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.

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 (PD) and the probability of false alarm (PFA), that can be readily evaluated using any mathematical software. Monte-Carlo simulations corroborate our analytical findings.

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.

Sums of Weibull variates arise in several communications fields, such as optical, mobile, and radar systems. However, due to the intricate task of evaluating the Weibull sums, only a few works deal with the exact sum statistics. Some of these works provide solutions in terms of nested infinite sums-products, approximate solutions, or in terms of especial functions that, unfortunately, have not yet been implemented in mathematical packages such as Maple, MATLAB, or Mathematica. Yet, these solutions are time-consuming and prone to convergence and instability problems as the number of Weibull summands increases. In this letter, based on a comprehensive calculus of residues, we derive novel exact expressions for the probability density function and the cumulative distribution function of the sum of independent and identically distributed Weibull random variables. Numerical results show that our derived solutions are faster and enjoy a lower computational burden than the state-of-the-art ones.

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 α-μ 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 α-μ 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.

Sparse code multiple access (SCMA) is an interesting proposal for supporting massive machine-type communications (mMTC) in future mobile networks. In this use case, mobile networks connect to Internet of Things (IoT) devices, which may have low computational processing capacities, and thus, they are exposed to different security threats. In this regard, physical-layer security (PLS) arises as an alternative technique to protect information. This work proposes a new scheme based on the design of unknown codebooks to an external eavesdropper aiming at guaranteeing PLS in the uplink of SCMA systems over generalized $\kappa$ - $\mu$ fading channels. Considering that the SCMA codebook design can be realized from the rotation of base quadrature-amplitude modulation (QAM) constellations using the signal-space-diversity (SSD) technique, a novel upper-bound expression to calculate the average bit error probability (ABEP) of multidimensional SSD systems is derived. Then, a metric to select the best rotation matrices is determined. With this, a set of optimal and suboptimal rotation matrices can be acquired. A strategy to obtain secret keys in the SCMA system is presented by considering imperfect channel estimation. The secret keys are used to select matrices for rotating the base QAM constellations used in the codebooks generation. Finally, an uncoded and turbo-encoded SCMA system is evaluated using Monte Carlo simulations. The results show that our proposal ensures a near-optimal SCMA performance while the eavesdropper cannot decode the information.