Exact error performance of square orthogonal space- time block coding with channel estimation

Consider a wireless communication system in flat fading with N transmit and M receive antennas using space-time block coding, where N×1 code vectors are transmitted over L symbol intervals, resulting in an N×L code matrix. A least-squares estimate (LSE) as well as a minimum mean-square estimate (MMSE) of the M×N channel matrix is obtained from a sequence of pilot code vectors. For the case of linear square (i.e., with N=L) orthogonal codes over constant envelope constellations, we obtain an expression for the exact decoding error probability (DEP) for coherent maximum-likelihood decoding. We also find the coding gain for high average signal-to-noise ratio (SNR) per diversity branch in the case of Rayleigh fading. A comparison between both channel-estimation techniques is done in terms of the average pilot-power-to-signal-power ratio (APPSPR). It is found that MMSE requires lower pilot power than LSE for the same DEP and the same average SNR per diversity branch. In addition, the error performance with LSE approaches that with MMSE, with an increase of average SNR per branch or an increase of APPSPR.