Single-carrier frequency-domain turbo equalization (SC-FDTE) has gained widespread adoption in the emerging broadband spatial modulation (SM) systems operating in frequency-selective channels, where the channel model considered is a quasi-static Rayleigh fading channel. In this paper, a new class of robust FDTE designs based on the minimum mean-square error (MMSE) criterion is conceived for broadband single-carrier SM (SC-SM) systems relying on realistic imperfect channel knowledge. First, a robust time-domain soft-decision feedback (TDSDF)-aided FDTE is proposed to cope with channel estimation errors at the receiver. Furthermore, its robust frequency-domain soft-decision feedback (FDSDF)-aided counterpart is derived to offer a low-complexity approximate solution. Finally, by exploiting the carefully selected reliable soft-decision output of the channel decoder as pilots, we refine the resultant decision-directed channel estimation. As a benefit, the performance of the two robust FDTEs can be further improved. Both our simulation results and our extrinsic information transfer (EXIT) chart analysis demonstrate that the proposed robust FDTEs achieve significant performance improvements over the conventional FDTEs.

In this paper, low-complexity time-domain turbo equalization (TDTE) detectors based upon soft-interference-cancellation (SIC)-aided minimum mean-square error (MMSE) criterion are proposed for single carrier generalized spatial modulation (SC-GSM) systems. First, a symbol-by-symbol-aided TDTE detector for application to the small-scale GSM systems is proposed, where the zero symbols are considered as constellation points when performing SIC. Then, vector-by-vector-aided TDTE (VV-TDTE) detectors for application to larger-scale antenna systems are introduced, where the GSM symbol is treated as an entire vector when performing SIC. As for the proposed VV-TDTE detectors, in addition, different time-varying filter coefficients are designed, in order to strike a flexible tradeoff between complexity and performance. By relying upon extrinsic information transfer chart analysis, we show that the proposed TDTE detectors are capable of providing considerable bit error rate performance gains over existing TDTE detectors and over the classic frequency-domain equalization-based MMSE detector, especially for the unbalanced antenna configurations.

In this paper, we design the low-complexity tree search-based detectors for generalized spatial modulation (GSM) aided single carrier (SC) systems over dispersive channels. Specifically, we commence with a brief review of the existing detection algorithms and then extend the sphere decoding-aided (SD) tree search algorithms designed for flat fading channels to GSM-aided SC systems. Moreover, a pair of reduced-complexity tree search algorithms are proposed by employing a hybrid concept of SD and M-algorithm to balance a tradeoff between the performance and complexity. Our proposed detectors are capable of recovering the transmit signal for both the overdetermine and underdetermine antenna configurations. Simulation results show that: 1) the extended SD-aided tree search algorithms are capable of providing the same performance as the maximum likelihood (ML) algorithm with reduced complexity; 2) the proposed novel algorithms exhibit lower complexity with negligible performance loss, compared with other tree search algorithms.