Quantifying Error Estimates as Functions of Signal-to-Noise Ratio in a Multi-Tier Weak Radio Signal Detection Process with N Simultaneous Signals

This paper quantifies error in estimates of signal parameters as functions of zero crossings and signal-to-noise ratio of a weak signal in a multi-tier weak radio signal detection process with N simultaneous signals. For situations in which the weak signal contains Gaussian white noise (e.g., SNR = 20dB), a zero crossing cluster contains multiple zero crossings. For each zero crossing cluster, the task is to extract an estimate of the mean zero crossing of each cluster and an estimate of the standard deviation of the cluster. From the estimates of the mean zero crossing and standard deviation of each zero crossing cluster, one may quantity estimates and the error in the estimates of the weak signal frequency using pairs of zero crossing clusters. In these situations, all of the zero crossings within each cluster are detected. As with prior work, the starting point is is the generationalization of Tsui's phase measurement approach to detection of N-l weak signals. The paper quantifies errors in the signal parameters obtained from estimates of the zero crossing within each zero crossing cluster obtained from sampled data values of the instantaneous frequency. Examples are provided for the situation in which N=2, the strong signal takes on a value of 850 MHz, the weak signal takes on a value of 855 MHz with SNR = 20dB, and the signal- to-interference ratio is SIR $= 10^{-4}$. For instantaneous frequency data for eight consecutive zero crossing clusters with SNR = 20dB, the method estimates the frequency of a weak signal as 854.980759 MHz with a standard deviation of 0.1969 MHz. This approach provides a method to quantity the capability of this method to account for noise in weak signal detection for identification of zero crossings and extraction of signal parameters.