Compressed Gridless Frequency Estimation by Segmented Atomic Norm Minimization for Random Demodulation

The fixed-dictionary based gridded frequency sparse representation in random demodulation systems faces the grid mismatch problem, which may lead to severe degradation of the compression algorithm to the extent that high precision signal parameters and signal reconstruction cannot be obtained. Gridless compressed sensing introduces the concept of atomic norm, which solves the grid problem caused by spectrum discretization and greatly improves the accuracy of signal frequency estimation. However, in practice, solving large-scale meshless compressed sensing problems directly can consume a lot of time and storage resources. In this paper, we borrow the idea of segmented random sampling to compress the signal by generating segmented pseudo-random sequences in a random demodulation system. Then each segment of the compressed sampled signal is reconstructed and frequency estimated by atomic norm separately, and the obtained frequency estimates of several segments are averaged to obtain the frequency estimates of the original signal. The algorithm can achieve a recovery signal-to-noise ratio of 68 dB for a signal with 256 points per segment, and the recovery accuracy is only related to the number of points within the segment, independent of the number of segments. The algorithm reduces the computational complexity and improves the solution size and the accuracy of frequency estimation.