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

Performance Analysis of Multiple Input Multiple Output Free Space Optical Communication Systems

The Free Space Optical (FSO) communication i.e. optical communication without fibers is slowly becoming quite popular as fiber and its installation cost as well as difficulties involved becomes zero. The FSO communication is already making its impact in deep space communication and is expected to replace the existing optical fiber communication systems in the near future. In order to further speed up the optical communication, the Multiple Input/Multiple Output (MIMO) technology from microwave MIMO systems is being investigated. The characteristics of the Multiple Input/Multiple Output Free Space Optical communication systems using APD receivers have been discussed. The APD-based receivers for MIMO FSO systems under normal working conditions are designed and the characteristics of the components, such as InGaAs APDs, GaAs MESFET transimpedance amplifiers, a matched filter and an equalizer, etc., are considered. The probabilistic analysis of a FSO channel, APDs and noise in the FSO systems has been carried out. The main contributions in this dissertation are: obtaining the detailed closed-form expressions for the upper bounds of the error probabilities, analyzing the impacts of different parameters in MIMO FSO systems, and thorough analysis of a more complex model of the MIMO FSO system involving Webb distribution for APD-based optical receiver, the probabilistic analysis of the detection for pulse position modulation signaling and the transmitted symbol matrix for MIMO FSO equal gain combining systems. Using this detailed analysis the average symbol error probability, average bit error probability and average pairwise probability are also obtained. The equations have been derived by using the Fourier series analysis method. The modified Gauss-Chebyshev method for error probability calculation is also proposed. Results for average SEP and average BEP under different parameters are obtained and the impact of these parameters on MIMO FSO systems is also discussed