Noise enhancement and SNR equivalence in Bernoulli nonuniform sampling

Abstract

This paper addresses the problem of nonuniform spectral analysis and spectrum sensing by means of Bernoulli sampling. The statistical treatment of sampling shows that nonuniformly sampling below the Nyquist rate produces in average the e ects of noise enhancement and power loss on the second-order statistics of the signal (correlation and spectrum). The main focus of the paper is to obtain an equivalence in terms of signal-to-noise ratio (SNR) to model the noise enhancement and power loss effects. The Bernoulli nonuniform sampling is further extended to matrix formulation, which allows the application of spectrum sensing for cognitive radio signal detection. Numerical results assess the noise enhancement eff ect and SNR equivalence in spectral analysis and spectrum sensing.