A quick simulation method for fading communications channels using a novel eigenvalue importance sampling technique

Abstract

In this paper, we introduce a quick simulation method for fading communications channels using a novel eigenvalue importance sampling technique. Our approach is motivated by the fact that many performance analyses involve metrics which are functions of the eigenvalues of the channel correlation matrix. More specifically in Rayleigh fading we often require the eigenvalues of the Wishart matrix HH† where H is the matrix of channel gains. Hence we propose direct simulation of the Wishart eigenvalues rather than simulation of the full channel matrix. If H is nR × nT then this idea in itself reduces simulation time since m = min(nR,nT) eigenvalues are required rather than the 2 × nR × nT real Gaussians. However, direct generation of the eigenvalues is complicated. Therefore we introduce a novel eigenvalue importance sampling technique which generates the eigenvalues from a simple biased density which "mimics" the real density. We call our approach Eigenvalue Importance Sampling (EVIS). Secondly, we try to reduce rare event simulation time by using biased eigenvalue densities to encourage the rare event of interest. We denote this approach Rare event Eigenvalue Importance Sampling (REVIS). Both methods are demonstrated via the example of simulating capacity outages and values for a MIMO system. Results show that considerable savings are offered by this novel approach even with simple implementations and small scale systems (m ≤ 4).