Report on the development of efficient metrological methods for key NR OTA RF parametric metrics (e.g. TRP, EIRP), for sub-6 GHz MIMO and mm-wave massive MIMO systems, and the quantification of the associated uncertainties (target the upper limits of measurement uncertainties for the measured quantities given in 3GPP documents e.g. ETSI TR 38.810, TR 38.884) based on using, for example, direct far-field (DFF), indirect far-field (IFF), near field-to-far-field (NF-FF), mid field and reverberation chamber (RC) methods with validation in an interlaboratory comparison

21NRM03 MEWS Deliverable D2: Report on the development of efficient metrological methods for key NR OTA RF parametric metrics (e.g. TRP, EIRP), for sub-6 GHz MIMO and mm-wave massive MIMO systems, and the quantification of the associated uncertainties (target the upper limits of measurement uncertainties for the measured quantities given in 3GPP documents e.g. ETSI TR 38.810, TR 38.884) based on using, for example, direct far-field (DFF), indirect far-field (IFF), near field-to-far-field (NF-FF), mid field and reverberation chamber (RC) methods with validation in an interlaboratory comparison Organisation name of the lead participant for the deliverable: National Physical Laboratory Authors: Yunsong Gui, Jerdvisanop Chakarothai, Tian Hong Loh, Martin Forsberg, Fredrik Harrysson, Ivan Bonev, Fengchun Zhang, Martin Hudlicka and Emrah Tas Due date of the deliverable: 30 September 2025 Actual submission date of the deliverable: 30 November 2025 Confidentiality Status: PU - Public, fully open (remember to deposit public deliverables in a trusted repository). Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or EURAMET. Neither the European Union nor the granting authority can be held responsible for them. Deliverable Cover Sheet The project has received funding from the European Partnership on Metrology, co-financed from the European Union’s Horizon Europe Research and Innovation Programme and by the Participating States. Abbreviations Acronym Description AC Anechoic Chamber AiP Antenna-in-Package ANN Artificial Neural Network AnUT Antenna under Test AUT Array under Test BS Base Station BTM Backward Transformation Method BW BandWidth CATR Compact Antenna Test Range CDF Cumulative Distribution Function CFR Channel Frequency Response CTIA Cellular Telecommunication and Internet Association DFT Discrete Fourier Transform DFF Direct-Far-Field DL downlink DUT Device under Test EIRP Effective Isotropic Radiated Power EIS Effective Isotropic Sensitivity FSPL Free-Space Path Loss HPBW Half Power Beamwidth IFFT Inverse Fast Fourier Transform IFBW Intermediate Frequency Bandwidth LoS Line of Sight LTE Long Term Evolution MIMO Multiple-input-multiple-output mmWave Millimeter Wave frequency band MPM Matrix Pencil Method MU Measurement Uncertainty NAC Non-Anechoic Chamber OFDM Orthogonal Frequency Division Multiplexing Omni-VAA Omnidirectional Antenna-Based VAA OTA Over the Air PADP Power Angle Delay Profile PL Path Loss PWG Plane Wave Generator QZ Quiet Zone RC Reverberation Chamber RBW Resolution Bandwidth REV Rotating Element Electric Field Vector method RF Radio Frequency RMSD Root-Mean-Square Deviation Rx Receiver 1 Acronym Description SA Spectrum Analyzer SIC Successive Interference Cancellation SNR Signal to Noise Ratio SGH Standard Gain Horn Sub-THz Sub-Terahertz band SS System Simulator THz-TDS THz Time-Domain Spectrometer Tx Transmitter UE User Equipment ULA Uniform Linear Array UL uplink URA Uniform Rectangular Array VNA Vector Network Analyzer VST Vector Signal Transceiver WP Work Package 3GPP Third Generation Partnership Project 4G 4th Generation Wireless Systems 5G 5th Generation Wireless Systems 6G 6th Generation Wireless Systems 2 Contents Abbreviations.......................................................... 1 Executivesummary....................................................... 5 1.Introduction ......................................................... 6 2. Multi-probe Enabled Over-the-air Calibration of Millimeter-wave Antenna Array: Concept and Experimental Validation ......................................................... 7 2.1Introduction...................................................... 7 2.2 Multi-probe enabled array calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Multi-probe scheme for improving measurement efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 Multi-probe scheme for improving measurement accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.5 Multi-probe scheme for reducing measurement distance . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.6Conclusion....................................................... 14 3. Over-the-Air Testing for Connecting Faults Diagnosis in Beamforming Antenna Arrays with Short MeasurementDistance....................................................... 16 3.1Introduction...................................................... 16 3.2 Proposed beam-steering diagnosis method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3Numericalsimulations................................................ 20 3.4Measurementvalidation............................................... 20 3.5Conclusion....................................................... 22 4 Gradient-Based Beam Peak Search for Over-the-Air Testing of Mmwave Phased Arrays . . . . . . . . . . . . . . 23 4.1Introduction...................................................... 23 4.2 Measurement setup. Search methods used in the standardization and proposed in the current work . 23 4.3Simulationresults .................................................. 26 4.4Measurementresults ................................................ 27 4.5Conclusion....................................................... 29 5 Single-Frequency Phaseless Data Based Echo Suppression for Antenna Pattern Measurement in a Non-ideal Chamber.......................................................... 30 5.1Introduction...................................................... 30 5.2 Proposed amplitude-only echo suppression method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.3 Numerical analysis: reliable region, reference antenna selection, zero-frequency pollution, required length of probe movement, number of probe positions (probe spacing) and robustness . . . . . . 35 5.4Experimentalvalidation............................................... 37 5.5Conclusion....................................................... 41 6. An Efficient Multi-Beam Pattern Measurement Campaign for Millimeter-Wave Phased Arrays . . . . . . . . . . 43 6.1Introduction...................................................... 43 6.2Measurementsetupandprocedure........................................ 43 6.3Measurementresults ................................................ 45 6.4Conclusion....................................................... 50 7. AC Direct Far-field (FF) Measurements of Total Radiated Power (TRP) . . . . . . . . . . . . . . . . . . . . . . . . 51 3 7.1Scope.......................................................... 51 7.2Introduction...................................................... 51 7.3 3GPP’s definition of Total Radiated Power with Anechoic Chamber Method . . . . . . . . . . . . . . . . . 51 7.4 Far-Field DL Testbed Implementation inside AC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 7.5 Measurement Procedure of Receiver Path Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 7.6TRPTestProcedure ................................................. 56 7.7TRPMeasurementResults.............................................. 56 7.8Conclusion ...................................................... 57 8. TRP measurements in RC for 5G FR2 Base Stations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 8.1TRPmeasurementsinRISERC ........................................... 58 8.2TRPmeasurementsinNPLRC ........................................... 65 9. Investigation of high-gain antenna effects during testing in RC at 77 GHz . . . . . . . . . . . . . . . . . . . . . 75 9.1Scope.......................................................... 75 9.2Measurementsetup ................................................. 75 9.3Evaluationofmeasurementdata ......................................... 75 9.4Conclusions...................................................... 78 10.Inter-laboratoryComparisons .............................................. 79 10.1Scope ......................................................... 79 10.2Introduction..................................................... 79 10.3 Measurement setups for total radiated power using reverberation chamber in RISE and NPL . . . . . 79 10.4Measurementresults................................................ 80 10.5Conclusion...................................................... 88 11.Conclusion.......................................................... 89 4 Executive summary This report is the third deliverable D2 of the MEWS project, covering the topics included in Work Package 2 (WP2) and it merges the knowledge of the direct far-field (DFF), indirect far-field (IFF), near-field-to-far-field (NF-FF), mid-field and reverberation chamber (RC) methods aiming to develop cost-effective and time-efficient metrological methods for the OTA conformance testing of new radio (NR) RF parametrics. The chapters of this deliverable report are organized as follows: Chapter 1 gives an overall introduction, while Chapter 2 presents the concepts and experimental validation of multi-probe enabled over-the-air (OTA) calibration of millimeter-wave (mm-wave) antenna array. Chapter 3 describes a novel diagnosis method for connecting faults’ detection in beamforming antenna arrays with short measurement distance. Chapter 4 shows an efficient gradient-based beam peak search technique for OTA testing of mm-wave phased array. Chapter 5 proposes a novel echo suppression method with a single-frequency phase-less measurement for recovering the antenna gain pattern measured in the non-anechoic chamber (NAC). Chapter 6 describes an effective multi-beam pattern measurement campaign using a fast multi-beam pattern measuring technique for mm-wave phased array antenna systems characterizations. Chapter 7 presents the total radiated power (TRP) measurements using the direct far field (DFF) method based on the actual 5G NR downlink signal in the anechoic chamber (AC). Chapter 8 presents TRP measurements using the reverberation chamber (RC) method based on the actual 5G NR downlink signal. Chapter 9 shows the investigation of high-gain antenna effects towards OTA conformance testing using RC method at 77 GHz. Chapter 10 shows the inter-laboratory comparisons on the TRP-related measurements between different methods. Finally, conclusions are made in Chapter 11. 5 1. Introduction The global shift from 4G to 5G, and soon towards 6G, represents more than just an increase in data rates, it signifies a transformation in how wireless networks are conceived, deployed, and used. Future systems will operate across vastly higher frequency ranges (mmWave and sub-THz), leverage massive antenna arrays, rely on artificial intelligence and edge computing, and serve mission-critical applications requiring extreme precision in timing and reliability [1], [2]. This technological leap introduces unprecedented complexity in the design, testing, and validation of wireless systems. Measurement science or metrology is essential to navigate these challenges, offering the traceable benchmarks necessary for innovation, standardization, regulation, and industrial deployment. However, existing metrology infrastructure and methodologies are not fully equipped to handle these emerging demands. The primary aim of the presented work in this document is to develop metrological methods that are not only scientifically rigorous, but also practical from an industrial and regulatory standpoint, i. e. minimizing cost and test time while maintaining measurement accuracy and repeatability. A key focus was placed on achieving traceability and uncertainty quantification in accordance with international standards and guidelines. The developed methods aligned with and extended relevant specifications such as [3], [4] and [5]. These metrological advancements support both Radio Frequency (RF) conformance testing (e.g., Total Radiation power (TRP), Effective Isotropic Radiated Power (EIRP)/Effective Isotropic Sensitivity (EIS) validation, spurious emissions, and receiver sensitivity) and end-to-end system performance assessments, including throughput, beam management, and mobility handling under realistic signal conditions. Where relevant, measurement procedures were validated through inter-laboratory comparisons and collaborative test campaigns to demonstrate repeatability and reproducibility across facilities. More specifically, the main objectives of the deliverable can be summarized as follows: • Multi-probe Enabled Over-the-air Calibration of Millimeter-wave Antenna Array: Concept and Experimental Validation • Gradient-Based Beam Peak Search for Over-the-Air Testing of Mmwave Phased Arrays • Over-the-Air Testing for Connecting Faults Diagnosis in Beamforming Antenna Arrays with Short Measurement Distance • Single-FrequencyPhaselessDataBasedEchoSuppressionforAntennaPatternMeasurementinaNon-idealChamber • An Efficient Multi-Beam Pattern Measurement Campaign for Millimeter-Wave Phased Arrays 6 2. Multi-probe Enabled Over-the-air Calibration of Millimeter-wave Antenna Array: Concept and Experimental Validation 2.1 Introduction Because mmWave technology has a larger spectrum resource than legacy bands (i.e. sub-6 GHz), it is crucial for achieving the high data-rate requirements of current 5G and future wireless communication systems. In dynamic propagation conditions, high-gain and beam-steerable array systems are necessary to maintain link reliability and produce a high Signal to Noise Ratio (SNR), because of the high transmission loss and blockage susceptibility in mmWave bands. Furthermore, because of cost considerations, technological trends in creating highly integrated radio transceiver designs willbeunavoidableinmmWavebands[6],[7]. Becauseofitsmorestringentrequirementsforsystemcomplexity,implementation cost, and measurement time, this has presented significant hurdles for its testing and measuring methodologies. Therefore, practical, rapid, precise, and affordable methods for evaluating integrated mmWave antenna arrays are urgently required [8], [9], [10] and [11]. To provide precise array radiation performance, rigorous array calibration is necessary. Finding the first complex excitations in the RF chains that are attached to the array elements and calibrating them out to guarantee homogeneous excitation across RF chains is the aim of calibration. Because mmWave radios use active components in the RF channels, array calibration is more important than in legacy frequency bands. For any multi-antenna/channel system to function as intended, array calibration is typically necessary. Research on array calibration has been ongoing for a long time, and numerous techniques have been documented. By taking off the antennas and using an RF cable to reach each antenna port, it is possible to undertake a direct measurement of the RF chain complex responses of individual branches, as demonstrated in [12]. The conducted method’s low cost and ease of use have led to its widespread adoption in the industry for legacy frequency bands. However, antenna connectors for testing purposes will not be available due to the highly integrated RF transceiver designs at mmWave and above. Furthermore, because of the higher density packaging made possible by the shorter wavelengths, the number of elements in mmWave phased arrays has increased significantly, making conducted testing impractical. Phased arrays must therefore be calibrated in a radiated Over the Air (OTA) way, particularly for mmWave radios. Antenna elements of the array under test (AUT) are used as interfaces to send and receive plane waves in the boresight direction during OTA array calibration. As a result, the responses in the RF chains and boresight radiation patterns of AUT elements make up the calibration coefficients. There have been reports of mmWave antennas using digital, analog, and hybrid beamforming designs [13] and [7]. The work [14], presented in this subchapter, is focused on calibration for analog-beamforming type phased arrays with amplitude and phase-toggling ability for each element. The park-and-probe technique is commonly used in the industry to simulate plane-wave impinging at each AUT element. It involves moving the probe antenna mounted on a mechanical scanner to line up with each activated AUT element while deactivating other AUT elements (by using of attenuators) and sequentially recording the complex responses for each RF chain [15], [16]. It was shown that mechanical movement is quite slow and inaccurate, especially for large-scale arrays, and thus measurement in this ”on-off mode” is not desirable for mmWave phased arrays [17]. By taking into account non-negligible mutual coupling effects between components, the ”all-on mode” is able to quantify component-to-component non-uniformity, unlike the ”on-off mode”. For the mmWave phased array [17], calibration carried out in the ”all-on” mode is therefore more accurate. The DFF, Compact Antenna Test Range (CATR), or Plane Wave Generator (PWG) setups can be used to approximate the plane-wave condition in which the AUT can be calibrated in the ”all-on mode” [18]. The DFF configuration 7 necessitates a long measuring distance, may frequently has link budget problems, and has high chamber needs. However, the expense of implementing the system is still significant even though CATR configurations can be used to create plane-wave fields at a distance shorter than the DFF. There have been numerous PWG prototypes suggested for base station (BS) testing in the sub-6 GHz bands [19], [20], and [21]. Although several works have been documented in the literature [22], [23], the applicability of PWGs in the mmWave frequency band is still in its early development, mostly because of the low-resolution of phase shifters and attenuators and the restricted supported bandwidth (BW). 2.2 Multi-probe enabled array calibration Detailed discussion on the boresight plane-wave methods can be found in [14]. Figure 1 shows the schematic of a multi-probe configuration using M probe antennas. Figure 1: Calibration system diagram of a multi-probe setup The multi-probe method is examined in two application scenarios: 1) A multi-probe FF setup to increase the measurement accuracy or measurement efficiency for beam-steering AUT. Plane waves are expected to impinge from probe directions to the AUT. 2) A multi-probe NF setup to shorten the necessary measurement distance. The probes are situated in the FF region of the AUT element, but they are located in the NF region of the AUT. Note that in certain works, this region is referred to as ”mid-field” [8], [24]. A single probe antenna can be moved to predetermined positions (a concept known as a virtual probe array) or numerous probe antennas can be used directly to implement the multi-probe system. Note that multi-PWG [25], [26], or multi-reflector compact range (to generate plane waves of varied impinging angles) can also be viewed as a multi-probe technique in a FF configuration. To keep things simple, we’ll assume that the probe antennas are turned on and off in sequence. The idea behind the multi-probe FF setup is that the beam-steering factors of the array can be derived from the array factors associated with the multi-probe locations. This allows for the effective expansion of the beam-steering angularrangewith sparselydistributed probes[27] andalso speedsup the calibrationprocess, because therearefewer 8 dB and phase errors of up to ±0.4◦, respectively. For the accuracy enhancement measurement, the three-probe setup can significantly reduce the calibration error, compared to a single-probe setup, especially when the beam-steering angle range is small. For the measurement range reduction measurement, one demonstrated that the distance can be decreasedfromtherequired39.2mforthesingleprobesetupto0.5m withtheuseof a10×10virtualprobearraysetup, which can achieve amplitude errors up to ±0.3 dB and phase errors up to ±3◦, respectively. The comparison of various calibration methods in both single-probe and multi-probe setups is summarized in Table I in [14]). The multi-probe scheme is promising for testing future advanced mmWave radios. 15 3. Over-the-AirTestingforConnectingFaultsDiagnosisinBeamformingAntennaArrayswithShort Measurement Distance 3.1 Introduction Communication systems use beamforming technology to increase the SNR [33]. In order to facilitate multiband operation, BSs in Long Term Evolution (LTE) systems may include up to five arrays, each of which may include eight to eleven dual-polarized antenna elements. The high number of antennas utilized in the BSs causes connecting faults, and this problem gets worse as the number of elements in the sub-6 GHz 5G BS systems increases [34]. The connecting faults include disconnection faults, which may be caused by the deterioration of associated RF components, such as antennas, cables, and connectors. Wrongmanual installationcan also lead to connecting faults (misconnectionfaults). Three forms of connecting faults can occur in dual-polarized BS antennas: unconnected antenna elements, switched ports of antenna elements (for the same polarization), and swapped ports of two polarizations of the same antenna element. In traditional array diagnosis methods, the first fault type is the same as the detection of failed elements [35], [36], [31], [37], and [38]. Since the misconnection could negatively impact the beamforming antenna’s steering precision, detecting the other two fault types is equally crucial. In fact, identifying connecting faults with assembled BS antennas in real-world production line environment can be extremely difficult for a number of reasons: 1) The inner antenna structures and feed ports of the assembled beamforming antenna are not visible, since the antenna is enclosed in a radome. Therefore, OTA testing is necessary to assess the device’s performance in a non-intrusive manner [39], [40]. 2)Forassembledantennas,itisnotfeasibletofreelycontrolthephaseoramplitudeofindividualarrayelements. Beamforming networks that can produce specific specified beam directions [41], [42] are used to create BS antennas with switched beams and electric downtilt capability. 3) To facilitate extensive BS testing, which requires detection based on a small number of measurement positions, the testing method must be quick. 4) It is preferable to use a robust approach that can withstand potential errors from nonideal testing conditions [43]. Without the need for an RF clean environment, i. e. an AC with virtually no environmental scatterings, it would save a significant amount of money. However, overcoming the aforementioned obstacles is not simple. Few works for achieving array diagnosis will be outlined. A possible method is the backward transformation method (BTM) [35]. It uses planar NF data to reconstruct the FF patterns of the array and the aperture field based on field transformation theory. However, to satisfy the Nyquist sampling theorem, large number of samples and scanners with high precision are required. The REV method [36], [31] is another reconstruction approach. It relies on analysis of thepowervariationinthearraysignalwhilethephaseofantennaelementsrotatesfrom0◦to360◦. Thematrixmethods [37], [38], compressed sensing techniques [44], [45] and artificial neural network (ANN)-based techniques ([46], [47] and [48]) have also been proposed as possible methods. However, each of the proposed method has its own limitation or condition in order to achieve a successful diagnosis. This subchapteris based on[49] andproposesa novelOTA testingmethod, which canbe conductedin a compact measurement setup when a BS antenna operates in its default beam-steering mode. The detection of faulty elements 16 for various types of connecting faults is achieved by solving the relevant linear equations and implementing a differential strategy. The comparisons between the proposed method and several representative array diagnosis methods mentionedabovearesummarizedinTable I in [49]. Theattractivefeaturesof theproposeddiagnosis methodarelisted as follows: 1) Default modemeasurement: That is, the measurements canbe conductedwhen theAUT, i.e., thebeamforming antenna array, steers its beam to the predefined directions using the built-in phase shift settings. 2) Fast: All the antenna elements are diagnosed simultaneously with only a few measurement positions in the NF of the AUT. The whole diagnosis process could be completed in several minutes with the help of a fully automated measurement process. 3) Robust: The proposed method can be achieved in practical indoor or production line scenarios with possible scattering in the testing environment. 3.2 Proposed beam-steering diagnosis method The schematic of the diagnosis setup is shown in Figure 7. Figure 7: BS diagnostics system schematic Lets assume a beamforming antenna array including Nantenna elements (located on the left side of the figure and enclosed by the black dashed line). The feed of the AUT is split into Nbranches with Nphase shifters (one for each branch) connected to the Nantenna elements. The phase shifters are used to mimic the built-in phase shift settings of a BS beamforming array. The total number of phase shifter settings is P, allowing for steering the beam into Pdifferent directions. The schematic presents also one of the fault types, in particular, the feeds of the third and fourth array elements are swapped. The probe array is located on the right side of Figure 7 and it is also enclosed by the black dashed line. The proposed diagnosis method requires the estimation of the complex S-parameters between 17 the AUT feed on the left and the probe feed(s) on the right for Mdifferent spatial locations. Practically, this could be achieved by either using a probe array with Mprobe antennas and a switch or by using a virtual probe array i.e., a single-probe antenna is moved to M different locations with the use of a mechanical positioner. The first scheme is preferable to achieve fast diagnosis, because of the possibility for automation of the measurement process. Therefore, the array with Mprobe antennas and a switch is the method we work with. The distance between the AUT and the probe array is D. Figure 7 presents only one polarization of the AUT and probe array. The other polarization would follow the same arrangement, parallel to the presented one. To detect any connecting faults in the AUT, the array diagnosis is based on estimation of the S-parameter received by Mprobes for Pdifferent phase shifter settings. The measured S-parameter at a single frequency (estimated as complex S21 by the VNA in our measurements) forms a matrix S∈CM×Pwith the (m,p)th entry is the S-parameter between the feed of the AUT and mth probe for the pth phase shifter setting (m∈[1, M],p∈[1, P ]). Matrix Scan be expressed as a matrix product of three matrices: S=A·C·B(3-1) where matrices A∈CM×N,C∈CN×N, and B∈CN×Pcharacterize three factors of the matrix S. Matrix A= [amn]is the coupling matrix between the AUT element ports and the probe antenna ports. Therefore, the elements of matrix Aare the transmission coefficients between the ports of the nth AUT element and the mth probe antenna. Considering that mth probe is placed in the FF of the nth antenna element, matrix Acan be estimated as [50]: amn =gnθA mn·gmθP nmjλe−jkrmn 4πrmn (3-2) Matrix B= [bnp]is composed of Pcolumn vectors of the complex excitation weights applied to the Nantenna elements. Its single element contains the complex excitation given to the nth AUT element in the pth phase shifter setting. Bcan be possibly represented by: bnp =Bejk(n−N+1 2)δsinαp(3-3) where Bis the magnitude weight for possible tapering, δis the distance between the AUT elements, and αpis the target beam steering angle for the pth phase shifter setting. In the following, B= 1, i.e. no tapering is assumed. Matrix Cis the connection matrix between the phase shifters and the AUT elements. Under normal condition, each phase shifter is connected to one antenna port and the Cmatrix is an identity matrix. However, if a fault occurs, matrix Cis not an identity matrix more. For example, if the nth port is disconnected, then the corresponding diagonal element cnn will be zero. If some ports are swapped, then the corresponding rows or columns in Cwill be swapped. Therefore, the matrix Cwhich gives the information about accidental disconnections of some antenna ports or port swappings, and the structure of the matrix Cshows which antenna ports are affected. To perform a successful diagnosis of the AUT, knowledge about matrix Cand matrix Sis needed. A diagnosis matrix Q, i.e., a matrix indicating the fault of the AUT, therefore must ideally be matrix Cfrom (3-1): 18 Q0=C=A−1·S·B−1(3-4) The elements of matrix Scan be directly estimated by measuring transmission coefficients between AUT and the probe array. Bis generally known and it is defined by (3-3). However, matrix Ais unknown, and the approximation of matrix Aand the inverse operation for both matrices Aand Bwill introduce errors to the diagnosis. Therefore, the accumulation of errors leads to large error and it is therefore not feasible to obtain matrix Cdirectly. To solve this problem, A·Cor C·Bcan be used instead as the updated diagnosis matrix: Q1=A·C=S·B−1(3-5) or Q2=C·B=A−1·S(3-6) The diagnosis matrix from (3-6) is considered as better than the one in (3-5). Matrix Ais estimated by using some simplifications. Moreover, a differential diagnosis is proposed, because it will be more accurate and robust. The reader can refer to [49] for further details. Then, the final diagnosis matrix can be expressed as: dQ=A−1 F·˜ S−˜ S(ref)≈(C−I)·B(3-7) where A−1 Fis the inverse of the simplified matrix Aconsidering only Free Space Path Loss (FSPL), ˜ S(ref)is the S matrix of the “golden array” (reference array) and Iis the identity matrix. dQ= [qnp]of Pcolumnvectorsrepresentsthe estimated connection situation of each array element with different scanning angles. A large value of |qnp|indicates a big amplitude deviation of the nth element between the AUT array and the “golden array”, showing a possible connecting fault. More specifically, the connecting faults of the nth element in the AUT can be determined by the magnitude of |qnp|by following the cases below: Case 1 : |qn1| ≈ |qn2| ≈ . . . ≈ |qnP | ≈ 0. In this case, the nth antenna element works correctly. Case 2 : |qn1|≈|qn2| ≈ . . . ≈ |qnP | ≫ 0. In this case, there is a disconnection fault or a misconnection of swapped ports for antenna element polarization on the nth antenna element. Case 3 : |qn1|<|qn2|<· · · <|qnP |. In this case, there is a misconnection fault of swapped ports (for the same polarization) on the nth antenna element. Note that |qnp|>0when the pth phase shift setting does not correspond to 0◦scanning angle for Case 3. 19 3.3 Numerical simulations CST Microwave Studio have been used to obtain the S-parameters of the reference array i.e., matrix ˜ S(ref), and simulationsinMATLABareusedtovalidatetheentirediagnosisprocess. An11-elementbeamformingantennaarraypresented in Figure 8 serves as the AUT in our simulation. Figure 8: Arrangement of the AUT and the probe array The antenna element is a ±45◦polarized antenna and it operates at 2.7 GHz. The array has 22 ports in total, with 11 ports for each polarization. The distance between elements is 72.2 mm (which is equivalent to 0.65λat 2.7 GHz). The beam can be steered from 0◦to 15◦with a step of 3◦. The array in Figure 8 is used for validation of the proposed diagnosis method. However, the proposed method is not limited to this particular type and arrangement of the array elements. As it is presented in the figure, the fault types are detected by a linear array of probes arranged opposite to the AUT. The probes should be dual-polarized in the same directions as the AUT. The distance between the AUT array and probe array is selected to be 40 cm (around 3.6λ) to obtain small system errors. Matrix Ais a matrix of transmission coefficients between the AUT and probes at 2.7 GHz obtained from the simulations in CST Microwave Studio. The effectiveness of the proposed method is demonstrated in Figure 9 and Figure 11, showing the simulation and the measurement results for different types of connecting faults. 3.4 Measurement validation A measurement system was built in a laboratory environment at Aalborg University for validation of the proposed method, as presented in Figure 10a, and photos of the measurements are shown in Figure 10b and Figure 10c. 20 (a) (b) Figure 9: Simulation results: Magnitude of the differential diagnosis matrix dQfor fault type of a) element 3 disconnected and b) elements 3 and 4 swapped (a) (b) (c) Figure 10: (a) Illustration of the measurement system, photos of (b) measurement system and (c) configuration of the AUT and probe antennas Forsimplicity,thediagnosisforan8-elementsingle-polarizedlineararraywasdemonstrated. Themeasurement datawererecordedatcenterfrequencyoftheAUT,i. e. 3.6GHz. TheAUTandtheprobeantennasarealigned,numbered, and set face-to-face as shown in Figure 10c. The distance between the AUT and the probe array was 100 cm (around 12λ). The height of the antennas is 150 cm. 21 (a) (b) Figure 11: Measurement results: Magnitude of the differential diagnosis matrix dQfor fault type of a) element 4 disconnected and b) elements 4 and 5 swapped As it is obvious from Figure 9 and Figure 11, for both simulation and measurement set-ups, the disconnected elements and the swapped elements have been detected successfully (by identifying the peaks in the amplitude values). As pointed out in [49], the precise magnitude of peaks is not crucial as rather the variation trend determines the typeoffault. Thehardwareusedintheexperiment[49]isnotideal. Forinstancethe8-waypowerdividermayintroduce amplitude balance up to 0.4 dB and phase error up to 8 ◦, the phase shifter specified accuracy is ±1.5◦. Moreover, the isolation among arms is reported to minimum 20 dB, which means in the worst case each transmission path is influenced by adjacent paths as well. The setup was first calibrated for these imperfections with typical amplitude deviation for different paths within ±0.15 dB and phase difference ±0.6◦whereas the MU of the transmission coefficient measuredusingVNAistypically±0.1 dB and±1◦, respectively, for transmission coefficients upto-70 dB.Compared with the magnitudes of the matrix elements, the type of fault can still be determined unambiguously even with a non-ideal hardware. 3.5 Conclusion Anoveldiagnosis methodbased on the measurementof S-parametersbetweenthe AUTanda probearrayis presented for connecting faults’ detection in beamforming antenna arrays. Generally, the probe array which must be the same as the AUT positioned at short simulation (measurement) distance from the AUT can be used for diagnosis, as the proposed method has been verified both by simulations and measurements. The proposed method functions for a beamforming antenna array working in its default beam-steering mode. The MU introduced by the hardware setup is negligible compared to magnitudes of matrices required to detect a fault in the antenna array. 22 4 Gradient-Based Beam Peak Search for Over-the-Air Testing of Mmwave Phased Arrays 4.1 Introduction EIS and EIRP are important metrics that must be precisely measured at the beam peak directions in order to assess the transmit and receive performance of mmWave antennas. It is time-consuming to properly record the entire radiation pattern of the DUT in order to determine the beam peak direction. The problem gets more complicated, because the more directive beam patterns generated by larger-aperture antennas in future mmWave systems require more dense sampling [51]. Thus, a beam peak search approach that is both precise and efficient is urgently needed. The maximum total component of EIRP defines the beam peak direction, including the corresponding polarization of the DUT used to form the beam, as defined in the Cellular Telecommunication and Internet Association (CTIA) and the Third Generation Partnership Project (3GPP) [52]. 3GPP and CTIA have provided clear instructions on the measuring process [53], [54]. [53] states that the beam peak search procedure in the spherical coverage test uses either a constant step size grid approach or a constant density grid method. In particular, the constant step size technique requires at least 1106 grid points for the reference 8 × 2 non-sparse antenna arrays used in smartphone UEs, and the constant density grid method requires 800 grid points. This procedure takes a lot of time and is not acceptable in the industry [55]. There is a significant need to limit the number of measurements in order to shorten the measurement time. This subchapter is based on the work in [56], and proposes a gradient-based search method, which reduces significantly the number of required measurement points compared to conventional search method, while maintaining the measurement accuracy. Moreover, a coarse and a refined strategies are presented to mitigate the problem of gradients potentially converging to local maxima rather than global maxima. Numerical simulations and experimental measurements have been performed to validate the effectiveness of the proposed algorithm. 4.2 Measurement setup. Search methods used in the standardization and proposed in the current work Measurement system for the beam peak search is presented in Figure 12. Figure 12: The schematic diagram of measurement system with measurement points (circle) Positioned on a turntable, the mmWave phased array DUT forms and fixes a beam in a predetermined direction. A probe antenna samples the radiation pattern of the DUT at each point of rotation (by using a constant step or density grid). To guarantee the robustness of the measurement process, the turntable is randomly rotated and the relative orientation of the antenna array and the measurement grid is also changed randomly in accordance with the 3GPP 23 specification. The antenna array model in [57] is used to construct the radiation pattern. The DUT is an 8 × 2 rectangle phased array with 0.5λ vertical and horizontal spacings. Each array element has a front-to-back ratio of 30 dB and a horizontal HPBW of 260°and a vertical HPBW of 130°. As shown in Figure 13a, the referenceantenna pattern has a beam peak at [0°,0°]. (a) (b) (c) Figure13: a) Theradiationpatternofreferenceantennaarraywithθ=0°,Diagramforcoarsemeasurement: b)Measured EIRP over the coarse grid c) The interpolated radiation pattern and vertices identified as the potential beam peak location According to the standardization, the probe antenna moves in the θ and ϕ directions with a step size of 7.5°, while the DUT rotates in a random direction, creating a grid of 1106 measurement points. For the duration of the measurement, the probe antenna is positioned at grid point [θ, ϕ] with the beam fixed toward the DUT. The signal sent by the DUT is then picked up by the probe antenna. A spectrum analyzer (SA), power meter, or gNB simulator is then used to process the received signal in order to precisely measure its power level. Next, EIRP is computed by summing themeasuredpowerwiththe compositelossesof theentiretransmissionpathandfrequency. Thebeampeakdirection is determined at the angular location where the maximum EIRP is found after the EIRP is measured at all grid points using the previously described steps. The steps of the proposed method are summarized in Algorithm 1. Algorithm 1 Proposed method Input: Size of sparse grid Gr×Gc Output: xpeak ,˜ Xmat = [x1,x2, . . . , xR]T 1: Measure Gr×Gcsparse grid matrix Exs1 a,band calculate the 181 ×181 matrix ˜ Eby interpolation 2: Identify potential beam peak location xs2 pand xs3 p,q 3: Measure xs2 pand Exs3 p,q,x1is the location with maximum EIRP among xs1,xs2and xs3 24 B(ϕ) = L X l=1 alδ(ϕ−ϕl)exp(jφl)(5-3) It is obvious that If the channel characteristics vector B(ϕ)is known, then the true (real) pattern A(ϕ)can be obtained from AM AUT (ϕ)via compensating out the channel vector B(ϕ). In [52], it is explained that after performing DFT for (5-2) in the angular domain, the convolution relationship is transformed into the multiplication relationship. Therefore, for the true (real) pattern A(ϕ)we obtain: ˜ AAUT =˜ AM AUT /˜ B(5-4) where ∼denotes the DFT operation. The division is implemented element-wise in the DFT vectors. Thus, if ˜ B is known, the true (real) pattern can be estimated by performing the IDFT for (5-4), and ˜ Bcan be considered as the calibration factor. Obviously, the key to spatial deconvolution for the true pattern is to obtain the calibration factor ˜ B. Generally, there are two main methods to estimate ˜ B, i.e. chamber channel sounding method [70] and reference antenna method [71]. In the chamber channel sounding method, the spatial matrix pencil method (MPM) is used with the formed virtual array in the chamber (i.e., by moving a single antenna to several preset spatial locations and measuring the chamber channel response at each spatial location) [70]. Therefore, the environment multi-path characteristics, i.e., the propagation angles, amplitudes, and phases, can be estimated. Then, B(ϕ)can be calculated from (5-3), and the calibration factor ˜ Bis estimated with the use of DFT. This method is used widely for channel parameter estimation in wireless communication [72]. However, the effectiveness of the method depends on the virtual array aperture (i.e., the spatial resolution) and therefore requires a high SNR. The other method, i.e. the reference antenna method, extracts the calibration factor by using a reference antenna with known pattern AREF (ϕ). Therefore, the pattern measurement for the reference antenna in the nonanechoic environment is firstly conducted, resulting in a measured pattern AM REF (ϕ)yielding: AM REF (ϕ) = AREF (ϕ)∗B(ϕ)(5-5) By applying DFT operation to (5-5), the calibration factor can be estimated as: ˜ B=˜ AM REF /˜ AREF (5-6) Without changing the channel environment, the AUT pattern AM AUT (ϕ)can be measured. Then, by substituting (5-6) into (5-4), the true pattern in the DFT domain can be reconstructed as: 31 ˜ AAUT =˜ AM AUT /˜ B =˜ AM AUT ˜ AREF ˜ AM REF (5-7) Thus, AAUT (ϕ)can be easily computed by performing the IDFT. In the proposed method, the probe antenna is placed in the FF of the AnUT and it is moved along the LOS path direction to M positions spaced by ∆d, as illustrated in Figure 16. Figure 16: Diagram of the FF antenna measurement in a NAC, where the AUT is rotated in a counterclockwise direction, starting from −180◦, as denoted by the gray arrow. Note that in this figure the antenna under test is denoted as AUT In general, the amplitude of the propagation paths over the multiple probe locations is distance-dependent due to the FSPL. However, since the FF measurement setup is considered here and the probe virtual array aperture is much smaller compared to the FF measurement distance d0, the variation in the path power among the probe virtual array introduced by the FSPL can be ignored. Neglecting the probe antenna pattern, with the measured antenna rotated to φ, the FF received signal can be represented as a vectorial summation of complex signals (complex field of direct path and reflected paths). The reader is advised to refer to equations (9)-(11) in [52]. The received power at the mth probe position for a given AnUT rotation angle ϕcan be represented as the squared magnitude of the complex received signal y(m, ϕ). If we considering the non-anechoic environment with an LOS propagation and two reflection paths, then the received power P(m, ϕ)at the mth position for a given AUT rotation angle ϕcan be calculated by using (10), where (·)His the conjugate operation. Note that y(m, ϕ)is the FF received signal, El(ϕ)is the complex amplitude of the lth propagation path at the original (m= 0) position with E1(ϕ) denoting the contribution of the LOS propagation, Φlis the received signal phase that is jointly determined by the lth wave propagation and antenna phase pattern response and klcan be considered as the spatial frequency of the lth propagation wave along the direction of movement. Terms I-III in (5-8) can be considered as the direct components, which are important in the proposed method. Terms IV-VI can be considered as the harmonic components, which are characterized by the spatial frequency differences (ki−kj)caused by the ith and jth propagation paths. 32 P(m, ϕ) =y(m, ϕ)·yH(m, ϕ) =|E1(ϕ)|2+|E2(ϕ)|2+|E3(ϕ)|2+E1(ϕ)E2H(ϕ)·exp(j2π(k1−k2)m∆d) + E1(ϕ)E3H(ϕ)·exp(j2π(k1−k3)m∆d) +E1H(ϕ)E2(ϕ)·exp(j2π(k2−k1)m∆d) + E1H(ϕ)E3(ϕ)·exp(j2π(k3−k1)m∆d) +E2(ϕ)E3H·exp(j2π(k2−k3)m∆d) + EH 2(ϕ)E3(ϕ)·exp(j2π(k3−k2)m∆d) =|E1(ϕ)| | {z } I +|E2(ϕ)| | {z } II +|E3(ϕ)|2 | {z } III + 2 |E1(ϕ)| |E2(ϕ)|cos(2π(k1−k2)m∆d+ Φ1(ϕ)−Φ2(ϕ)) | {z } IV + 2 |E1(ϕ)| |E3(ϕ)|cos(2π(k1−k3)m∆d+ Φ1(ϕ)−Φ3(ϕ)) | {z } II + 2 |E2(ϕ)| |E3(ϕ)|cos(2π(k2−k3)m∆d+ Φ2(ϕ)−Φ3(ϕ)) | {z } VI (5-8) Further, the reader can refer to Fig. 2 - Fig. 14 and equations (13)-(20) in [52], which for the sake of simplicity are not included in the deliverable. However, they will be briefly discussed. The most important part of the proposed method is to extract the direct components in (5-8). Considering as an example a simulated measurement with M= 32 positions, the procedure is detailed as follows: 1. Measure the received power at all Mpositions and obtain the power sequence (shown in Fig. 2(a) in [52]). 2. Perform DFT for the obtained power sequence (the harmonic frequency spectrum is shown in Fig. 2(b) in [52]). 3. The direct components must appear at zero frequency. The harmonic spectrum value at zero-frequency point must be directly extracted. More specifically, by nulling the harmonic frequency components except that at zero frequency (as illustrated in Fig. 2(c) in [52]), the direct components in the DFT domain can therefore be estimated. 4. Perform IDFT for the obtained harmonic frequency spectrum after nulling operation in procedure 3. The desired direct components can be obtained (as presented in Fig. 2(d) in [52]). Perform procedures 1-4 for each measured field angle ϕ, and the direct components can be estimated. Θ(ϕ) = |E1(ϕ)|2+|E2(ϕ)|2+|E3(ϕ)|2+|σ(ϕ)|2(5-9) where |σ(ϕ)|2is the interference power component due to the the spectrum leakages of the harmonic terms and is also the error source of the proposed method. Note that the scenario with L= 3 propagation paths is only chosen as an example, and the extension to a more generic multipath propagation environment is straightforward and doable. By using equations (9) and (10) in [52]), (5-9) can be represented as: 33 Θ(ϕ) = L X l=1 |El(ϕ)|2+|σ(ϕ)|2 = L X l=1 a2 l· |A(ϕ−ϕl)|2+|σ(ϕ)|2 = L X l=1 gl·T(ϕ−ϕl) + |σ(ϕ)|2(5-10) Actually, (5-10) is a circular convolution of PL l=1 glδ(ϕ−ϕl)and T(ϕ)as: Θ(ϕ) = T(ϕ)∗G(ϕ) + |σ(ϕ)|2(5-11) with T(ϕ) = |A(ϕ)|2(5-12) G(ϕ) = L X l=1 a2 lδ(ϕ−ϕl)(5-13) By performing DFT to (5-11) in the rotation angle domain, we obtain: ˜ Θ=˜ T·˜ G+˜ σ(5-14) ˜ σis the interference term |σ(ϕ)|2in the DFT domain. As it was discussed when explaining the second method (i.e. the reference antenna method), a reference antenna to obtain the chamber response characteristic ˜ G(i.e. the environment factor) can be used. More specifically, ΘAUT (ϕ)and ΘREF (ϕ)are assumed to be the extracted direct components for each rotation angle from the AnUT and reference antenna measurement, respectively, where TREF (ϕ) is the known power pattern of the reference antenna. Therefore, the environment factor can be obtained via elementwise division: ˜ G=˜ ΘREF /˜ TREF (5-15) Therefore, the AnUT power pattern in the DFT domain ˜ TAUT can be estimated via element-wise division as: ˜ TAUT =˜ ΘAUT /˜ G =˜ ΘAUT ˜ TREF ˜ ΘREF (5-16) 34 Afterwards, by performing IDFT for ˜ TAUT and take the square root, the antenna gain pattern |AAUT (ϕ)|is recovered. The reason, the DFT procedure is performed, is the error analysis. The investigation in the DFT domain provides an insight into the undesired interference component, helping us to investigate the algorithm error and derive the guideline of the virtual array design. 5.3 Numerical analysis: reliable region, reference antenna selection, zero-frequency pollution, required length of probe movement, number of probe positions (probe spacing) and robustness A non-anechoic environment is simulated in [52]) to study the performance and robustness of the proposed method. The measurement frequency is set to 28 GHz. An omnidirectional antenna is used as the probe positioned in the ϕ1 direction. InadditiontotheLOS propagation(a1= 1(0 dB)and ϕ1= 0◦), two reflectionwaves witha2= 0.5(−6dB)and ϕ2=−40◦and a3= 0.3(−10.5dB)and ϕ3=−25◦are introduced to mimic the non-anechoic environment. As the AnUT, a horn antenna with HPBW of 20◦is used. Two types of synthetic radiation patterns, i. e. specified by the 3GPP in [73], with HPBW of 20◦(antenna A) and 40◦(antenna B), respectively, are used as the reference antenna for the proposed technique. The synthetic pattern, flowchart of the simulation framework and comparison of the patterns are shown respectively in Fig. 3, Fig. 4 and Fig. 5 in [52]). By using the proposed echo suppression with reference antenna A, it is shown that the radiation pattern is successfully recovered, in terms of the pattern shape, HPBW, and gain. In practical applications, the environment or measurement system would introduce noise. Therefore, the complex random noise was added to the simulated measurement, with the SNR chosen to be 40 dB, and the Monte Carlo simulation with 1000 realizations was performed. Reference antenna A was used in this simulation. For the most realizations, the results similar to the presented in Fig. 5 in [52] could be obtained. However, in some extreme cases, noticeable errors may occur in weak signal directions (far from the main lobe direction in the antenna pattern). This would be expected, because weak signals are more sensitive to noise, compared to the main beam region. Further, the reader is advised to review Fig. 6 - Fig. 14 in [52], where a detailed analysis on the reconstructed patterns is discussed and presented. The comparison between the true and the reconstructed AnUT power patterns, with and without noise, in the DFT domain, and all the curves match to a good extend within the reliable region. However, significant deviations were found outside the reliable region in the case with noise. The components referred to as the spurious components, presented considerable power. Actually, the spurious components are the main cause of the deteriorated performance, because the other high-frequency components, deviating from the target, contribute a bit to the pattern, because of their negligible power. However, this problem can be solved by applying a rectangular window for the obtained pattern in the DFT domain, i.e. by gating the components outside the reliable region, the recovered pattern (shown as the blue curve in Fig. 6(a) in [52]) is significantly improved. The proposed strategy is examined by comparing the results using the reference antenna A and those for using the reference antenna B (antenna B has a larger HPBW compared to the AUT). It was found that the proposed algorithm with reference antenna B would not work. Moreover, gating operation would not help improving the results. It is well known fact that a less directional antenna will have a narrower main lobe in the DFT domain. The latter leads to narrower reliable region (reference antenna B). Therefore, the spurious components in the AnUT DFT pattern appears in the position close to 0◦, which can not be filtered by gating. The main conclusion is that the reliable region of the reference antenna must be broader than that of the AnUT. In other words, the reference antenna must be more (or at least equally) directional than the AnUT. 35 Theharmoniccomponentsin(5-8)shouldbeideallydelta-shapeimpulseresponsesintheDFTdomain. However, they are not, because of the finite length of the power measurement sequence from the virtual probe array. Therefore, thepower leakagein the frequencyspectrum isnotavoidableandwill resultin interferingpower onthe zerofrequency in the DFT domain, introducing undesired components ˜ σto ˜ Θ. The interfering power introduced by the spectrum leakage is referred to as zero-frequency pollution. We discuss how zero-frequency pollution would affect the proposed algorithm and how to mitigate the adverse effects (reference antenna Ais used). The spectrum leakage is determined by the length of the processed power sequence. Therefore, the longer the length of the power sequence, the less leakage will be introduced [74]. However, longer sequence length means also more measurement locations and longer measurement time. Two configurations are considered here, i.e. case α: 15 probe positions and case β: 30 probe positions. The same moving step ∆d=λis used. Fig. 8 in [52] presents the results. It was observed a noticeable accuracy deterioration for configuration αcompared to that with M= 30 probe positions. This phenomenon can be explained by looking at the individual harmonic frequency spectrum of all the components in (5-8) at a certain field angle. As it was expected, the components in the DFT domain act in the form of the sinc function [74]. When the larger sampling length is adopted, all the components in the harmonic frequency spectrum become closer to the Dirac impulse, and less zero-frequency pollution will be introduced. Therefore, using a large virtual probe array for the proposed algorithm is important to reduce the zero-frequency pollution and improve the recovery precision. IfthelengthofprobemovementisD,thespatialBWis1/D.˜ kisassumedtobetheminimumharmonicfrequency A.Dshould satisfy the relationship: D > 2 ˜ k(5-17) Equation (5-17) shows a practical guideline for the required distance of the probe movement. However, ˜ kis typically unknown. The selection of Ddepends on the differences in the impinging angle of propagation paths. A large separation would need a small D. If the roughly estimation of the dominant echoes in the environment is possible, then the Dcan be set accordingly. Moving the probe to many locations will typically require long measurement time. Therefore, we will derive the relationship between the number of probe positions and the precision of the algorithm. From the main principle of the Fourier transform, it is known that the length of the sequence determines the lobe width and decaying rate of the sinc function in the DFT domain. On the other hand, for a fixed sequence length, the number of sampling points, i.e., samplingrate,determinesthespectrumaliasingintheDFTdomain. WithgivenprobemovementlengthD,thesampling rate is fs= (M−1)/D.k′is assumed to be the maximum harmonic frequency in (5-8). All signal processing algorithms would satisfy the Nyquist sampling theorem to avoid spectrum aliasing in the DFT domain. However, the proposed method is concerned with zero-frequency fidelity, and the aliasing at other frequency points is not significant. Fig. 12 in [52] presents an example of the harmonic spectrum and the periodically extended spectrum introduced by the finite Fourier transform (the Hamming window is used). It could be observed that although the spectrum aliasing exists, the zero-frequency point is not impacted as well. Therefore, a criteria that the sampling rate should follow: fs> k′+B(5-18) 36 or after some transformations: M=fsD+ 1 >(k′+B)D+ 1 =k′D+BD + 1 =k′D+ 3.(5-19) During a long measurement (especially when considering the phase measurement), the chamber environment may normally not remain stationary. Therefore, the phases of propagation paths are not stable. However, the spatial deconvolution(asdiscussedinthesecondsection)wouldrequireanaccuratephaseinformation. Fig. 14in[52]presents the recovered patterns for 200 realizations with the conventional spatial deconvolution algorithm and the proposed algorithm, using the data with and without phase noise. The unstable phase was modeled by adding small random phasedeviationsrangingfrom−3.6◦to3.6◦. Inthissimulation,D= 60λ, ϕ1=−28◦, ϕ2=−25◦, andtenprobepositions are used. It can be observed that in the ideal scenario, the reference method presents excellent accuracy, while the performance significantly deteriorates, when the measurement environment is changed, even for a rather small phase variation. However, the proposed method is relatively not susceptible to the unstable phases, especially in the main beam and first sidelobe regions. It can be concluded that the phase deviations are associated with the impacts of zero-frequency pollution and pseudo path, leading to variations of the recovered pattern. 5.4 Experimental validation The measurements are conducted in a large AC at Aalborg University, Aalborg, Denmark. The test scenario is presented in Figure 17. Figure 17: Experimental setup in a non-anechoic scenario A metal plate with the size of 1 m × 1 m is used to construct a non-anechoic environment. The plate location is configured to create strong reflection paths towards the probe. The probe and the AnUT used LGF-11-1800-WB-DL 37 antenna with HPBW of 40◦, as presented in Figure 18a. A standard gain horn (SGH) antenna Flann 22240-20 with HPBW of 20◦(Figure 18b) was employed as the reference antenna. The measurement frequency was 28 GHz and bwas the wavelength. (a) (b) Figure 18: Photos of (a) probe (AnUT) antenna and (b) reference antennas The implementation of the virtual probe array in the validation measurement can be summarized by the following steps: 1) Place the reference antenna (with a known pattern) on the turntable. 2) Move the probe antenna to the first spatial location, where the distance from the probe to the reference antenna (or AnUT) is 9.22 m in our measurement setup. 3) The reference antenna is rotated in the azimuth plane and measured for the first spatial location. 4) Repeat the antenna pattern measurement for probe antenna at other spatial locations (with the help of a slider) and obtain the received power response of reference antenna PREF (m, ϕ)for all spatial locations, i.e., (10). The movement direction is along the LOS path propagation. In our measurement, the probe is moved to M= 38 points with ∆d= 0.5λbcovering the 19.82 −cm measurement range. 5) Replace the reference antenna with AnUT. Repeat the procedures (1)–(4) for the AnUT to obtain the received power response of AnUT PAUT (m, ϕ)for all spatial locations, i.e. (5-8). A single measurement (at one probe position) of the AnUT pattern or the reference antenna pattern in a 2-D azimuthplanetakesonlyoneminute. Thepowerdivergenceofthe propagationpathamongtheprobearrayintroduced by the FSPL is not more than 0.18 dB and it can be ignored. To examine the environment characteristics, the AnUT is rotated and the frequency responses at the frequency band 28–30 GHz by using a VNA are measured. For each angle, 101 frequency points are recorded. Note that the wideband complex-signal measurement aims to show the power angle delay profile (PADP) of the employed non-anechoic environment, while for the proposed algorithm only singlefrequency amplitude-only data at 28 GHz is used. Figure 19 presents the results for the obtained PADP. 38 (a) (b) Figure 19: PADPs of (a) anechoic and (b) NAC environments Except the LOS path and reflection, there are also some weaker propagation paths, as indicated by the yellow arrow, which may be caused by system nonideality, the scattering path caused by the setup components, and the diffraction paths introduced by the edges of the plate. It is observed that a path appears with a delay smaller than that ofthe LOS.Itis a signalpath that shouldbe introducedbythe loose connectorbehind theprobeantennaor insufficient isolation between the Transmitter (Tx) and the Rx. Furthermore, it can be concluded that the diffraction paths may be not only from 2-D plane, but also in the 3-D direction, due to the top and bottom edges of the plate. Note that the presented results are without normalization to demonstrate the agreement between the reconstructed and the true antenna patterns. For the algorithm validation, the reference antenna and AnUT are first measured in the AC and then measured at 28GHzintheconstructednon-anechoicenvironmentforthepreset38probepositions. Theantennapatternsmeasured in a NAC are presented in Figure 20. 39 Figure 20: Reconstructed patterns using different sets of probe positions The red curve indicates that due to the multipath interference, −20-dB gain deviations are introduced in the region around −30◦. Furthermore, the gain, HPBW, and location of the main beam can not be accurately measured. By applying the proposed processing algorithm, Figure 20 illustrates that a significant improvement of the antenna pattern can be achieved, and the amplitude of the main beam is well recovered. Slight deviations at the angles about −100◦can be caused by MU and zero-frequency pollutions. Additionally, marginal discrepancy appears in the regions of φ = −130◦to 180◦and 130◦to 180◦, which is attributed to the low SNRs in these regions in the measurement. To examine the inference about the required numbers of probe positions, different sets of probes are employed for algorithm validation. The maximum harmonic frequency is assumed to be contributed by the echo from −45◦and the LOS path. The derived number should be larger than 8.4 positions when applying the window function. Thus, the probe position index with the spacing of 2, 3, and 4 is selected, i.e., the index [1, 3, 5, . . . , 37] (M= 19), [1, 4, 7, . . . , 37] (M= 13), and [1, 5, 9, . . . , 37] (M= 10), respectively, to perform the proposed algorithm. The recovered results are shown in Figure 20, and the excellent matches validated the effectiveness of the proposed criteria, and the peak deviationis only0.2dB. Figure19 showsthat the reflectionpathis actuallyat approximately−28◦. Thederivedrequired number of probe locations is M= 5.1, and at least six locations should be used. As expected, when M= 5, obvious pattern distortions can be observed in Figure 20. The obtained minimum length of probe movement for the algorithm implementation is ˆ D= 0.183 m. Figure 21 shows the patterns reconstructed with the lengths of 100%ˆ D, 75%ˆ D, 50%ˆ D, and 25%ˆ D. 40 (a) (b) (c) (d) (e) (f) (g) Figure 24: ULA pattern comparison between the target and the reconstructed for 7 beams a) 0°b) -17°c) 17°d) -35°e) 35°f) -59°and g) 59° 47 (a) (b) (c) (d) (e) (f) (g) Figure 25: URA pattern comparison between the target and the reconstructed for 7 beams a) 0°b) -17°c) 17°d) -35°e) 35°f) -59°and g) 59° 48 The number of sampling angles within [−90°, 90°] is decreased from 181 points with a uniform step of 1◦to 19 points with a uniform step of 10°and to 7 points with a uniform step of 30°in order to better illustrate the effectiveness of the measurement campaign. The number of mechanical rotations needed in the current hardware configuration or thenumberofprobesneededinamulti-probearrangementcanbothbedecreasedbyloweringthenumberofsampling angles. The URA, for instance, is sampled with an angle step of 10°and 30°to produce the all-on measured element patterns, which are then interpolated with an angle step of 1°. Ultimately, different array patterns are reconstructed with an angle step of 1°by combining the interpolated element patterns and the beam-steering weights from different beams. For beams 0°, −17°, −35°, and −59°, respectively. The array patterns reconstructed by 10°and 30°angle sampling steps are compared with the target array pattern with an angle step of 1°in Figure 26. (a) (b) (c) (d) Figure26: URApatterncomparisonbetweenthetargetandtheall-onreconstructedusingtwoelementpatternsampling steps for 4 beams a) 0°b) -17°c) -35°and d) -59° Although there is an error in terms of sidelobes and nulls, the two angle sampling stages produce the same main beam pattern as the target for four beams. Compared to 30°sampling, the sidelobe and null errors obtained by 10°sampling are smaller. Note that depending on the application, a trade-off between the pattern accuracy and the sparse sampling step should be taken into account. For instance, in mmWave UE applications, where sparse angle sampling can be used, the primary beam is the focus. The sampling step will be lowered for more accurate pattern performance in applications like mmWave BS where precise measurements of sidelobes and nulls are required. 49 6.4 Conclusion Using a fast multi-beam pattern measuring technique of mmWave phased array antenna systems, an effective multibeam pattern measurement campaign has been described. For multi-beam pattern reconstruction of phased arrays, it is possible to precisely extract all element complex patterns in the practical all-on mode of arrays throughout the measurementcampaign. Furthermore,asparsesampleofelementpatternswithawidebeamwidthcanmoreeffectively reconstruct the multi-beam array patterns. Extending the measuring technique based on a NF setup with a shorter measurement distance would be ideal for future research. The free space propagation coefficients between array elements and probes need to be carefully calibrated out from the measured element fields. Due to the inaccessible antenna connectors and the difficulties of phase measurement at mmWave frequencies, the requirement for complex measurement may be challenging. Therefore, in practical mmWave systems, it would be also preferable to retrieve the element complex pattern by amplitude-only measurements. 50 7. AC Direct Far-field (FF) Measurements of Total Radiated Power (TRP) 7.1 Scope This chapter shows results for an anechoic-chamber-based method for the measurement of TRP from 5G BSs in the FR2 frequency range (39 GHz). The 5G NR FR2 signal at 39 GHz was generated by a vector signal transceiver (VST) NI PXIe-5840, together withmixerstoupconvertand down-convertIF signal at3.5 GHzinto39 GHz. All measurementswere performed at the NPL SMART chamber facility in Teddington, United Kingdom. The measurements were performed as a part of Activity A1.2.5 in the 21NRM03 MEWS project. 7.2 Introduction In 5G NR, especially in FR2, radio systems integrate the antenna array with the RF front-end, making it difficult to perform conducted power measurement. Beamforming and direction-dependent antenna gain also cause large variations in radiated power that cannot be captured at a connector port. Therefore, 3GPP defines transmitter performance using TRP, which represents the spatially averaged power radiated into free space. TRP enables consistent OTA evaluation across different antenna architectures and ensures that minimum output power, spurious emissions, and other transmitter requirements reflect real-world radiated behavior rather than internal RFIC characteristics. The NR System Simulator (SS) and the DUT shall be configured in accordance with TS 38.521-1 [87], Section 6.2.1 (UE maximum output power), using the default settings defined in TS 38.521-1 [87] and TS 38.508-1 [88] as applicable. The measurement shall be performed based on the detailed test parameters specified for each band in Table 4.3.3-1 of TR 38.834 [89]. Meanwhile, in mm-wave FR2 testing, OTA measurements face a major imbalance between downlink (DL) and uplink (UL) power levels. Due to very large free-space path loss at millimeter-wave frequencies, the transmit power in UL becomes extremely weak, often approaching the noise floor, making reliable EIRP/TRP measurement difficult. Conversely, DL signaling from the test equipment must be strong enough to maintain link stability, which can drive the UE receiver into saturation during EIS sensitivity tests. This “high-DL / low-UL” mismatch leads to measurement dynamic-range limitations, receiver overload, excessive attenuation requirements, poor SNR in UL, and unreliable OTA results, motivating the need for near-field methods, hybrid FF/NF techniques to maintain the test feasibility. 7.3 3GPP’s definition of Total Radiated Power with Anechoic Chamber Method Transmitter power measurements shall be performed using TRP as a measurement metric. This definition will be used to calculate the TRP value of NR FR1 DUT where the TRP with AC method is defined as: TRP =1 4πZπ θ=0 Z2π ϕ=0EIRPθ(θ, ϕ) + EIRPϕ(θ, ϕ)sinθdϕdθ. (7-1) where the effective isotropic radiated power (EIRP) is defined as: EIRP(θ, ϕ) = PTGT(θ, ϕ).(7-2) where is the product of the power delivered to the antenna PTand the antenna’s power gain GT. Note that EIRPθand EIRPϕdenote the EIRP components in the corresponding θand ϕ-polarizations. The discrete forms of 51 angle interval in the θand ϕ-directions are represented by ∆ϕ=2π Mand ∆θ=π N, respectively. Therefore, the discrete summation form of TRP for the AC method, using the sinθ∆θweighting, is expressed as [90]: TRP ≈π 2NM N−1 X n=0 M−1 X m=0EIRPθ(θn, ϕm) + EIRPϕ(θn, ϕm)sinθn.(7-3) where N and M are the number of sampling intervals for θ and ϕ axes, respectively. θnand ϕmare the measurement angles. In theory, there is no singularity or loss of information at the pole (θ = 0°), because the polar axis corresponds to a single point with zero solid angle, and the integration is mathematically well-defined. However, in practical numerical integration, the radiation pattern is sampled at discrete θ values, typically at uniform angular steps such as 1°, 2°, or 5°. If the maximum radiation beam is directed exactly toward θ = 0°, two following problems may occur: 1. The measurement points at θ = 0° have a weight of sinθ = 0, resulting in zero contribution to TRP calculation in (7-3). 2. The next available sampling point (e.g., θ = 15°) may already be significantly below the actual peak level, especially for highly directive millimeter-wave antennas. As a result, the discrete approximation may underestimate the radiated power in the vicinity of the main beam. To solve this problem, the Clenshaw-Curtis quadrature may be used in the integral instead. The summation form based on the Clenshaw-Curtis quadrature integral approximation of TRP with AC method is defined as: TRP ≈1 2M N X n=0 M−1 X m=0EIRPθ(θn, ϕm) + EIRPϕ(θn, ϕm)W(θn).(7-4) where the value of W(θn)follows Table 1 below (Table 5.1-1 in TR 38.834 [89]). Table 1: Weights for Clenshaw–Curtis Quadrature with ∆θ= 15◦. Clenshaw–Curtis θ[deg.] Weights 0 0.0070 15 0.0661 30 0.1315 45 0.1848 60 0.2270 75 0.2527 90 0.2620 105 0.2527 120 0.2270 135 0.1848 150 0.1315 165 0.0661 180 0.0070 52 7.4 Far-Field DL Testbed Implementation inside AC Figure27showsthe measurementsystemconfigurationdevelopedforevaluatingtheTRP or effectiveisotropicradiated power (EIRP) in the millimetre-wave frequency range. The antenna under test (Tx) is mounted on a rotatable positioner inside an anechoic chamber, which allows both azimuth and elevation scanning. This enables the acquisition of the radiated power distribution in all spatial directions, from which the TRP is calculated by spatial integration. The chamber walls are covered with RF absorbers to suppress reflections and to emulate free-space conditions. A receiving antenna (Rx) with known gain value is fixed at a specific position to detect the electromagnetic waves radiated from the Tx antenna. Figure 27: FR2 TRP OTA test system implemented in our study for 38.5 GHz band; AMP: amplifier, MX: mixer, DCP: directional coupler, PDV: power divider, SG: signal generator In the transmit and receive signal paths, a set of high-frequency amplifiers, band-pass filters, and frequency mixers are used for frequency conversion and unwanted signal suppression. The millimeter-wave LO signal at 35 GHz (output power: 4 dBm) is generated by an LO signal generator (Rohde and Schwarz, SMB100B). Because coaxial-cable loss at 35 GHz is significantly higher than in the microwave region below 18 GHz, the LO generator is placed inside the chamber to minimize cable length and reduce transmission loss for the common LO distribution. The LO signal is then amplified by an amplifier (Agilent, 83050A, 2–50 GHz) and delivered through a power divider (Mini-Circuits, ZC2PD5R263-S+)totwo10-dBdirectionalcouplers(Mini-Circuits,ZCDC10-5R263-S+)toincreaseisolationand suppressleakage RF signals from the transmitter path to the receiver path. The LO signals fed from the directional couplers are upconverted to 38.5 GHz by a mixer (Mini-Circuits, ZMDB-653H-E+) using a 3.5-GHz baseband IF signal with a bandwidth of 40MHzgeneratedbyanVSTNIPXIe-5840. Theresulting38.5-GHzRFsignalisamplifiedbyapoweramplifier(ERZIA,ERZHPA-2400-5000-28) andthen passedthrougha cavity band-passfilter(Aaren Technology, AT22F-WS422-KF) beforebeing transmitted to the antenna under test (AUT).On the receiving side, the signal captured by a well-calibrated Rx antenna (A-Info, LB-180400-15-C-KF) is amplified by a low-noise amplifier (ERZIA, ERZ-LNA-2600-4000-30-2.5) and filtered using a cavityband-pass filter(AarenTechnology, AT22F-WS422-KF) beforebeing down-convertedtoan intermediatefrequency 53 (IF) by the mixer (Mini Circuits, ZMDB-653H-E+). The resulting IF signal at 3.5 GHz is then amplified by an amplifier (Agilent, 83020A) and goes through an LTCC lowpass filter (Mini Circuits, DC - 3800 MHz). Finally, the signal is digitized by an NI PXIe-5840 VST, which performs integrated I/Q demodulation, frequency sweeping, and power computation. This system enables broadband and highly accurate radiated power measurements in the millimeter-wave band and is suitable for characterizing the radiation performance of 5G/6G wireless terminals and antenna modules. 7.5 Measurement Procedure of Receiver Path Loss According to the procedure stated in TR 38.834 [89], the relative power values of the measurement points will be transformed to absolute radiated power values (in dBm) by performing a range path loss measurement. The DUT is placed at the center of the QZ inside the chamber, and the attenuation of the complete receiver path, Ltotal, from the receiving antenna end to the measurement receiver should be calibrated out beforehand. Firstly, direct connection between the end of the cable at the transmitter side to that of the receiver side inside the chamber is done as shown in Figure 28 and the power at the output of the cable at the transmitter side is then measured. Figure 28: Measurement of receiver path loss Ltotal; AMP: amplifier, MX: mixer, DCP: directional coupler, PDV: power divider, SG: signal generator A conventional RF and microwave power meter measures the total in-band power integrated over the entire occupied signal bandwidth, rather than the power at individual frequency components. Since typical power meters employ thermoelectric or diode-based sensing without frequency-selective filtering, all signal components entering the sensor within its specified operating frequency range are summed to produce a single average power value. Figure 29 shows the receiving signal at the VST when the total in-band power at the end of the transmitter side is equal to -26.88 dBm, -37.08 dBm, -47.09 dBm, and -57.10 dBm, respectively. 54 Figure 29: Measurement of received power at the receiver in the IF band The band-integrated average powers measured at the receiver or VST for four cases, i.e., without attenuator, with 10 dB, 20 dB, and 30 dB attenuator, are equal to -6.33 dBm, -13.14 dBm, -22.58 dBm, and -32.41 dBm, respectively. Figure 30 shows the relationship between the measured power at the cable end and the received power at the VST. Figure 30 indicates the linear relationship between the received power at the receiver and the input power measured at the cable end. The data points align closely with the fitted straight line, indicating a high degree of linearity when the input power is below around -40 dBm. The slope of the fitted line represents the proportionality factor between the input and output power. Finally, we can determine the path loss at the receiver side by subtracting the received power with the input power which lies in the linear range, i.e., Lcable =Pmeas−PT=−32.41−(−57.10) = 24.69dB. Since Lcable has a positive value, the receiving side experiences a gain rather than a loss since amplifiers were used in the receiving path. Figure 30: Linearity between the input power measured at the cable end and the received power at the receiver 55 7.6 TRP Test Procedure According to the TRP test procedure stated in TR 38.834 [89], the TRP of the DUT is measured by sampling the radiated transmit power of the DUT with a 3D scan at various locations surrounding the device. The measurement is performed with a constant sampling step of 15 degrees in both θand φ-direction for TRP measurement. As per 3GPP standard, number of sampling points in θand φ-direction are set to N = 13 and M = 24, respectively. This accounts for a total numberof312measurementsforeachoftwoorthogonalcomponents. Allthemeasuredpowervalueswillbeintegrated into TRP, as defined in Clause 5.1 of TR 38.834 [89]. The measurement procedure includes the following steps: 1. Place the DUT inside the QZ following the positioning guideline defined in Clause 6 of TR 38.834 [89]. 2. Connect the NR SS with the DUT through the link antenna following Steps 1 and 2 in Section 6.2.1.4.2 of TS 38.521-1 [91] and ensure the DUT transmits with its maximum power. 3. Measure the power at each measurement point, and calculate EIRP(θ, φ) by subtracting the composite loss of the entire receiver path. TheTRPvalueiscalculatedusingtheTRPintegrationapproachesoutlinedinClause5.1in[92]andheredescribed in Section 7.3. 7.7 TRP Measurement Results The measured power results using VST in NPL are shown in Figure 31. The power measured at the VST can be converted into EIRP using the following equation: Pmeas [dBm] = PT[dBm] + GT[dBi] + GR[dBi] + 20 log10λ 4πddB +Lcable [dB].(7-5) Therefore, EIRP[dBm] = PT+GT=Pmeas −GR−20 log10λ 4πd−Lcable.(7-6) where PTis the transmitting power supplied to the transmitting antenna, GTand GRare the transmitting and receiving antenna gains, respectively. Pmeas is the power measured at the VST, λis the wavelength, d is the distance between transmitting and receiving antennas. Here d = 1.7 m and λ= 7.79mm at 38.5 GHz. Lcable represents the path loss of the receiver side from the end of the receiving cable to the VST, which is measured using procedures in subchapter 7.5. A standard gain horn antenna (Flann Microwave, Model no. 22240-20) with a typical gain of 20 dBi and a double-ridge guided horn antenna (A-Info, LB-180400-15-C-KF) with a typical gain of 15 dBi were used as transmitting and receiving antennas, respectively. From 31, the maximum receiving power of -63.66 dBm at 38.5 GHz for combined polarization is obtained when θ = 0° and φ = 345°, which is slightly shifted from the boresight direction of the antenna. This may be caused by antenna misalignment. The EIRP at θ = 0° and φ = 345° is calculated as: EIRP =−63.66 dBm −17.22 dB −−68.76 dB−24.69 dB =−36.81 [dBm].(7-7) Since PT measured at the cable end before connecting to the transmitting antenna is -58.52 dBm at 38.5 GHz, the transmitting antenna gain is then determined as 21.71 dBi. Meanwhile, the simulated antenna gain derived by using the 56 Signalling Bandwidth 200 MHz. Figure 40: Comparison between reference measurement (left) and RC TRP measurement (right) with signalling bandwidth of 200MHz. The difference between the measurements is 0.76 dB. Figure 41: Comparison between TRP for antenna without 3 dB attenuator (left) and with 3 dB attenuator (right) for a signalling bandwidth of 200 MHz. Difference between measurements is 3.61 dB. 8.1.3.4 2x2 MIMO Signalling Bandwidth 100 MHz Figure 42: Comparison between reference measurements (left) and RC TRP measurement (right) with signalling bandwidth of 100MHz in 2x2 MIMO mode. The difference between the measurements is 0.41 dB. 63 Figure 43: Comparison between reference measurements (left) with attenuator on the second antenna and RC TRP measurement (right) with signalling bandwidth of 100MHz. The difference between the measurements is 0.07 dB. Signalling Bandwidth 200 MHz Figure 44: Comparison between reference measurements (left) and RC TRP measurement (right) with signalling bandwidth of 200MHz in 2x2 MIMO mode. The difference between the measurements is 0.55 dB. Figure 45: Comparison between reference measurements (left) with attenuator on the second antenna and RC TRP measurement (right) with signalling bandwidth of 200MHz. The difference between the measurements is 0.38 dB. 64 8.1.4 Measurement uncertainty The measurement uncertainty was estimated according to table 3. Table 3: Measurement uncertainty for TRP measurements. 8.1.5 Conclusions This subsection shows a straightforward proposal for a RC TRP measurement method for FR2 frequencies of 5G BS. To decrease the measurement uncertainty a smaller RC can be used to increase the OTA power levels in calibration and DUT measurements. If doing so, care should be taken to avoid line of sight coupling between DUT/calibration antenna and measurement antenna, which might be a problem when reducing RC size. Another improvement is to use more measurement samples in the DUT measurements, but there is a trade-off between uncertainty and measurement time that has to be made. The measurement time can probably be improved with an effective implementation of the method in software and control of measurement equipment. 8.2 TRP measurements in NPL RC 8.2.1 Introduction The adoption of complex 5G NR signals and multi-antenna technologies in emerging wireless systems has made their verification increasingly challenging. Thorough conformance testing of such NR systems is essential to evaluate wireless performance under real propagation scenarios in laboratory conditions, and to ensure that RF metrics fulfill the standard requirements before massive roll-out. These tests will move exclusively towards an over-the-air OTA radiated testing approach with antennas included, due to the lack of antenna connectors and their compact and highly integrated design incorporation in NR systems. Industry, research bodies and standards organizations, such as 3GPP [95], International Association for the Wireless Telecommunication Industry (CTIA) [92], and EuropeanTelecommunicationStandardsInstitute(ETSI)[96]areactivelyseekingimprovedNROTAtestingmethods. Accurate measurement of three-dimensional (3D) radiation patterns for device under test (DUT) with narrow beamwidths requires fine spatial resolution. OTA conformance testing for multiple-input-multiple-output (MIMO) RF parametrics has been studied in technical report TR 38.810 [97]. However, conventional methods are costly, time-consuming and cumbersome due to the beam-steering capabilities of 5G NR systems. According to TR 38.810 [97], such measurements can take several days, highlighting the need for more efficient approaches. 65 Measurement of TRP for radio equipment, both BSs and user equipment (UE), is essential as the EU Radio Equipment Directiveimposes itas an essential requirement[[98], [99]]. The purposeof thesemeasurementsis toensurethat anyradioequipment should support the efficientuseof the radiospectrum and conformityshouldbe demonstratedby using OTA metrics such as TRP and equivalent isotropic radiated power (EIRP), as defined in the harmonized standards [[90], [100]]. Methodological details of the TRP measurements for millimetre-wave (mm-wave) MIMO BS systems and UE are outlined in 3GPP test specifications, namely, ETSI TS 138.141-2 [90] and ETSI TS 138.521-2 [91], respectively. However, conventional TRP measurement methods such as DFF, CATR, and near-field-to-far-field (NF-FF) techniques, share a major common drawback – long measurement time. TRP requires integration over the full radiation sphere so both DFF and CATR methods must mechanically scan azimuth/elevation with fine angular steps to avoid under-sampling, especially for narrow beams at mm-wave frequencies; when combined with multiple frequency bands, output power levels, and large sets of beam configurations, further increase complexity and the required number of measurement configurations explodes. High path loss at 5G NR FR2 frequencies further stretches the dwell times, as more averaging is needed to satisfy dynamic-range and repeatability targets. NF-FF method is even more time-consuming, requiring dense spatial sampling, dual polarization, phase stability, and extensivepost-processing, such asprobe correctionand far-field reconstruction, especially for mm-wave MIMO equipment. These challenges highlight the urgent need for a faster, accurate, and traceable TRP measurement approach that can significantly reduce test time while maintaining accuracy and traceability. Reverberation chamber (RC) is an over-moded reflecting environment providing statistically homogeneous and isotropic fields within its working volume [101]. Such capability makes RC a faster and often more cost-effective alternative to an anechoic chamber for the TRP testing. This subchapter presents a newly developed cost-effective and time-efficient method for measuring TRP for conformance testing of a 5G NR BS using the RC technique. A new testbed setup has been configured to rigorously evaluate the transmission characteristics between antennas inside the chamber, as well as the reflection power from thetransmittingantennawithintheRC.Themeasurementmethod has undergonecalibrationandverificationtoensure reliability. The antenna efficiency, which can be used to calculate TRP, is obtained by using the proposed testbed. Its validity is confirmed by comparing results with those from a conventional VNA. 8.2.2 Testbed setup The testbed architecture is shown in Figure 46(a). There are two stages of test procedure, i.e., calibration and measurement stages. In the calibration stage (the relevant setup involved are shown in Figure 46(b), a Zadoff-Chu (ZC) orthogonal frequency division multiplexing (OFDM) signal with intermediate frequency (IF) of 3.2 GHz and a bandwidth of 40 MHz is generated using a National Instruments (NI) PXIe-5451 waveform generator and in-phase andquadrature(IQ)modulator(NIPXIe-5611). ThissignalisupconvertedtoRFat26GHzusinga22.8GHzlocaloscillator (LO) signal from a Keysight N5173B EXG source. 66 (a) (b) (c) Figure 46: Illustrative diagram for: (a) the testbed architecture; (b) its calibration setup; (c) its measurement setup The resulting mm-wave signal passes through a band-pass filter (AMWAV AWBPF25.5-26.5GC2), a power splitter (Mini-Circuits ZN2PD2-50-S+), RF switches (NI PXI-2599) and a four-port downconverter (Keysight M9362A-D01) into the four-channel vector transceiver (NI PXIe-5644R). At the receiver, fractional-delay and phase-difference estimation for 67 each channel are performed; the resulting corrections are applied in real time so that all channels remain phasealigned over long runs. Digital signal processors can then perform channel estimation and analyses on the coherent data. The signal from one channel is utilized as the power/phase reference versus the other three channels. With the proposed scheme, reliable measurements can be carried out, and the measured data can be stabilized against the time-varying drift. As a result, this setup enables stable, coherent measurements and accurate frequency response estimation across all receiver channels. At the measurement stage (the relevant setup involved are shown in Figure 46c, the RF switches are switched to the measurement route (yellow color route as illustrated in Figure 46. A 5G NR waveform is transmitted from the Anritsu base-station emulator (BSE) MT8000A to a mm-wave extender MA80003A for up-conversion to FR2 signals at 26 GHz, then they pass through a coupler module, which is comprised of a 10-dB hybrid coupler and a power splitter (Mini-Circuits, ZN2PD-183W-S+). Using this combination, one can reduce the interference by the signals reflected from the antenna to the reference signals, i.e., suppressing amplitude of S32. The main path (through the S21 route) feeds the transmitting antenna Tx1 inside the RC, while two taps of the coupler module provide references; one from the coupler module with the route S31 (forward sample) for the phase and power normalization at each measurement and the other from the power divider at the route S42 (reverse sample) to monitor the mismatch power from the transmitting antenna. A coherent four-channel receiver ingests signals from route S31,S42, and from the two receiving antennas (Rx2, Rx3) inside the RC under acommonLO signal distributedvia a powersplitter. The RF signalsare thendownconvertedintoIF signals, which are transmitted into the transceiver for digitization and signal processing. As a result, one can obtain time-aligned, self-referenced data required in deriving the transmission characteristics between antenna pairs or the S-parameters of SRx2-Tx1 and SRx3-Tx1. These data will be used to determine antenna efficiency and TRP of the transmitting antenna Tx1. 8.2.3DesignoftheSoftwareforReal-Time Processing The main challenge of the proposed method lies in measuring S-parameters using real 5G NR signals generated by the DUT, as required by 3GPP standards, rather than relying on traditional VNA techniques. To address this challenge, in this paper, a real-time, multi-channel software solution has been developed. It enables S-parameter measurements between multiple receiving channels by leveraging the 5G NR downlink waveform, ensuring compliance with standard requirements while maintaining measurement accuracy and efficiency. This software, incorporating the real-time processing capabilities of the multi-channel VST platform, can provide up to four channels with 80 MHz bandwidth per channel real-time measurement capability. Due to its inherited wide-band demodulation feature, it can hugely reduce the measurement duration compared with the sweepingfrequency-based VNA method. Figure 47 illustrates the real-time processing program structure, which consists of two consecutive steps, i.e., the calibration and measurement steps, respectively, same as the architecture shown in Figure 46. The calibration step, which is required to launch regularly during the measurement period, aims to measure and eliminate the channel response differences existing in the multiple RF receiving measurement channels. A ZCOFDM waveform is generated by a dedicated RF generator in the calibration branch, see Figure 46. At the receiver side, a channel frequency response (CFR) estimation algorithm is applied to obtain the deviations in the relative CFRs of each RF channel, normalized to the reference channel, i.e. the receiving Channel 1 (denoted as Ch1). An iterative sampling adjustment is applied to eliminate the errors and uncertainties caused by sampling timing differences by a fractional delay resampling module with the estimated delay offsets as inputs. Since the measurement of relative CFRs is operation in the calibration RF branch, all differences between the measurement branch and calibration RF branch, 68 including cables, different ports in the RF switch, power dividers, adapters. etc., are carefully considered, measured in advance, and compensated in the CFR estimation processing. After measuring the relative CFRs, the whole system is switched to the measurement stage by simply switching the RF path to import the 5G NR downlink signal and executing the corresponding processing program, without interrupting the continuous signal streaming at the receivers. The measurement stage involves full data processing of the 5G NR downlink signal. It begins with time and frequency synchronization using the Synchronization Signal Block (SSB), followed by blind detection of the Physical Downlink Control Channel (PDCCH) to extract the Downlink Control Information (DCI) required for subsequent Physical Downlink Shared Channel (PDSCH) demodulation. As shown in Figure 46, the receive channel 1, Ch1, typically connected to the DUT’s RF output through a coupler, serves as the reference channel due to its superior signal quality compared to the rest of the channels. In the next step, PDSCH demodulation processing is performed on the receiver Ch1, including channel estimation, equalization, and bit-level demodulation. The detected bit sequence is then used to reconstruct the transmitted downlink waveform through modulation, enabling accurate S-parameter measurements in the following stage. In the final step of the measurement stage, all receiving channels (Ch1, Ch2, Ch3, and Ch4) perform channel estimation using the reconstructed waveform as the reference waveform. To evaluate the OTA transmission characteristics, the influence of the RF measurement paths is removed by compensating with the previously stored relative CFR. This process, analogous to calibration in a VNA, effectively sets the calibration plane at the inputs of the VST receivers. As a result, accurate and traceable S-parameter measurements can be obtained. Figure 47: Two-step VST-based S-parameters measurement program structure. The acronym definitions are: FFT – Fast Fourier-Transform; IFFT – Inverse FFT; CFR – Channel Frequency Response; PBCH – Physical Broadcast Channel; PDCCH – Physical Downlink Control Channel 8.2.4 Testbed verification To verify the testbed’s performance for transmission measurements, we use a coupler module as a DUT by connecting the output port of the DUT to Ch2 and measure the transmission between Ports 1 and 2 or S21. Figure 48 illustrates the configuration for the direct connection to the Ch2 cable. The insertion loss of all measurement cables was measured in advance using a VNA and then de-embedded with the postprocessing. The reference planes were set at the coupler input Port 1 and at the output Port 2 as shown in Figure 48. The transmission 21 of the coupler module was then measured using the proposed testbed and compared with the VNA results. 69 Figure 48: Testbed configuration for measurement of transmission characteristics of the coupler module Figures 49–51 (a) and (b) show the amplitude and phase, respectively, of the coupler module’s transmission coefficient 21 measured with a VNA and with the proposed testbed by connecting to different receiving channel at the downconverter. Many spikes seen at the edge of the band in the plots of amplitude and phase are attributed to the processing of the fast Fourier transform, so we excluded the corresponding data points in this band. The amplitude results from the VNA and the testbed agree well within 0.3 dB, confirming that the proposed testbed setup can accurately characterize the DUT transmission and evaluate the relevant S-parameters. As observed in Figures 49-51 (b), the phase obtained from the testbed slightly differs from that obtained using the VNA. This may be attributed to cable bending when the setup was changed. Although small discrepancies are observed in the measured phase, the RC procedure for antenna-efficiency measurements averages over multiple stirring steps (e.g., stirrer positions and frequency steps), so these phase differences have only a marginal effect on the results. (a) (b) Figure 49: Amplitude and phase of measured S21 of the coupler module using the VNA and the proposed testbed when directly connected the output port of the coupler module to the receiver Ch2: (a) Amplitude; (b) Phase 70 (a) (b) Figure 50: Amplitude and phase of measured S21 of the coupler module using the VNA and the proposed testbed when directly connected the output port of the coupler module to the receiver Ch3: (a) Amplitude; (b) Phase (a) (b) Figure 51: Amplitude and phase of measured S21 of the coupler module using the VNA and the proposed testbed when directly connected the output port of the coupler module to the receiver Ch4: (a) Amplitude; (b) Phase 8.2.5 Measurement Results To determine antenna efficiency by the three-antenna method inside RC [102], we need to know the S-parameters of S21,S31 and S32. By using the proposed testbed, one can measure the transmission from antennas 1 to 2 and 1 to 3, which correspond to S21 and S31 while the S32 is separately obtained using the conventional VNA. Measurement setup inside the RC is shown in Figures 52. After obtaining all S21,S31, and S32, total efficiency of the transmitting antenna is determined as: ηtot =CRC |S21,s|2|S31,s|2 ω τRC |S32,s|2(8-7) where ⟨.⟩means the average value of the S-parameter using any stirring method, ω is the angular frequency, TRC is the chamber decay constant which can be extracted from the time-domain response of the chamber, Sij,s is the stirred part of the S-parameter or Sij,s =Sij − ⟨Sij⟩, and CRC is a constant defined as: CRC =16π2V λ3(8-8) 71 Here, V is the volume of the RC and λ is the free-space wavelength. Figures 53(a) and (b) indicate the amplitude and phase of the transmission S21, while Figures 54(a) and (b) show those of S31, respectively. It is demonstrated that both results measured by the VNA and VST (the proposed testbed) resemble each other. The minor difference may be caused by different cable positions or bending when swapping the cables between the VNA setup and the testbed setup since the RC is a high-Q resonator where small differences in cable positions, antenna setup angle, or bending of the cable may affect total results. A high peak at the center frequency as indicated in Figure 53(a) and Figure 54(a) is caused by the DC component when the IF signals are converted into the baseband signal. This peak is cut off by using the average value between two neighboring values instead. Then, we performed the measurement of S21 and S31 on 400 step stirrer positions and calculated the antenna efficiency. (a) (b) Figure 52: Experimental setup for antenna efficiency measurement using the RC: (a) illustrative diagram; (b) photo (a) (b) Figure 53: Measured S21 between Antennas 2 and 1 placed inside the RC: (a) Amplitude; (b) Phase 72 10. Inter-laboratory Comparisons 10.1 Scope This chapter shows results for an anechoic-chamber-based and reverberation-chamber based method for the measurement of TRP from 5G Base Stations in the FR2 frequency range (39 GHz) provided in Chapter 7 and 8, respectively. These comparisons were performed as a part of Activity A1.2.5 in the 21NRM03 MEWS project. 10.2 Introduction Due to increase in number of measurement conditions over multiple frequency bands, output power levels, and large sets ofbeam configurations, there isan increasingneed in developing anew rapid measurement methodfor evaluating the performance of 5G NR FR2 devices. To compare these to current standardized approaches, two new mm-Wave mMIMO testbeds are developed for the measurement of the NR OTA RF parametric measurement of the total radiated power and the effective isotropic radiated power. One testbed is developed by NPL (United Kingdom) and the other by RISE (Sweden). 10.3 Measurement setups for total radiated power using reverberation chamber in RISE and NPL One of the mm-Wave mMIMO testbed has been developed using a base station emulator MT8000A, along with two frequency converters (MA80002A) from Anritsu Co. The measurements were performed at the RISE reverberation chamber which has a dimension of 3.7 m × 2.6 m × 4.5 m in Borås, Sweden. Measurement setup diagram is illustrated in Figure 61. It composed of a radio communication test station (Anritsu, MT8000A), an RF converter (Anritsu, MA80002A), a standard gain horn antenna (Flann Microwave, Model no. 22240-20), a double ridge guided horn antenna (EMCO, Model no. 3116), and a spectrum analyzer (Rhode and Schwarz, FSW43). Figure 61: Measurement setup for total radiated power in RISE, Sweden; BSE: base-station emulator, SA: spectrum analyzer The other mm-Wave mMIMO testbed using a VST has been developed by NPL for total radiated power and effective isotropic radiated power measurements in an NR FR2 frequency band. The schematic diagram of the testbed is shown in Figure 46(a) and details of the architecture and software design are given in Sections 8.2.2 and 8.2.3, respectively. This system has been validated in both 26 GHz and 38 GHz bands. The measurements were performed inside the 79 NPL reverberation chamber with a dimension of 6.55 m × 5.85 m × 3.5 m. Measurement procedure of TRP is described in subchapter 7.7 and, hence, is omitted here. 10.4 Measurement results 10.4.1 RC (RISE) With the base-station emulator or a communication tester, the tethered (cable-bound) power fed to the downlink antenna in the RC can be measured and compared to the TRP measurement inside the RC. The standard gain horn antennas are used in experiments, and it is expected that the TRP will be close to the power fed into the antenna since high efficiency of the standard gain horn antenna. The measurements were carried out using the setup shown in Figure 61. Each TRP measurement is processed from 50 RC samples with the stirrers in a stepped motion mode while measurement of ⟨|S21|2⟩M(see subchapter 8.2) and chamber loss was done with 200 RC samples. Figure 62, Figure 63, and Figure 64 show comparison between reference measured power and RC TRP measurements with a signal bandwidth of 50 MHz, 100 MHz, and 200 MHz, respectively. The reference power is measured by connecting the cable end before the transmitting antenna. (a) (b) Figure 62: Comparison between (a) reference measurements and (b) RC TRP measurements with a signal bandwidth of 50 MHz. The difference between two measurements is 0.18 dB 80 (a) (b) Figure 63: Comparison between (a) reference measurements and (b) RC TRP measurements with a signal bandwidth of 100 MHz. The difference between two measurements is 0.42 dB (a) (b) Figure 64: Comparison between (a) reference measurements and (b) RC TRP measurements with a signal bandwidth of 200 MHz. The difference between two measurements is 0.75 dB It is shown that the measured TRPs are close to the reference power since the antenna efficiency is high for standard gain horn antenna. However, the reason that the differences between the reference power and TRP were larger for wider signal bandwidth is still unclear and needs further investigation. It might be attributed to the mode fluctuation nature of the reverberation chamber. 10.4.2 RC (NPL) using VST Before measuring the TRP using the NPL-developed testbed, the S-parameters between two standard gain horn antennas were measured and compared with those obtained using a VNA. Figure 65 shows the 81 measurement setup inside the RC. Three standard gain horn antennas (Flann Microwave, Model 22240-20) were used. The transmitting antenna is the same one employed in the experiments conducted at RISE, Sweden, for consistency and comparison. The center frequency of the 5G NR FR2 signal is 38.5 GHz with a bandwidth of 40 MHz. The designed testbed setup is used to measure the transmission from the Tx antenna to the Rx antenna. First, we compare the measured S21 results with those obtained using the conventional VNA method. Figure 65: Measurement of TRP by using three-antenna method in NPL reverberation chamber Figure 66 shows the ensemble S-parameter results obtained from the VNA and the testbed over 400 RC samples. It can be seen that both results agree reasonably well, with differences within approximately 3 dB, demonstrating the validity of the developed measurement system using VST. 82 Figure 66: Comparison between the ensemble S-parameter of S21 measured using VNA and that obtained from the developed testbed over 400 RC samples. Effective band indicates the band of the transmitted NR FR2 signal Figure 67 shows the antenna efficiency of the Tx antenna measured by the testbed and the conventional VNA. Measurement results using the testbed are indicated in a red box around the center frequency at 38.5 GHz since the bandwidth of the receiver is only limited to 40 MHz. Both results are in good agreement with the difference smaller than 3 %, demonstrating again the validity of our testbed at the 38.5 GHz band. For average power of 0 dBm with 40 MHz bandwidth at the input port of the base station, the TRP of 5G NR FR2 signal is determined as −1.37 dBm or 0.73 mW using the testbed. 83 Figure 67: Total radiation efficiency of the standard gain horn antenna measured by using three-antenna method and the developed testbed 10.4.3 AC Direct Far-Field (DFF) Using VST (NPL) A testbed using the VST for direct far-field TRP measurement method inside the anechoic chamber has been developed. The architecture of the measurement setup is shown in Figure 27. Figure 68 shows the measurement inside the SMART chamber facility in NPL. The antenna tower at the transmitter side has a U-shaped arm for rotation in a roll direction. In order not to get the coaxial cable tangled with the tower and rotation arm, 2.92 mm-type joint rotation connector is used and attached to the end of the antenna tower. To make a rotation in azimuth direction, the antenna tower is set on the rotation stage with absorbers to reduce the reflection from the stage. A standard gain horn antenna (Flann Microwave, Model no.22240-20) is used as a transmit antenna and a broadband double ridge guided horn antenna (A-Info, Model no. LB-180400-15-C-KF) is used as a receiving antenna. The receiving antenna is fixed on antenna tower at 1.7 m far from the aperture of the transmitting antenna. Angle steps in both θand φ-directions are ∆θ= ∆ϕ= 9°. Number of sampling points in θand φ-direction are then set to N = 21 and M = 40, respectively. This accounts for a total number of 840 measurements for each of two orthogonal components. 84 Figure 68: Measurement setup for AC direct far-field method in SMART chamber in NPL Figures 69(a), (b), and (c) show the power measured at the VST for θ-polarization, φ-polarization, and combined polarization, respectively. The maximum receiving power of -61.92 dBm, corresponding to EIRP of -35.07 dBm at 38.5 GHz for combined polarization is obtained when θ = 0° and φ = 297°. The TRP is evaluated as -54.27 dBm. 85 (a) (b) (c) Figure 69: Measured power at the VST for (a) θ-polarization, (b) ϕ-polarization, and (c) combined polarization with number of measurement points of N= 21 and M= 40. 10.4.4ACMid-Field(NPL)UsingVST The AC mid-field, or CFFNF (Combined Far-Field / Near-Field) method described in TR 38.884 is required because conventional direct far-field (FF) over-the-air (OTA) measurements for FR2 signals suffer from fundamental limitations caused by high path loss and cable loss. These limitations make certain RF test cases, particularly those involving high DL power and low UL power, either inaccurate or entirely untestable. In the FR2 bands (24–52 GHz), the free-space path loss is extremely high; for a typical far-field distance of 1 m, the loss exceeds 60–65 dB at 28–40 GHz. As a result, the radiated power becomes too weak to measure and often approaches the noise floor of the test system. Increasing the far-field distance only worsens the SNR problem, making TRP measurements unreliable or even infeasible. The key idea of using AC mid-field is to move the probe or the receiving antenna much closer to the DUT, e.g., 0.2–0.3 m. This can reduce path loss by 10–15 dB and dramatically improve SNR of the system. In TR 38.884, the signal received by the probe antenna from a transmitting antenna array is modelled as a superposition of the contributions of individual antenna elements: Signal(θ, ϕ) = X k akFk(θk, ϕk)Gprobe(αk, βk)e−jkRk Rk(10-1) where akis excitation coefficient of antenna element k, Fkis antenna element pattern, Gprobe indicates probe antenna pattern, Rkdenotes distance from element k to the probe, and k=2π/λ is the wavenumber. For a fixed angular direction (θ,ϕ), changing the measurement distance r(probe position) slightly changes all the element-to-probe distances Rk(r), and therefore the measured power: 86 p(r) = Signal2(10-2) exhibits a specific distance dependence. The AC mid-field or CFFNF method approximates this distance dependence by using a power-series expansion in terms of 1/r, and extracts the far-field EIRP/EIS as the constant (zerothorder) term of this expansion. Received power can be expressed in terms of distance d as: p(d)≈C0+C1 d2+C2 d4(10-3) C0correspondstothe far-fieldEIRP/EIS (thetermasd→∞)and the 1/d4termis thedominant near-fieldresidual after normalization. Figure 70 shows the measurement setup inside the anechoic chamber at NPL. The transmitting antenna is a standard gain horn antenna (Flann Microwave, Model 22240-20), and the receiving antenna is a double-ridge guide horn antenna (A-Info, Model LB-180400-15-C-KF). The gain of the receiving antenna must be known beforehand using (7-6). The testbed used for this measurement is the same as that used for the direct far-field method, shown in Figure 27. Measurement distances of 0.4, 0.5, and 0.6 m were selected, which lie within the radiating near-field. In this region, the far-field gain pattern of the receiving antenna is sufficiently accurate to be used as a correction term. Table 5 summarizes the measured power, the power corrected using (7-6), and the power further corrected by compensating for the known 1/r2free-space decay at 0.4, 0.5, and 0.6 m. By applying the distance-dependent fitting defined in (10-3), the far-field EIRP, corresponding to the fitting coefficient C0, is obtained as –32.21 dBm. Meanwhile, the EIRP measured directly at 0.9 m is –33.40 dBm, giving a difference of approximately 1.19 dB. This discrepancy may be attributed to the measurement distance at 0.9 m where the far-field condition is still insufficiently satisfied. It is also observed that while the measured power at 1.7 m was –63.66 dBm, the measured powers at 0.4, 0.5, and 0.6 m were –47.36, –49.01, and –50.27 dBm, respectively, more than 10 dB higher than that measured at 1.7 m, thereby significantly improving the SNR of the measurement. These results demonstrate that, using the proposed testbed, the EIRP can be accurately estimated at reduced distances, leading to improved SNR and enhanced measurement reliability, particularly when dealing with NR FR2 signals in the millimeter-wave frequency band. Figure 70: Measurement setup for CNFF method inside the SMART chamber in NPL 87 Table 5: Measurement results for measured power, corrected power, and corrected power compensated with its distance. Distance (m) Measured power (dBm) Corrected power Pcorr (dBm) Pcorr ×d2(dBm) 0.4 -47.36 -33.03 -40.99 0.5 -49.01 -32.74 -38.76 0.6 -50.27 -32.42 -36.85 10.5 Conclusion This section presents a new cost-effective and time-efficient method for measuring the TRP of 5G NR BS using a RC. A testbed employing real 5G NR signals is designed to accurately characterize transmission between transmitting and receivingantennasinside theRC.Its validityisconfirmedby comparingresultswith those fromaconventionalVNA.The testbed is then used to evaluate antenna efficiency via three-antenna method. Finally, TRP is derived for conformance testing, and the time-efficiency of the proposed method is demonstrated by comparing the total measurement time with the VNA-based approach. 88 [100] User Equipment (UE) conformance specification; Radio transmission and reception; Part 4: Performance. “TS 38.521-4 version 18.2.0 Release 18”. In: European Telecommunications Standards Institute (ETSI) (2024). [101] T Loh and J Li. “The Effect of Receiving Antenna Orientation and Polarization on Measurements of Antenna Efficiency in a Reverberation Chamber”. In: 11th European Conference on Antennas and Propagation (EuCAP 2017) (2017). [102] C Hollway et al. “Reverberation chamber techniques for determining the radiation and total efficiency of antennas”. In: IEEE Transactions on Antennas and Propagation (2012). [103] International Electrotechnical Commission. IEC 61000-4-21: Electromagnetic Compatibility (EMC) – Part 4-21: TestingandMeasurementTechniques–ReverberationChamberTestMethods.https://webstore.iec.ch/publication/ 4191. Second Edition. 2011. [104] David A. Hill. ElectromagneticTheory of ReverberationChambers. Technical Report Technical Note 1506. Boulder, CO, USA: National Institute of Standards and Technology, 1998. URL: https://nvlpubs.nist.gov/nistpubs/ Legacy/TN/nbstechnicalnote1506.pdf. 95