A new ML detector for trellis-coded spatial modulation using hard and soft estimates

In this paper we propose a new detector for the spatial modulation (SM) receiver. In trellis coded spatial modulation (TCSM) schemes, the joint detection is used for identifying both the antenna index and the transmitted symbol. We define a hybrid maximum-likelihood (ML) SM detector, which determines the transmit antenna index soft estimate and the transmitted symbol hard estimate. The antenna indexes soft estimates are decoded using the logarithmic maximum a posteriori probability (log-MAP) algorithm. It is shown that for at least four receive antennas, the hybrid ML-SM detector offers a coding gain of at least 2 dB over the hard-output solutions in spatially correlated (SC) channels. The proposed detector is less complex than soft-output one, with a negligible bit error rate (BER) performance decrease. The BER is estimated by simulation for QPSK-TCSM transmissions over stationary Rayleigh and SC fading channels with additive white Gaussian noise (AWGN).