An experiment with an S-band radar using pulse compression andrange sidelobe suppression for meteorological measurements

A major technology barrier to the application of pulse compression for the meteorological functions required by a next generation ATC radar is range/time sidelobes which mask and corrupt observations of weak phenomena occurring near areas of strong extended meteorological scatterers. Techniques for suppressing range sidelobes are well known but without prior knowledge of the scattering medium's velocity distribution their performance degrades rapidly in the presence of Doppler. Recent investigations have presented a “doppler tolerant” range sidelobe suppression technique. The thrust of the work described herein is the extension of previous simulations to actual transmitted dispersed/coded waveforms using the S-band surveillance radar located at Rome Laboratory Surveillance Facility. The objectives of the experiment are: 1) to extend the verification of the simulation of the Doppler tolerant technique; and 2) to demonstrate that the radar transmitter, waveform generator, and receiver imperfections do not significantly degrade resolution, performance or reliability of meteorological spectral moment estimates     

Closed-Form Expressions for Noncoherent Radar Integration Gain and Collapsing Loss

Closed-form formulas allow rapid determination of noncoherent integration gain and integration loss when the single-sample IF signal-to-noise ratio (SNR) is known. In addition, if the required SNR is known for any number of integrated pulses, the required SNR for any other number is easily determined. A closed-form expression is given for radar collapsing loss, expressed in terms of the equivalent integrated signal-to-noise ratio required to produce a given combination of false-alarm and detection probabilities. Alternatively, the single-sample signal-to-noise ratio of a set of samples may be used together with the closed-form expression for integration gain to get the equivalent integrated signal-to-noise ratio.     

Geometric aspects of long-term noncoherent integration

Long-term integration is defined as integration, perhaps interrupted, over time periods long enough for targets to move through volumes in space resolvable by the radar. Because the motion of the target is unknown prior to detection, long-term integration must be performed along multiple paths representing plausible target paths. The geometry of such a set of integration paths affects detection performance in several ways. The simplest implementation of long-term integration, using constant radial velocity paths, is investigated. The effects of path geometry on detection is quantified and optimized for a target whose motion is nearly radial but otherwise unknown     

Expressions in Closed Form for the Angular Accuracy of a Scanning Radar

Closed-form expressions are given for the standard deviation of the error in estimating angle (usually azimuth) in a scanning radar. The formulas apply to Swerling's lower bound and to the error using a pulse-to-pulse two-pole filter. They apply to non-fluctuating and Swerling II targets and hold for all signal-to-noise ratios. Comparison with graphical results in the literature shows that the average deviation obtained using the formulas is less than 4 percent.     

The Effect of Weighting upon Signal-to-Noise Ratio in Pulse Bursts

The Doppler sidelobes of a received pulse burst may be partially controlled by varying the amplitudes of the pulses in the burst or sequence upon transmission and/or reception. When there is a peak power limitation, weighting the amplitudes produces a loss in signal-to-noise ratio. A general expression is derived for the loss factor under the peak power limitation, and loss factor formulas are given for the following cases: Case A: Full nominal weights upon reception. Uniform weights on transmission. Case B: Square roots of the nominal weights on both transmission and reception. Case C: Full nominal weights on both transmission and reception. These cases are listed in order of increasing loss. Numerical results are tabulated for regular spacings and for the following nominal weights: 1) Dolph-Tchebycheff, 2) Taylor, 3) Hamming, and 4) Hann.     

Energy Detection of a Random Process in Colored Gaussian Noise

A likelihood receiver for a Gaussian random signal process in colored Gaussian noise is realized with a quadratic form of a finite-duration sample of the input process. Such a receiver may be called a "filtered energy detector." The output statistic is compared with a threshold and if the threshold is exceeded, a signal is said to be present. False alarm and detection probabilities may be estimated if tabulated distributions can be fitted to the actual distributions of the test statistic which are unknown. Gamma distributions were fitted to the conditional probability densities of the output statistic by equating means and variances, formulas for which are derived assuming a large observation interval. A numerical example is given for the case in which the noise and signal processes have spectral densities of the same shape or are flat. The optimum filter turns out to be a band-limited noise whitener. The factors governing false alarm and detection probabilities are the filter bandwidth, the sample duration, and the signal level compared to the noise. Two sets of receiver operating characteristic curves are presented to complete the example.     

Reduction of sidelobe self-interference in an agile beam radar

In an agile beam phased array radar, the beam is often multiplexed over several angular positions, and “listens” in each position only over an instrumented range that may be a fraction of the unambiguous range as determined by the pulse repetition period in each position. After transmitting a pulse in a given direction, the beam is switched, essentially instantaneously, to another position, after the instrumented range delay. In this second position, echoes from the first position, from multiple trips of the instrumented range, enter the one-way angular sidelobes of the first position. This interference is compounded if there are several beam positions in a pulse repetition period. The author proposes a method of phase coding the pulses in such a way that the pulse-to-pulse phase variation in each direction is orthogonal to every other phase code in the other directions. The codes are Walsh functions. These are sets of binary valued (+1 or -1) functions such that all of the functions in the set are mutually orthogonal. Not every possible number N of pulses in each direction and number K of beam positions can be accommodated, but a large variety of such combinations can be accommodated. Several examples are given. The combination of low one-way sidelobes and orthogonality (or near orthogonality) of the phase codes should provide for very stringent sidelobe self interference rejection     

Some High-Velocity Clutter Effects in Matched and Mismatched Receivers

A generalized ambiguity function including the effects of Doppler dispersion is defined as the time cross correlation of the complex envelopes of two signals, both derived from the same basic waveform but with different delays and Doppler effects. The Doppler effects include the frequency shift and expansion or contraction of the modulation time scale. This expansion or contraction is the Doppler dispersion. While the general ambiguity function cannot be expressed directly in terms of the Woodward or undispersed ambiguity function, its squared magnitude can be expressed in terms of the Woodward ambiguity function. The relation is not simple, being an integral form. Nevertheless, since the Woodward ambiguity function is known for many signals, the relation may simplify the determination of the squared magnitude of the general ambiguity function. We consider the clutter output of a matched filter or correlation receiver where the receiver is matched to a waveform having a specific delay and specific time compression. The variance of the clutter output is the two-dimensional convolution of the clutter ``scattering function' with the squared magnitude of the general ambiguity function. This is a generalization of an earlier result which is formally the same but using the Woodward ambiguity function. This last result is generalized for a mismatched receiver. In such a case, the variance of the clutter output is the double convolution of the clutter scattering function with the cross ambiguity function of the transmitted waveform, modified by the average velocity of the clutter, and the receiver reference waveform.