Frequency estimator performance analysis with compressive sensing or non-uniform sampling

Uniform sampling may ensure alias-free signal representation. Using complex-valued samples, the uniform sampling rate must exceed the analog bandwidth. Consequently, the system analog bandwidth requirement constrains the time spanned by N uniformly spaced samples. Ultimately, acquiring this limited timespan constrains frequency estimator variance as evidenced by the Cramer-Rao lower bound. Frequency estimators commonly use maximum-likelihood estimation for a signal corrupted by Gaussian noise. These estimators compute the peak frequency correlation between the received samples and a known waveform template. Since the hypothesized basis functions are known, compressive sensing or non-uniform sampling provides an alternative. Either alternative may observe a greater timespan while preserving the same alias-free analog bandwidth and without recording more samples. This increases the average Fisher information per sample and decreases the Cramer-Rao lower bound. As a result, these alternative sampling techniques can deliver improved frequency estimates.