Multi-stream iterative SVD for massive MIMO communication systems under time varying channels

Singular value decomposition (SVD) plays an important role in signal processing for multi-input multi-output (MIMO) communication systems. Under massive MIMO scenarios, as the channel matrix is very large, implementing SVD at every frame is highly inefficient. Existing literature on iterative SVD algorithms are mostly heuristic based, and the associated tracking performance under time-varying channels is not clear. The difficulties of deriving and analyzing SVD algorithms are due to the non-convexity of the associated optimization problem and the time-varying nature of the MIMO channel. In this paper, we formulate the problem on Grassmann manifolds and derive a multi-stream iterative SVD algorithm using optimization techniques. To enhance the tracking performance under time-varying channels, we propose a compensation algorithm to offset the motion of the time-varying target eigenspace. We analyze the convergence behavior of the proposed algorithm, where we show that under some mild conditions, the proposed iterative SVD algorithm with compensations has zero tracking error, despite the underlying problem being non-convex and the channel being time-varying. The complexity of the algorithm is only O(n²p) for estimating p singular vectors, compared with O(n³) for the SVD of a n × n channel matrix.