On the approximation of the optimum detector by the energy detector in detection of colored Gaussian signals in noise

We demonstrate that the optimum detector of colored Gaussian signals in white Gaussian noise can be approximated, without serious degradation in detection performance, by the so-called energy detector which is optimum only when the signal is also white. Contrary to intuition, such an approximation is possible when the signal which is colored dominates the noise which is white. The demonstration is made analytically by deriving the optimum detection statistic and also numerically by simulating the detection performance of both detectors. A comparison of data processing complexity of the two detectors is also given.