This paper addresses the estimation of the frequency of a sinusoid from compressively sensed measurements. Normally in parameter estimation, measurements are assumed to contain the signal and additive white Gaussian noise (AWGN). Under the paradigm of compressive sensing (CS), the measurements no longer contain AWGN but correlated noise. Frequency estimation of a sinusoid from measurements obtained through CS using the A WGN assumption will be non-optimal. This paper provides near-optimal frequency estimates for a sinusoid obtained through CS. Estimation of frequency of a sinusoid from CS measurements is cast as a linear least squares problem. A near-optimal solution in closed-form is presented by applying generalized total least squares (GTLS) technique to avoid bias caused by the correlated noise. The accuracy of the closed-form solution is close to the theoretical bound as confirmed by simulations.

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Keywords Compressed sensing, Cramer-Rao lower bound, Frequency estimation, Random modulator pre-integrator, Total least squares
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Conference 2018 IEEE Canadian Conference on Electrical and Computer Engineering, CCECE 2018
Chan, Y.-T. (Yiu-Tong), Chan, F. (Francois), & Rajan, S. (2018). Estimation of Frequency of a Sinusoid from Compressive Sensing Measurements. In Canadian Conference on Electrical and Computer Engineering. doi:10.1109/CCECE.2018.8447886