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.     

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.     

Group-Complementary Array Coding for Radar Clutter Rejection

A radar waveform design technique which utilizes Lagrange's method of multipliers to control temporal sidelobes and to reduce Doppler sidelobes is described. This classical method of constrained optimization is applied to the problem of synthesizing a radar wave-form where mismatch loss is the objective function to be minimized. The associated constraints are taken from expressions for the composite temporal sidelobes of the cross-correlation response and the peak correlation response where sets of code words are used to modulate a series of radar pulses. The resulting code sets and receiver reference sets are called group-complementary and produce a trench parallel to or on the range axis of the cross-ambiguity surface.     

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.     

Nullifying ACF grating lobes in stepped-frequency train of LFM pulses

An effective way to increase the bandwidth of a coherent pulse-train is to add a frequency step /spl Delta/f between consecutive pulses. A large /spl Delta/f implies a large total bandwidth, hence improved range resolution. However, when the product of the frequency step times the pulse-duration t/sub p/, is larger than one (t/sub p/ /spl Delta/f > 1), the autocorrelation function (ACF) of the stepped-frequency pulse-train suffers from ambiguous peaks, known as "grating lobes." It is well known that replacing the fixed-frequency pulses with linear FM (LFM) pulses of bandwidth B can reduce those grating lobes. We present a simple analytic expression for the ambiguity function (AF) and ACF of such a signal and derive from it very simple relationships between /spl Delta/f, B, and t/sub p/ that will place s exactly where the grating lobes are located, and thus remove them completely.     

Performance of a Pseudorandom Binary Phase Code with Errors and Doppler-Shifted CW

The effects that various code imperfections have on the peak of the mainlobe and on the time sidelobes of the compressed coded signal are described. The imperfections considered are finite pulse rise time, timing errors, code integration mismatch, and Doppler shift of the coded signal.     

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。     

Resolution in Doppler and Acceleration with Coherent Pulse Trains

The resolution properties and clutter performance of a simultaneous Doppler and acceleration measurement are investigated in detail with particular emphasis given to coherent pulse trains. The analysis is based on the concept of a matched-filter receiver, although receiver weighting of the type that reduces Doppler sidelobes is also analyzed in detail. Near the main lobe of the acceleration response is a pedestal-ike sidelobe region, the height of which is about 1/N of the main response lobe power where N is the number of pulses in the train. The extent of this pedestal along the acceleration axis is proportional to N. The acceleration measurement in a clutter environment is best performed when both targets and clutter are confined to this pedestal region, since some response sidelobes outside of this region are extremely large.     

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.     

Interception Algorithm of S-cubed Signal Model in Stealth Radar Equipment

Radar equipment of stealth platforms such as aircraft have adopted the newest modern technology to design the signal waveforms. One of the important and effective methods is the hybrid waveform called spread spectrum stretch (S-cubed) which combines linear frequency modulation (LFM) and discrete phase code. In order to investigate the function of enemy’s stealth radar equipment, the interception algorithm of S-cubed is needed. In this paper, a novel detection and parameter estimation approach for the reconnaissance S-cubed radar signal is presented. First, the generalized time-frequency representation of Zhao, Atlas, and Marks (ZAM-GTFR) and Hough transforms (HT) are applied to detecting the signal, and then the initial frequency and modulation slope of LFM are estimated from the ZAM-GTFR. On the basis of LFM information, the reconstructing signal is generated. Finally, the code rate of discrete phase code is extracted from the negative peaks of the ZAM-GTFR. Simulation results show that the proposed algorithm has higher estimation accuracy when the signal to noise ratio (SNR) is above 3 dB.     

一种组合型的探干一体化信号设计分析

针对雷达信号资源利用率有待提升、低截获性能不足的问题,提出 1种复合调制的创新型探干一体化信号波形。线性调频信号本身具有良好的低截获性能,伪随机码序列分量具有较好的干扰性,同时又能一定程度上扩展信号带宽,两者的复合调制信号具有良好的探测和干扰性能。对基于 LFM的探干一体化信号波形进行了调制原理分析,并分别从时域、频域、功率谱、模糊函数、自相关特性等角度分析其探测、干扰特性。仿真实验证明,相较于单一调制的线性调频信号,一体化信号具有更宽的频带、更优良的干扰特性和探测性能,同时,有更高效的雷达资源利用率。     

Doppler Compensation & Single Pulse Imaging using Adaptive Pulse Compression

The effects of target Doppler are addressed in relation to adaptive receive processing for radar pulse compression. To correct for Doppler-induced filter mismatch over a single pulse, the Doppler-compensated adaptive pulse compression (DC-APC) algorithm is presented whereby the respective Doppler shifts for large target returns are jointly estimated with the illuminated range profile and subsequently incorporated into the original APC adaptive receive filter formulation. As a result, the Doppler-mismatch-induced range sidelobes can be suppressed thereby regaining a significant portion of the sensitivity improvement that is possible when applying adaptive pulse compression (APC) without the existence of significant Doppler mismatch. In contrast, instead of compensating for Doppler mismatch, the single pulse imaging (SPI) algorithm generalizes the APC formulation for a bank of Doppler-shifted matched filters thereby producing a sidelobe-suppressed range-Doppler image from the return signal of a single radar pulse which is applicable for targets with substantial variation in Doppler. Both techniques are based on the recently proposed APC algorithm and its generalization, the multistatic adaptive pulse compression (MAPC) algorithm, which have been shown to be effective for the suppression of pulse compression range sidelobes thus dramatically increasing the sensitivity of pulse compression radar.     

Modulation Diversity for Pulse-Compressing Radars

Radars using wideband FM pulses in the same band are less likely to interfere if one of them uses linear FM and the other uses hyperbolic FM. This can be done without sacrificing Doppler tolerance and without separate software to accommodate the range-Doppler coupling.     

Radar/sonar acceleration estimation with linear-period modulatedwaveforms

Doppler and acceleration tolerance of wideband LPM/HFM (linear period-modulated, hyperbolic frequency-modulated) and linear frequency-modulated (FM) signals are compared. A bank of filters matched to frequency-shifted versions of a wideband LPM/HFM transmission system yields a joint maximum likelihood estimate of range and acceleration and avoids acceleration-induced degradation in detection performance. Analytical and neurophysiological results suggest that such processing can be used in bat echolocation for detection and classification of insect wing motion since wideband LFM waveforms are much less Doppler-tolerant than HFM waveforms but have greater acceleration tolerance     

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.     

Principle and Design of a Vernier FM Radar System

This paper describes the principle and the signal design of a proposed new FM radar system. In order to measure the surface characteristics of a small target at a long distance, or to discriminate among multiple targets, very accurate range or Doppler resolutions are necessary [1]. The proposed system satisfies the range resolution requirement by detecting the target with two different resolutions: coarse resolution for measuring range, and fine resolution for measuring the target details. The principal advantage of the system is in the vernier scale for the measurement of a distance. The system is just as easily realizable as conventional FM radar, requires no special filters in the receiver, and represents a saving in the required bandwidth for the same range resolution.     

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     

Advances in non-linear apodization

Selected new methods and applications of non-linear apodization for irregularly-shaped and parse coherent apertures and arrays are presented. The benefits include unproved impulse response performance, i.e., reduced peak sidelobes and integrated sidelobe power, along with improved mainlobe resolution, compared to classic windowing techniques. Nonlinear apodization (NLA) techniques can also serve as powerful engines for effective superresolution and bandwidth extrapolation of coherent data for filling sparse apertures. The sparse aperture filling property of superresolution algorithms for radar data forms the basis for a new concept which is introduced here: synthetic multiple aperture radar technology (SMART). Increased swath and/or reduced antenna size are some of the benefits postulated for SMART applied to synthetic aperture radar (SAR) systems. The benefits of these new methods and applications for nonlinear apodization are then demonstrated for two specific applications: 1) sidelobe control for Y-type synthetic aperture radiometers, such as the European Soil Moisture and Ocean Salinity (SMOS) system (Kerr et al.) and JPL's proposed GeoSTAR (Lambrigsten) concept; and, 2) filling of sparse synthetic aperture radar data by exploiting the bandwidth extrapolation properties of nonlinear apodization based superresolution techniques. The methods that have been developed and demonstrated herein have potential application to a wide range of passive and active microwave remote sensing and radar systems.     

Mitigating Range Ambiguity in High PRF Radar using Inter-Pulse Binary Coding

The paper proposes a way to increase the energy within a coherent processing interval (CPI) using more pulses instead of longer pulses. Long coded pulses result in masking targets at close range and poor Doppler tolerance. Increasing the number of pulses implies high pulse repetition frequency (PRF), which suffers from range ambiguity and target folding. These drawbacks of a high PRF can be mitigated by inter-pulse coding. The approach suggested here should be attractive for close and mid range applications of radar, ground penetrating radar, ultrasound imaging, and more.     

机载调频无线电高度表敏感特性分析

在国际国内频谱资源有限性、稀缺性日益凸显的大背景下,多种业务共用频段已是必然。通过试验和仿真分析方法研究机载调频无线电高度表对雷达脉冲信号的敏感特性,期望实现二者的同频段共用。研究结果表明,处于同一频段的雷达脉冲信号会对机载调频无线电高度表产生有害干扰,雷达脉冲信号会影响高度表指示,使高度表示值不断增大直至满刻度,从而危及飞行安全。