Noise Calibration, Delay Coherence and SNR Walls for Signal Detection

In this paper we consider the problem of robustly detecting the presence/absence of signals in uncertain low SNR environments. Our previous results have shown the existence of fundamental SNR thresholds called SNR walls below which robust detection is impossible. For signals with narrowband pilots, we had shown earlier that a simple modification to the matched filter provides significant robustness gains. This technique is called runtime noise calibration. In this paper we show that runtime noise calibration can also be applied to improve the robustness of other feature detectors. We use a 50% duty-cycle pulse-amplitude-modulated signal as an example to illustrate the gains from noise calibration. Robustness results for this example give us important insights which also apply in the general case of cyclostationary signals. Our results suggests that for cyclostationary signals, frequency-selective fading and uncertain noise color are the main reasons for detector non-robustness. Furthermore, we introduce the notion of delay coherence for frequency-selective channels. We also characterize the location of the SNR wall as a function of the delay-coherence time of the channel.