Presented here is a unified approach to evaluating the error-rate performance of digital communication systems operating over a generalized fading channel. What enables the unification is the recognition of the desirable form for alternate representations of the Gaussian and Marcum Q-functions that are characteristic of error-probability expressions for coherent, differentially coherent, and noncoherent forms of detection. It is shown that in the largest majority of cases, these error-rate expressions can be put in the form of a single integral with finite limits and an integrand composed of elementary functions, thus readily enabling numerical evaluation.

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A unified approach to the performance analysis of digital communication over generalized fading channels

We present new exponential bounds for the Gaussian Q function (one- and two-dimensional) and its inverse, and for M-ary phase-shift-keying (MPSK), M-ary differential phase-shift-keying (MDPSK) error probabilities over additive white Gaussian noise channels. More precisely, the new bounds are in the form of the sum of exponential functions that, in the limit, approach the exact value. Then, a quite accurate and simple approximate expression given by the sum of two exponential functions is reported. The results are applied to the general problem of evaluating the average error probability in fading channels. Some examples of applications are also presented for the computation of the pairwise error probability of space-time codes and the average error probability of MPSK and MDPSK in fading channels.

New exponential bounds and approximations for the computation of error probability in fading channels

We present a unified analytical framework to determine the exact average symbol-error rate (SER) of linearly modulated signals over generalized fading channels. The results are applicable to systems employing coherent demodulation with maximal-ratio combining multichannel reception. The analyses assume independent fading paths, which are not necessarily identically distributed. In all cases, the proposed approach leads to an expression of the average SER involving a single finite-range integral, which can be easily computed numerically. In addition, as special cases, SER expressions for single-channel reception are obtained. These expressions reduce to well-known solutions, give alternative (often simpler) expressions for previous results, or provide new formulas that are either closed-form expressions or simple to compute numerically.

A unified approach for calculating error rates of linearly modulated signals over generalized fading channels

We derive analytical expressions for the symbol error probability (SEP) for a hybrid selection/maximal-ratio combining (H-S/MRC) diversity system in multipath-fading wireless environments. With H-S/MRC, L out of N diversity branches are selected and combined using maximal-ratio combining (MRC). We consider coherent detection of M-ary phase-shift keying (MPSK) and quadrature amplitude modulation (MQAM) using H-S/MRC for the case of independent Rayleigh fading with equal signal-to-noise ratio averaged over the fading. The proposed problem is made analytically tractable by transforming the ordered physical diversity branches, which are correlated, into independent and identically distributed (i.i.d.) "virtual branches," which results in a simple derivation of the SEP for arbitrary L and N. We further obtain a canonical structure for the SEP of H-S/MRC as a weighted sum of the elementary SEPs, which are the SEPs using MRC with i.i.d. diversity branches in Rayleigh fading, or equivalently the SEPs of the nondiversity (single-branch) system in Nakagami fading, whose closed-form expressions are well-known. We present numerical examples illustrating that H-S/MRC, even with L/spl Lt/N, can achieve a performance close to that of N-branch MRC.

Virtual branch analysis of symbol error probability for hybrid selection/maximal-ratio combining in Rayleigh fading

We present new exponential bounds for the Gaussian Q-function or, equivalently, of the complementary error function er f c(.). More precisely, the new bound is in the form of the sum of exponential functions that, in the limit, approaches the exact value. Then, a quite accurate and simple approximated expression given by the sum of two exponential functions is reported. Moreover, some new simple bounds for the inverse er f c(.) are derived. The results are applied to the general problem of evaluating the average error probability in fading channels. An example of application to the computation of the pairwise error probability of space-time codes is also presented.

V. Mandrekar

Papers

Simplified Relationships for the Prohahijity Distribution of the Phase of a Sine Wave in Narrow-Band Normal Noise