Efficient Receive Antenna Selection Algorithms and Framework for Transmit Zero-Forcing Beamforming

MIMO wireless downlinks using transmit zero-forcing beamforming (TZFBF) with M-T transmit antennas can serve up to K=M-T receivers, each equipped with one antenna. To maximize the sum rate, waterfilling can be used. It is shown that unlike classical waterfilling, TZFBF waterfilling cannot simply drop the poorer spatial modes during optimization. Instead, receive antenna selection (RAS) must be incorporated and achieving the maximum sum rate requires an exhaustive search over Sigma(vertical bar S vertical bar)(C-MT(vertical bar S vertical bar))= 2(MT)-1 iterations to find the optimal subset S of active receivers where vertical bar S vertical bar = 1,...,M-T. In principle, a separate RAS algorithm can be used in conjunction with waterfilling to reduce the exponential complexity O(2(MT)) of the exhaustive search to linear complexity O(M-T). We develop optimization algorithms that emulate classical waterfilling by progressively reducing the effects of poor spatial modes in M-T iterations. They do so by performing RAS jointly during the waterfilling process at little additional complexity. By avoiding a separate RAS process, complexity is thus further reduced. For the typical case where K > M-T, we propose a 2-phase framework that helps reduce the overall complexity while meeting the TZFBF dimensional constraints. Numerical results over different channel conditions are given.