This paper introduces two comprehensive composite fading models: the α-FMixture and the α-GMixture. These models unify a broad spectrum of previously reported composite fading distributions and enable the systematic construction of hundreds of new ones. Their first-order statistics (namely, probability density function (PDF), cumulative distribution function (CDF), moment-generating function, and higher-order moments) are derived in compact, tractable forms that, for specific cases, yield singularity-free expressions improving upon existing state-of-the-art solutions. By consolidating a wide range of multiplicative shadow (MS) and LOS shadow (LOSS) fading families into a single parameterized framework, they provide a unified analytical basis for obtaining the key statistics of numerous composite fading scenarios. Serving asplug-and-playbase models, they enable direct evaluation of metrics such as outage probability (OP) and average symbol error rate (ASER) for both established and new composite fading models without rederiving channel statistics. Their unified structure and flexible parameterization also support systematic analysis of fading and shadowing in emerging scenarios, providing practical and extensible tools for next-generation wireless channel characterization.

The aim of this paper is threefold: 1) we introduce a unified statistical characterization for the instantaneous power of a plethora of Gaussian-based fading models; 2) we propose a general framework for the power sum of either independent and identically distributed (i.i.d.) or independent and non-identically distributed (i.non-i.d.) fading distributions; and 3) we provide a unified performance assessment of wireless communications systems in the presence of small-scale fading channels. To accomplish these three goals, we first show that the instantaneous power of a broad Gaussian class of fading models is governed by a mixture of gamma (MG) distribution. Later, we propose novel, tractable, and efficient solutions for the exact sum statistics of i.i.d. and i.non-i.d. MG variates. Lastly, we show that two key performance indicators—namely, the average bit-error rate and the outage probability—of a maximal-ratio combining (MRC) diversity receiver subject to a wide variety of Gaussian-based fading channels can be expressed, in a unified fashion, as a weighted sum of the performance indicators of a single-branch wireless system subject to independent Nakagami-m fading channels. Extensive numerical simulations reveal the outstanding improvement in computational efficiency and mathematical tractability of our derived expressions when compared with state-of-the-art solutions.

Two generalizations of the fluctuating two-ray (FTR) fading model have recently appeared in the literature. In particular, in these FTR-based models, the specular components of the complex baseband signal are modulated by the square root of either (i) the product (Cascade FTR) or (ii) the ratio of products (Ratio-Product FTR) of Gamma random variables (RVs). Leveraging the applicability of the sum of RVs in performance analysis of communications systems, this paper explores the sum statistics of these two newly introduced FTR-based RVs. More precisely, we obtain novel exact formulations for the probability density function (PDF), the cumulative distribution function (CDF), and the raw moments of the sum of independent and identically distributed (i.i.d.) squared FTR-based RVs. Moreover, we carry out a truncation error analysis for the derived PDFs and CDFs. Finally, we obtain in an exact and asymptotic manner essential performance metrics such as outage probability (OP) and symbol error probability (SEP) for a maximal-ratio combining (MRC) receiver.

In the context of synthetic aperture radar (SAR) systems, the Gamma distribution stands out as a strong contender for clutter modeling. The cell-averaging constant false alarm rate (CA-CFAR) detector has frequently been employed as a well-balanced detection technique, ensuring a blend of high performance and comparatively low complexity. In this study, we evaluate, in an exact manner, the CA-CFAR detector’s performance in an SAR system, assuming the presence of correlated Gamma-distributed clutter. To this aim, we derive novel exact expressions for the probability of detection (PD) and the probability of false alarm (PFA), simplifying their runtime evaluations without depending on specific mathematical software. The independent and identically distributed (IID) and independent not identically distributed (INID) cases are also analyzed. In particular, for the IID case, our derived PD and PFA expressions are given in closed form. Our analytical findings are validated through Monte Carlo simulations.

Sea clutter has been a long-standing issue in old and modern radars. Under this context, the K-distribution has emerged as a promising clutter model to accurately mimic sea signal variations in a large variety of radar systems. To guarantee an adequate radar performance in the presence of sea clutter, the family of constant false-alarm rate (CFAR) detectors has been commonly used. In particular, due to its adequate balance between performance and implementation, the cell-averaging CFAR (CA-CFAR) detector has been considered an attractive detection mechanism to enhance radar performance over various clutter environments. In this work, we assess radar performance considering a CA-CFAR detector operating over K-distributed sea clutter with fully correlated texture. More precisely, we derive novel closed-form expressions for the probability of detection ( $P_{\text {D}}$ ) and the probability of false alarm ( $P_{\text {FA}}$ ) that can be readily evaluated using any mathematical software. Monte-Carlo (MC) simulations corroborate our analytical findings.

The sum of random variables (RVs) appears extensively in wireless communications, at large, both conventional and advanced, and has been subject of longstanding research. The statistical characterization of the referred sum is crucial to determine the performance of such communications systems. Although efforts have been undertaken to unveil these sum statistics, e.g., probability density function (PDF) and cumulative distribution function (CDF), no general efficient nor manageable solutions capable of evaluating the exact sum PDF and CDF are available to date. The only formulations are given in terms of either the multi-fold Brennan’s integral or the multivariate Fox$H$-function. Unfortunately, these methods are only feasible up to a certain number of RVs, meaning that when the number of RVs in the sum increases, the computation of the sum PDF and CDF is subject to stability problems, convergence issues, or inaccurate results. In this paper, we derive new, simple, exact formulations for the PDF and CDF of the sum of$L$independent and identically distributed$\alpha $-$\mu $RVs. Unlike the available solutions, the computational complexity of our analytical expressions is independent of the number of summands. Capitalizing on our unprecedented findings, we analyze, in exact and asymptotic manners, the performance of$L$-branch pre-detection equal-gain combining and maximal-ratio combining receivers over$\alpha $-$\mu $fading environments. The coding and diversity gains of the system for both receivers are analyzed and quantified. Moreover, numerical simulations show that the computation time reduces drastically when using our expressions, which are arguably the most efficient and manageable formulations derived so far.

In this letter, we derive a novel exact expression for the probability of false alarm (PFA) and an approximate closed-form solution for the probability of detection (PD) of a smallest of cell-averaging constant false alarm rate (SOCA-CFAR) detector operating over Weibull-distributed clutter. For the analysis, we consider an exponentially distributed target and allow arbitrary values for the shape parameter of clutter interference. To the best of our knowledge, there are no exact or approximate performance evaluations for an SOCA-CFAR detector considering arbitrary values for the shape parameter of the Weibull interference samples (i.e., different from 1) contained within the CFAR window. Therefore, our analytical derivations generalize previous performance evaluation studies and take a small step toward a better understanding of more realistic SOCA-CFAR detectors. Moreover, we obtain exact formulations for the probability density function (PDF) and the cumulative distribution function (CDF) for a minimum of two sums of independent and identically distributed (i.i.d.) Weibull random variables. Numerical results indicate that the system performance improves as the shape parameter of the Weibull interference increases. The validity of all our expressions is confirmed via Monte Carlo simulations.

In this letter, we provide a general cell-averaging constant false alarm rate (CA-CFAR) performance analysis considering homogeneous Weibull-distributed clutter environments. To do so, we provide generalized expressions for the probability of detection (PD) and probability of false alarm (PFA). Notably, these expressions permit arbitrary values for the shape parameter of the Weibull interference. So far, all CA-CFAR performance analyses were carried out by setting the shape parameter of the Weibull samples within the CFAR window equal to one, which narrows the overall evaluation spectrum. In this study, we allow the shape parameter to take values greater than or equal to one—regime of paramount importance in many practical applications—and still manage to derive manageable and easy-to-implement solutions. All our expressions are confirmed via Monte-Carlo simulations. Numerical results indicate that radar detection is improved as the shape parameter increases.

Modern radar systems use square-law detectors to search and track fluctuating targets embedded in Weibull-distributed ground clutter. However, the theoretical performance analysis of square-law detectors in the presence of Weibull clutter leads to cumbersome mathematical formulations. Some studies have circumvented this problem by using approximations or mathematical artifacts to simplify calculations. In this work, we derive aclosed-formandexactexpression for the probability of detection (PD) of a square-law detector in the presence of exponential targets and Weibull-distributed ground clutter, given in terms of the Fox H-function. Unlike previous studies, no approximations nor simplifying assumptions are made throughout our analysis. Furthermore, we derive a fast convergent series for the referred PD by exploiting the orthogonal selection of poles in Cauchy’s residue theorem. In passing, we also obtain closed-form solutions and series representations for the probability density function and the cumulative distribution function of the sum statistics that govern the output of a square-law detector. Numerical results and Monte Carlo simulations corroborate the validity of our expressions.

This work assesses the performance of a phased array radar working in background noise. To do so, we consider the presence of a nonfluctuating target embedded in complex white Gaussian noise (CWGN), in which the amplitude of the target echo and the noise power are assumed to be unknown. Making use of the generalized likelihood ratio test (GLRT), we design and analyze a detector based on the phased-array front end. We obtain exact closed-form expressions for the probability density functions (PDFs) corresponding to the detection statistics. In addition, we derive a fast convergent series for the probability of detection (PD). The derived series presents a low computational cost while maintaining a tractable and efficient solution. Numerical results and Monte Carlo simulations corroborate the validity of our expressions. The performance of the proposed detector is also compared with the idealized Neyman-Pearson (NP) detector to quantify the practical losses in terms of the signal-to-noise ratio (SNR).

This letter presents a novel and exact formulation for the probability of detection of a cell-averaging, constant false-alarm rate (CFAR) radar system operating in a homogeneous Weibull clutter environment. We consider a realistic scenario with both target returns and clutter residues within the cell under test by the radar processing. In passing, we derive novel closed-form expressions for the probability density function and the cumulative distribution function of the sum of an exponentially fluctuating target embedded in Weibull clutter. The derived exact expressions are given in terms of both: 1) bivariate Fox H-function, for which we provide a portable and efficient MATHEMATICA code and 2) easily computable series representations. The validity of all expressions is confirmed via Monte Carlo simulation. The derived results are compared with the idealized Neyman-Pearson detector so as to quantify the CFAR losses, and they indicate that even a small change in the shape parameter of the clutter distribution can significantly affect the radar detection performance.