Comments on “New Method of Performance Analysis for Diversity Reception With Correlated Rayleigh-Fading Signals”

The purpose of this comment is to provide a critical discussion of the new method of performance analysis of diversity systems proposed in the abovementioned paper. It is shown that this method provides incorrect results for equal-gain and selective combining. A new method of performance analysis of two-branch receive diversity systems has been presented in the paper mentioned above.1 The main idea of this method is to transform the two received correlated signals into uncorrelated ones and to then apply the existing techniques of uncorrelated signal-combining analysis: “Based on the conversion process proposed in Section III, the performance analysis can be conducted by the following steps for the dual-branch diversity reception in correlated Rayleigh-fading environments. Step 1) Convert two correlated signals into two independent ones with the proposed transformation. Step 2) Conduct the performance analysis of diversity reception with new independent Rayleigh-fading signals by using existing analysis methods reported in the literature. Manuscript received February 6, 2001; revised November 28, 2001 and February 27, 2002. S. Loyka is with the School of Information Technology and Engineering (SITE), University of Ottawa, Ottawa, ON K1N 6N5, Canada (e-mail: [email protected]). C. Tellambura is with the School of Computer Science and Software Engineering, Monash University, Clayton, Vic. 3168, Australia (e-mail: [email protected]). A. Kouki and F. Gagnon are with the Department of Electrical Engineering, Ecole de Technologie Superieure, Montreal, PQ H3C 1K3, Canada (e-mail: [email protected]). A. Annamalai is with the the Bradley Department of Electrical and Computer Engineering, Virginia Polytechnic Institute and State University, Alexandria, VA 22314 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TVT.2003.811342 1L. Fang, G. Bi, and A. C. Kot, IEEE Trans. Veh. Technol., vol. 49, pp. 1807–1812, Sept. 2000. Fig. 1. (a) Block diagram of a diversity-combining system and (b) the transformed system. r and r are the received correlated signals, ~ r and ~ r are the transformed uncorrelated signals. The analysis result achieved in Step 2 is the performance of diversity reception with original correlated Rayleigh-fading signals.” The implicit assumption behind this approach, which leads to the statement in the last sentence, is that the transformation proposed in Section III does not change the performance of the diversity-combining system. However, the paperfails to provide a proof for this crucial assumption. As the detailed analysis below shows, this assumption is true for maximal-ratio combining (MRC), but not true for equal-gain combining (EGC) and selection combining (SC). Thus, the method above cannot be applied in the latter two cases. Let us now consider the method proposed in the paperin more detail. Without going into a complex statistical analysis, we examine the basic equations that describe the operation of a diversity-combining system. Fig. 1(a) shows the original diversity-combining system under the analysis, which can be MRC, EGC, or SC. Fig. 1(b) shows the modified system by using the transformation in the paper. The instantaneous signal-to-noise power ratio (SNR) at the output of the original system is = F (r) 2N ; r = r1 r2 (1) where r is the received complex envelope-signal vector (without noise), F is the signal-combining function, and N is the noise power per branch (for simplicity, we consider the case of equal noise powers). For MRC, EGC, and SC, correspondingly, it takes the following form [2]: