A Simple and Effective Approach for Transmit Antenna Selection in Multiuser Massive MIMO Leveraging Submodularity

Massive MIMO systems are expected to enable great improvements in spectral and energy efficiency. Realizing these benefits in practice, however, is hindered by the cost and complexity of implementing large-scale antenna systems. A potential solution is to use transmit antenna selection for reducing the number of radio-frequency (RF) chains at the base station. In this paper, we consider the NP-hard discrete optimization problem of performing transmit antenna selection in the downlink of a single cell, multiuser massive MIMO system by maximizing the downlink sum-rate capacity with fixed user power allocation subject to various RF switching constraints. Whereas prior work has focused on using convex relaxation based schemes, which lack theoretical performance guarantees and can be computationally demanding, we adopt a very different approach. We establish that the objective function of this antenna selection problem is monotone and satisfies an important property known as submodularity, while the RF switching constraints are expressible as the independent sets of a matroid. This implies that a simple greedy algorithm can be used to guarantee a constant-factor approximation for all problem instances. Simulations indicate that greedy selection yields a near-optimal solution in practice and captures a significant fraction of the total downlink channel capacity at substantially lower complexity relative to convex relaxation based approaches, even with very few RF chains. This paves the way for substantial reduction in hardware complexity of massive MIMO systems while using very simple algorithms.