Analysis of the Boundary Effect on Signal Detection in Unwrapped Phase Noise

This paper analyzes signal detection in the phase domain and the boundary effect due to the phase noise. Considering the sum of a complex function and additive zero-mean complex Gaussian noise, the phase model is developed under the assumption of perfect phase unwrapping. Then, based on the matched filter, two detectors are proposed, depending on if the phase boundary is employed. The analysis shows that the boundary introduces zero likelihood in the maximum likelihood criterion and so changes the decision rule greatly, resulting in a significant improvement on the detection performance. The binary phase shift keying is analyzed for wireless communication via the phase domain.