Compressive Sensing for the Capacity of a Rayleigh Fading Channel

A given objective function, I(px(x)), is to be maximized over the argument px(x), where px(x) is a continuous function of x ∈ R¹. Rather than optimizing I(px (x)) over the domain of functions, where the optimal solution p*_x (x) is non-zero only at a few but unknown discrete points x ∈ {x₁, x₂,_⋯, x_S}, is it possible to solve the optimization problem by optimizing the objective function over S discrete components only? This is the main problem addressed and is solved using compressive sensing (CS) with application to the determination of the capacity of a discrete memoryless Rayleigh-fading channel with peak and average input power constraints. A novel optimization algorithm is developed and applied to a known example. Simulation results, using this novel optimization algorithm, are generated which provides an accurate estimate of the optimizing distribution and the resultant capacity. The significance of this approach is that it can be applied to optimization problems in general and specifically, to communication systems where the domain can be compressed.