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Doppler detection for linear FM waveform using extended matched filter

This paper proposes a Doppler detection method for Linear FM (LFM) waveform by identifying its location within the extended Matched Filter (MF). The extended MF of a LFM waveform is constructed by extending its frequency sweep on both sides. Doppler shift results in shifting the frequency sweep of the LFM waveform along the instantaneous frequency of its extended MF. Thus, identifying the location of the received LFM waveform within its extended MF results in detecting the Doppler shift of the LFM waveform. At the receiver, after carrier demodulation the highly sampled received signal is first passed into the extended MF. Timing of the mainlobe of the extended MF output is used to identify the highly sampled received signal containing the LFM waveform within the extended MF. Then, a running sum of these samples over a length equal to that of the highly sampled LFM waveform is computed. The maximum of this running sum occurs at the location of the LFM waveform within the extended MF which in turn results in identifying its Doppler shift. In comparison with the method of Doppler detection using a triangular FM waveform, it is shown that the proposed method has superior performance in the presence of additive noise.