Over-sampled polyphase code design for physical implementation with spectral and correlation consideration

This paper presents an approach for designing continuous phase modulation (CPM) waveform with good spectral compatibility and low correlation properties. The suggested approach is to first design over-sampled polyphase code with stopband and correlation constraint, and then transform the polyphase code into CPM waveform. Applying over-sampling ensures that the resulting CPM waveform would well inherit the spectral and correlation properties from the designed polyphase code. To cope with such over-sampled code optimization, special considerations on both spectral and correlation penalty function are illustrated, and an efficient alternating projection method based on (I)FFT is proposed accordingly. Numeric results validate both the CPM waveform design approach and the over-sampled polyphase code optimization method.