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 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 paper investigates the achievable sum rate and the outage capacity of generalized frequency division multiplexing systems (GFDMs) with minimum mean-square error (MMSE) receivers over frequency-selective Rayleigh fading channels. To this end, a Gamma-based approximation approach for the probability density function of the signal-to-interference-plus-noise ratio is presented, based on which accurate analytical formulations for the achievable sum rate and outage capacity are proposed. The accuracy of our analysis is corroborated through Monte Carlo simulation assuming different GFDM parameters. Illustrative numerical results are depicted in order to reveal the impact of the key system parameters, such as the number of subcarriers, number of subsymbols, and roll-off factors, on the overall system performance.

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.

Two new methods of radial velocity estimation for distributed targets in arc-scanning synthetic aperture radar (ArcSAR) systems, namely, the maximum-likelihood estimator (MLE) and the suboptimal method based on the least squares estimation (LSE), are proposed, derived, and analyzed. To this end, we establish that n scatterers of the distributed target are uniformly dispersed within the radar resolution cell of dimensions a × b and they move randomly at different velocities. Furthermore, the effect of the antenna pattern is considered to characterize the amplitude of the scattered signal. Thus, from the coherent integration of the scatters at each pulse repetition interval in radar scanning, m data sequences are obtained as samples of the composite signal, which follows a multivariate normal distribution. From this, the covariance matrix, upon which the methods are based, is derived. Simulations have been carried out to compare the new methods with existing methods, namely, phase, energy, and correlation, as a function of the signalto-noise ratio. Finally, the results show that the MLE and LSE methods outperform the conventional methods, providing a gain of more than 10 dB.

Channel state information (CSI) is fundamental to the performance of massive multiple-input multiple-output systems. However, systems that rely on pilots for the CSI estimation are susceptible to pilot contamination, as neighboring cells may reuse the same pilot sequences. Independent component analysis (ICA) has been widely used in recent studies to perform blind decoding, in order to circumvent the effects of pilot contamination. In this letter, we introduce a modified version of fastICA, the phase corrected ICA that reduces phase rotation on the estimated constellations, and thus, results in better performance of blind receivers. Through simulations, we show that our method significantly reduces symbol error rates compared to standard ICA based methods. Furthermore, we show that the increase in complexity is small at high signal-to-noise rate.

The computation of the achievable sum rate for integer-forcing (IF) linear receivers requires the search for the shortest set of linearly independent lattice vectors (SIVP). Since SIVP is considered an NP-hard problem, we propose two approximations to the IF achievable sum rate. The first approximation is suitable for systems with two antennas at both transmitter and receiver (2 × 2 arrays) and is based on the analysis of the Gauss-Lagrange algorithm. The second approximation considers n × n array systems and is based on Minkowski's second theorem. Assuming a block-fading channel with Rayleigh distribution, we have derived the exact probability density function of both approximations. We have used these results to obtain the mean sum-rate, outage probability, and outage rate for uncorrelated fading channels. For the second approximation, the effect of channel correlation on these metrics was also analyzed. An exhaustive series of simulations have been conducted to assess the tightness and robustness of both solutions.

Integer-forcing (IF) precoding, also known as downlink IF, is a promising new approach to communication over multiple-input multiple-output (MIMO) broadcast channels. Inspired by the integer-forcing linear receiver for multiple-access channels, it generalizes linear precoding by inducing an effective channel matrix that is approximately integer, rather than approximately identity. Combined with lattice encoding and a pre-inversion of the channel matrix at the transmitter, the scheme has the potential to outperform any linear precoding scheme, despite enjoying similar low complexity. In this paper, a specific IF precoding scheme, called diagonally scaled exact IF (DIF), is proposed and shown to achieve maximum spatial multiplexing gain. For the special case of two receivers, in the high SNR regime, an optimal choice of parameters is derived analytically, leading to an almost closed-form expression for the achievable sum rate. In particular, it is shown that the gap to the sum capacity is upper bounded by 0.27 bits for any channel realization. For general SNR, a regularized version of DIF (RDIF) is proposed. Numerical results for two receivers under Rayleigh fading show that RDIF can achieve performance superior to optimal linear precoding and very close to the sum capacity.

The channel capacity for the multiple-input multiple-output (MIMO) relay channel is still an open problem. In view of this gap, upper and lower bounds were found by Wang et al., 2005. This paper presents an extensive study of mutual information and outage probability of Rayleigh fading MIMO relay channels based on the eigenvalues distribution for the sum of complex Wishart matrices. Interestingly, for certain scenarios, upper and lower bounds are coincident providing the real channel capacity. To compute outage probability, a Gaussian approximation for mutual information has been used. Furthermore, it was proposed an equivalent distribution for the sum of Wishart matrices, which proves to be excellent in all scenarios. Closed-form expressions for probability density function and outage probability have been found for the general case of any number of antennas and any SNR values. Analytical expressions have been validated by means of Monte Carlo simulations.

This paper derives a general analytical expression for the correlation coefficient of signals received by two identical spaced antennas in a radar system used to detect meteorological phenomena such as rain and clouds. Such a correlation coefficient is found as a function of the relevant physical parameters, namely, distance between antennas (baseline distance), signal bandwidth, and antenna directivity. One of the antennas transmits the signal and receives its echoes from the scatterers, characterizing a monostatic radar, whereas the other antenna only receives these echoes, characterizing a bistatic radar. Our approach can be easily extended to nonidentical antennas.

The purpose of this paper is to derive a general analytical expression for the correlation coefficient of signals received by two different antennas as a function of the distance between them (baseline distance), the signal bandwidth, and the antenna beamwidth. The two antennas are supposed to be part of a radar system for detecting meteorological phenomena such as rain and clouds. One of the antennas transmits the radar signal and receives the echoes; the other antenna only receives the echoes. The good functioning of such a radar system depends on the correlation between the two antenna signals. The exact analytical framework derived here has been recently used in practice to assist in the design of a meteorological radar system for Orbisat Indústria e Aerolevantamento S.A. (a branch of Embraer Defense and Security).

In this work we compare full-duplex (FD) and half-duplex (HD) relaying in terms of outage probability and throughput. We consider a practical FD relay model where the loop interference between transmitted and received signals is taken into account. We analyze two modes for FD transmission, block Markov encoding and multi-hop transmission without interference cancellation, and two different modes for HD transmission, which are based on selective and incremental decode-and-forward protocols. Results show that there is a tradeoff between SNR and information rate in which each scheme becomes more suitable.

In this paper, exact expressions for the level crossing rate (LCR) and average fade duration (AFD) for two-branch selection, equal-gain and maximal-ratio combining systems in a Hoyt fading environment are presented. The expressions apply to unbalanced, non-identical, correlated diversity channels and have been validated by specializing the general results to some particular cases whose solutions are known. In passing, the joint bidimensional envelope-phase Hoyt distribution with arbitrary fading parameters is obtained.

This paper presents the multiple-input multiple-output (MIMO) channel capacity over the Nakagami-m fading channel. The joint eigenvalue density function of W = HH' where H is the channel matrix, is derived in closed form for H (2 times 2) and any integer values of m, as well as for H (2 times 3) with to = 2 and to = 3. The marginal eigenvalue distribution of W is also derived in a closed-form expression. All the results are validated by numerical Monte Carlo simulations and are in excellent agreement.

In this work, a number of new closed-form expressions for the eta-mu fading channels involving the joint statistics of the envelope, phase, and their time derivatives are obtained. Level crossing rate (LCR), average fade duration (AFD), and phase crossing rate (PCR) are also derived. The expressions are thoroughly validated by reducing them to some particular known cases and, more generally, by means of Monte Carlo simulation. We then provide alternative (i) singlefold integral exact formulations and (ii) highly-accurate approximations to the level-crossing statistics of multibranch maximal-ratio combining (MRC) and equal-gain combining (EGC) systems, respectively, operating over independent Hoyt fading channels, for which the exact solutions appear in the literature in multifold integral forms.

This paper presents the MIMO channel capacity over the Nakagami-m fading channel. The joint eigenvalue density function of W = HHdagger, where H is the channel matrix, is derived in a closed form in the 2 times 2 case and for integer values of m, as well as for m rarr infin. The marginal eigenvalue distribution of W is also derived in closed form solution. For the more general r times t case, an asymptotic formulation is presented and is shown to be close to simulations, even for a small number of antennas. All the results are validated by numerical Monte Carlo simulations and are in excellent agreement.

This paper derives exact expressions for the level crossing rate and average fade duration of multibranch pure-selection, equal-gain, and maximal-ratio combiners operating over independent non-identical α-μ (also called generalized Γ or Stacy) fading channels. The derived expressions are in closed form for pure-selection combining and in integral form for equal-gain and maximal-ratio combining. For the two latter schemes, accurate closed-form approximations are then provided. The analytical results are validated by reducing the general expressions to known particular cases and, more generally, by means of simulation. Numerical examples are also given to illustrate the high accuracy of the proposed closed-form approximations.

General exact expressions for the level crossing rate and average fade duration of dual-branch selection, equal-gain, and maximal-ratio combiners operating over non-identical correlated Ricean channels are derived. Sample numerical results are discussed by specializing the general expressions to a space-diversity system with horizontally spaced omnidirectional antennas at the mobile station. When the antennas are perpendicular to the direction of the vehicle motion, the average fade duration is loosely dependent on the antenna spacing and on the Ricean factor, being almost identical to that of the independent fading condition. When the antennas are parallel to the direction of the vehicle motion, the level crossing rate can be reduced below the value obtainable for independent fading signals. In this case, if a line-of-sight component exists, a further improvement in the average fade duration over the independent condition may be also achieved.

This paper specializes and parameterizes the general result presented elsewhere in the literature in order to propose, fully characterize, and investigate the symmetrical n-k distribution. It yields estimators for the involved parameters and uses field measurements to validate the distribution. The symmetrical n-k distribution includes, as special cases, important distributions such as Rayleigh, Rice, Hoyt, Nakagami-q, and one-sided Gaussian. The fact that the symmetrical n-k distribution has one more parameter than the well-known distributions renders it more flexible. Of course, in situations in which those distributions included in it give good results a better fitting is given by the symmetrical n-k distribution. In addition, in many other situations in which these distributions give poor results a good fitting may be found through the symmetrical n-k distribution. More specifically, its non-monomodal feature finds applications in several circumstances, examples of which are given in this paper.