A Low-Complexity Krylov-Beamspace Beamforming for FDD Massive MIMO

Beamspace beamforming, which is advantageous in reducing channel estimation efforts and the subsequent precoding complexity, has great potential for massive Multiple Input multiple Output (MIMO) systems with extremely large antenna arrays. Sub-6 GHz will still play an essential role for a wide coverage and a reliable connectivity in future wireless communications. It is thus of prime interest to investigate efficient beamspace beamforming technologies for Frequency Division Duplex (FDD) massive MIMO. Standard beamspace beamforming schemes can be realized by either downlink grid-of-beam or uplink sounding, where beams are selected from the Discrete Fourier Transformation (DFT) codebook or calculated by Eigen-Value Decomposition (EVD) from the measured channel covariance matrix. However, in FDD when channel reciprocity does not hold, it is difficult to design efficient beamspace beamforming algorithms that not only delivers high performance but also has low complexity and low induced overhead. This paper proposes a novel Krylovbeamspace beamforming scheme for FDD massive MIMO. Taking advantages of angular reciprocity in FDD, we develop a generalized algorithm to compensate the uplink channel covariance matrix for the downlink use, which is more robust against scattered channels and imperfect reciprocity than the conventional counterpart. The beamspace beamforming matrix is designed by the derived beam signature vector and the compensated channel covariance matrix, resulting in the so called "beam"-Krylov subspace. Two concepts utilizing limited downlink feedback and/or uplink sounding are proposed, which can provide enough flexibilities in implementing the new scheme. The proposed algorithm does not need any complicated EVD calculations and even outperforms the baseline method, which is low-complexity/low-overhead and quite applicable for FDD massive MIMO.