Low-Complexity Massive MIMO Subspace Estimation and Tracking from Low-Dimensional Projections

Massive MIMO is a variant of multiuser MIMO, where the number of antennas $M$ at the base-station is large, and generally much larger than the number of spatially multiplexed data streams to/from the users. It has been observed that in many realistic propagation scenarios as well as in spatially correlated channel models used in standardizations, although the user channel vectors have a very high-dim $M$, they lie on low-dim subspaces due to their limited angular spread. This low-dim subspace structure remains stable across many coherence blocks and can be exploited in several ways to improve the system performance. A main challenge, however, is to estimate this signal subspace from samples of users' channel vectors as fast and efficiently as possible. In a recent work, we addressed this problem and proposed a very effective novel algorithm referred to as Approximate Maximum-Likelihood (AML), which was formulated as a semi-definite program (SDP). In this paper, we address two problems left open in our previous work: computational complexity and tracking. The algorithm proposed in this paper is reminiscent of Multiple Measurement Vectors (MMV) problem in Compressed Sensing and is proved to be equivalent to the AML Algorithm for sufficiently dense angular grids. It has also a very low computational complexity and is able to track sharp transitions in the channel statistics very quickly. Although mainly motivated by massive MIMO applications, our proposed algorithm is of independent interest in other related subspace estimation applications. We assess the estimation/tracking performance of our proposed algorithm empirically via numerical simulations, especially in practically relevant situations where a direct implementation of the SDP would be infeasible in real-time. We also compare the performance of our algorithm with other related subspace estimation algorithms in the literature.