Modular XL-MIMO beam training stops sweeping the full codebook: parallax lays out candidates, statistics prune the noise-only sectors
Synopsis
Beam training for modular extremely large antenna arrays in hybrid near- and far-field environments no longer keeps a fixed candidate codebook. Prior subarray schemes relied on predefined codebooks or activation patterns and adapted poorly to spatially non-stationary channels; this scheme builds a parallax-aware initial codebook covering each subarray's angular shift, then learns online with a multi-armed bandit, and once a statistical steady state is detected it projects beams across subarrays and prunes noise-only sectors with a likelihood ratio test, compressing the action space. In simulation the scheme's effective spectral efficiency exceeds three comparison schemes across the evaluated SNR range, with markedly reduced training overhead.
Interpretation
Beam training for modular extremely large arrays turns the candidate codebook from a fixed set into a set that shrinks during training, so each subarray searches only its retained beam indices. Earlier subarray beam training relied on predefined codebooks or predefined activation patterns, which limited adaptability to dynamic, spatially non-stationary channels. In simulations at 100 GHz carrier, 8 modules of 32 antennas each and a minimum uniform power distance of 1.3 m, effective spectral efficiency exceeds the TH BT, Dual-UCB BT and Hybrid BT comparison schemes across the evaluated SNR range.
Training runs in two stages: probing over an initial codebook that covers each subarray's parallax shift, then online decisions over the compressed candidate set. The initial codebook is built from the beam index redundancy required between adjacent subarrays, set by the ratio of subarray spacing to the minimum uniform power distance. With 1, 2 and 3 scattering clusters, effective spectral efficiency rises during exploration and converges to a steady value, highest at one cluster.
Codebook compression is triggered by a statistical steady-state test comparing empirical quantiles of effective spectral efficiency in current and historical windows. Once the steady-state criterion is met, spatial-frequency gradients project validated high-gain beams onto other subarrays, and a likelihood ratio test removes pure-noise beams from the candidate set. Simulations use window length 20, step 5, correlation threshold 0.95, relative threshold 0.2 and likelihood ratio threshold 10, with the training overhead budget equal to the number of scattering clusters.
Perspective
The demonstrated scope is numerical simulation of a single-user frequency-division-duplex downlink with a modular extremely large array at 100 GHz carrier, 8 modules of 32 antennas each, with channel statistics quasi-static over 667 coherence blocks.
The conclusions rest on simulation, and the assumption that channel statistics stay fixed over the statistical period runs through the whole training process; future work will study spatial non-stationarity from partial visibility in single-user and multi-user scenarios.