Comparative study of two-sensor(magnitude-squared coherence) and single-sensor(square-law) receiver operating characteristics

An approximation for the Probability Density function (PDF) of the Magnitude-Squared Coherence (MSC) estimate is presented. The analysis is valid for the case of two ergodic Gaussian random processes, partitioned into n
d
independent data segments. The Probability of False Alarm (P
fa
) is related directly to the decision threshold. Also, the true MSC is given as a function of signal-to-noise ratio (SNR), for equal and nonequal SNR conditions in each sensor. Associated plots are included. The detection performance of an MSC estimate processor is analyzed. This investigation is valid when Gaussian noise inputs to the two sensors are uncorrelated, and have the same auto-spectral density. The Probability of Detection (P
D
) is plotted against the SNR for certain values of n
d
between 26 and 8000. Also, the detection performance of the coherence estimator (two-sensor) is compared to that of a single-sensor square law detector, assuming a narrowband Gaussian input signal, with rectangular spectrum. Curves of P
D
vs SNR, for the processors, are presented together.