A method for coarse frequency acquisition for Nyquist filtered MPSK

In mobile satellite communications, frequency offsets are important to estimate before further processing and detection of the received signal. In this work, we devise a straightforward technique for coarse frequency acquisition through the discrete Fourier transform (DFT) computation for samples of the received waveform with a set of special preamble sequences suitable for any Nyquist pulse shape and which can also be used for timing recovery. The technique can be applied to any L-ary phase shift keying (LPSK) modulation scheme, though we apply it to binary phase shift keying (BPSK) and show how to use it with a LPSK scheme. Also, the analysis takes into account the effect of the receiver´s narrowband low-pass filter (LPF) on attenuating the noise power which also results in correlated noise samples. Such a treatment of performance with correlated noise is not considered in the literature as the noise is usually assumed to be uncorrelated for simplicity in analysis. The presented results are obtained through theory and verified by computer simulation. A new discrete Fourier transform (DFT) search algorithm, based on the maximum-likelihood principle, and which takes into account the preamble structure, is introduced and examined