Switching rate of generalized selection combining with non-identical branches in Rayleigh fading channels

Generalized selection combining (GSC), whereby the receiver selects M out of N received replicas of the same signal for combining, is an effective mean to achieve reliable transmission in fading channel. However, in order to perform coherent combining, the selected signals must be individually tracked for sufficiently long time before accurate channel estimates can be produced for combining purpose. This tracking operation, unfortunately, is incompatible with the inherently antenna switching that takes place inside the GSC receiver. In this paper, we extend the switching rate analysis of M out of NGSC receivers in [3] to the case of independent but statistically non-identical branches. Despite the fact that non-identical branches introduces a correlation between the difference of the M-th and the M+1-th strongest signals, u(t), and its derivative, u'(t), we were able to derive an analytical expression for the switching rate of the GSC receiver under this condition (independency between u(t) and u'(t) is crucial in obtaining the simple results in [3]). Our numerical results agree with the intuition that having nonidentical branches reduces the switching rate. The more dissimilar the branches are, the larger the reduction. While this lowering of the switching rate allows the GSC receiver more time to dwell on the selected signals and hence producing more accurate channel estimates for coherent combining, the bit-error rate of GSC, unfortunately, is higher when the branches are not identical.