Effects of Micro-Scale Mobility and Beam Misalignment in On-Body mmWave Systems

682 IEEE COMMUNICATIONS LETTERS, VOL. 28, NO. 3, MARCH 2024 Effects of Micro-Scale Mobility and Beam Misalignment in On-Body mmWave Systems Asad Ali , Member, IEEE, Olga Galinina , Member, IEEE, Jiri Hosek , Senior Member, IEEE, and Sergey Andreev , Senior Member, IEEE Abstract— Wearable devices positioned on a human body have challenges in millimeter-wave (mmWave) communication due to micro-scale mobility, such as subtle shakes and rotations. These movements can compromise the radio link performance. It may be problematic for high-rate immersive applications, where this can lead to substantial degradation in the user’s quality of experience. In this letter, we propose a framework to quantify the impact of micro-scale mobility and beam misalignment on the performance of on-body mmWave links. Our findings reveal that for varying levels of beam misalignment, it is possible to adjust the antenna half-power beamwidth to enhance the data rates. Index Terms— Beam misalignment, micro-scale mobility, personal wearable devices, millimeter-wave communication. I. INTRODUCTION ONE of the envisioned 5G/6G scenarios [1] involves the support of mobile augmented reality (AR) and mixed reality (MR) applications. These can be deployed on wearable devices, such as AR glasses, tethered to a device with better computing capabilities and longer battery life, such as a smartphone, tablet, or puck. The resulting network of interconnected wearable devices located in close proximity to an individual – referred to as a wearable Personal IoT Network (PIN) [2] – is expected to offer users higher data rates at lower latency and increased network capacity for AR/MR applications. As a result, PINs enable a seamless immersive experience, while the computing device serves dual roles as a processing unit and a gateway providing IP connectivity. The microwave frequency band lacks the capacity to meet the demands of future immersive applications [3]. A more suitable alternative is the millimeter-wave (mmWave) frequency band, which offers a larger bandwidth and extremely high data rates. However, the use of highly directional mmWave antennas can lead to beam misalignment, which occurs when a directional beam deviates from the intended receiver due to changes in the relative distance and orientation of antennas caused by micro-scale user mobility, such as smaller shakes and rotations [4]. Beam misalignment can Manuscript received 26 October 2023; revised 5 December 2023; accepted 24 December 2023. Date of publication 2 January 2024; date of current version 12 March 2024. This work was supported by the H2020 A-WEAR ITN/EJD and by the Academy of Finland (projects RADIANT, IDEA-MILL, and SOLID). The associate editor coordinating the review of this letter and approving it for publication was A. Li. (Corresponding author: Asad Ali.) Asad Ali and Sergey Andreev are with the Unit of Electrical Engineering, Tampere University, 33720 Tampere, Finland, and also with the Department of Telecommunications, Brno University of Technology, 61600 Brno, Czech Republic (e-mail: [email protected]; sergey[email protected]). Olga Galinina is with the Tampere Institute for Advanced Study, Tampere University, 33100 Tampere, Finland (e-mail: [email protected]). Jiri Hosek is with the Department of Telecommunications, Brno University of Technology, 61600 Brno, Czech Republic (e-mail: [email protected]). Digital Object Identifier 10.1109/LCOMM.2023.3349349 potentially lead to disruptions in the operation of the emerging rate-hungry services [5] if not compensated for by frequent beamforming procedures. Most research efforts were focused on studying the effects of beam misalignment in mediumand long-range links, such as in [5] and [6], while there has been limited exploration of directionality effects for short-range on-body communications. The impact of highly directional connectivity was studied in the context of terahertz (THz) networks [7] and [8]. In our previous work [9], we examined the system-level performance of mmWave PINs by considering off-body interference. However, micro-scale mobility and beam misalignment were only addressed in the context of off-body communication [4]. A comparison of the state-of-the-art is summarized in Table I. In on-body mmWave systems, the relative positions and orientations of the antennas may deviate considerably between transmissions, as also observed in [10], which can result in a substantial decrease in antenna gain, hence impacting the received signal strength. For shorter links, micro-mobility and beam misalignment are the primary sources of randomness and data rate fluctuations. Consequently, understanding the impact of these factors on on-body mmWave systems is instrumental to optimizing their performance and selecting better radio settings. In this letter, we aim at analyzing the effects of random beam misalignment and micro-scale mobility on mmWave link performance. Our contributions can be summarized as follows: •We propose a novel theoretical framework for on-body mmWave systems that incorporates arbitrary distributions of beam misalignment and micro-scale mobility of a wearable device. We provide analytical expressions for the distribution of the data rate. •We conduct numerical analysis to study the interplay between the transmit power, antenna beamwidth, microscale mobility, beam misalignment, and the resulting data rate. •We provide insights on reducing the data rate fluctuations and enhancing the data rates by appropriately selecting the transmit power and antenna beamwidth. The proposed framework can serve as a valuable tool for other researchers and practitioners by enabling further in-depth mathematical analysis, theoretical sensitivity assessment, and reduction of data rate fluctuations caused by micro-mobility. II. SYSTEM MODEL A. User Model and Device Placement We consider a scenario where a user is equipped with advanced wearable technology, such as AR glasses, and a © 2024 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ ALI et al.: EFFECTS OF MICRO-SCALE MOBILITY AND BEAM MISALIGNMENT 683 TABLE I STATE-OF-THE-ART COMPARISON Fig. 1. User micro-scale mobility and beam misalignment. companion computing device, referred to as the Rx and the Tx, respectively. The user is modeled as a cylinder with a fixed radius of rand height of hB. The Tx and Rx devices are placed on the surface of the cylinder at fixed heights of hT and hR, respectively. The position of the Rx determines the front-facing direction of the user, and the Tx is placed such that its projection onto the 2D plane is located at an angular distance ψfrom the Rx projection. We consider an arbitrary truncated distribution fψ(ψ)of angle ψ, with the range limited to [Φmin,Φmax]. To reflect the forward placement of the Tx device, we intentionally limit the maximum angle Φmax to π 2. The employed geometrical abstraction is illustrated in Fig. 1. B. Directional Connectivity The devices are considered to be wirelessly tethered, thereby forming a wearable PIN. They communicate using a directional medium access control protocol with omnidirectional reception, e.g., IEEE 802.11ad/ay. We assume that Tx forms a directional 3D beam, which is axially symmetric around the antenna boresight and has no side lobes due to antenna tapering. The degree of directivity is determined by the halfpower beamwidth (HPBW), θ, measured at the half-power or −3dB point of the main lobe of the beam. The gain of the antenna array is approximated by a product of two components: the maximum directivity gain Gmax achieved by a transmission along the antenna boresight and the directivity reduction factor ρ(α)corresponding to a gain decrease due to the deviation αfrom the axis, such that Gtx =Gmax ·ρ(α). Here, αrepresents the angle between the antenna beam boresight and the direct path from the Tx to the Rx, which we regard as the angle of beam misalignment. We also allow αto follow an arbitrary truncated distribution fα(α)with its range limited to [0, αmax]. The maximum achievable directionality gain is estimated as a ratio between the area covered by a directional beam on a sphere and the surface area of a sphere, which may be expressed as Gmax =2 1−cos θ 2 . Coefficient ρ(α)is determined by the antenna radiation pattern in 3D space and can be approximated as suggested in [11]: ρ(α)=1−α θ, α ≤θ. (1) C. Received Signal Power and Data Rate Let ddenote the 3D distance between the devices. Then, the average path gain can be modeled as: g(d) = Ld−γ,(2) where Land γare referred to as the propagation constant and the propagation exponent for the on-body channel, respectively. The reception is assumed to be omnidirectional, e.g., Grx = 1; therefore, for α≥0, the received power at the Rx can be calculated as a function of the transmit power Ptx as Prx(d, α)=PtxGtxGrxg(d)=PtxGmax 1−α θLd−γ.(3) Using the Shannon-Hartley theorem, we can estimate the data rate ˜ras follows: ˜r=wlog (1 + SNR) ,(4) where wis the bandwidth, SNR is the signal-to-noise ratio (SNR) defined as SNR = Prx Pnwith Pnrepresenting the noise power. Notably, in practical systems, the maximum achievable data rate (denoted as rSNR) is dependent on the selected modulation and coding scheme (MCS). The MCS defines a combination of modulation and error-correction coding used for wireless data transmission, thereby determining the maximum achievable data rate. Higher MCS levels with more sophisticated modulation and coding enable higher maximum data rates. As a result, the upper limit on the data rate can be expressed as rSNR =wlog (1 + SNRmax), where SNRmax is the SNR level corresponding to the selected MCS. Consequently, the effective data rate is obtained as r= max(˜r, rSNR). In the following section, we explore the performance of mmWave links in a wearable PIN during an immersive AR session. Particularly, we contribute an expression that allows one to obtain the mean data rate for arbitrary distributions of angle ψdefining the position of a wearable device and angle αcharacterizing the beam misalignment. III. ON-BODY mmWAVE PERFORMANCE EVALUATION In this section, we derive an expression for the distribution of the data rates on on-body directional links that can incorporate various distributions of micro-scale changes in the antenna position and beam misalignment. We employ the transformation of random variables and distribution marginalization techniques to obtain our sought distribution. The distribution of the central angle, fψ(ψ), characterizes the position of the Tx when transmitting data to the Rx for an AR application. For a user at a fixed height, we express the distance between the Rx and the Tx as a function of the central angle ψat the center of the user, as shown in Fig. 1. With this distribution, we can obtain the distribution of distances between the devices, which can then be used along with the distribution of beam misalignment angles to obtain 684 IEEE COMMUNICATIONS LETTERS, VOL. 28, NO. 3, MARCH 2024 the distribution of the data rate. We first express the distance between the Rx and the Tx as follows: d(ψ) = r4r2 bsin2ψ 2+d2 v,(5) where dv=hT−hRis the vertical distance between the devices. According to our system model, the central angle ψcan range between Ψmin and Ψmax, which implies that the on-body distance dbetween the devices ranges between d=dmin =d(Ψmin)and d=dmax =d(Ψmax). With these definitions, we can proceed to derive the expressions that allow to numerically calculate our target metrics of interest. The data rate ris dependent on the distance dbetween the devices and the beam misalignment α. We may express the data rate ras a function of distance dand beam misalignment αas r=wlog 1 + P dγ1−min(α,θ) θ, where P=PtxGmaxL Pnis introduced for brevity. The data rate ˜rwithout the rSNR limit ranges from the minimum data rate ˜rmin =r(dmax, αmax), where the distance is the longest and the misalignment is maximum, to the maximum data rate ˜rmax =r(dmin,0), where the distance is the shortest and the beams are perfectly aligned. Proposition: For arbitrary truncated distributions of the beam misalignment angle fα(α)and the central angle fψ(ψ), the distribution of the data rate without the MCS-imposed limit f˜r(˜r)can be expressed as f˜r(˜r) = 2(1 −C0)P2γ−1θe ˜r w γwCrθ(e˜r/w −1)1+2/γ min(α(˜r,dmin),θ) Z 0 fα(α) ×fψ2 arcsin 1 2rbpz(˜r)−d2 v ×(θ−α)2/γ−1(θdγ(e˜r/w −1)+P(θ−α)) q(z(˜r)−d2 v)(d2 v−z(˜r)+4r2 b)dα +C0δ(˜r),˜r∈[˜rmin,˜rmax],(6) where the coefficient Cr=Fr,0(rmax)−Fr,0(rmin)and the coefficient C0=Fα(max(θ, αmax)) −Fα(θ). Proof: The data rate ˜rdepends on the angle of misalignment αand the distance d, subject to the placement of Tx determined by the internal angle ψ. However, it is essential to address the situation of complete beam misalignment (α > θ), which leads to a transmission failure with ˜r= 0. To quantify the probability of the event where α > θ, we introduce the coefficient C0, which can be calculated as C0=Zmax(θ,αmax) θ fα(α)dα=Fα(max(θ, αmax)) −Fα(θ). (7) Consequently, the distribution of the data rate ˜rbecomes a mixture of a discrete distribution and a continuous distribution, due to the fact that for α > θ, the data rate ˜ris zero. The probability density function (PDF) of this mixture can be obtained as f˜r(˜r) = f˜r,0(˜r)(1 −C0) + C0δ(˜r),(8) where f˜r,0(r)is the distribution function for ˜r > 0without the rSNR limit and δ(˜r)is the Dirac delta function at ˜r= 0. To derive the expression for f˜r,0(˜r), we marginalize the joint distribution f˜r,α(˜r, α|α≤θ). By marginalizing, we integrate over all possible values of αthat satisfy the condition α≤θ. Hence, in the remainder of this work, the conditional part of this notation is omitted for brevity, and the joint distribution is then presented as f˜r,α(˜r, α). To obtain the joint distribution f˜r,α(˜r, α), we employ a bivariate transformation represented by the following expression: f˜r,α(˜r, α)=fψ,α(ψ(˜r, α), α)|J|=fψ(ψ(˜r, α))fα(α)|J|,(9) where |J|is the absolute value of the determinant for the Jacobian matrix. For the considered transformation, the latter is given as |J|= ∂ψ(˜r, α) ∂˜r ∂ψ(˜r, α) ∂α ∂α(˜r, d) ∂˜r ∂α(˜r, d) ∂α  =∂ψ(˜r, α) ∂˜r ∂α(˜r, d) ∂α −∂ψ(˜r, α) ∂α ∂α(˜r, d) ∂˜r.(10) By utilizing the joint distribution f˜r,α(˜r, α)given by (9), we can derive f˜r,0(˜r)by marginalizing it with respect to α. The resulting expression is then: f˜r,0(˜r) = min(α(˜r,dmin),θ) Z 0 fψ(ψ(˜r, α))fα(α)|J|dα =2P2/γ−1θe ˜r w γwCrθ(e˜r/w −1)1+2/γ min(α(˜r,dmin),θ) Z 0 fα(α) ×fψ2 arcsin 1 2rbpz(˜r)−d2 v ×(θ−α)2/γ−1(θdγ(e˜r/w −1)+P(θ−α)) q(z(˜r)−d2 v)(d2 v−z(˜r)+4r2 b)dα, ˜r∈[˜rmin,˜rmax], (11) where the coefficient Cr=F˜r,0(˜rmax)−F˜r,0(˜rmin). Notably, the expression for F˜r,0(˜r)is as follows: F˜r,0(˜r) = 2P2/γ−1 γwθ2/γ ˜r Z ˜rmin ex w (ex/w−1)1+2/γ min(α(x,dmin),θ) Z 0 fα(α) ×fψ2 arcsin 1 2rbpz(x)−d2 v ×(θ−α)2/γ−1(θdγ(ex/w−1)+P(θ−α)) q(z(x)−d2 v)(d2 v−z(x)+4r2 b)dαdx, ˜r∈[˜rmin,˜rmax]. (12) By substituting (11) into (8), we arrive at the distribution of the data rate without the rSNR limit, which can be expressed as (6). Since the data rate without the rSNR limit ˜rcan range between ˜rmin and ˜rmax, it is possible that the SNR at the Rx is greater than SNRmax. In this case, the data rate ˜ris limited to the maximum achievable data rate rSNR corresponding to the selected MCS. Therefore, the effective data rate r after considering the limitation imposed by the MCS ranges from rmin = min (˜rmin, rSNR)to rmax = min (˜rmax, rSNR). Theorem: For any truncated distribution of the beam misalignment angle fα(α)and the central angle fψ(ψ), the ALI et al.: EFFECTS OF MICRO-SCALE MOBILITY AND BEAM MISALIGNMENT 685 distribution of the effective data rate fr(r)may be given as fr(r) = 2(1−C0)(1−Cs)P2γ−1θe r w γwCrθ(er/w −1)1+2/γ min(α(r,dmin),θ) Z 0 fα(α) ×fψ2 arcsin 1 2rbpz(r)−d2 v ×(θ−α)2/γ−1(θdγ(er/w−1)+P(θ−α)) q(z(r)−d2 v)(d2 v−z(r)+4r2 b)dα+ (1 −Cs)C0δ(r) +Csδ(r−rSNR), r ∈[rmin, rmax],(13) where Cs=F˜r,0(rmax)−F˜r,0(rmin)is a scaling coefficient. Proof: Considering the effective data rate, any values ˜r≥rSNR are replaced with a fixed data rate r=rSNR. As a result, the distribution of the data rate rcan be obtained as a mixture of two distributions: the Dirac delta distribution δ(r−rSNR)and the distribution f˜r(r). Hence, the resulting distribution may be represented as fr(r) = f˜r(r)(1 −Cs) + Csδ(r−rSNR), r ∈[rmin, rmax], (14) where Cs=F˜r,0(˜rmax)−F˜r,0(rmax)is a coefficient representing the probability that ˜r≥rSNR. We can now derive our metrics of interest by using the distribution fr(r). For any distribution function of the beam misalignment angle fα(α)and the central angle fψ(ψ), the expected data rate can be obtained as E[r] = Rrmax rmin rfr(r)dr. Additionally, this expression may be used to calculate the standard deviation of the data rate as σr=pEr2−E[r]2. Our framework enables the incorporation of micro-scale mobility, as characterized by the movement of devices and modeled by the internal angle ψ, and of beam misalignment, as modeled by the misalignment angle α. The derived distribution can be employed for further mathematical analysis and optimization, which may be challenging to achieve with simulations only. IV. NUMERICAL RESULTS AND DISCUSSION In this section, we present our numerical results to illustrate the impact of various parameters. We consider a user equipped with AR glasses (Rx) and an accompanying processing unit (Tx). Both devices are wirelessly paired to each other via a direct directional mmWave link using IEEE 802.11ay radio technology. We require the Tx to be on the front side of the user’s torso and assume to have the line of sight to the Rx. We also utilize the log-distance pathloss model from [13] and adapt it to g(d) = Ld−γpathloss format. For simulations, we use realistic antenna radiation patterns obtained from MATLAB’s sensorArrayAnalyzer app for uniform rectangular array (URA) antennas. For the results obtained from our analytical expressions, we utilize θthat corresponds to the HPBW of the URA radiation pattern (e.g., θ= 30 corresponds to 4×4 URA). Specifically, the analytical results utilize the antenna pattern obtained by using (1). The parameters employed in this section are summarized in Table II. We assume that the Tx position, which is determined by the central angle ψ, follows a truncated normal distribution with the mean µψand the standard deviation σψ, having its range limited to [0,π 2]. To address misalignment, we introduce TABLE II NOTATION AND PARAMETERS OF OUR NUMERICAL STUDY a variable x, which follows a truncated normal distribution with the mean µα= 0 and the standard deviation σα. The misalignment angle is then defined as α=|x|, thus resulting in a folded distribution centered at zero with the range of [0, π]. While our framework can incorporate different distributions, we use these examples for the sake of exposition. In Fig. 2a, we present the standard deviation of the data rate σrwith respect to the increasing deviation in the central angle µψfor different Tx positions and transmit powers. Here, µψrepresents the mean position of the Tx and σψis the degree of variation in the Tx position (e.g., during sitting, walking, running, etc.). From Fig. 2a, we learn that an increase in the value of σψleads to a corresponding growth for the standard deviation of the data rate σr. In statistics, an empirical rule states that for a normal distribution, 99.7%of values lie within 3σrof the E[r]. For the standard deviation of the data rate σr, the value of the data rate can also change by 3σraround the mean data rate E[r], e.g., with a standard deviation of 125 Mbps, it is possible to have a drop of up to 375 Mbps around the mean data rate. Immersive applications are characterized by both high data rates and stringent packet delay budgets (PDBs); hence, significant fluctuations in the data rate can result in exceeding the PDB and thereby failing to satisfy the user’s expectations. Additionally, we observe that higher transmit power leads to a wider deviation in the data rate. Furthermore, as the Tx moves away (e.g., by increasing µψ), the deviation of the data rate grows for higher σψand vice versa for lower σψ. We conclude that employing a Transmit Power Control (TPC) mechanism to lower the power can help reduce fluctuations in the data rate. In Fig. 2b, we display the mean data rate E[r]with respect to an increasing misalignment σαfor different numbers of antenna elements (HPBW) and transmit powers. In practice, the value of σαcan be impacted by various factors, including the angular and displacement velocities of the antenna, the employed beamforming algorithm, and the size of the antenna array. Essentially, these factors influence the beam realignment delay in response to changes in the antenna location and orientation. For a shorter realignment delay, the value of σα is expected to be small. We compare our analytical results obtained from (1) with the simulation results using realistic antenna patterns. Fig. 2b shows that with a growing misalignment, there is a corresponding decline in the data rate. We observe that wider beams are more robust as the data rate decreases gradually for an increasing misalignment as compared to narrower beams. The performance improvement from larger numbers of antenna elements for narrow beams diminishes as the data rate 686 IEEE COMMUNICATIONS LETTERS, VOL. 28, NO. 3, MARCH 2024 Fig. 2. Impact of micro-scale mobility and beam misalignment on data rate in on-body communication. (a) Standard deviation of rate w.r.t. σψ. (b) Mean data rate vs. σα. (c) Mean data rate vs. HPBW. approaches rSNR. As the power grows and the beams become narrower, the data rate saturates at rSNR imposed due to MCS. We also observe that under a lower transmit power, when the standard deviation of the misalignment angle σαincreases, antennas with higher numbers of elements perform better than those with lower numbers of elements, provided that the mean data rate E[r]for the perfectly aligned beams (σα= 0) is not equal to rSNR. Narrow beams and high transmit powers typically lead to improved data rates. However, for a higher transmit power, antennas with fewer antenna elements (wider beams) can outperform those with higher numbers of elements (narrow beams) in terms of the data rate due to beam misalignment. Narrower beams are more susceptible to misalignment, thus, making wider beams preferable in the cases of strong misalignment, such as during increased user movement. This leads to an important insight that applying a TPC mechanism in situations with a high degree of beam misalignment may benefit from using higher transmit power. In Fig. 2c, we present the mean data rate with respect to an increasing beamwidth θfor a varying standard deviation of the misalignment angle σα. The simulation results (depicted by ∗) are provided alongside the analytical results using the beam pattern given by (1) instead of the realistic patterns obtained from MATLAB’s sensorArrayAnalyzer. We consider a large range of values, including those that do not directly correspond to the number of antenna elements. Knowing the statistical aspects of the beam misalignment can help deliver higher data rates. This knowledge can be highly beneficial in improving the system performance when coupled with an adaptive beamwidth control algorithm, wherein the HPBW can be adjusted by partially deactivating the antenna array [14]. For the antenna arrays with a limited number of antenna elements, such as those in devices like smart AR glasses, the achievable HPBW is constrained, thus, simplifying the selection of HPBW. V. CONCLUSION In this letter, we propose a novel framework for evaluating the performance of on-body mmWave systems in the presence of micro-scale mobility of wearable devices and beam misalignment. Our methodology incorporates arbitrary distributions modeling the positions of wearable devices and beam misalignment angles. Our results demonstrate that increasing the transmit power can effectively mitigate the performance decline caused by beam misalignment, albeit with higher fluctuations in the data rate. Additionally, the findings highlight that the HPBW of an antenna array can be appropriately adjusted with statistical knowledge of the beam misalignment for any selected transmit power to achieve higher data rates. Wider beams prove advantageous in the scenarios with a high degree of misalignment, i.e., during increased user movement. 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