Sampling walls in signal detection of Bernoulli nonuniformly sampled signals

In this work, we show the existence of sampling walls in signal detection of nonuniformly sampling wideband signals in the presence of noise uncertainty. A sampling wall is the sampling rate below which the target error probabilities (namely the missed detection and false alarm probabilities) cannot be achieved at a given signal to noise ratio (SNR) regardless the number of acquired samples. Contrary to existing works, we address the signal detection as a binary hypotheses testing problem without having to reconstruct neither the signal nor the spectrum from the observations. Specifically, we adopt a Bernoulli distributed sampler as it exhibits good tradeoff properties between complexity and performance. We show that Bernoulli nonuniform sampling suffers from noise enhancement, which translates into a whitening effect in the correlation of the legacy signal. Therefore, in the presence of noise uncertainty, we derive explicit expressions for sampling walls as a function of the legacy signal occupation, the SNR and the noise uncertainty level. Finally, numerical results are further provided to assess the behavior of the sampling walls and signal detection performance.