Adaptive MIMO antenna selection via discrete stochastic optimization

Abstract

Abstract-Recently it has been shown that it is possible to improve the performance of multiple-input multiple-output (MIMO) systems by employing a larger number of antennas than actually used and selecting the optimal subset based on the channel state information. Existing antenna selection algorithms assume perfect channel knowledge and optimize criteria such as Shannon capacity or various bounds on error rate. This paper examines MIMO antenna selection algorithms where the set of possible solutions is large and only a noisy estimate of the channel is available. In the same spirit as traditional adaptive filtering algorithms, we propose simulation based discrete stochastic optimization algorithms to adaptively select a better antenna subset using criteria such as maximum mutual information, bounds on error rate, etc. These discrete stochastic approximation algorithms are ideally suited to minimize the error rate since computing a closed form expression for the error rate is intractable. We also consider scenarios of timevarying channels for which the antenna selection algorithms can track the time-varying optimal antenna configuration. We present several numerical examples to show the fast convergence of these algorithms under various performance criteria, and also demonstrate their tracking capabilities.

Adaptive antenna selection and Tx/Rx beamforming for large-scale MIMO systems in 60 GHz channels

“…In [10], the stochastic approximation method is introduced to solve the problem of the form (8). The basic idea is to generate a sequence of the estimates of the optimal antenna subset where the new estimate is based on the previous one by moving a small step in a good direction towards the global optimizer.…”

“…Due to the potentially large search space in the present problem, which not only limits the convergence speed but also makes it difficult to maintain the occupation probability vector, the algorithms in [10] can become inefficient. Here, we propose a modified version of the stochastic approximation algorithm that is more efficient to implement, and more importantly, it fits naturally to a procedure for estimating the principal singular value of H ω based on the receive beamformer output y(ω, w, u) only.…”

“…Since the search space is quite large, i. e., ( 32 10 ) = 64512240, in the same figure, we also plot the largest eigenvalues of the best and the worst subsets among 1,000 randomly selected antenna subsets. Moreover, the single-run performance of the antenna selection algorithm in [10] is also shown. In Figure 5, the average performance of 100 runs for the above schemes is plotted in a larger span of iterations.…”

“…First, it is seen that the G-circle estimates are quite close to the actual largest eigenvalues, which validates the use of G-circle as a metric for antenna selection in strong line-of-sight channels. Secondly, Algorithm 1 has a much faster convergence rate than the algorithm in [10], which at each iteration picks the next candidate subset randomly and independent of the current subset, whereas Algorithm 1 searches for the next candidate subset in the neighborhood of the current subset. Thirdly, Algorithm 1 can lock onto a near-optimal antenna subset very quickly, e.g., in 10-20 iterations, and it significantly outperforms the exhaustive search over a large number (e.g., 1,000) of subsets.…”

“…is smaller than the number of antenna elements, and the antenna selection technique is used to fully exploit the beamforming gain afforded by the large-scale MIMO antennas. Although various schemes for antenna selection exist in the literature [7][8][9][10], they all assume that the MIMO channel matrix is known or can be estimated. In the 60 GHz WPAN system under consideration, however, the receiver has no access to such a channel matrix, because the received signals are combined in the analog domain prior to digital baseband due to the analog beamformer or phase shifter [11].…”