Reply to "Comments on \´New method of performance analysis for diversity reception with correlated Rayleigh-fading signals\´"

Fang et al. (2000) attempted to simplify the procedures of performance analysis for maximal ratio combining (MRC), selection combining (SC), and equal gain combining (EGC) diversity systems of two correlated Rayleigh-fading channels by using a known transformation technique. It was then found by Loyka et al. (for comment see ibid., vol. 52, no. 3, p. 725-726 (2003)) that this transformation technique is correct for MRC, but leads to some performance-prediction deviations for SC and EGC diversity systems compared to the results produced by other reported approaches. Because the transformation process redistributes the signal energy among different antennas, the bit error ratio (BER) achieved after the transformation may be different from that without transformation. For SC and EGC, the transformation technique can provide the same BER as that achieved without the transformation technique when the correlation is not strong and the signal-to-noise ratio (SNR) is large (p² < 0.8 and SNR > 8 dB, for example). In the case of small SNR and strong correlation, desirable performance gain in BER can be achieved by the transformation technique for the SC diversity system. However, the transformation technique produces an undesirable performance loss in terms of the BER for the EGC diversity system. It is not sufficient to use one example, as in Loyka et al. (fig. 2), to assess when the transform technique for SC predicts performance that deviates from reported approaches.