Low-Complexity Block-Krylov-Beamspace Beamforming for Extreme Massive MIMO

The upper mid-band, spanning from 7 GHz to 20 GHz, emerges as a promising candidate spectrum for 6G, offering extensive coverage and remarkable capacity. It drives massive Multiple Input Multiple Output (MIMO) to adopt extremely large antenna arrays and the so-called extreme massive MIMO will play an essential role. However, as the number of antennas at base stations increases, the demands on signal processing intensify significantly, imposing substantial limitations on product implementation. Reduced-rank beamforming such as beamspace beamforming can reduce the complexities associated with channel estimation and precoding. This paper introduces a low-complexity block Krylov-beamspace beamforming, targeting the implementation of two-stage long-term/short-term fully digital rank-reduction beamforming in 6G extreme massive MIMO at upper mid-band. The key lies in the concept of using the derived multiple signature vectors to calculate the beamspace beamforming matrix that spans the block Krylov subspace. An adaptive and fast-converging beamspace determination scheme is also developed for the proposed algorithm. We further investigate its implementation in the practical cross-polarized antenna systems. The proposed beamforming is able to provide an eigen-based performance but with a significant complexity reduction, exhibiting a great potential in the evolution of extreme massive MIMO for 6G.