Distribution of Compressive Measurements Generated by Structurally Random Matrices

Structurally random matrices (SRM) have been proposed as a practical alternative to fully random matrices (FRM) for generating compressive sensing measurements. If the measurements are transmitted over a communication channel they need to be efficiently quantized and coded, which requires knowledge of the measurements statistics. In this paper we study the statistical distribution of measurements generated by SRMs (and FRMs), give conditions for asymptotic normality and point out the implication for measurements quantization and coding.