Analog Compressed Sensing for Sparse Frequency Shift Keying Modulation Schemes

There is a growing interest in signaling schemes that operate in the wideband regime due to the crowded frequency spectrum. However, a downside of the wideband regime is that obtaining channel state information is costly, and the capacity of previously used modulation schemes such as code division multiple access and orthogonal frequency division multiplexing begins to diverge from the capacity bound without channel state information. Impulsive frequency shift keying and wideband time frequency coding have been shown to perform well in the wideband regime without channel state information, thus avoiding the costs and challenges associated with obtaining channel state information. However, the maximum likelihood receiver is a bank of frequency-selective filters, which is very costly to implement due to the large number of filters. In this work, we aim to simplify the receiver by using an analog compressed sensing receiver with chipping sequences as correlating signals to detect the sparse signals. Our results show that using a compressed sensing receiver allows for the simplification of the analog receiver with the trade off of a slight degradation in recovery performance. For a fixed frequency separation, symbol time, and peak SNR, the performance loss remains the same for a fixed ratio of number of correlating signals to the number of frequencies.