Detection performance of the circular correlation coefficient receiver

The complex circular correlation detector is analyzed for the case of one complex sinusoid in complex white Gaussian noise. The distribution function of the squared modulus of the circular serial correlation coefficient is found when no signal is present, allowing computation of the detection threshold. For small data records, as is typical in radar applications, the performance of the correlation coefficient detector is compared to a standard DFT detector. The correlation detector outperforms the DFT detector for some sinusoidal frequencies but performs more poorly for others. The correlation detector is also shown to be a constant false alarm rate receiver and requires less computation and storage than an FFT.