Frank F. Kretschmer

Linear Frequency Modulation Derived Polyphase Pulse Compression Codes

Two new polyphase pulse compression codes and efficient digital implementation techniques are presented that are very Doppler tolerant and that can provide large pulse compression ratios. One of these codes is tolerant of precompression bandwidth limitations.

A New Class of Polyphase Pulse Compression Codes and Techniques

A new class of symmetric radar pulse compression polyphase codes is introduced which is compatible with digital signal processing. These codes share many of the useful properties of the Frank polyphase code. In contrast with the Frank code, the new codes are not subject to mainlobe to sidelobe ratio degradation caused by bandlimiting prior to sampling and digital pulse compression. It is shown that bandlimiting the new codes prior to pulse compression acts as a waveform amplitude weighting which has the effect of increasing the mainlobe to sidelobe ratios.

Doppler Properties of Polyphase Coded Pulse Compression Waveforms

Doppler properties of the Frank polyphase code and the recently derived P1, P2, P3, and P4 polyphase codes are investigated and compared. An approximate 4 dB cyclic variation of the peak compressed signal is shown to occur as the Doppler frequency increases. The troughs in the peak-signal response occur whenever the total phase shift across the uncompressed pulse, due to Doppler, is an odd multiple of ¿ radians. It is shown that while the P3 and P4 codes have larger zero-Doppler peak sidelobes than the other codes, the P3 and P4 codes degrade less as the Doppler frequency increases. Also, the effects of amplitude weighting and receiver bandlimiting for both zero and nonzero Doppler are investigated.

Low sidelobe radar waveforms derived from orthogonal matrices

Novel waveforms are described that have low sidelobes when individual or multiple waveforms are approximately processed. They are related to orthogonal matrices that may be associated with complementary sequences and also with periodic waveforms having autocorrelation functions with constant zero-amplitude sidelobes. Also described are sets of sequences whose cross-correlation functions sum to zero everywhere. A potential application is the elimination of ambiguous range stationary clutter. >

An Improved Algorithm for Adaptive Processing

The Widrow-Hoff least mean square (LMS) algorithm based on the method of steepest descent is conditionally stable. A modified algorithm is given which is unconditionally stable, capable of better performance when used in adaptive filter processing, and provides a more realistic means for simulating the Applebaum-Howells adaptive loop.

New radar pulse compression waveforms

Pulse compression waveforms are described which have low sidelobe levels. Emphasis is on individual waveforms or multiple dissimilar waveforms. Processing the single waveforms consists of matched filtering while the multiple waveforms are individually matched, filtered, time-aligned, and summed. The multiple waveforms consist of complementary waveforms whose compressed pulses sum to zero in the sidelobes. These waveforms, in turn, were related to the underlying theory of orthogonal matrices. Multiple waveforms are discussed that, when filtered using a filter matched to a different waveform of the set, have a small output or cross-correlation response after combination of the individual responses. These waveforms have potential applications in reducing ambiguous range stationary clutter returns.<<ETX>>

A Digital Open-Loop Adaptive Processor

A new technique for adaptive processing applications, which is superior to the conventional Applebaum-Howells adaptive loop, is presented. The new technique is based on open-loop digital processing and does not have the limitations of the conventional closedloop analog processor. In contrast with the conventional adaptive loop, the open-loop processor has effectively infinite gain, is unconditionally stable, and does not depend on the power level of the auxiliary signal.

Reciprocal radar waveforms

Digitally coded radar waveforms can be used to obtain large time-bandwidth products (pulse compression ratios). It is demonstrated that periodic radar waveforms with zero sidelobes or almost zero sidelobes can be defined. A perfect periodic code is a periodic code whose autocorrelation function has zero sidelobes and whose amplitude is uniform (maximum power efficiency=1). An asymptotically perfect periodic code has the property that as the number of elements in the code goes to infinity the autocorrelation function of the code has zero sidelobes and its power efficiency is one. The authors introduce a class of radar waveforms that are either perfect or asymptotically perfect codes. These are called reciprocal codes because they can be derived through a linear transformation of known codes. The aperiodic performance of the reciprocal code is examined. >

Angle measurement in the presence of mainbeam interference

The estimation of the angle of arrival of a desired signal in the presence of mainbeam interference is discussed. Adaptive antenna arrays are incorporated to form adapted sum and difference beams in which the interference signals are suppressed. Monopulse error curves are then obtained, providing the necessary distortion correction curves across the entire mainbeam tracking angle region. New Cramer-Rao (C-R) bounds on the angle estimation error are derived with generalized assumptions on the signal amplitude and phase. The bounds previously derived by others are valid under different conditions. With these generalized assumptions on the signal characteristics, a Monte Carlo simulation is performed based on a suggested estimation procedure to determine the angle estimation error. These errors are compared with the C-R bounds. Good performance is shown for sufficient S/N/sub 0/ and angular separation between the target and the interference sources.<<ETX>>

Estimators of Generalized Chi-Square Parameters

The maximum likelihood estimators of the parameters of the genalized chi-square distribution are derived and approximated. These estimators are compared with those based on the method of moments.