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.     

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     

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.     

Performance of phased-array antennas with mechanical errors

The performance of planar phase-array antennas with mechanical errors is investigated. Errors in array element positions as a result of structural distortions are considered as deterministic and predictable. Detailed calculations for two assumed modes of distortion reveal that their effects on antenna performance are the loss of peak response in the scan direction and the broadening of the mainlobe, while the far-out sidelobe structure remains relatively intact. For large antennas, performance improvement can be expected by suitable phase compensation. Performance of antennas with random errors in their element positions must be treated statistically. Expressions of average directivity and sidelobe level corresponding to arbitrary error magnitudes in element position, amplitude and phase of excitation as well as finite rate of failure of element modules were derived and verified by direct numerical calculations from the antenna directivity patterns. For a planar phased-array antenna typical for space-based radars, the standard deviation of element position errors must not exceed 1% of the operating wavelength in order to maintain a -10 dBi sidelobe level     

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     

Mismatched Filtering of Sonar Signals

A replica correlator (matched filter) is an optimum processor for a receiver employing a pulse of continuous wave (CW) signal in a white Gaussian noise background. In an active sonar, however, when the target of interest has low Doppler shift and is embedded in a high reverberation background, this is not so. High sidelobes of the correlator frequency response pass a significant portion of the signal contained in the mainlobe of the reverberation spectrum. In order to reduce the sidelobes of the correlator output spectrum and at the same time keep the increase in its 3 dB bandwidth to a small amount, we propose lengthening of the replica of the transmitted signal and weighting it by a Kaiser window. It is demonstrated that by extending the weighted replica by 50 percent compared with the transmitted signal, it is possible to reduce the sidelobe levels to at least 40 dB below the mainlobe peak, with the concomitant increase of the 3 dB band-width by less than 5 percent. The degradation in signal-to-noise ratio (SNR) performance for such a ?mismatched? filter receiver with respect to the matched filter is less than 1.5 dB.     

Generalized Response of a Linear FM Pulse Compression Matched Filter

A pulse compression matched filter is analyzed so that the response may be computed when the pulse width, FM rate, and center frequency simultaneously differ from design conditions. Unilateral and bilateral time domain amplitude weighting for sidelobe reduction is included. A general cross-ambiguity function is defined to include these effects and some basic computed results are presented for the peak envelope response with various degrees of Hamming weighting. Computer evaluation of this cross-ambiguity function allows one to choose a combination of mismatches for signal design trade-off between resolution and detection performance. Since no restrictions are placed upon the mismatch parameters, this analysis may also be used to evaluate the filter discrimination against various interfering signals.     

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。     

Doppler Processor Rejection of Range Ambiguous Clutter

Doppler processors are used in radar to separate target returns from clutter. When the clutter is at a range farther than the unambiguous range of the radar, the ability to reject the clutter is degraded. In this article the degradation is analyzed for an N-pulse batch processor with Dolph weighting, and the results show how degradation varies with design sidelobe level.     

Removing autocorrelation sidelobes by overlaying orthogonal coding on any train of identical pulses

A coherent train of identical linear FM (LFM) pulses is used extensively in radar because of its good range and Doppler resolution. Its relatively high autocorrelation function (ACF) sidelobes are sometimes reduced through spectrum shaping (e.g., nonlinear FM, or intrapulse weighting on receive). We show how to completely remove most of the ACF sidelobes about the mainlobe peak, without any increase to the mainlobe width, by diversifying the pulses through overlaying them with orthonormal coding. A helpful byproduct of this design is reduced ACF recurrent lobes. The overlaid signal also results in reduced Doppler tolerance, which can be considered as a drawback for some applications. The method is applied to several trains of identical pulses (LFM and others) using several orthonormal codes. The effect on the three important properties of the radar signal: ACF, ambiguity function (AY), and frequency spectrum is presented. The effect on Doppler tolerance is studied, and implementation issues are discussed. The new design is also compared with complementary and sub-complementary pulse trains and is shown to be superior in many aspects.     

Clutter Suppression by Complex Weighting of Coherent Pulse Trains

Uniform coherent pulse trains offer a practical solution to the problem of designing a radar signal possessing both high range and range-rate resolution. The Doppler sensitivity provides some rejection of off-Doppler (clutter) returns in the matched filter receiver. This paper considers the use of a processor in which members of the received pulse train are selectively weighted in amplitude and phase to improve clutter suppression. The techniques described are particularly suitable for rejecting interference entering the processor through ambiguous responses (range sidelobes) of the signal. The complex weights which are derived are optimum in the sense that they produce the maximum clutter suppression for a given detection efficiency. In determining these weights, it is assumed that the distribution of clutter in range and range rate relative to targets of interest is known. Thus, clutter suppression is achieved by reducing the sidelobe levels in specified regions of the receiver response. These techniques are directly applicable to array antennas; the analogous antenna problem would be to reduce sidelobe levels in a particular sector while preserving gain. Complex weighting is most successful when the clutter is limited in both range and velocity.     

Adaptive resolution of mainlobe and sidelobe detections using model order determination

This work presents the development and performance evaluation of a methodology for distinguishing between mainlobe and sidelobe detections that arise in adaptive radar systems operating in adverse environments. Various adaptive detection test statistics such as the adaptive matched filter (AMF), the generalized likelihood ratio test (GLRT), and adaptive coherence estimate (ACE), and combinations of these, have been previously analyzed with respect to their sidelobe rejection capabilities. In contrast to these methods which are based on detecting a single target with known direction and Doppler, the present method uses model order determination techniques applied to the AMF or GLRT data observed over the range of unknown angle and Doppler parameters. The determination of model order, i.e., the number of signals present in the data, is made by using least-squares model fit error residuals and applying the Akaike Information Criterion (AIC). Comprehensive computer simulation results are presented which demonstrate substantial improvement in sidelobe rejection performance and detections of multiple sources compared with previous methods.     

Robust SVA method for every sampling rate condition

Linear apodization, or data weighting, is the traditional procedure to improve sidelobe levels in a finite sampled signal at the expense of resolution. New apodization methods, such as spatially variant apodization (SVA), apply nonlinear filtering to the signal in order to completely remove sidelobes without any loss of resolution. However, the results are strongly influenced by signal sampling rate. Some variations which improve results have been previously published, but sidelobe cancellation gets worse since sampling frequency is not settled at Nyquist (or a multiple). This paper presents a new and efficient technique based on SVA that drastically reduces sidelobe levels for every sampling rate condition. The algorithm is, essentially, a parameter optimization of a variant filter for each pixel of the image. A one-dimensional case and a two-dimensional generalization are presented, as well as some applications to target detection capability in a synthetic aperture radar (SAR) system.     

Clutter Performance of Coherent Pulse Trains for Targets with Range Acceleration

The clutter performance of coherent pulse trains is examined when the duration of the pulse train is increased to values for which range acceleration effects must be taken into account. The problem of target detection against a clutter background with differential Doppler is studied in terms of the range acceleration effects on the conventional Doppler response. Specifically considered are the consequences on the sidelobe level and width of the main Doppler lobe. The analysis shows that the sidelobe level remains essentially unchanged when the range acceleration mismatch becomes significant. However, the main Doppler response broadens in proportion to the magnitude of the acceleration mismatch. Thus, an increase of the signal duration for better Doppler resolution is useful only until acceleration effects spread the Doppler spectrum of the clutter and eliminate the differential Doppler between targets and clutter.     

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.     

两种自适应方向图峰值副瓣控制方法比较

自适应阵列（或称自适应波束形成）目前已广泛应用到雷达、声纳和通信领域中用来抑制各种干扰（有意的干扰，杂波干扰和多用户干扰等）。在雷达应用中，为了减轻脉冲欺骗式干扰或旁瓣目标并利用单脉冲雷达来准确测量目标波达方向．要求自适应方向图具有低副瓣和稳定的主瓣形状。在实际应用中，各种失配误差将降低自适应阵列的性能．这些误差包括由于目标的波达方向不精确引起的信号指向误差，由通道失配和位置扰动引起的阵列校准误差和由小样本教引起的协方差矩阵估计误差。在此情况下，自适应波束形成的性能大大下降（干扰抑制性能变差。主瓣失真和高的副瓣）。已提出了一种基于二次约束的集成峰值副瓣控制（integrated peak sidelobe control，简称IPSC）方法。该方法可以精确地控制峰值副瓣电平并产生具有稳定的主瓣形状的自适应方向图。研究IPSC中目标信号的影响和信号消除方案以进一步提高IPSC的性能。并将IPSC方法和最新提出的基于二阶锥规划（second-order cone programming，简称SOCP）的分布式峰值副瓣控制（distfibuted peak sidelobe control，简称为DPSC）新方法在性能上进行了比较。仿真结果表明。在干扰抑制性能和方向图控制质量方面IPSC比DPSC性能优越。此外IPSC比DPSC计算高效。     

Matched-Filter Responses of the Linear FM Waveform

Although the properties of the linear FM signal have been studied previously in considerable detail, such studies have involved rather narrow aspects of the theory. This paper extends the work in several respects. By presenting three-dimensional projections of the conventional ambiguity function of the linear FM signal in more detail than was available before, we can study the sidelobe behavior off as well as on the axes, without weighting, with unilateral weighting in the receiver, and with bilateral weighting. These plots reveal interesting properties related to the signal symmetry in time and frequency. The matched-filter response is then extended to include Doppler distortions of the modulation function. The results show that Woodward's ambiguity function is valid only for signals with relatively modest sophistication, even though in most practical situations one is interested only in those undistorted parts of the matched-filter response in the vicinity of the delay axis. Plots of the response are presented for various degrees of distortion, for signals with and without weighting. Lastly, we consider the effects of a mismatch in range acceleration, again for the various cases of interest. The results convey a thorough insight into the properties of chirp radar under a broad range of operational conditions.     

Jamming Susceptibility

Generalized equations are developed to evaluate the effects of interference upon communications systems. Interference may be due to natural causes and accidental or sophisticated jamming. One- and two-way communication systems are considered. The equations are applicable to near and deep space communication links as well as radar in both friendly and unfriendly environments. Both mainlobe and sidelobe reception and collocated and diversely located interference and signal sources may be analyzed. A practical discussion for each of the variables, as well as a sample solution, is included.     

Some Results on Digital Chirp

Generating chirp waveforms by means of phase coding yields a simple, cost-effective mechanization. The coding process, however, introduces phase errors whose effect must be included in the design. An approximate analysis is presented, valid for moderate to high compression ratios, which allows error effects on compressed pulse amplitude and sidelobes to be calculated in a simple manner. The anaylsis provides criteria for selecting the coding bit width (sample rate), weighting network bandwidth, and phase-coder quantization interval and transition times. Weighting functions for maximizing the signal-to-noise ratio (SNR) or for producing desired close-in sidelobe performance are derived, as is an exact expression for the transmitted spectrum. Numerical results are presented for Gaussian and the maximum-SNR weighting. The results indicate that performance will be satisfactory for many applications.     

Design of Broadband Circular Sonar Arrays Using Linear Programming

The design of a circular acoustic array with uniformly spaced elements is carried out using linear programming. The size of the linear program to be solved is reduced by imposing symmetry conditions on the complex element weights. The cost function used minimizes the beamwidth over a range of frequencies for a specified maximum sidelobe level.