On the performance analysis of binary non-coherent modulations with selection combining in double rice fading channels

In this paper, we examine the bit error probability (BEP) performance of binary non-coherent modulations over L-branch selective combining (SC) diversity in frequency-flat, slowly-varying double Rice fading channels. The double Rice fading channel is constructed as the product of two independent but not identically distributed Rice processes. In addition, we assume that the double Rice processes affecting the signal received over the L branches of the diversity system are independent and identically distributed. Under these assumptions, and by using the cumulative distribution function (CDF) approach, we derive an expression for the average BEP performance of binary noncoherent frequency-shift keying (FSK) and differential phase-shift keying (DPSK) modulations. The result elaborated is generic in that it includes the propagation environments described by Rayleigh × Rice and double Rayleigh fading models as special cases. The result is in the form of semi-infinite range integrals, that are easy to compute numerically. Additionally, for the special case of dual-branch SC diversity, i.e., L = 2, relatively simplified expressions for the BEP performance are obtained. Moreover, illustrative numerical results are presented together with corresponding simulation quantities to check the validity of the derived analytical quantities, and analyze the impact of the fading parameters on the BEP performance. The results are useful in assessing the performance of amplify-and-forward (AF) dual-hop vehicle-to-vehicle (V2V) communications with line-of-sight (LOS) paths, and where the additive noise in the relay station can be neglected.