OPTICAL MULTIBEAM BEAMFORMER BASED ON XBAR ARCHITECTURE

OPTICAL MULTIBEAM BEAMFORMER BASED ON XBAR ARCHITECTURE Ronis Maximidis(1),(2), Stefanos Kovaios(1),(2), Ioannis Roumpos(1),(3), Apostolos Tsakyridis(1),(2), George Giamougiannis(1),(2), Miltiadis Moralis-Pegios(1),(2), Dimitra Ketzaki(1),(2), Nikos Pleros(1),(2) (1)School of Informatics, Aristotle University of Thessaloniki Thessaloniki, Greece Email: ma[email protected]th.gr (2) Center of Interdisciplinary Research & Innovation, Balkan Center Thessaloniki, Greece (3) Department of Physics Thessaloniki, Aristotle University of Thessaloniki, Thessaloniki, Greece Abstract – This paper proposes a novel optical multibeam beamformer architecture capable of supporting multiple independent beams simultaneously. The architecture is based on a crossbar design, enabling efficient routing and combining of optical signals to form the desired beam patterns. A comprehensive theoretical analysis of the crossbar beamformer is presented, including performance metrics that demonstrate the efficiency and effectiveness of the crossbar architecture. Additionally, a comparison between the proposed beamformer and the traditional Blass matrix highlights an improvement of over 100 dB in insertion loss for a 1 dB phase shifter loss, as well as superior beamformer fidelity exceeding 99% for the crossbar architecture. I. INTRODUCTION Beamsteering and beamforming networks are essential for achieving higher communication speeds in the dynamic and fast-changing environments of Low Earth Orbit (LEO) satellite networks [1]. Photonic Integrated Circuit (PIC) technologies are emerging as a transformative solution in the RF domain, offering key advantages such as large bandwidth, compact size, reduced energy consumption, and cost-effectiveness. In contrast to traditional RF chains and mechanical steering methods, which tend to be costly, energyintensive, or bulky, PIC technology presents a promising alternative by delivering compact, costeffective, and energy-efficient beamforming solutions [2]. This paper introduces a novel optical multibeam beamformer architecture designed that harness the benefits of PICs. The proposed architecture utilizes a crossbar (XBAR) design, which facilitates efficient routing, amplitude, and phase modulation, and the combination of optical signals to generate the desired beam patterns. The experimental validation of this beamformer was demonstrated in [3] using a 4x4 Silicon Photonic (SiPho) photonic integrated circuit. The measured performance of the phase-shifting elements confirmed the beamformer's ability to independently steer two beams to angles of up to 8 degrees. In this work, a thorough theoretical analysis is conducted to elucidate the advantages of the proposed beamformer. This includes mathematical modeling of signal propagation within the XBAR beamformer and an evaluation of the beamformer fidelity. Additionally, the proposed architecture is compared to the traditional Blass matrix, a well-established beamforming method that has also seen some photonic implementations [4]. The comparison underscores that our design offers superior scalability and robustness, making it more suitable for the demands of modern satellite communication systems. II. XBAR BEAMFORMER ANALYSIS A. XBAR Operational Principles Fig. 1 illustrates a layout of an N×M optical beamformer architecture that is based on the crossbar architecture. In this setup, each of the N input signals, xn, with n=1, ⋯, N, is divided into M outputs via log2(M) splitting stages. Subsequently, each of the sn,m signals is directed to an XBAR node, comprising an amplitude modulator (ΑΜ) and a phase modulator (PM). Following this, the modulated signals from each of the M outputs are consolidated through log2(N) coupling stages to the M output signal, ym. This arrangement ensures that the first outputs of each of the N rows are combined to form output #1 of the beamformer, the second outputs to form output #2, and so on until M combined outputs of each N input are obtained. In this way, each combined output comprises N signals modulated in amplitude and phase, ym= s1,m + s2,m + ⋯ + sN-1,m + sn,m. This architecture allows independent programming of nodes with one-step programming avoiding cascaded nodes which leads to the lowest loss linear optical architecture [5]. The independent amplitude and phase control translates to the generation of multiple beams which can be controlled independently and are robust to fabrication errors. For the conversion of the optical signal back to the RF domain an array of PD is employed. To retain the change in the phase after o/e conversion the initial optical signal is fed to the photodiode as well [4]. Fig. 1. Architecture of crossbar multibeam photonic beamformer B. Insertion Loss Analysis The insertion loss of the propagation path with maximum loss of the XBAR beamformer is given by: 𝐼𝐿 𝑝𝑎𝑡ℎ =𝑙𝑜𝑔2 𝑀 𝐼𝐿𝑠𝑝+ 10𝑙𝑜𝑔10 𝑀 + 𝐼𝐿𝑁 + 𝑀−1 𝑙𝑜𝑔2 𝑁 𝐼𝐿𝑥 + 𝑙𝑜𝑔2 𝑁 𝐼𝐿𝑐 + 10𝑙𝑜𝑔10 𝑁 +𝐿∗𝐼𝐿𝑤𝑔 (1) The terms of the equation (1) are:  1st term 𝑙𝑜𝑔2 𝑀 𝐼𝐿𝑠𝑝 represents the losses induced by the 3dB splitting stages, with 𝐼𝐿𝑠𝑝 being the splitter loss  2nd term 10𝑙𝑜𝑔10 𝑀 represents power splitting between each antenna element of the antenna array.  3rd term where: 𝐼𝐿𝑁=𝐼𝐿𝑠𝑝+ 2𝐼𝐿𝑝ℎ+𝐼𝐿𝑐 is the node loss, where 𝐼𝐿𝑝ℎ and 𝐼𝐿𝑐 are the phase shifter loss and 3dB coupler loss respectively.  4th term 𝑀−1 𝑙𝑜𝑔2 𝑁 𝐼𝐿𝑥 is responsible for the crossing losses, with 𝐼𝐿𝑥 to be a crossing loss.  5th term 𝑙𝑜𝑔2 𝑁 𝐼𝐿𝑐 represents the losses induced by the beam coupling stage at the output of the beamformer.  6th term 10𝑙𝑜𝑔10 𝑁 represents the power lost at every coupling stage at the output of the beamformer.  7th term 𝐿∗𝐼𝐿𝑤𝑔 represents waveguide losses with 𝐿 and 𝐼𝐿𝑤𝑔 to be the waveguide lengths and the waveguide losses per unit length respectively. The values for individual component losses that can be found in the literature are presented in Table 1. Table 1. Individual components losses Components Loss Value 𝐼𝐿𝑤𝑔 [6] 0.1dB/cm 𝐼𝐿𝑐𝑜𝑢𝑝𝑙𝑒𝑟 [7] 0.06 dB 𝐼𝐿𝑐𝑟𝑜𝑠𝑠𝑖𝑛𝑔 [8] 0.02 dB 𝐼𝐿𝑠𝑝𝑙𝑖𝑡𝑡𝑒𝑟 [7] 0.06 dB Utilizing (1) and Table 1 the loss analysis of the XBAR beamformer was performed assuming variable phase shifter loss as its value strongly depends on the speed, power consumption, and footprint requirements of beamformer applications [9],[10]. The results of the loss analysis for XBAR beamformers of various dimensions and for phase shifter loss in the range of 02 dB are shown in Fig. 2. Fig. 2. XBAR beamformer’s insertion loss of the path with the maximum transmission losses. To compare the losses of the XBAR beamformer with the losses of the Blass matrix its losses were calculated for beamformers of the same dimensionality and are presented in Fig 3. Fig. 3. Blass beamformer’s insertion loss of the path with the maximum transmission losses. Fig. 4. Insertion losses of the path with the maximum transmission losses for XBAR beamformer (solid line) and Blass beamformer (dashed line). Fig. 3 indicates the insertion loss higher than 50dB even for small beamformers and low phase shifter loss of 0.5dB. Furthermore, for phase shifter loss of 2dB the Blass beamformer suffers around 320 dB insertion loss for 8×64 configuration, while for the same beamformer size XBAR beamformer demonstrated an insertion loss of only 41 dB. Finally, to compare the XBAR and Blass beamformers insertion loss for ultra-low phase shifter loss up to 0.1 dB zoom on this part of Fig. 3 is shown in Fig. 4. Fig. 4 clearly shows that even for very low losses the use of the XBAR beamformer is beneficial for beamformers with large antenna elements. C. Fidelity Analysis The robustness of a beamformer to the fabrication errors can be estimated by calculating the output signal fidelity given by: 𝐹= 𝑌𝐹𝐴𝐵𝑌𝐸𝑋𝑃 † 𝑌𝐹𝐴𝐵𝑌𝐹𝐴𝐵† 𝑌𝐸𝑋𝑃𝑌𝐸𝑋𝑃 † 2 , (2) where 𝑌𝐹𝐴𝐵 and 𝑌𝐸𝑋𝑃 are the signals at outputs fabricated and expected beamformer respectively. Fidelity equal with one means that signals are the same and it decreases as the vector difference between the vectors increases. Fig.5 shows the fidelity of 64×64 beamformers, where a loss with uniform distribution is applied to the nodes with the maximum node loss value varying from 0 to 3dB, and a mean value of 1000 analyzed matrix was taken. Fig 5(a) indicates that the fidelity of the XBAR beamformer is higher than 0.99 even for a maximum node loss of 3dB and it’s the same for all beams. On the other hand, in Fig 5b we can see that the fidelity of the Blass beamformer drops significantly with the beam number and maximum node loss, which is an inherent attribute of the Blass matrix (a) (b) Fig. 5. Fidelity of a 64x64 beamformer a) XBAR b) Blass III. CONCLUSIONS In this paper, the performance of the XBAR beamformer in terms of insertion losses and fidelity was theoretically analyzed and compared with that of the Blass matrix. The XBAR beamformer demonstrated clear superiority, with an insertion loss of around 41 dB for an 8x64 configuration, whereas the Blass beamformer exhibited significantly higher losses, around 320 dB for the same beamformer size. Additionally, the fidelity of the 64×64 XBAR beamformer, even when considering fabrication errors leading to up to 3 dB node maximum loss, was compared to that of the Blass beamformer. The XBAR beamformer maintained a fidelity higher than 0.99, while the Blass matrix was severely impacted by fabrication errors, resulting in a fidelity lower than 0.2 for high beam counts. IV. 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