On the Monotonicity of the Generalized Marcum and Nuttall Q-Functions

Monotonicity criteria are established for the generalized Marcum Q-function, \emph{Q}_{M}, the standard Nuttall Q-function, \emph{Q}_{M,N}, and the normalized Nuttall Q-function, $\mathcal{Q}_{M,N}$, with respect to their real order indices M,N. Besides, closed-form expressions are derived for the computation of the standard and normalized Nuttall Q-functions for the case when M,N are odd multiples of 0.5 and $M\geq N$. By exploiting these results, novel upper and lower bounds for \emph{Q}_{M,N} and $\mathcal{Q}_{M,N}$ are proposed. Furthermore, specific tight upper and lower bounds for \emph{Q}_{M}, previously reported in the literature, are extended for real values of M. The offered theoretical results can be efficiently applied in the study of digital communications over fading channels, in the information-theoretic analysis of multiple-input multiple-output systems and in the description of stochastic processes in probability theory, among others.Comment: Published in IEEE Transactions on Information Theory, August 2009. Only slight formatting modification

Ergodic Capacity Analysis of Amplify-and-Forward MIMO Dual-Hop Systems

This paper presents an analytical characterization of the ergodic capacity of amplify-and-forward (AF) MIMO dual-hop relay channels, assuming that the channel state information is available at the destination terminal only. In contrast to prior results, our expressions apply for arbitrary numbers of antennas and arbitrary relay configurations. We derive an expression for the exact ergodic capacity, simplified closed-form expressions for the high SNR regime, and tight closed-form upper and lower bounds. These results are made possible to employing recent tools from finite-dimensional random matrix theory to derive new closed-form expressions for various statistical properties of the equivalent AF MIMO dual-hop relay channel, such as the distribution of an unordered eigenvalue and certain random determinant properties. Based on the analytical capacity expressions, we investigate the impact of the system and channel characteristics, such as the antenna configuration and the relay power gain. We also demonstrate a number of interesting relationships between the dual-hop AF MIMO relay channel and conventional point-to-point MIMO channels in various asymptotic regimes.Comment: 40 pages, 9 figures, Submitted to to IEEE Transactions on Information Theor

MIMO Networks: the Effects of Interference

Multiple-input/multiple-output (MIMO) systems promise enormous capacity increase and are being considered as one of the key technologies for future wireless networks. However, the decrease in capacity due to the presence of interferers in MIMO networks is not well understood. In this paper, we develop an analytical framework to characterize the capacity of MIMO communication systems in the presence of multiple MIMO co-channel interferers and noise. We consider the situation in which transmitters have no information about the channel and all links undergo Rayleigh fading. We first generalize the known determinant representation of hypergeometric functions with matrix arguments to the case when the argument matrices have eigenvalues of arbitrary multiplicity. This enables the derivation of the distribution of the eigenvalues of Gaussian quadratic forms and Wishart matrices with arbitrary correlation, with application to both single user and multiuser MIMO systems. In particular, we derive the ergodic mutual information for MIMO systems in the presence of multiple MIMO interferers. Our analysis is valid for any number of interferers, each with arbitrary number of antennas having possibly unequal power levels. This framework, therefore, accommodates the study of distributed MIMO systems and accounts for different positions of the MIMO interferers.Comment: Submitted to IEEE Trans. on Info. Theor

Approximation to Distribution of Product of Random Variables Using Orthogonal Polynomials for Lognormal Density

We derive a closed-form expression for the orthogonal polynomials associated with the general lognormal density. The result can be utilized to construct easily computable approximations for probability density function of a product of random variables, when the considered variates are either independent or correlated. As an example, we have calculated the approximative distribution for the product of Nakagami-m variables. Simulations indicate that accuracy of the proposed approximation is good with small cross-correlations under light fading condition.Comment: submitted to IEEE Communications Lette

Performance Analysis of Project-and-Forward Relaying in Mixed MIMO-Pinhole and Rayleigh Dual-Hop Channel

In this letter, we present an end-to-end performance analysis of dual-hop project-and-forward relaying in a realistic scenario, where the source-relay and the relay-destination links are experiencing MIMO-pinhole and Rayleigh channel conditions, respectively. We derive the probability density function of both the relay post-processing and the end-to-end signal-to-noise ratios, and the obtained expressions are used to derive the outage probability of the analyzed system as well as its end-to-end ergodic capacity in terms of generalized functions. Applying then the residue theory to Mellin-Barnes integrals, we infer the system asymptotic behavior for different channel parameters. As the bivariate Meijer-G function is involved in the analysis, we propose a new and fast MATLAB implementation enabling an automated definition of the complex integration contour. Extensive Monte-Carlo simulations are invoked to corroborate the analytical results.Comment: 4 pages, IEEE Communications Letters, 201

A novel equivalent definition of modified Bessel functions for performance analysis of multi-hop wireless communication systems

A statistical model is derived for the equivalent signal-to-noise ratio of the Source-to-Relay-to-Destination (S-R-D) link for Amplify-and-Forward (AF) relaying systems that are subject to block Rayleigh-fading. The probability density function and the cumulated density function of the S-R-D link SNR involve modified Bessel functions of the second kind. Using fractional-calculus mathematics, a novel approach is introduced to rewrite those Bessel functions (and the statistical model of the S-R-D link SNR) in series form using simple elementary functions. Moreover, a statistical characterization of the total receive-SNR at the destination, corresponding to the S-R-D and the S-D link SNR, is provided for a more general relaying scenario in which the destination receives signals from both the relay and the source and processes them using maximum ratio combining (MRC). Using the novel statistical model for the total receive SNR at the destination, accurate and simple analytical expressions for the outage probability, the bit error probability, and the ergodic capacity are obtained. The analytical results presented in this paper provide a theoretical framework to analyze the performance of the AF cooperative systems with an MRC receiver