Weighted sums of Rayleigh random variables occur in diverse problems in wireless, and particularly in interference systems. Previous work has reported upper bounds on the cumulative distribution function of weighted Rayleigh sums. New lower bounds to the cumulative distribution function of weighted Rayleigh sums are derived. The new lower bounds to the cumulative distribution function are used as an intermediate result in deriving a new upper bound on the ratio of a Rayleigh random variable to a weighted sum of Rayleigh random variables shifted by a nonnegative constant. Special cases of this ratio occur in the context of cognitive radio systems and synchronization components. Novel approximations, that are tighter than any known bounds, to the cumulative distribution function of weighted Rayleigh sums are also presented.

The multiple-user interference (MUI) in time-hopped impulse-radio ultrawide bandwidth (UWB) systems is impulse-like and poorly approximated by a Gaussian distribution. Therefore, conventional matched filter receiver designs, which are optimal for Gaussian noise, are not fully efficient for UWB applications. Several alternative distributions for approximating the MUI process and the MUI-plus-noise process in UWB systems are motivated and compared. These distributions have in common that they are more impulsive than the Gaussian approximation, with a greater area in the tails of the probability density function (pdf) compared to a Gaussian pdf. The improved MUI and MUI-plus-noise models are utilized to derive new receiver designs for UWB applications, which are shown to be superior to the conventional matched filter receiver. Multipath propagation is abundant in UWB channels and is exploited by a Rake receiver. A Rake receiver uses multiple fingers to comb the multipath rays with a conventional matched filter implemented in each finger. Rake structures utilizing the new receiver designs that are suitable for reception of UWB signals in multipath fading channels are provided. An optimal performance benchmark, based on an accurate theoretical model for the interference that fully explains the features of the MUI pdf, is also presented. Analysis and simulation results are shown for the novel receivers, which demonstrate that the new designs have superior performance compared to the conventional linear receiver when MUI is significant. Several adaptive receivers are shown to always match or exceed the performance of the conventional linear receiver in all MUI-plus-noise environments. Parameter estimation for the new receivers also is discussed.

This paper provides a power-margin-based measure of the quality of computer-generated random variates having a distribution that derives from the multivariate Gaussian distribution. The measure is designed to be simple to compute, and to provide assessments which are meaningful and intuitive in communication system simulation applications. For example, the measure can be used to assess and compare the qualities of different methods of generating Rayleigh fading samples for simulation.

The lack of a well-defined and meaningful measure of the quality of computer-generated correlated random variates complicates the design and comparison of generation algorithms for communications system simulation applications. This paper presents quantitative quality measures for computer-generated random variates having a multivariate Gaussian distribution or having a distribution that derives from the multivariate Gaussian distribution. These measures are, in particular, useful for digital communication system simulation applications. A theoretical basis for the definition of the measures is given and it is shown that the measures also possess useful intuitive interpretations. Examples of the use of these quality measures are provided.

A number of different algorithms are used for the generation of correlated Rayleigh random variates. This paper presents an analysis of the statistical properties of methods based on the inverse discrete Fourier transform (IDFT). A modification of the algorithm of Smith (1975) is presented, the new method requiring exactly one-half the number of IDPT operations and roughly two-thirds the computer memory of the original method. Evaluations of and comparisons between various variate generation methods using meaningful quantitative measures are believed to be lacking. New quantitative quality measures for random variate generation have been proposed that are, in particular, meaningful and useful for digital communication system simulation. This paper presents the application of these measures to the IDFT method and three other methods of correlated variate generation, comparing the algorithms in terms of the quality of the generated samples and the required computational effort.

The lack of a well-defined and meaningful measure of the quality of computer generated correlated random variates complicates the design and comparison of generation algorithms for communications system simulation applications. This paper presents quantitative quality measures for computer-generated random variates having a multivariate Gaussian distribution or having a distribution that derives from the multivariate Gaussian distribution. These measures are, in particular, useful for digital communication system simulation applications. A theoretical basis for the definition of the measures is given and it is shown that the measures also possess useful intuitive interpretations. Examples of the use of these quality measures are provided.