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

The average bit-error rate of transmit antenna selection combined with receive maximum-ratio combining is computed as a function of the transmit antenna update rate when using binary phase-shift keying in flat Rayleigh fading channels. This scheme achieves an order of diversity equal to the product of the number of transmit and receive antennas. Therefore, it can gain significant diversity benefits over traditional receive diversity schemes by distributing the antennas over the transmit and receive side.

Performance analysis of combined transmit-SC/receive-MRC

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 alternate (often simpler) expressions for previous results, or provide new formulas which are either closed-form expressions or simple to compute numerically.

We evaluate and optimize the performance of switch and stay diversity systems which have the advantage of offering one of the least complex solutions to mitigating the effect of fading. We study the impact of fading type and severity, unbalanced branches, fading correlation, and imperfect channel estimation on the performance of these systems, and compare this performance with that of more complex diversity schemes such as maximal-ratio combining and selection combining. We also propose, analyze, and optimize the performance of a generalized switched diversity scheme. In summary, the presented results offer a simple, generic, and useful analytical tool for the accurate performance evaluation and optimization of switched diversity systems.

Analysis and optimization of switched diversity systems

An analytical technique well suited to numerical analysis is presented for computing the average bit-error rate (BER) and outage probability of M-ary phase-shift keying (PSK) in the land-mobile satellite channel (LMSC) with microdiversity reception. Closed-form expressions are found for L-branch microdiversity using both selection diversity combining (SDC) and maximal ratio combining (MRC). These expressions are extended to include both M-ary coherent PSK (M-PSK) and differential PSK [M-differential PSK (DPSK)]. Following previous empirical studies, the LMSC is modeled as a weighted sum of Rice and Suzuki distributions. Numerical results are provided illustrating the achievable performance of both M-PSK and M-DPSK with diversity reception. Using measured channel parameters, the performance in various mobile environments for various satellite elevation angles is also found.

Analysis of M-ary phase-shift keying with diversity reception for land-mobile satellite channels

M-ary phase-shift keying and differential phase-shift keying (DPSK) on a slow fading Rayleigh channel without diversity is investigated. Expressions for the distribution of the phase angle between a vector with Rayleigh amplitude distribution and a noiseless reference, and between two vectors both with Rayleigh amplitude distribution perturbed by Gaussian noise are obtained. >

Probability of error of M-ary PSK and DPSK on a Rayleigh fading channel

An expression is derived for the probability of error of an Nth-order selection diversity system for the case where the receiver is forced to swell on one channel for several symbols before being allowed to make a decision regarding the best channel. It is found that the time-varying nature of a fading channel causes significant degradation of the probability of error when the dwell time becomes longer than about 10% of the inverse of the fading bandwidth of the channel. The onset of degradation is a function of the signal-to-noise ratio and of the order of diversity. Specific probabilities of error are calculated for differential phase-shift keyed modulation (DPSK). However, the calculations can be done for any other modulation technique. >

C.K. Pauw

Papers

Probability of error of M-ary PSK and DPSK on a Rayleigh fading channel

Probability of error for selection diversity as a function of dwell time