Fast Two-Stage Max-Log MAP Detection Schemes for the Soft-Input Soft-Output Detection of Coded Generalized Spatial Modulation Signals

We study soft-input soft-output (SISO) maximum logarithmic maximum a posteriori (max-log-MAP) detection of coded generalized spatial modulation (GenSM) signals for the iterative detection and decoding receiver. Due to the property of GenSM, extrinsic bit log-likelihood ratio associated with each bit of the transmit antenna combination index and transmit symbol vector needs to be computed. By extending our sorting assisted successive sphere decoding algorithm (SA-SSDA) for the hard-output detection of GenSM signals, we study two-stage detection schemes here to conduct multiple single tree search sphere decoding algorithms (STS-SDAs) for the second stage computation, where the order of the multiple STS-SDAs is determined in the first stage computation. Unlike previous two-stage detectors, our emphasis is on studying the ordering metrics for determining the order of STS-SDAs and is on giving suggestions about the scenarios to use adequate ordering metrics for the purpose of complexity reduction. Accordingly, incorporating the tricks used by the SA-SSDA and STS-SDA, we arrive at a fast SA-SSTS-SDA for exactly max-log-MAP detection of GenSM signals. Our proposed detector is feasible for hardware implementation and may motivate future research on the SISO detection of coded GenSM signals.