Performance Analysis of Full-Rate Coordinate Interleaved Orthogonal Designs Over Time-Selective Fading Channels

Coordinate interleaved orthogonal designs (CIOD) (Khan and Rajan in IEEE Trans Inform Theory 52(5):2062–2091, 2006) can offer desirable properties, such as full rate, full diversity and single-symbol maximum likelihood decoding for two, three and four transmit antennas under quasi-static fading channels. When fading is time-selective, zero-forcing decoder can applied to achieve good performance while still maintain low decoding complexity. In this paper, theoretical analysis of symbol error rate performance for CIOD codes over time-selective fading channels with a zero-forcing linear receiver is derived. Firstly, a closed-form expression (i.e., not in integral form) is derived for the average symbol pair-wise error probability (SPEP) in time-selective frequency-nonselective independent identically distributed (i.i.d.) Rayleigh fading channels. Then, the SPEP is used to derive a tight upper bound (UB) for the symbol-error rate (SER) of CIOD codes. Simulation results indicate that our theoretical UB often coincides (within 0.05 dB) with the true SER obtained via Monte-Carlo simulation. The UB can thus be used to accurately predict and optimize the performance of CIOD codes over time-selective fading channels.