Sparse space codes for multi-antenna systems

Sparse space codes (SSC) are proposed as a novel transmission scheme for an under-determined MIMO channel. Each SSC codeword is a sparse vector of the size of the number of transmit antennas. The information is imparted through: (i) uncertainty in the positions of non-zero elements, and (ii) uncertainty in the symbol-space of non-zero elements. Basis-pursuit (BPD) and LASSO detectors are used with knowledge of code sparsity to detect SSC. However, their performance is found to be degraded compared to the Maximum Likelihood Detector (MLD). A runner-up basis pursuit algorithm is proposed that provides MLD-like performance with a small increment in complexity over BPD. Analytical and simulation results show that SSC outperforms orthogonal space time block codes in terms of word error rate at varying SNR ranges.