Joint iterative channel estimation and frequency-domain turbo equalization for single-carrier spatial modulation

Single carrier frequency-domain turbo equalization (SC-FDTE) has gained widespread adoption in the emerging broadband spatial modulation (S-M) 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 broad-band 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 counter-part 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