A Semidefinite Relaxation Approach to OFDM-IM Detection in Rapidly Time-Varying Channels

In this paper, the signal detection of orthogonal frequency division multiplexing with index modulation (OFDM-IM) in the rapidly time-varying channel is studied. Due to the inter-carrier interference, the conventional block detectors based on the successive interference cancellation (SIC) strategy, e.g., the signal power (SP) detector, suffer from severe error propagation especially in the case with large normalized Doppler frequency. To address this problem, a semidefinite relaxation (SDR) approach is first proposed. In the proposed SDR detector, the signal feature of OFDM-IM is presented properly as the convex constraints in the SDR programming problem and utilized in the randomization procedure. The SDR detector can avoid the error propagation effectively with a cost of higher polynomial complexity. To reduce the complexity, the group-based SIC-SDR detector is then proposed, where the subcarriers in one OFDM symbol is partitioned into multiple groups, and the SDR detection is performed over each group successively in conjunction with the ordered SIC strategy. However, similar with the SP detector, the SIC-SDR detector also suffers from the error propagation. To boost the performance, we propose to take the solution of the SIC-SDR detector as the initial estimation of a further local search algorithm (LSA). Concretely, after a proper definition of the nearest neighbors of an OFDM-IM signal vector, the proposed combined detector employing the likelihood ascent-search as the LSA is presented. Finally, the validity of the proposed detectors is justified by simulation results, and the combined detector achieves an excellent performance-complexity trade off.