Maximal ratio combining with channel estimation errors

An ideal coherent maximal ratio (MR) combiner multiplies the signals on all the incoming channels by the complex conjugate of their complex channel gains and then sums the resultant products to provide the optimum combined signal. However, the channel gains can not be estimated perfectly in any practical system. Thus, system performance will be degraded because there will be an error in the estimation of the combiner weighting factors in realistic combiners. In the paper closed form results are obtained for the bit error rates (BER) of MFSK, MPSK (M=2,4,8) and MDPSK (M=2,4) using imperfect MR combining in Rayleigh fading. These results are used to approximate the BER performance of equal gain (EG) combining with imperfect co-phasing. The MFSK results are also compared with those of the optimum non-coherent square-law (SL) combiner to determine how good channel estimation must be to surpass the performance of the optimum non-coherent combiner