Multiple-symbol differential detection based on combinatorial geometry

In this paper, the application of combinatorial geometry to noncoherent multiple-symbol differential detection (MSDD) is considered. The resulting algorithm is referred to as CG-MSDD. Analytical expressions for the complexity of CG-MSDD are derived and it is shown that it is polynomial in the length N of the MSDD observation window if the rank of the N times N channel autocorrelation matrix is fixed, but in fact exponential in N if standard fading models are considered. Compared to popular sphere-decoder based MSDD, CG-MSDD is superior (i) in low-signal-to-noise power ratio (SNR) slow-fading channels as its complexity is independent of the SNR, (ii) as its complexity is constant, i.e., independent of the particular channel and noise realization, and (iii) asymptotically, as its complexity exponent only scales linearly with the bandwidth of the fading process.