The pulse-pair algorithm as a robust estimator of turbulent weather spectral parameters using airborne pulse Doppler radar

Original publisher: [Washington, D.C.] : National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Program ; [Springfield, Va. : For sale by National Technical Information Service], 1991. OCLC Number: ocm27873891 Subject: Doppler radar. Excerpt: ... III. The Radar Return Autocorrelation Considering System Phase Jitter Effects The transmitted radar signal at each pulse time is a burst of a sinusoid defined by J ( 2_fct + _ ) v ( t ) = V0e ( I0 ) where _ is a random phase considered constant throughout the pulse duration and fc is the transmitted carrier frequency. The complex demodulated video signal at the receiver output can be represented as j [ 2_fdt + _ ( t ) ] Z ( t ) = Z0 ( t ) e ( ii ) where the envelope function Zo ( t ) is a narrowband random process determined primarily by the nature of the source of the radar return, fd represents the mean Doppler frequency of the return, and _ ( t ) is a random process associated with the phase of the return. The process _ ( t ) is considered to have stationary increments where statistical changes are very slow as compared to the interpulse period T s. The phase process modelled in terms of _ ( t ) might include STALO oscillator phase drift, phase instabilities within the modulator or demodulator, or platform motion, i.e., anything that might contribute to uncertainty in the phase of the return signal from pulse to pulse. Any short term intrapulse phase fluctations associated with the source of the return, e.g., the weather, are considered to be a part of the process Zo ( t ). The interpulse phase variations modelled in terms of _ ( t ) will be referred to as phase jitter and are isolated for further study. Assuming that the envelope process is statistically independent of the phase jitter process, the autocorrelation of the return can be characterized as R ' ( T s ) = E { z * ( t ) Z ( t + Ts ) } = R ( Ts ) E { e-j_ ( t ) eJ_ ( t