Exact expressions for the probability density function (PDF) and cumulative distribution function (CDF) of cascaded Rayleigh fading channels with arbitrary correlation but not necessarily identically distributed are derived. Furthermore, the PDF and CDF of the instantaneous signal‐to‐noise ratio are obtained. The cascaded channels are assumed to have slow frequency non‐selective arbitrarily correlated Rayleigh fading with arbitrarily values of fading parameters. Indeed, the expressions of the outage probability and average normalised channel capacity for this channel model are derived. The average bit error probability for coherently detected binary signals in additive white Gaussian noise channel as well as in arbitrarily correlated cascaded Rayleigh fading channels is obtained. Numerical results are also provided and authenticated by Monte Carlo simulation. To the best of the authors' knowledge, the derived expressions for this channel model are new and have not been reported in the literature.

Novel expressions for the multivariate probability density function (PDF), cumulative distribution function (CDF) and moment generating function (MGF) of arbitrarily correlated and unbalanced α - μ fading channels are derived. The derived expressions are expressed in terms of well known functions which are available in common mathematical software. The new results are then used to derive the MGF of the signal-to-noise ratio (SNR) at the equal gain combiner (EGC) output. For such a scenario, the derived MGF of the SNR at the EGC output is used directly to evaluate the average bit error probability for differential quadrature phase shift keying (DQPSK) signals, with postdetection diversity reception and combining over additive white Gaussian noise and slow nonselective arbitrarily correlated and unbalanced α - μ fading channels.

This paper derives a simple general closed form expression of the bit error probability for differentially detected signals with post-detection equal gain combining in additive white Gaussian noise and slow frequency nonselective fading channels. The derived expression is then used to study the performance of Gaussian minimum shift keying (GMSK) and quadrature Differential phase sift keying (QDPSK) signals when transmitting over non-identical and correlated Weibull fading channels in which each diversity branch can have unequal signal to noise ratio (SNR) and different severity parameter β as well.

This paper studies the performance of diversity applied to an efficient modulation/coding scheme using M-ary frequency-shift keying (MFSK) signals, with postdetection noncoherent diversity reception and combining over slow nonselective arbitrarily correlated and unbalanced Nakagami-m fading channels, in which the diversity branches can have unequal signal-to-noise ratios (SNRs), as well as different severity parameter m. This modulation/coding scheme is referred to as multiple tone MFSK (MT-MFSK) and is implemented based on balanced incomplete block design (BIB-design) from combinatorial theory. In MT-MFSK modulation, the number of tones used to represent the signals set is reduced compared with the conventional MFSK modulation, and each MT-MFSK signal is represented by a number of distinct orthogonal tones selected according to BIB-design. This mechanism drastically increase the bandwidth efficiency of the modulated signal and allows the modulator to create implicit frequency diversity. In this paper, we show that by combining the implicit frequency diversity of MT-MFSK signals with the diversity reception introduced by employing multiple receiving antennas, substantial improvements in performance can be obtained. A noncoherent square-law combining (SLC) soft-decision receiver is introduced and a union bound expression for the average symbol error probability is obtained. The effects of arbitrarily values of fading severity parameter m and the arbitrarily correlation between the unbalanced L diversity channels are considered. The system performance is compared with that of the conventional MFSK system. The results show that this modulation/coding scheme creates a multiplicative diversity and, therefore, performs better than the conventional MFSK system in terms of power and bandwidth efficiency.

This paper studies the performance and determine the advantages and limitations of diversity, applied to binary and quadrature differential phase shift keying (DPSK) signals under Nakagami-m (1960) fading in the presence of additive white Gaussian noise. The DPSK signals on the several diversity channels are presumed to be perturbed independently by Nakagami-m fading and additive white Gaussian noise. Also, it is assumed that the fading is slow and frequency nonselective. The postdetection diversity combining method is chosen so that the receiver performs a noncoherent detection, where equal gain combining (EGC) is used. Average bit error probability expressions are derived for both binary and quadrature DPSK. The derived expression for binary DPSK is in closed form, while that of QDPSK is in terms of a finite integral that can be easily computed via numerical integration routines, and, hence, can be usefully exploited in the performance evaluation of digital mobile radio systems.

This paper studies the design and performance analysis of a noncoherent multiple tone-frequency shift keying (MT-FSK) modulation based balanced incomplete block design (BIB-design) from combinatorial theory. The performance analysis of MT-FSK signals in Rayleigh fading channels with diversity and diversity combining is studied. A noncoherent diversity receiver and combiner is introduced and a union bound expression for the bit error rate is obtained. The results show that MT-FSK with diversity create a multiplicative diversity and therefore performs better than the conventional MFSK system in terms of power and bandwidth efficiency with less complexity.

This paper studies the performance of frequency hopped/coherent M-ary PSK signals in the presence of partial-band multitone jamming. The probability density function for the jammed received signal phase is found and utilized in obtaining a probability of error expression. The analytical expressions to assess the performance under worst case multitone jamming are provided.

This paper studies the design and performance analysis of a noncoherent hybrid modulation scheme derived from multifrequency and multiphase signals, and referred to as joint frequency-phase modulation (JFPM). This modulation class includes many formats, which can be classified as efficient bandwidth-limited modulation or power-limited modulation techniques. A noncoherent receiver structure for JFPM signals is introduced, and an exact expression for the probability of a bit error over AWGN channels is obtained. The results show that noncoherent JFPM perform better than M-ary DPSK and/or noncoherent M-ary FSK systems. The power spectral density and the spectral efficiency of JFPM are analyzed. Fractional out-of-band power containment bandwidths are obtained numerically for different JFPM formats. These analytical results show that the power spectral density of JFPM does not contain a discrete component and the same bandwidth efficiency can be obtained by using different JFPM formats. Overall, JFPM can be classified as a bandwidth- and power-efficient modulation technique.>