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Although the widely linear least mean square error (WLMMSE) receiver has been an appealing option for multiple-input-multiple-output (MIMO) wireless systems, a statistical understanding on its pose-detection signal-to-interference-plus-noise ratio (SINR) in detail is still missing. To this end, we consider a WLMMSE MIMO transmission system with rectilinear or quasi-rectilinear (QR) signals over the uncorrelated Rayleigh fading channel and investigate the statistical properties of its SINR for an arbitrary antenna configuration with $N_t$ transmit antennas and $N_r$ receive ones. We first derive an analytic probability density function (PDF) of the SINR in terms of the confluent hypergeometric function of the second kind, for WLMMSE MIMO systems with an arbitrary $N_r$ and $N_t=2, 3$. For a more general case in practice, i.e., $N_t>3$ , we resort to the moment generating function to obtain an approximate but closed form PDF under some mild conditions, which, as expected, is more Gaussian-like as $2N_r-N_t$ increases. The so-derived PDFs are able to provide key insights into the WLMMSE MIMO receiver in terms of the outage probability, the symbol error rate, and the diversity gain, all presented in closed form. In particular, its diversity gain and the gain improvement over the conventional LMMSE one are explicitly quantified as $N_r-(N_t-1)/2$ and $(N_t-1)/2$ , respectively. Finally, Monte Carlo simulations support the analysis. [ABSTRACT FROM AUTHOR]

Optical wireless networks, particularly free-space optical (FSO) in outdoor environments and visible light communication (VLC) in indoor environments, suffer from severe deterioration in signal quality due to various factors such as the availability of line-of-sight link, the turbulence of the atmosphere, or pointing errors. To enable high-quality service point-to-point transmission through optical wireless communication, an efficient and reliable backhaul link is essential. Towards this objective, this paper proposes a novel optical backhauled non-orthogonal multiple access (NOMA) in VLC systems. Unlike earlier works, our model considers the effects of various transmission parameters in a mixed cooperative FSO/radio over a fiber backhaul link with NOMA-VLC to serve two users. The closed-form expressions of outage probability, sum throughput, ergodic sum capacity, and average bit error rate are delivered for a variety of channel conditions using Meijer's G and Gaussian hypergeometric functions. More specifically, both the theoretical and simulation results demonstrate that the performance gain of the proposed optical-based NOMA systems can improve the performance of the users in comparison with the conventional OMA systems at medium to high SNR ranges. Furthermore, a deep learning-based framework is proposed to accurately estimate the ergodic capacity of the proposed system and significantly reduce the complexity cost of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article will present exact analytical expressions for the components of the magnetic field from an ideal and conically shaped permanent magnet that may be employed for parametric studies, optimization studies, as well as for design purposes. These types of magnets find applications in areas where the magnetic flux needs to be concentrated in a smaller region of space. If conically shaped permanent magnets are manufactured from the Neodymium material, for example, then strong magnetic fields are possible. This becomes relevant in applications such as nuclear magnetic resonance (NMR), sensor technology, and magnetometers. [ABSTRACT FROM AUTHOR]

Approximate outage probability and rate expressions are derived for systems employing maximum ratio combining, when both the desired signal and the interfering signals are subjected to $\eta -\mu$ fading, with the interferers having unequal power. The approximations are in terms of the Gauss hypergeometric function. A close match is observed between the results obtained through the derived analytical expression and the one obtained through Monte-Carlo simulations. Also, the utility of the applications is established in a vehicular application. [ABSTRACT FROM AUTHOR]

A number of new results aiming at facilitating the use of the $\alpha $ - $\eta $ - $\kappa $ - $\mu $ fading model are presented. These results include: 1) fast convergent, with no recursions, series representations for the envelope probability density function (PDF) and cumulative distribution function (CDF); 2) higher order moments of the envelope; 3) moment generating function (MGF) of the envelope; 4) asymptotic behavior of the envelope PDF and also of the envelope CDF; 5) a procedure for parameter estimation; 6) new closed-form expressions for particular cases of the envelope distribution; 7) new mathematical identity for the generalized Laguerre polynomial and the generalized hypergeometric function; and 8) approximate, but tight, series representation for the phase PDF. As application examples, the following are given: 1) outage probability; 2) outage capacity; 3) amount of fading; and 4) bit error rate, for which the asymptotic behavior is also presented. [ABSTRACT FROM AUTHOR]

While the performance analysis of linear zero-forcing (ZF) and minimum mean-square error (MMSE) receivers has received much attention, there has been no exact closed-form distribution of signal-to-interference-plus-noise ratio (SINR) for MMSE multiple-input multiple-output (MIMO) systems in the arbitrary fading environments for over the past 20 years. In this paper, an exact and general distribution of SINR for MMSE MIMO systems is presented under uncorrelated Rayleigh fading environments. We start our analysis by finding regular patterns from the probability density function (PDF) of SINR for small dimensions, and using the regular patterns, we extend the PDF to arbitrary dimensions. From the exact and general PDF of SINR for MMSE MIMO systems, the cumulative distribution function and the moment-generating function are derived in terms of the incomplete gamma function and the confluent hypergeometric function of the second kind, respectively. As applications, the error probability, outage probability, and achievable sum rate are investigated by using the distribution of SINR for MMSE MIMO systems. Most notably, the achievable sum rates for ZF and MMSE MIMO systems are defined by using the Meijer $G$ -function, which are the first closed-form expressions in the literature. [ABSTRACT FROM AUTHOR]

Approximate symbol error rate (SER), outage probability, and rate expressions are derived for receive diversity system employing optimum combining when both the desired and the interfering signals are subjected to Rician fading, for the cases of equal power uncorrelated interferers, unequal power interferers, and interferer correlation. The derived expressions are applicable for an arbitrary number of receive antennas and interferers and for any quadrature amplitude modulation constellation. Furthermore, we derive a simple closed-form expression for SER in the interference-limited regime, for the special case of Rayleigh faded interferers. A close match is observed between the SER, outage probability, and rate results obtained through the derived analytical expressions and the ones obtained from Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

We provide new analytical results for the two-wave with diffuse power (TWDP) fading model. Specifically, we derive a closed-form expression for its generalized moment generating function in terms of a finite number of standard hypergeometric functions. This result is used to compute the moments of the TWDP distribution, as well as to analyze the performance of wireless communication systems operating under TWDP fading channels in the context of energy detection, error and outage performances, and physical layer security. [ABSTRACT FROM AUTHOR]

The inductance integrals of air-core circular coils with rectangular cross section and parallel axes are difficult to tackle with analytical method due to the inclusion of Struve functions. Using the inverse Mellin transform, these Bessel–Struve integrals will be continued analytically to the complex plane, and then by virtue of contour deformation and residue theorem, they can be expanded to the series containing the generalized hypergeometric functions which are easy to execute in common mathematical software packages. The series solutions are preferable in case the difficulties arise in the evaluations of Bessel–Struve integrals, though they do not cover the whole region of coil geometric parameters. In addition, the obtained series were compared numerically with the corresponding integrals, complete consistency was shown clearly. By means of the proposed method, the computation efficiency can be improved by several orders of magnitude compared to that of the corresponding integral methods. [ABSTRACT FROM AUTHOR]

In this paper, novel closed-form expressions for the level crossing rate and average fade duration of $\kappa-\mu$ shadowed fading channels are derived. The new equations provide the capability of modeling the correlation between the time derivative of the shadowed dominant and multipath components of the $\kappa-\mu$ shadowed fading envelope. Verification of the new equations is performed by reduction to a number of known special cases. It is shown that as the shadowing of the resultant dominant component decreases, the signal crosses lower threshold levels at a reduced rate. Furthermore, the impact of increasing correlation between the slope of the shadowed dominant and multipath components similarly acts to reduce crossings at lower signal levels. The new expressions for the second-order statistics are also compared with field measurements obtained for cellular device-to-device and body-centric communication channels, which are known to be susceptible to shadowed fading. [ABSTRACT FROM PUBLISHER]

In this paper, the performance of a dual-hop multiuser underlay cognitive network is thoroughly investigated by using a decode-and-forward (DF) protocol at the relay node and employing opportunistic scheduling at the destination users. A practical scenario where cochannel interference signals are present in the system is considered for the investigation. Considering that transmissions are performed over nonidentical Rayleigh fading channels, first, the exact signal-to-interference-plus-noise ratio (SINR) of the network is formulated. Then, the exact equivalent cumulative distribution function (cdf) and the outage probability of the system SINR are derived. An efficient tight approximation is proposed for the per-hop cdfs, and based on this, the closed-form expressions for the error probability and the ergodic capacity are derived. Furthermore, an asymptotic expression for the cdf of the instantaneous SINR is derived, and a simple and general asymptotic expression for the error probability is presented and discussed. Moreover, adaptive power allocation under the total-transmit-power constraint is studied to minimize the asymptotic average error probability. As expected, the results show that optimum power allocation improves the system performance compared with uniform power allocation. Finally, the theoretical analysis is validated by presenting various numerical results and Monte Carlo simulations. [ABSTRACT FROM PUBLISHER]

In this correspondence, fractional negative-order moments are used to estimate the K-clutter plus noise parameters. Combining the fractional positive and negative moments, we aim to improve the accuracy of the estimation outcomes. This is achieved through the reduction of the effect of the two first intensity moments involved in the equation of the unknown parameters. For instance, the proposed fractional positive- and negative-order moments? estimator, given in terms of two confluent hypergeometric functions, is solved numerically to yield the shape parameter. Using single pulse and multiple pulses in various clutter plus noise scenarios, we show, via both simulated and IPIX real data, a comparison of the new estimator with the estimators based on the higher-order moments, the fractional positive-order moments, the [zlog(z)], and the constrained maximum likelihood. [ABSTRACT FROM PUBLISHER]

We examine the adaptive detection problem in the presence of colored noise with an unknown covariance matrix, by exploiting a persymmetric structure in the received signal. The persymmetric adaptive matched filter (PS-AMF) is used to address this problem, which can significantly alleviate the requirement of secondary data. In G. Pailloux et al. “Persymmetric adaptive radar detectors,” (2011) the probability of false alarm of the PS-AMF has been obtained in terms of the Gaussian hypergeometric function. In this paper, finite-sum expressions for the probability of false alarm of the PS-AMF are derived, which are more convenient to use in calculating the detection threshold. Moreover, the detection probabilities of the PS-AMF for both nonfluctuating and fluctuating target models are derived. In the fluctuating model, the amplitude of the target echoes is described by a generalized Chi distribution that involves the Rayleigh distribution as a special case. These theoretical results are all confirmed using Monte Carlo (MC) simulations. [ABSTRACT FROM PUBLISHER]

The estimation of the K-distributed radar clutter plus thermal noise parameters can be improved by employing fractional moments instead of the existing higher order moments. In order to achieve this, we provide first an asymptotic expression of the moments in terms of the confluent and Gauss hypergeometric functions. For fractional orders of the latter, the new estimation method is derived so that the estimates of the shape parameter are achieved via numerical computations of nonlinear equations. For lower fractional orders of moments and different values of the parameters, the numerical simulations demonstrate the effectiveness of the proposed estimation procedure when compared with the standard higher order moments method. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel [z log(z)]-based approach to the evaluation of estimators of the K-distributed clutter plus thermal noise parameters. In doing this, we start by deriving expressions of log-based moments of the received data, i.e., means of [log(z)] and [z log(z)], which are related to the parameters of the K plus noise distribution, the digamma, and the hypergeometric functions. Then, by accommodating a single pulse and noncoherent integration of N pulses, respectively, we first determine the new estimators in terms of log-based moments and first- and second-order moments. As the computation of these nonlinear estimates requires the use of numerical routines, we resort to the inverse of the harmonic mean of the received data to get equivalent but more interesting estimates in which expressions are independent of the confluent hypergeometric functions. Monte Carlo simulations show that the proposed estimators are more efficient than existing methods for various clutter plus noise situations. [ABSTRACT FROM AUTHOR]

This paper presents a new connection between the generalized Marcum-Q function and the confluent hypergeometric function of two variables, \Phi3. This result is then applied to the closed-form characterization of the bivariate Nakagami-m distribution and of the distribution of the minimum eigenvalue of correlated noncentral Wishart matrices, both important in communication theory. New expressions for the corresponding cumulative distributions are obtained and a number of communication-theoretic problems involving them are pointed out. [ABSTRACT FROM AUTHOR]

In this paper, we derive exact closed-form expressions for the bivariate Nakagami-m cumulative distribution function (CDF) with positive integer fading severity index m in terms of a class of hypergeometric functions. Particularly, we show that the bivariate Nakagami-m CDF can be expressed as a finite sum of elementary functions and bivariate confluent hypergeometric Φ_3 functions. Direct applications which arise from the proposed closed-form expression are the outage probability (OP) analysis of a dual-branch selection combiner in correlated Nakagami-m fading, or the calculation of the level crossing rate (LCR) and average fade duration (AFD) of a sampled Nakagami-m fading envelope. [ABSTRACT FROM AUTHOR]

In this paper, an improvement for calculating the self-inductance of circular coils of rectangular cross section is presented. An integral of elementary functions is applied to replace the Bessel and Struve functions in the integrand of the inductance expression, and the term of improper integral without the exponential factor is solved to a closed form which consists of the complete elliptic integrals of the first and second kind and generalized hypergeometric functions. Due to this method, the main difficulties of the numerical evaluations of the inductance expression are overcome. Excellent agreement with published method is confirmed by the numerical comparisons and the calculations can be accelerated to several tens to hundreds of times depending on the shape factors of the coils. Similar expressions of the special cases (thin-wall solenoids and disk coils) are also given and compared with previous methods. Furthermore, the asymptotic behaviors of the special coils which tend to be a circular ring are obtained and numerically validated. [ABSTRACT FROM AUTHOR]

A closed form expression for the Cramer Rao lower bound (CRB) for parameter estimation in the presence of a two component Gaussian mixture noise model is derived. It is further shown that this closed form expression can be lower bounded by a simple two term expression. Closed form expressions are also derived for the variance of the maximum likelihood estimator (MLE) when the parameters of the Gaussian mixture model are misspecified. It is then shown that the MLE can handle a significant amount of misspecification of the parameters of the Gaussian mixture model and yet maintain a variance close to the CRB. [ABSTRACT FROM AUTHOR]

One of the oldest problems in the theory of quantum stabilizer codes is solved by proving the nonexistence of quantum [[13,5,4]]-codes. [ABSTRACT FROM AUTHOR]

The closed-form expressions for the exact average symbol error probability (SEP) and bit error probability (BEP) of arbitrary M-ary cross quadrature amplitude modulation (XQAM) signaling with maximal-ratio combining (MRC) diversity reception over independent but not necessarily identical \eta-\mu fading channels are derived. The results are presented in terms of a finite (in proportion to \sqrtM) sum of Lauricella hypergeometric functions FD^{(n)}, which can be numerically evaluated using its integral or converging series representation. For some special fading scenarios of interest, the formulas are expressed by some simpler functions, such as Gauss's single hypergeometric function 2F1 and Apell's double hypergeometric function F1, both of which are available functions in standard numerical software. For Rayleigh channels and some special cases of Nakagami-m channels, the results are presented in the form of a finite sum of trigonometric functions. The analytical expressions show excellent agreement with the simulation results. Numerical evaluation with the proposed expressions reveals that cross-QAM can obtain at least 1.1-dB gain, compared with rectangular QAM when SEP < 0.3. [ABSTRACT FROM PUBLISHER]

In the context of η-μ generalized fading scenarios, this paper provides a general closed-form expression for the average symbol error probability (SEP) of arbitrary M-ary quadrature amplitude modulation (QAM) constellations in maximal-ratio combining (MRC) schemes over non-identical correlated channels. For such a scenario, the moment-generating function (MGF) of the signal-to-noise ratio (SNR) at the combiner output is obtained by rearranging the Gaussian components used to model the correlation between the diversity branches. The average SEP is then derived in terms of Lauricella multivariate hypergeometric functions, which can be implemented in most popular numerical softwares, such as Mathematica. The proposed analytical expressions are validated through Monte Carlo simulations, and insightful discussions are provided from the numerical results. [ABSTRACT FROM AUTHOR]

Pulsed circular arrays are collecting growing interest in radar applications such as automotives and indoor navigations. This contribution presents the analytic derivation of the spacetime and energy patterns of pulsed circular arrays in terms of geometrical and electrical parameters as well as of the signal distortion produced by the antennas' response. It is shown that the field emitted by circular arrays with many elements can be represented as a summation of a practically finite set of high-order Hermite-Rodriguez waveforms, while the energy pattern is a generalized Hypergeometric Function. The angular and temporal resolutions are finally related, through handy formulas, to the array size, the input signals and to the antenna types. [ABSTRACT FROM AUTHOR]

This letter addresses the problem of finding a tractable expression for the symbol error outage (SEO) in flat Nakagami-m fading and shadowing channels. We deal with M-ary phase shift keying (M-PSK) and quadrature amplitude modulation (M-QAM) which extends our previous results on BPSK signaling. We propose a new tight approximation of the symbol error probability (SEP) holding for M-PSK and M-QAM signals which is accurate over all signal to noise ratios (SNRs) of interest. We derive a new generic expression for the inverse SEP which facilitates the derivation of a tight approximation of the SEO in a lognormal shadowing environment. [ABSTRACT FROM AUTHOR]

In this contribution, we derive exact closed-form expressions for the average symbol error probability (SEP) of arbitrary rectangular quadrature amplitude modulation (QAM) for single- and multichannel diversity reception over independent but not-necessarily identically distributed Nakagami-m fading channels. The diversity branches may hence exhibit identical or distinctive power levels and their associated Nakagami indexes need not be the same. Our work extends previous results pertaining to nondiversity reception of M-ary rectangular QAM over Rayleigh fading channels and multichannel reception of M-ary square QAM over Nakagami-m fading channels. For a given number L of diversity branches and a corresponding set of arbitrary real-valued Nakagami indexes not less than 1/2, our SEP results are expressed in terms of Gauss's hypergeometric function 2F1 and Lauricella's multivariate hypergeometric function FD(L) of L variables, both of which can be efficiently evaluated using standard numerical softwares. [ABSTRACT FROM AUTHOR]

The memoryless noncoherent single-input-single-output (SISO) Rayleigh-fading channel is considered. Closed-form expressions are derived for the mutual information between the output and the input of this channel when the input magnitude distribution is discrete and is restricted to having two mass points. It is subsequently shown how these expressions can be used to obtain closed-form expressions for the capacity of this channel for signal to noise ratio (SNR) values of up to approximately 0 dB, and a tight capacity lower bound for SNR values between 0 dB and 10 dB. The expressions for the channel capacity and its tower bound are given as functions of a parameter which can be obtained via numerical root-finding algorithms. [ABSTRACT FROM AUTHOR]

The performances of cyclic delay diversity and space-time block-coded multicarrier code-division multiple-access (MC-CDMA) systems operating in a Nakagami-m fading channel with correlated subcarriers are investigated. By using the moment-generating function of the correlated Nakagami-m random variable, explicit closed-form formulas for the exact average symbol error rate (SER) of M-ary signals for an MC-CDMA system employing the aforementioned diversity techniques are derived with a maximum ratio combining detection technique. The average SERs are expressed in terms of higher transcendental functions, such as the Gauss and Appell hypergeometric functions. Both numerical and simulation results are presented, showing excellent agreement. [ABSTRACT FROM AUTHOR]

This paper is aimed at exposing the reader to certain aspects in the design of the best approximants with Gaussian radial basis functions (RBFs). The class of functions to which this approach applies consists of those compactly supported in frequency. The approximative properties of uniqueness and existence are restricted to this class. Functions which are smooth enough can be expanded in Gaussian series converging uniformly to the objective function. The uniqueness of these series is demonstrated by the context of the orthonormal basis in a Hilbert space. Furthermore, the best approximation to a given band-limited function from a truncated Gaussian series is analyzed by an energy-based argument. This analysis not only gives a theoretical proof concerned with the existence of best approximations but addresses the problems of architectural selection. Specifically, guidance for selecting the variance and the oversampling parameters is provided for practitioners. [ABSTRACT FROM AUTHOR]

Optimum combining (OC) is a powerful means for combatting co-channel interference. Its performance, however, is difficult to analyze. The prevailing methodology in current use is to neglect the influence of additive white Gaussian noise (AWGN). Inclusion of AWGN into the analysis usually leads to mathematical intractability, except for some extreme cases. In this letter, we formulate the problem in the framework of hypergeometric functions, so that their good properties can be exploited to enable the analysis to account for the influence of AWGN and co-channel interference simultaneously. We obtain closed-form solutions to the characteristic function (CHF) of the signal-to-interference-plus-noise ratio at the OC output for three important operational scenarios in Rayleigh fading, although the general solution still needs further effort to simplify. The assumptions made here are that both signal and interferers suffer from Rayleigh fading, and the number of interferers is not less than the number of antennas. The use of resulting CHF formulas is illustrated through their application to the bit-error and outage performance evaluation of OC. [ABSTRACT FROM AUTHOR]

This is a tutorial presentation of the Mellin-transform (MT) method for the exact calculation of one-dimensional definite integrals, and an illustration of the application of this method to antenna/electromagnetics problems. Once the basics have been mastered, one quickly realizes that the MT-method is extremely powerful, often yielding closed-form expressions very difficult to come up with other methods or to deduce from the usual tables of integrals. Yet, as opposed to other methods, the MT-method is very straightforward to apply; it usually requires laborious calculations, but little ingenuity. In fact, the MT-method is used by Mathematica to symbolically calculate definite integrals. The first part of this paper is a step-by-step tutorial, proceeding from first principles. It includes basic information on Mellin-Barnes integrals and generalized hypergeometric functions, and summarizes the key ideas of the MT-method. In the remaining parts, the MT-method is applied to three examples from the antenna area. The results here are believed to be new, at least in the antenna/electromagnetics literature. In our first example, we obtain a closed-form expression, as a generalized hypergeometric function, for the power radiated by a constant-current circular-loop antenna; this quantity has been extensively discussed recently. Our second example concerns the admittance of a 2-D slot antenna. In both these examples, the exact closed-form expressions are applied to improve upon existing formulas in standard antenna textbooks. In our third example, finally, we obtain a very simple expression for an integral arising in recent, unpublished studies of unbounded, biaxially anisotropic media. [ABSTRACT FROM AUTHOR]

In this letter, we take a close look at the performance of maximal ratio combining (MRC) schemes operating in a flat-Nakagami-m fading environment with arbitrary fading parameters. We derive an expression for the probability density function (pdf) of the output signal-to-noise ratio (SNR) by expressing the moment generating function of the output SNR in the form of multiple Barnes-type contour integrals. By evaluating the inverse transform and converting the multiple contour integrals into infinite series, we are able to derive an expression for the pdf of the output SNR when the Nakagami fading parameters along the diversity branches take on real and arbitrary values. Consequently, the average bit-error rate can now be expressed in terms of Lauri-cella's multivariate hypergeometric function, which can be easily evaluated numerically. Special cases of the main results reduce to known results in the literature. The results, which apply to independent as well as correlated diversity branches, will be useful for predicting the system performances when the Nakagami fading parameters are real and arbitrary. [ABSTRACT FROM AUTHOR]

Moments of the multibranch equal gain combiner (EGC) output signal-to-noise ratio (SNR) are only known for independent fading channels or exponentially correlated Nakagami-m fading channels. In this paper, we derive the moments of the EGC output SNR in equally correlated Rayleigh, Rician, and Nakagami-m fading channels. Our moment expressions can be used to evaluate the outage and the average error rate as well as purely moments-based measures such as the average output SNR and the amount of fading as functions of the fading correlation. Numerical results that illustrate the effect of fading correlation on the distribution of the EGC output SNR are also provided. [ABSTRACT FROM AUTHOR]

In this letter, we present new closed-form formulas for the exact average symbol-error rate (SER) of binary and M-ary signals over Nakagami-m fading channels with arbitrary fading index in. Using the well-known moment generating function-based analysis approach, we express the average SER in terms of the higher transcendental functions such as the Gauss hypergeometric function, Appell hypergeometric function, or Lauricella function. The results are generally applicable to arbitrary real-valued in. Furthermore, with the aid of reduction formulas of hypergeometric functions, we show previously published results for Rayleigh fading (m = 1) as special cases of our expressions. [ABSTRACT FROM AUTHOR]

Presents a study which focused on the towers of function fields meeting with Drinfeld-Vladut bound with equality. Information on the hypergeometric analogs of the Arithmetic-Geometric Mean; Interpretation of the algorithms used.

It is shown that the Binomial(n,p) distribution maximizes the entropy in the class of ultra-tog-concave distributions of order n with fixed mean np. This result, which extends a theorem of Shepp and Olkin (1981), is analogous to that of Johnson (2007), who considers the Poisson case. The proof constructs a Markov chain whose limiting distribution is Binomial (n, p) and shows that the entropy never decreases along the iterations of this Markov chain. [ABSTRACT FROM AUTHOR]

The recent paper by Shnidman [1] introduced two new models for radar target fluctuation. One of them is the noncentral gamma-gamma (NCGG) distribution, specified by a density function expressed as an infinite sum. It is shown here that one can actually derive an expression for the density in terms of the confluent hypergeometric function. A general elementary expression is provided for the associated moments. [ABSTRACT FROM AUTHOR]

Various explicit and closed-form expressions are derived for the moments of the Rician process considered by Kim et at. [ABSTRACT FROM AUTHOR]

A theoretical analysis is performed on thicknessshear vibrations of a contoured AT-cut quartz resonator with a hyperbolic thickness variation using the Legendre equation and hypergeometric function. Based on the solution, resonant frequencies and modes are calculated. Strong energy trapping of the modes is observed. The effects of the parameters of the hyperbolic contour on resonant frequencies and modes are examined. A comparison with the conventional contoured resonator in the literature with a quadratic thickness variation is made. The behaviors of the two types of resonators are qualitatively similar, with small but significant quantitative differences. [ABSTRACT FROM PUBLISHER]

In this paper, infinite integrals involving the product of Bessel functions of different arguments are solved in closed-form. The obtained solutions form a framework for the error probability analysis of wireless amplify and forward (AF) systems with an arbitrary number of variable-gain relays operating over independent but not necessarily identical Nakagami-m fading channels. Here we show that the error probability can be described by generalized hypergeometric functions, namely, Gauss's and Lauricella's multivariate hypergeometric functions. This work represents a significant improvement over previous contributions and extends previous formulas pertaining to dual-hop transmissions over identical Nakagami-m fading channels. Numerical examples show an excellent match between simulation and theoretical results. [ABSTRACT FROM PUBLISHER]

In this comment, it is shown that the semi-numerical algorithm for computation of the ergodic channel capacity, which has been suggested in the paper cited by the headline above, can be replaced by a closed-form solution — either based on generalized hypergeometric functions or, in a more concise and elegant approach, on Meijer's G-function. [ABSTRACT FROM AUTHOR]

An explicit expression is derived for the probability density function (pdf) of the square magnitude of the normalized cross wavelet spectrum for the self-normalized Morlet cross wavelet spectrum (NCM) detector considered for Plett. The expression involves the well-known Gauss hypergeometric function. [ABSTRACT FROM AUTHOR]