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A pulse-compression radar system which utilizes a linear FM waveform has a theoretical upper limit to the magnitude of its compression ratio or time-bandwidth product. This limit is a function of the observed target's relative radial velocity, and the effect on the return signal is characterized by both a pulse stretching and amplitude reduction if the limit is exceeded. The use of a logarithmic phase-modulation signal waveform and a corresponding ``matched'' receiver possesses the desirable characteristics of the linear FM and in addition has no upper limit to the magnitude of the compression ratio. A single receive pulse-compression filter is matched for all target velocities. A linear FM signal can be thought of as a very good approximation to a logarithmic phase-modulation signal for compression ratios less than the maximum limit. A general method of implementing a variety of systems employing pulse-compression ratios up to 105 and utilizing logarithmic phase modulation is presented.