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.     

Range-time-sidelobe reduction technique for FM-derived polyphase PCcodes

A simple, easy to implement technique is presented that can significantly reduce the range-time-sidelobes of a class of polyphase pulse compression codes. This technique reduces the highest sidelobes to only one code element magnitude independent of effective pulse compression ratio. The codes considered are polyphase codes that are derived from the step-approximation-to-linear-frequency-modulation and linear-frequency-modulation waveforms such as the P1, P3, P4, and the Frank codes. The characteristics of these codes that make this possible are explained     

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.     

Range Sidelobe Suppression for Barker Codes

The utility of Barker-type phase-reversal codes is extended by the use of sidelobe suppression techniques that can be easily implemented in digital form. It is shown that sidelobe suppression techniques can be found where the tapped delay line used to reduce the sidelobes has only a few distinct tap weights, in which case the complexity of the digital processor is greatly reduced. An example is given where the technique is applied to Barker codes with positive sidelobes, specifically, the 13-element Barker code. If higher pulse compression factors are desired than are obtainable with Barker codes, multistage Barker codes may be used. The sidelobes then may be suppressed for any one or all of the different coding stages.     

Design and analysis of new p(n,k) polyphase pulse compression codes

P(n,k) codes as a new class of polyphase pulse compression codes are introduced and analyzed in detail. The P(n,k) codes are conceptually derived by step approximation of the phase function of a nonlinear-frequency modulated (NLFM) Chirp signal with a favorable energy density spectrum. The significant advantages of P(n,k) codes over conventional polyphase codes are lower autocorrelation sidelobes and an improved tolerance of low Doppler shifts and precompression bandwidth limitations. The primary disadvantage of the P(n,k) codes over conventional codes is a loss in range resolution. The uniform P(n,k) codes are especially attractive for radars employing digital signal professing because their favorable correlation properties also remain when quantization effects are taken into account     

A multiobjective optimization approach to determine the parameters of stepped frequency pulse train

Frequency stepping techniques are commonly used in modern radar system to get high range resolution with the disadvantage that its autocorrelation function (ACF) yield undesirable “grating lobes”. Wider mainlobe deteriorates the range resolution capability of the waveform and higher peak sidelobe either hides the small targets or causes the false target detection. Several techniques have been used to choose the parameters of linear frequency modulated (LFM) pulse train to suppress the grating lobes without paying much attention to the mainlobe width and peak sidelobe level. In this paper a multiobjective optimization (Nondominated Sorting Genetic Algorithm-II (NSGA-II)) approach is proposed to optimize the parameters of the LFM pulse train to achieve reduced grating lobes, low peak sidelobe level and narrow mainlobe width. The optimization problem has been studied in two different ways: first one is associated with the reduction of grating lobes and the minimization of peak sidelobe level of the ACF with constraints and second one is related to the minimization of the peak sidelobe level and mainlobe width of the ACF with constraints. Simulation studies have been carried out to justify the potentiality of the proposed approach.     

Poly-phase codes and optimal filters for multiple user ranging

A technique is introduced to select poly-phase codes and optimal filters of a pulse compression system that have specific temporal and frequency characteristics. In the particular problem under study, multiple vehicles are assigned unique codes and receiver filters that have nearly orthogonal signatures. Narrowband users, that act as interference, are also present within the system. A code selection algorithm is used to select codes which have low autocorrelation sidelobes and low cross correlation peaks. Optimal mismatched filters are designed for these codes which minimize the peak values in the autocorrelation and the cross correlation functions. An adjustment to the filter design technique produces filters with nulls in their frequency response, in addition to having low correlation peaks. The method produces good codes and filters for a four-user system with length 34 four-phase codes. There is considerable improvement in cross and autocorrelation sidelobe levels over the matched filter case with only a slight decrease in the signal-to-noise ratio (SNR) of the system. The mismatched filter design also allows the design of frequency nulls at any frequency with arbitrary null attenuation, null width, and sidelobe level, at the cost of a slight decrease in processing gain     

Adaptive digital beamforming for angle estimation in jamming

A radar digital beamforming (DBF) architecture and processing algorithm is described for nulling the signal from a mainlobe electronic jammer and multiple sidelobe electronic jammers while maintaining monopulse angle estimation accuracy on the target. The architecture consists of a sidelobe jamming (SLJ) cancelling adaptive array (AA) followed by a mainlobe jamming (MLJ) canceller. A mainlobe maintenance (MLM) technique or constrained adaptation during the sidelobe cancellation process is imposed so that the results of the SLJ cancellation process do not distort the subsequent mainlobe cancellation process. The SLJ signals and the MLJ signals are thus cancelled sequentially in separate processes. This technique was developed for improving radar processing in determining the angular location of a target, and specifically for improving the monopulse technique by maintaining the accuracy of the target echo monopulse ratio in the presence of electronic jamming by adaptive suppression of the jamming signals before forming the monopulse sum and difference beams     

A new algorithm to optimize Barker code sidelobe suppressionfilters

The authors suggest a new algorithm for binary coding waveform sidelobe reduction after matched filtering and present a general method by which optimized sidelobe suppression filters for Barker codes can be obtained with a peak output sidelobe 2.62 dB lower than the results found in the literature (for 13-b Barker code). This optimization algorithm is also promising for other binary coding waveforms, such as truncated pseudonoise (PN) sequences and concatenated codes. This new approach can readily be applied to sidelobe-reduction filter design for other binary coding waveforms, such as truncated PN sequences, concatenated codes, etc., which often find their applications in radar systems and spread spectrum communication systems     

Improving performance in pulse radar detection using neuralnetworks

A new approach using a multilayered feed forward neural network for pulse compression is presented. The 13 element Barker code was used as the signal code. In training this network, the extended Kalman filtering (EKF)-based learning algorithm which has faster convergence speed than the conventional backpropagation (BP) algorithm was used. This approach has yielded output peak signal to sidelobe ratios which are much superior to those obtained with the BP algorithm. Further, for use of this neural network for real time processing, parallel implementation of the EKF-based learning algorithm is indispensable. Therefore, parallel implementation has also been developed     

Nonlinear apodization for sidelobe control in SAR imagery

Synthetic aperture radar (SAR) imagery often requires sidelobe control, or apodization, via weighting of the frequency domain aperture. This is of particular importance when imaging scenes containing objects such as ships or buildings having very large radar cross sections. Sidelobe improvement using spectral weighting is invariably at the expense of mainlobe resolution presented here is a class of nonlinear operators which significantly reduce sidelobe levels without degrading mainlobe resolution implementation is via sequential nonlinear operations applied to complex-valued (undetected) SAR imagery. SAR imaging is used to motivate the concepts developed in this work. However, these nonlinear apodization techniques have potentially broad and far-ranging applications in antenna design, sonar, digital filtering etc., i.e., whenever data can be represented as the Fourier transform of a finite-aperture signal     

Biphase Sequence Generation with Low Sidelobe Autocorrelation Function

Since Barker-like sequences could not be found for sequence lengths greater than 13, radar system designers have been searching for biphase sequences with discrimination (ratio of the magnitude of the mainlobe to the magnitude of the peak sidelobe of the autocorrelation function of the sequence) greater than 13. We present new results on biphase Legendre sequences for all prime lengths. The results of the paper are as follows. 1) Two lemmas on the symmetric properties of the Legendre sequences are stated and using these lemmas and simple rules of modulo arithmetic, a method is suggested for generating long sequences which does not require multiplications and divisions. 2) From the properties of autocorrelation function of the cyclically shifted Legendre sequence (LS) for prime lengths, a computationally efficient method is evolved for carrying out systematic search for sequences with discrimination greater than 13. The proposed method reduces the computational load by a factor of approximately 16. Using these techniques, we generated codes up to length 1019. In each case we searched for the code which gives the maximum discrimination for that length.     

Properties of Dolph-Chebyshev Weighting Functions

Dolph-Chebyshev amplitude weighting is used with FFT signal processors and array antennas when a low sidelobe response is required. This particular weighting minimizes the width of the mainlobe response while forcing all of the sidelobes to a specified sidelobe level. As the specified sidelobe level is reduced, the mainlobe width increases, as does the loss in signal-to-noise ratio. This correspondence describes how the Dolph-Chebyshev weights may be easily calculated, and gives design data showing how signal-to-noise loss and mainlobe width vary with the specified sidelobe level.     

Sparse frequency transmit-and-receive waveform design

A computationally efficient algorithm derives complex digital transmit and receive ultra-wideband radar and communication waveforms with excellent arbitrary frequency band suppression and range sidelobe minimization. The transmit waveform minimizes a scalar function penalizing weighted spectral energy in arbitrary frequency bands. Near constant power results from another penalty function for deviations from constant power, or constant power is enforced by a phase-only formulation. Next, a least squares solution for the receive waveform minimizes a weighted sum of suppressed band spectral energy and range sidelobes (for pulse and continuous wave operation), with a mainlobe response constraint. Both waveforms are calculated by iterative algorithms whose updates require only linear order in memory and computation, permitting quick calculation of long pulses with thousands of samples.     

Improved Range Resolution Filters for Rectangular-Pulse Radar Systems

The performance of several new clutter-reduction filters suitable for rectangular-pulse radar systems is investigated. The new filters consist of various approximations and modifications of two filters known to be optimal for certain criteria: the well-known Urkowitz filter which optiizes the clutter improvement ratio, and the newer sidelobe reduction filter which minimizes output noise power subject to peak sidelobe constaints. The new filters are compared usig five basic criteria: clutter improvement ratio, signal-to-noise ratio, sidelobe peak ratio, pulse compression ratio, and filter complexity. The results are summarized in tabular and graphical form.     

Digital and Analog Subcomplementary Sequences for Pulse Compression

Golay's complementary pairing has been a method to increase the utility of binary sequences, because of the temporal sidelobe suppression in the autocorrelation vector summation. Complementary sets of Tseng and Liu and of Hollis exhibit the same effect when several autocorrelations are combined. These complementary pairs and sets of sequences can be extended into long complementary chains by a simple transformation. This transformation is extended here to all pulse compression waveforms. By this method, even though analog complementary sequences cannot be formed, a new class of waveforms, called subcomplementary waveforms, can be formed. Following these rules, repetition of waveforms such as linear frequency modulation (LFM) or linear stepped frequency modulation (LSFM) in a prescribed manner is possible without creating autocorrelation grating lobes or repetitive sidelobes. This method is equally applicable to all analog or digital pulse compression waveforms.     

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     

11位巴克码的LP滤波器及其在多普勒频移下的性能

本文介绍使最大旁瓣值最小的11位巴克码滤波器（LP滤波器）的计算结果。并介绍多普勒频移对这种滤波器性能影响。LP滤波器长度为53时,旁瓣电平降到—39.5dB,比匹配滤波器改善18.7dB。对加权序列长度L为41、45、49和53的11位巴克码的LP滤波器计算结果表明,其性能受多普勒频移的影响表现为:它们的主瓣电平下降、主瓣展宽、最小旁瓣电平上升、旁瓣电平平方和上升和信噪比损失增大。在较小的多普勒频移（f_d）时,L大的LP滤波器其性能优于L小的LP滤波器,在多普勒频移交大时,这种优势逐渐消失,不同长度LP滤波器性能大体一致。     

Efficient exhaustive search for optimal-peak-sidelobe binary codes

The work presented here describes an exhaustive search for minimum peak sidelobe level (PSL) binary codes, combining several devices for efficiency. These include combinatoric tree search techniques, the use of PSL-preserving symmetries to reduce search space, data representations and operations for fast sidelobe computation, and a partitioning scheme for parallelism. All balanced 64-bit minimum PSL codes are presented, and the upper limit on known consecutive lengths to have PSL = 4 codes is extended to 70. In addition, a technique for determining balance properties of a code for given PSL-preserving transformations is developed.