Distributions of Radar Angels

A foremost characteristic of large dot radar angels is the wide variation of basic parameter values which they exhibit. This variation is traceable to the nature of the underlying phenomena, i.e., birds and flocks of birds. In this paper, statistical distribution models for the mean radar cross section (RCS) and density of radar angels are obtained, based on a combination of radar and direct ornithological data. The radar cross-section distribution model has been derived from a dimensionless RCS versus wavelength model for individual birds, obtained from measured RCS data which have been scaled to a dimensionless form. This model is applied to ornithological data on populations of birds. The density distribution model is based on statistical reduction of migratory bird data obtained by Lowery's moon watching experiment, and observed seasonal and diurnal variations of radar angel activity. Both resulting distribution models are closely appproximated by the log-normal distribution. The model parameters for these distributions are given.     

Exact Angular Accuracy of an Amplitude Comparison Sequential-Lobing Processor

Assume E1 and E2 are the squares of two sequential envelopes from the sequential lobing of an antenna in a given plane. Independent thermal noise is generally present in the envelopes. The statistic e = (E2 ? E1)/(E2 + E1) has been used as an estimate of the angle to a target for the significant region of small angles compared to a beamwidth. For a nonfading target, the probability density and characteristic function of e are obtained in closed form. Thence, the exact bias, standard deviation, and rms error in estimating the noise-free value e of e are obtained for all e and signal-to-noise ratios. The same type of statistic as e can be used to estimate time delay in a split range gate tracker.     

Angular Tracking of Two Closely Spaced Radar Targets

Bounds on the accuracy of unbiased estimates of the angular coordinates of a target, in the presence of a nearby interfering target, have previously been determined. These bounds allow for the angular resolution of two CW targets to an extent limited only by the signal-to-noise ratio (SNR). An SNR of 40 dB will allow two targets to be resolved at less than one-fifth beamwidth (?/2 X) separation, for most values of target relative phase angles. The maximum-likelihood estimator for this problem, based on the outputs of a plane circular array of receiving elements, is found and simplified. An analog realization of the two-target maximum-likeli-hood processor is presented. This realization has the simple form of two single-target trackers each tracking one of the targets, linked by a decoupling network which accounts for the interference produced in each by the presence of a second target, when the targets are separated by less than a beamwidth. Results of an analog-computer simulation of the system are given and discussed. Finally an application to the finite-size single-target problem is given.     

A Semicoherent Detection and Doppler Estimation Statistic

Consider a uniform train of M coherent short pulses transmitted by a radar and received with a Doppler shift. When thermal noise is present, let the mth sample of the return at the video be represented by the complex process Zm. A novel detection and Doppler estimation criterion is analyzed which depends on the semicoherent statistic begin{equation*}{Z_{K}}^prime = sum_{m=k+1}^{M} {^{z}m^{z}m-k}^{ *}end{equation*} where the asterisk stands for complex conjugate. Its characteristics are also studied when the real and imaginary parts of Zm are digitized to one bit.