Asymptotic Information-Theoretic Optimality of Channel Model Substitution by Monte Carlo Sampling

Channel model substitution (CMS) has been widelyapplied as a powerful toolkit to enable closed-form communication performance analysis. Minimizing the Kullback-Leiblerdivergence (KLD) between an original channel model (OCM)and its distributional substitute (DS) can achieve informationtheoretic optimality. However, for most CMS applications, theexpression of KLD cannot be derived in closed form, leading togreat challenges in minimizing such implicit objective functions.To tackle this analytical difficulty, we propose to use MonteCarlo sampling (MCS) to eliminate the integration of the objective function in these intractable KLD minimization problems.Through MCS, one can take the numerical estimate of KLD in asummative form as the objective function and proceed with theoptimization to approach asymptotic optimality. By employingthe generalized Newton-Raphson (N-R) method, the informationtheoretic optima for a majority of CMS applications can benumerically obtained with guaranteed existence and uniqueness.