An Analytical Framework for Performance Analysis of UWB Systems in Log-Normal Multipath Channels via Pearson Type IV Distribution

In this paper, we propose an analytical framework for the accurate analysis of Rake and transmitted reference (TR) ultra wide band (UWB) receivers in multipath channels with log-normal fading. The framework relies on approximating the logarithm of the signal-to-noise ratio (SNR) at the detector input by the Pearson type IV distribution, which turns out to provide a simple but surprisingly effective and accurate approximation for the whole SNR probability density function (pdf). The framework includes the analytical derivation of i) the average bit error probability (ABEP) via Gauss-Legendre Gaussian quadrature rules (GQR), ii) the SNR cumulative distribution function (CDF) via the hypergeometric function ₂F₁ (middot, middot; middot; middot), which is useful for outage probability (Pout) analysis and iii) the SNR moment generating function (MGF) via Gauss-Legendre GQR. The validity and accuracy of the theoretical approach are also substantiated via Monte Carlo simulations.