Impacts of hardware nonlinearities on compressive sensing performance

In previous work, we have exploited prior knowledge of target signals to design compressive measurement kernels for fast-time sub-Nyquist sampling. The kernels were designed to maximize the Shannon mutual information between the measurement and the target signals to be estimated. We showed that in cases where the radar system is resolution-limited rather than noise-limited, compressive sensing (CS) could provide a performance benefit for these applications, despite the signal-to-noise ratio (SNR) loss inherent in radio frequency compressive sensing. Hence, the largest performance gains were seen at high SNR. On the other hand, both the kernel optimization and the signal reconstruction are model based, meaning they are highly dependent on an accurate forward model of the sensing process. Because sub-Nyquist analog-to-digital conversion requires analog multiplication and lowpass filtering, the forward model must accurately quantify the signal operations in order for CS-based techniques to reach their full utility. In this paper, we model inaccuracies in the analog multiplier via third-order non-linear terms in the sensing model and quantify their effect on overall performance.