Matched Filter Criteria and Range Weighting for Weather Radar

The effective weighting function for weather radar is defined. This weighting function considers the effects of both the transmitted signal and the receiver filter. It is used to assign effective ranges to samples taken at prescribed times. For uniformly distributed targets it is shown that "signal"-to-noise ratio depends on the receiver filter, transmitted signal envelope, and receiver noise spectral density. Maximization of this signal-to-noise ratio when range resolution constraints are imposed is discussed, and a receiver design approach specifically adapted for Doppler weather radars is developed.     

Spectrum Width Estimtes for Weather Echoes

Doppler spectrum width relates to wind shear and turbulence and thus is an important parameter which characterizes severe weather phenomena. The need to scan large volumes of space quickly and to obtain real-time estimates introduces stringent requirements on the signal processing. The Fourier transform and the autocovariance methods are candidate techniques. In particular, the autocovariance estimator is attractive due to low storgage and ease of computation. Statistics of an improved and asymptotically ubiased (for Gaussian spectra) autocovariance estimator of width are presented. Spurious effects on the complex video signal such as dc offsets and imbalances are assessed. Performance of the improved estimator on weather data is shown.     

Effective Antenna Pattern of Scanning Radars

It is shown that weather radar signal averaging causes a broadened apparent pattern of the scanning radar antenna. The apparent pattern is obtained by convolving the original pattern with the averaging circuit impulse response. Echo displacement and pattern broadness are examined for square law, linear, and logarithmic detectors having exponential and finite time integrators.     

Moments of Estimated Input Power for Finite Sample Averages of Radar Receiver Outputs

Closed-form solutions for all the estimated power moments as a function of the number of independent samples were found for the linear and logarithmic receiver. Incoming signal envelope distribution is assumed to be Rayleigh. The estimates' expected value and standard deviations are plotted and compared with those of a square-law receiver. It is shown that the bias in the expected value for both receivers depends on the number of samples. Only when the number of samples is large does the bias become constant, and the standard deviation around the unbiased mean becomes inversely proportional to the square root of the number of samples. The logarithmic receiver produces the largest standard deviation. When the input samples are dependent, an expansion of the method is suggested to obtain approximate moments.     

Reverse Error Coefficients

Expansion of tracking servo-system errors in terms of the derivatives of the output is proposed. Conditions under which the expansion of the complete output response coverages are found and a simplified example of a radar servo subsystem are discussed.     

Mean Power Estimation with a Recursive Filter

Power estimates from smoothed detector outputs of stationary signals are analyzed for linear, square law, and logarithmic receiverdetectors. Smoothing is accomplished with a first-order recursive digital filter. lnput amplitude is assumed to be Rayleigh distributed and detector output samples independent. Expansion of results to other distributions is indicated.     

Spectral Moment Estimates from Correlated Pulse Pairs

Estimates statistics of the first two power spectrum moments from the pulse pair covariance are analyzed. The input signal is assumed to be colored Gaussian and the noise, white Gaussian. Perturbation formulas for the standard deviation of both mean frequency and spectrum width are applied to a Gaussian shaped power spectrum, and so is a perturbation formula for the bias in the width estimate. Mean frequency estimation from interlaced pulse pairs is presented. Throughout this study, estimators from independent, spaced, and contiguous pulse pairs are compared to provide a continuum of statistics from equispaced tightly correlated to statistically independent pulse pairs.