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31 May 2013 Random-phase radar waveforms with shaped spectrum
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A random phase signal will also have random phase differences between two independent random phases. A phase increment across a time increment is in fact a phase-rate, or frequency. A phase-rate change is in fact a frequency-hop. By controlling the phase-rate, that is the characteristics of the phase increments, we can control the spectrum of the random-phase waveform. Spectrum precision and sharpness is enhanced by holding a frequency for some ‘chip’ length. For digitally generated phase samples, this means that the chip length needs to be many samples. This is a time-bandwidth issue. The definition of ‘many’ will depend on the sharpness desired, but often several tens’ of samples will be adequate. To shape the Energy Spectral Density (ESD) of a random-phase signal, we need to control the average energy at various phase-rates. This can be done with either or a combination of 1) Controlling the likelihood of specific phase increments, and/or 2) Controlling the duration of a specific phase increment chip length. For range-Doppler images, it is the 2-dimensional Impulse Response (IPR) that is of principal concern. This will tend to average out the random effects of any single pulse.
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A. W. Doerry and B. Marquette "Random-phase radar waveforms with shaped spectrum", Proc. SPIE 8714, Radar Sensor Technology XVII, 87141G (31 May 2013);

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