Frequency domain detection of sinusoidal signal under coloured Gaussian noise

Signal detection in coloured Gaussian noise usually requires preprocessing the received signal firstly to remove its correlation, resulting in a complicated calculation process. This study transforms the received signal into the frequency domain for detection and systematically studies both the real part (imaginary part) test and the approximate amplitude test (AAT). The study shows that the detection performance of the former is greatly affected by the initial phase of the signal, while that of the latter is basically independent of the initial phase. Frequency domain detection and the best detection are compared under a Gauss-Markov process, and the simulation results show that the detection performance of the AAT is similar to the best detection. In addition, the calculation of the AAT is obviously improved, so the AAT is easier to be applied in engineering compared to the best detection.