Performance of complex orthogonal M-ary transmission with Amicable Hadamard matrices over diversity Rayleigh fading channels

This paper proposes and analyzes a complex orthogonal multiplexing scheme based on the use of Amicable Hadamard matrices for non-selective Rayleigh fading channels. A thorough analysis provides exact closed-form mathematical formulas or upper and lower bounds together with simulation results for the estimation of the system bit error probability (BEP) with maximum likelihood vector detection. The proposed system is evaluated for various order configurations and M-ary information input with or without external diversity, assuming perfect channel state information at the receiver and interleaving. The results show great performance enhancement, in terms of BEP compared to regular MPAM modulation schemes. Furthermore, the proposed scheme presents similar or better performance in comparison to conventional MPAM with maximum ratio combining diversity or Alamouti 2×1 space-time block coding. This is achieved by the inherent time diversity gain without altering the original information rate and mean transmission power and leads to hardware antenna implementation complexity reduction.