Lattice-Based mmWave Hybrid Beamforming

Conventional hybrid precoding and combining based transceivers require a large number of high-resolution radio frequency (RF) phase shifters (PSs), which impose prohibitive hardware costs and power consumption. To address the above issue, both partially connected RF PSs and low-resolution PSs have been proposed. However, the performance limits of these low-cost designs have not been investigated theoretically. Furthermore, there is room for improvement in their spectral efficiency. To fill this knowledge gap, we derive the mean square error performance discrepancy between an optimal precoder/combiner and the hybrid analog-digital precoder/combiner under the constraint of 1-bit PSs relying on lattice theory. Then, by observing that this performance gap can be reduced by deactivating parts of the PSs whilst improving both the spectral and energy efficiency, we develop an adaptive RF PS connection network. To resolve the associated hybrid precoding and combining problems, we appropriately adapt Babai’s algorithm from the lattice decoding literature. Our simulation results demonstrate the superiority of the proposed scheme both in terms of its spectral and energy efficiency.