Asymptotically Exact Approximations for the Symmetric Difference of Generalized Marcum-Q Functions

(c) 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works. DOI: 10.1109/TVT.2014.2337263In this paper, we derive two simple and asymptotically exact approximations for the function defined as ΔQm(a, b) =Δ Qm(a, b) - Qm(b, a). The generalized Marcum Q-function Qm(a, b) appears in many scenarios in communications in this particular form and is referred to as the symmetric difference of generalized Marcum Q-functions or the difference of generalized Marcum Q-functions with reversed arguments. We show that the symmetric difference of Marcum Q-functions can be expressed in terms of a single Gaussian Q-function for large and even moderate values of the arguments a and b. A second approximation for ΔQm(a, b) is also given in terms of the exponential function. We illustrate the applicability of these new approximations in different scenarios: 1) statistical characterization of Hoyt fading; 2) performance analysis of communication systems; 3) level crossing statistics of a sampled Rayleigh envelope; and 4) asymptotic approximation of the Rice Ie-function.Universidad de Málaga. Campus de Excelencia Internacional. Andalucía Tech

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

An Approximation of the First Order Marcum QQ-Function with Application to Network Connectivity Analysis

An exponential-type approximation of the first order Marcum $Q$-function is presented, which is robust to changes in its first argument and can easily be integrated with respect to the second argument. Such characteristics are particularly useful in network connectivity analysis. The proposed approximation is exact in the limit of small first argument of the Marcum $Q$-function, in which case the optimal parameters can be obtained analytically. For larger values of the first argument, an optimization problem is solved, and the parameters can be accurately represented using regression analysis. Numerical results indicate that the proposed methods result in approximations very close to the actual Marcum $Q$-function for small and moderate values of the first argument. We demonstrate the accuracy of the approximation by using it to analyze the connectivity properties of random ad hoc networks operating in a Rician fading environment.Comment: 6 pages, 4 figures, 1 tabl

Predictor Antenna Systems: Exploiting Channel State Information for Vehicle Communications

Vehicle communication is one of the most important use cases in the fifth generation of wireless networks (5G). The growing demand for quality of service (QoS) characterized by performance metrics, such as spectrum efficiency, peak data rate, and outage probability, is mainly limited by inaccurate prediction/estimation of channel state information (CSI) of the rapidly changing environment around moving vehicles. One way to increase the prediction horizon of CSI in order to improve the QoS is deploying predictor antennas (PAs). A PA system consists of two sets of antennas typically mounted on the roof of a vehicle, where the PAs positioned at the front of the vehicle are used to predict the CSI observed by the receive antennas (RAs) that are aligned behind the PAs. In realistic PA systems, however, the actual benefit is affected by a variety of factors, including spatial mismatch, antenna utilization, temporal correlation of scattering environment, and CSI estimation error. This thesis investigates different resource allocation schemes for the PA systems under practical constraints.Comment: Licentiate thesis, Chalmers University of Technolog

Predictor Antenna Systems: Exploiting Channel State Information for Vehicle Communications

Vehicle communication is one of the most important use cases in the fifth generation of wireless networks (5G).\ua0 The growing demand for quality of service (QoS) characterized by performance metrics, such as spectrum efficiency, peak data rate, and outage probability, is mainly limited by inaccurate prediction/estimation of channel state information (CSI) of the rapidly changing environment around moving vehicles. One way to increase the prediction horizon of CSI in order to improve the QoS is deploying predictor antennas (PAs).\ua0 A PA system consists of two sets of antennas typically mounted on the roof of a vehicle, where the PAs positioned at the front of the vehicle are used to predict the CSI observed by the receive antennas (RAs) that are aligned behind the PAs. In realistic PA systems, however, the actual benefit is affected by a variety of factors, including spatial mismatch, antenna utilization, temporal correlation of scattering environment, and CSI estimation error. This thesis investigates different resource allocation schemes for the PA systems under practical constraints, with main contributions summarized as follows.First, in Paper A, we study the PA system in the presence of the so-called spatial mismatch problem, i.e., when the channel observed by the PA is not exactly the same as the one experienced by the RA. We derive closed-form expressions for the throughput-optimized rate adaptation, and evaluate the system performance in various temporally-correlated conditions for the scattering environment. Our results indicate that PA-assisted adaptive rate adaptation leads to a considerable performance improvement, compared to the cases with no rate adaptation. Then, to simplify e.g., various integral calculations as well as different operations such as parameter optimization, in Paper B, we propose a semi-linear approximation of the Marcum Q-function, and apply the proposed approximation to the evaluation of the PA system. We also perform deep analysis of the effect of various parameters such as antenna separation as well as CSI estimation error. As we show, our proposed approximation scheme enables us to analyze PA systems with high accuracy.The second part of the thesis focuses on improving the spectral efficiency of the PA system by involving the PA into data transmission. In Paper C, we analyze the outage-limited performance of PA systems using hybrid automatic repeat request (HARQ). With our proposed approach, the PA is used not only for improving the CSI in the retransmissions to the RA, but also for data transmission in the initial round.\ua0 As we show in the analytical and the simulation results, the combination of PA and HARQ protocols makes it possible to improve the spectral efficiency and adapt transmission parameters to mitigate the effect of spatial mismatch