Probabilistic Analysis of Received Composite Wireless Signals for Random Number of Multipaths

Abstract

ABSTRACT In wireless communication, the received random signal is composed of the sum of several random sinusoidal signals e.g., multipath fading or interference in communication channels, clutter and target cross section in radars, wave propagation in random media/channels and light scattering. According to the correspondence between a random wireless signal and a random vector, the sum of random vectors can be considered as an abstract mathematical model. It is desired to obtain the probability density function (pdf) of the length of the resulting vector. This report presents a technique to obtain pdf for the most general cases in which the lengths of vectors are arbitrary dependent random variables. The obtained pdf is in the form of definite integral, which may be inappropriate for analytic manipulations and numerical computations. Therefore, an appropriate infinite integral form called laguerre expansion is derived. The obtained results are applied in computing the scattering cross-section of random scatterers resulting from a small number of constant amplitude scatterers each having a random phase, and also achieve expressions for pdf of scattered signal intensity. The methods for computing the coefficients of aforementioned infinite series are also discussed. An arbitrary random nonzero real number is incorporated; whose appropriate value can reduce truncation error. This report is mainly focused on the computation of probability density function of the received composite wireless signals for random number of multipaths in a single antenna element of multi-input-multi-output wireless systems, and also selecting an optimum value of to minimize the truncation error.