A Semicoherent Detection and Doppler Estimation Statistic

Consider a uniform train of M coherent short pulses transmitted by a radar and received with a Doppler shift. When thermal noise is present, let the mth sample of the return at the video be represented by the complex process Zm. A novel detection and Doppler estimation criterion is analyzed which depends on the semicoherent statistic \begin{equation*}{Z_{K}}^\prime = \sum_{m=k+1}^{M} {^{z}m^{z}m-k}^{ *}\end{equation*} where the asterisk stands for complex conjugate. Its characteristics are also studied when the real and imaginary parts of Zm are digitized to one bit.