A Blind Antenna Selection Scheme for Single-Cell Uplink Massive MIMO

This paper considers the uplink of a single-cell large-scale multiple-input multiple output (MIMO) system in which $m$ mono-antenna users communicate with a base station (BS) outfitted by $n$ antennas. We assume that the number of antennas at the BS and that of users take large values, as envisioned by large-scale MIMO systems. This allows for high spectral efficiency gains but obviously comes at the cost of higher complexity, a fact that becomes all the more critical as the number of antennas grows large. To solve this issue is to choose a subset of the available $n$ antennas. The subset must be carefully chosen to achieve the best performance. However, finding the optimal subset of antennas is usually a difficult task, requiring one to solve a high dimensional combinatorial optimization problem. In this paper, we approach this problem in two ways. The first one consists in solving a convex relaxation of the problem using standard convex optimization tools. The second technique solves the problem using a greedy approach. The main advantages of the greedy approach lies in its wider scope, in that, unlike the first approach, it can be applied irrespective of the considered performance criterion. As an outcome of this feature, we show that the greedy approach can be applied even when only the channel statistics are available at the BS, which provides blind way to perform antenna selection.