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

摘要

In this paper, we introduce a quick simulation methodfor fading communications channels using a novel eigenvalue importancesampling technique. Our approach is motivated by thefact that many performance analyses involve metrics which arefunctions of the eigenvalues of the channel correlation matrix.More specifically in Rayleigh fading we often require the eigenvaluesof the Wishart matrix HH† where H is the matrix of channelgains. Hence we propose direct simulation of the Wishart eigenvaluesrather than simulation of the full channel matrix. If H isnR × nT then this idea in itself reduces simulation time since m =min(nR, nT ) eigenvalues are required rather than the 2×nR×nTreal Gaussians. However, direct generation of the eigenvalues iscomplicated. Therefore we introduce a novel eigenvalue importancesampling technique which generates the eigenvalues from asimple biased density which "mimics" the real density. We call ourapproach Eigenvalue Importance Sampling (EVIS). Secondly, wetry to reduce rare event simulation time by using biased eigenvaluedensities to encourage the rare event of interest. We denote this approachRare event Eigenvalue Importance Sampling (REVIS). Bothmethods are demonstrated via the example of simulating capacityoutages and values for a MIMO system. Results show that considerablesavings are offered by this novel approach even with simpleimplementations and small scale systems (m ≤ 4).