Demodulation of sparse PPM signals with low samples using trained RIP matrix

Compressed sensing (CS) theory considers the restricted isometry property (RIP) as a sufficient condition for measurement matrix which guarantees the recovery of any sparse signal from its compressed measurements. The RIP condition also preserves enough information for classification of sparse symbols, even with fewer measurements. In this work, we utilize RIP bound as the cost function for training a simple neural network in order to exploit the near optimal measurements or equivalently near optimal features for classification of a known set of sparse symbols. As an example, we consider demodulation of pulse position modulation (PPM) signals. The results indicate that the proposed method has much better performance than the random measurements and requires less samples than the optimum matched filter demodulator, at the expense of some performance loss. Further, the proposed approach does not need equalizer for multipath channels in contrast to the conventional receiver.