Nonuniform Sampling Walls in Wideband Signal Detection

This work shows the existence of sampling walls in detection of wideband signals from Bernoulli nonuniform sampling (BNS) in the presence of noise uncertainty. A sampling wall is defined as the sampling density below which the target error probabilities, i.e., the missed detection and false alarm probabilities, cannot be guaranteed at a given signal to noise ratio (SNR) regardless the number of acquired samples. The BNS is adopted because it exhibits good tradeoff properties between complexity and performance. It is shown that BNS suffers from noise enhancement, which translates into a whitening effect in the correlation of the legacy signal. Contrarily to the existing literature, the signal detection problem is addressed without having to reconstruct neither the signal nor its spectrum. More specifically, the optimal low SNR detector is formulated as a generalized likelihood ratio test (GLRT) to exploit the available side information of the problem, i.e., the noise variance, the sampling density and the legacy signal autocorrelation. By deriving the asymptotic performance of the GLRT in the presence of noise uncertainty, explicit expressions for sampling walls are obtained as a function of the legacy signal occupancy, the SNR and the noise uncertainty. Further, numerical results are provided to assess the behavior of the sampling walls and signal detection performance.