Compressive Sensing Aided Determination of OFDM Achievable Rate

In our previous work, we studied a novel approach employing compressive sensing to reduce the dimensionality of a convex optimisation problem, where the optimal feasible solution from a feasible subset of R^N is S-sparse, S<;<;N. This approach is also applicable if we wish to perform an "S-sparse optimisation", minimising a convex objective function over an S-sparse subset of the feasible set in R^N. In this paper, we provide an alternative derivation leading to an equivalent optimisation problem for a convex optimisation problem with an S-sparse optimal feasible solution. We first transform the original optimisation problem formulated in R^N into an equivalent problem in an "incoherent" domain in R^N. Then, we maximise the objective function using an arbitrary M-component subset of coordinates, i.e. function arguments. We apply the proposed method to reduce the dimensionality of a relevant information theory optimisation problem, the determination of the single user achievable rate for a multi-band multi-user OFDM system over a doubly-dispersive WSSUS fading channel. The vector channel model used is derived using WSSUS spaced-time spaced-frequency correlation function, which models fading decorrelation both in time and in frequency. The data symbols transmitted via OFDM signal tones have a finite alphabet.