Maximum a Posteriori OMP Detection for Generalized Space Shift Keying

We consider extensions of orthogonal matching pursuit (OMP) and oblique matching pursuit (ObMP) detectors for generalized space shift keying (GSSK). In particular, the maximum a posteriori (MAP) principle is incorporated with the OMP/ObMP so that the posteriori ratio can be maximized iteratively. Due to the fact that the posteriori ratio cannot be evaluated at the receiver unless the activated transmit antennas are known, two types of approximated posteriori ratios are derived. One is a simple approximation that ignores the terms in the posteriori ratio which need the information on transmit antenna activity, and the other is a more complex approximation developed by exploiting the transmit antenna activation probabilities. As a result, two types of MAP-OMPs and MAP-ObMPs are proposed based on these approximations. The performances and computational loads of the proposed schemes are examined and compared with existing OMP-based GSSK detectors. The results demonstrate that incorporating the MAP policies can significantly enhance performances of OMP/ObMP detectors and can yield efficient detectors that can outperform existing methods with little increase in complexity.