Transmit antenna selection schemes for spatial modulation systems: search complexity reduction and large-scale MIMO applications

Euclidean distance optimized antenna selection (EDAS) has proven to be able to achieve high transmit diversity gains for spatial modulation (SM) multiple-input multiple-output (MIMO) systems, but the exhaustive search over all possible antenna subsets may result in an intractable search complexity, especially for large-scale MIMO (LS-MIMO) systems. In this paper, a novel EDAS-equivalent criterion, relaying on matrix dimension reduction, is proposed to reduce the search complexity. Based upon this criterion, for small-scale SM-MIMO systems, a pair of transmit antenna selection (TAS) schemes, namely, the tree search based antenna selection (TSAS), and the decremental antenna selection (D-AS) schemes, are developed. Specifically, the TSAS scheme works by iteratively splitting the original Euclidean distance (ED) matrix into submatrices with smaller dimensions. TSAS achieves the same bit error rate (BER) performance as that of the exhaustive search at the cost of exponential search complexity. To address this issue, D-AS is carried out by excluding one specific transmit antenna from all the possible candidates in each iteration based on the channel information. D-AS is able to offer a near-optimal BER performance with a further reduction in terms of the search complexity. Moreover, we extend the D-AS scheme to LS-SM-MIMO systems by sorting all the ED elements with the low-complexity heapsort algorithm. Our simulation results show that the proposed D-AS algorithm outperforms conventional TAS schemes conceived for LS-SM-MIMO systems