Beam-focusing Analysis for Modular XL-arrays: Effect of Time Synchronization Errors
This work provides insights for system designers on the impact of synchronization errors in modular XL-arrays, which is crucial for near-field communications.
The paper analyzes how time synchronization errors among subarrays in modular XL-arrays affect beam-focusing performance. It finds that with two subarrays, beam-focusing persists but with a bounded angle offset; with multiple subarrays, errors cause an imbricated beam pattern that degrades multi-user communication.
For near-field communications, it is a hardware-efficient means to form an extremely large-scale array (XL-array) by concatenating multiple modular arrays (also referred to as subarrays). In this letter, we aim to investigate the effect of time synchronization errors among transmissions of different subarrays on the beam-focusing performance. To this end, we first characterize the beam pattern function when the transmit beamforming is designed based on maximum ratio transmission (MRT) under the premise of perfect time synchronization. As this function is highly difficult for analysis, we then consider a typical case with two subarrays. Interestingly, we show that for this case, the beam-focusing effect still persists even in the presence of time synchronization errors, while the focused location is deviated from the user location with an angle offset upper-bounded by 1/M, where M denotes the number of antennas in each subarray. Subsequently, for the general case with multiple subarrays, despite analytical intractability, we numerically show that time synchronization errors give rise to an imbricated (instead of focused) beam pattern. This may significantly degrade multi-user communication performance in practice due to the reduced desired signal power and increased inter-user interference.