The Doppler sensitivity of large TW phase modulated waveforms

The narrowband approach to coherent processing of large-TW waveforms in Doppler delay multiplies the data stream by the complex conjugate of the undilated envelope and uses FFT processing to test Doppler. This results in a correlation loss that depends fundamentally on the TW product of the waveform envelope and the amount of Doppler-induced time-base dilation occurring in the data. It is shown that it is possible to reduce the number of dilated envelope replicas required to cover a given Doppler band by dividing the band into subbands. Each narrowband is processed using an envelope replica with a fixed dilation parameter, and the width of each band is a function of a specified correlation loss limit, the TW product, and a Doppler sensitivity parameter that depends on the specific time-frequency allocation of the envelope. Examples are provided for envelopes with both continuous and discrete (FSK) allocations with emphasis on the class of unit allocation (UA) codes that includes all full Costas arrays, for which upper and lower bounds for Doppler sensitivity are derived