Designing Unimodular Sequence Sets With Good Correlations—Including an Application to MIMO Radar

A multiple-input multiple-output (MIMO) radar system that transmits orthogonal waveforms via its antennas can achieve a greatly increased virtual aperture compared with its phased-array counterpart. This increased virtual aperture enables many of the MIMO radar advantages, including enhanced parameter identifiability and improved resolution. Practical radar requirements such as unit peak-to-average power ratio and range compression dictate that we use MIMO radar waveforms that have constant modulus and good auto- and cross-correlation properties. We present in this paper new computationally efficient cyclic algorithms for MIMO radar waveform synthesis. These algorithms can be used for the design of unimodular MIMO sequences that have very low auto- and cross-correlation sidelobes in a specified lag interval, and of very long sequences that could hardly be handled by other algorithms previously suggested in the literature. A number of examples are provided to demonstrate the performances of the new waveform synthesis algorithms.     

Range Compression and Waveform Optimization for MIMO Radar: A CramÉr–Rao Bound Based Study

A multi-input multi-output (MIMO) radar system, unlike standard phased-array radar, can transmit via its antennas multiple probing signals that may be correlated or uncorrelated with each other. This waveform diversity offered by MIMO radar enables superior capabilities compared with a standard phased-array radar. One of the common practices in radar has been range compression. We first address the question of ldquoto compress or not to compressrdquo by considering both the Cramer-Rao bound (CRB) and the sufficient statistic for parameter estimation. Next, we consider MIMO radar waveform optimization for parameter estimation for the general case of multiple targets in the presence of spatially colored interference and noise. We optimize the probing signal vector of a MIMO radar system by considering several design criteria, including minimizing the trace, determinant, and the largest eigenvalue of the CRB matrix. We also consider waveform optimization by minimizing the CRB of one of the target angles only or one of the target amplitudes only. Numerical examples are provided to demonstrate the effectiveness of the approaches we consider herein.     

集中式MIMO雷达研究综述

多输入多输出(MIMO)雷达作为一种新体制雷达,利用其发射波形分集的特点,在目标检测、参数估计、射频隐身及抗干扰等诸多方面展现出了突出的性能,经过学者们近20年的深入研究,基于正交波形的MIMO雷达相关理论日臻完善,并在汽车辅助驾驶、安全防卫等领域得到广泛应用。近年来,随着电磁环境感知及知识辅助等概念的引入,基于波形优化的MIMO雷达主动抗干扰、射频隐身、以及探测-通信一体化等技术受到学者们的关注并得到深入研究。该文力图对学者们近20年来围绕MIMO雷达的研究工作进行归纳与综述,内容主要包括:正交波形MIMO雷达原理、目标探测性能分析、典型应用;正交波形MIMO雷达波形设计与特点;基于知识的认知MIMO波形设计与算法;基于MIMO的探测-通信一体化波形设计与算法;MIMO雷达信号处理、数据处理及资源管理。论文最后对MIMO雷达在机载应用中的空时处理(STAP)、MIMO雷达在成像中的信号处理、以及基于时分多波形分集的线性调频毫米波MIMO雷达信号处理等进行了讨论。      

面向频谱共存的MIMO雷达波形设计综述

多输入多输出（multiple-input multiple-output, MIMO）雷达良好的空间分集和波形分集能力使其在目标检测和参数估计等方面有着传统雷达无法比拟的突出优势。然而,随着信息技术的快速发展,雷达和通信系统对频谱资源的需求日益增长。频谱资源稀缺导致雷达和通信系统势必出现竞争频谱资源的问题,进而使得二者相互干扰并导致性能下降。针对面向频谱共存的MIMO雷达波形设计问题,介绍了MIMO雷达的基本概念、信号模型以及信号处理任务,对MIMO雷达波形设计问题的一般形式,以及面向典型应用场景的波形设计问题进行了概述。为通过发射波形设计提高MIMO雷达在频谱拥塞环境中的性能,对频谱约束下的MIMO雷达波形设计、MIMO雷达与通信系统协同设计和雷达通信一体化等领域的研究进展进行了系统的评述和总结,并展望了下一步的研究方向。     

MIMO Radar with Colocated Antennas

We have provided a review of some recent results on the emerging technology of MIMO radar with colocated antennas. We have shown that the waveform diversity offered by such a MIMO radar system enables significant superiority over its phased-array counterpart, including much improved parameter identifiability, direct applicability of adaptive techniques for parameter estimation, as well as superior flexibility of transmit beampattern designs. We hope that this overview of our recent results on the MIMO radar, along with the related results obtained by our colleagues, will stimulate the interest deserved by this topic in both academia and government agencies as well as industry.     

Additional degree of freedom in phased-MIMO radar signal design using space-time codes

In this paper, an additional degree of freedom in phased multi-input multi-output (phased-MIMO) radar with any arbitrary desired covariance matrix is proposed using space-time codes. By using the proposed method, any desired transmit covariance matrix in MIMO radar (phased-MIMO radars) can be realized by employing fully correlated base waveforms such as phased-array radars and simply extending them to different time slots with predesigned phases and amplitudes. In the proposed method, the transmit covariance matrix depends on the base waveform and space-time codes. For simplicity, a base waveform can be selected arbitrarily (ie, all base waveforms can be fully correlated, similar to phased-array radars). Therefore, any desired covariance matrix can be achieved by using a very simple phased-array structure and space-time code in the transmitter. The main advantage of the proposed scheme is that it does not require diverse uncorrelated waveforms. This considerably reduces transmitter hardware and software complexity and cost. One the receiver side, multiple signals can be analyzed jointly in the time and space domains to improve the signal-to-interference-plus-noise ratio.     

基于量子遗传算法的MIMO雷达正交信号波形设计

正交信号波形设计是MIMO雷达领域的研究热点,随着技术的发展,MIMO雷达对正交信号波形的性能要求越来越高。针对现有MIMO雷达正交信号波形互相关峰值较高且算法收敛速度慢的问题,为了提高码长较长的正交信号波形的性能,本文使用量子遗传算法,将量子计算与遗传算法相结合,进一步降低了波形的互相关峰值,一方面降低了不同目标回波之间的相互干扰,提高了雷达系统的检测性能,另一方面使雷达系统更难被敌方定位,提高了雷达的战场生存能力。仿真试验的结果表明,该方法能有效提高波形的正交性能,并加快了优化的速度。      

MIMO Radar Ambiguity Properties and Optimization Using Frequency-Hopping Waveforms

The concept of multiple-input multiple-output (MIMO) radars has drawn considerable attention recently. Unlike the traditional single-input multiple-output (SIMO) radar which emits coherent waveforms to form a focused beam, the MIMO radar can transmit orthogonal (or incoherent) waveforms. These waveforms can be used to increase the system spatial resolution. The waveforms also affect the range and Doppler resolution. In traditional (SIMO) radars, the ambiguity function of the transmitted pulse characterizes the compromise between range and Doppler resolutions. It is a major tool for studying and analyzing radar signals. Recently, the idea of ambiguity function has been extended to the case of MIMO radar. In this paper, some mathematical properties of the MIMO radar ambiguity function are first derived. These properties provide some insights into the MIMO radar waveform design. Then a new algorithm for designing the orthogonal frequency-hopping waveforms is proposed. This algorithm reduces the sidelobes in the corresponding MIMO radar ambiguity function and makes the energy of the ambiguity function spread evenly in the range and angular dimensions.      

MIMO Radar Waveform Constraints for GMTI

Ground moving-target indication (GMTI) provides both an opportunity and challenge for coherent multiple-input multiple-output (MIMO) radar. MIMO techniques can improve a radar's angle estimation and the minimum detectable velocity (MDV) for a target. However, the challenge of clutter mitigation places significant constraints on MIMO radar waveforms. In this paper, the loss of target return because of clutter mitigation (signal-to-noise ratio (SNR) loss) is the driving performance metric. The ideal, orthogonal repeated-pulse waveform is shown not to exist. Pulse-to-pulse time-varying waveforms, such as Doppler-division multiple access (DDMA), are shown to offer SNR loss performance approaching ideal MIMO systems.      

基于MIMO阵列的一体化射频技术研究进展及展望

基于多输入多输出（multiple-input-multiple-output， MIMO）阵列的一体化射频系统通过充分利用空间自由度和波形自由度，不仅能够同时实现雷达探测、数据通信、电子干扰等多种功能，而且具有目标探测可靠性好、参数估计精确度高、反侦察识别能力强等突出特点，在高动态强对抗环境中展现了巨大的潜力。从基于MIMO阵列的一体化射频系统的检测性能分析入手，剖析了一体化射频系统的检测性能极限以及影响检测性能的主要因素；针对MIMO阵列参数高精度估计问题，提出通过单个发射脉冲完成参数估计以及一种增强参数估计精度的波形优化算法；考虑到目标角度估计误差不可避免，提出了一种稳健的一体化波形设计算法；针对杂波环境中一体化射频系统性能下降的问题，提出了发射波形和接收滤波器联合优化算法，该算法不仅能够实现同时多功能，而且有效地抑制了杂波，提高了目标检测性能。最后，展望了一体化射频系统参数估计精度极限、高精度参数估计、稳健波形设计、波形设计算法快速实现等有待突破的信号处理关键技术。     

MIMO Radar Waveform Optimization With Prior Information of the Extended Target and Clutter

The concept of multiple-input multiple-output (MIMO) radar allows each transmitting antenna element to transmit an arbitrary waveform. This provides extra degrees of freedom compared to the traditional transmit beamforming approach. It has been shown in the recent literature that MIMO radar systems have many advantages. In this paper, we consider the joint optimization of waveforms and receiving filters in the MIMO radar for the case of extended target in clutter. A novel iterative algorithm is proposed to optimize the waveforms and receiving filters such that the detection performance can be maximized. The corresponding iterative algorithms are also developed for the case where only the statistics or the uncertainty set of the target impulse response is available. These algorithms guarantee that the SINR performance improves in each iteration step. Numerical results show that the proposed methods have better SINR performance than existing design methods.      

集中式MIMO雷达研究进展：正交波形设计与信号处理

集中式多输入多输出（Multiple Input Multiple Output,MIMO）雷达通常利用正交波形增加发射波形自由度,采用数字阵列拓展空间收发自由度,使得雷达接收机的天线孔径获得明显扩展,最终带来空间分辨率、测角精确度、杂波抑制能力等大幅度提升。但是,这些性能提升的前提是发射波形具有正交特性。事实上,在实际应用中,在不牺牲时域/频域资源情况下,受限于时宽带宽积,无法获得完全正交的波形集合,从而限制了MIMO雷达系统性能。本文对集中式MIMO雷达正交波形复用的技术原理进行了系统回顾,分别归纳了三种快时间发射波形设计方法：时分复用（Time Division Multiplexing, TDM）、码分复用（Code Division Multiplexing,CDM）和频分复用 （Frequency Division Multiplexing, FDM）,以及两种慢时间发射波形设计方法：多普勒分复用（Doppler Division Multiplexing,DDM）和随机相位编码波形,并对其优缺点进行对比。同时,对快时间MIMO和慢时间MIMO的信号处理流程进行归纳综合,给出基于匹配滤波的集中式MIMO雷达统一信号处理框架。为了展示不同波形对成像性能的影响,本文给出了基于三维匹配滤波的MIMO雷达成像结果。最后,结合实际应用问题,指出当前MIMO雷达面临的技术难点和发展趋势。     

MIMO雷达正交混沌调频波形集设计

正交波形设计是实现MIMO雷达的关键技术之一,目前正交波形设计方法主要多采用统计优化算法,如模拟退火、遗传算法等,此类方法主要缺点是算法耗时长、效率低,且所设计的波形集性能随着波形个数的增加而下降,针对此问题,提出一种基于混沌调频的MIMO雷达正交波形集设计方法,采用混沌调频信号作为MIMO雷达的发射波形,利用混沌序列良好的统计特性,无需寻优处理即可得到性能优越的正交波形集,且理论上可以得到任意数目的波形而不损失波形集性能,因此,该方法在算法效率和波形多样性方面具有优势,计算机仿真实验验证了设计方法的有效性。      

调频连续波MIMO雷达OFDM波形设计

对于多输入多输出调频连续波雷达,正交波形设计是其最关键的技术之一。传统频分波形采用频率调制方法,使得各信号在频域上互不重叠,通过带通滤波实现多通道分解,该方法信号带宽大、系统复杂,且由于采用带通滤波,信号相干性差。因此针对调频连续波雷达,本文提出了一种新的正交波形设计方法。该方法基于正交频分复用原理,一个信号周期包含M个线性扫频周期,其中M为正交信号个数,去调频接收后,作快时间离散傅里叶变换,通过多相分解实现信号分解。该方法不需要带通滤波,信号相干性好、带宽窄、系统简单。论文最后,通过仿真实验验证了波形设计的正确性和有效性。      

基于交替方向惩罚法的低精度量化MIMO雷达恒模波形设计方法

在MIMO雷达中配备大量有源天线单元可以获得优异的波束形成性能,但会导致系统能耗大、电路复杂及成本高等问题。采用低精度的DAC组件可有效克服上述问题,但现有基于无限精度DAC条件所设计的MIMO雷达波形往往难以直接适用于低精度DAC系统。为此,该文提出了一种离散相位约束下基于最小化积分副主瓣比的低精度量化MIMO雷达恒模波形设计方法。该方法首先采用丁克尔巴赫(Dinkelbach)算法将目标函数二次分数形式转换成减法形式,再利用交替方向惩罚法求解非凸恒模离散相位约束问题。最后通过数值仿真与其他方法进行对比,分析了所提方法的发射方向图与积分副主瓣比性能,验证了该方法的有效性。      

Spatial diversity in radars-models and detection performance

Inspired by recent advances in multiple-input multiple-output (MIMO) communications, this proposal introduces the statistical MIMO radar concept. To the authors' knowledge, this is the first time that the statistical MIMO is being proposed for radar. The fundamental difference between statistical MIMO and other radar array systems is that the latter seek to maximize the coherent processing gain, while statistical MIMO radar capitalizes on the diversity of target scattering to improve radar performance. Coherent processing is made possible by highly correlated signals at the receiver array, whereas in statistical MIMO radar, the signals received by the array elements are uncorrelated. Radar targets generally consist of many small elemental scatterers that are fused by the radar waveform and the processing at the receiver, to result in echoes with fluctuating amplitude and phase. It is well known that in conventional radar, slow fluctuations of the target radar cross section (RCS) result in target fades that degrade radar performance. By spacing the antenna elements at the transmitter and at the receiver such that the target angular spread is manifested, the MIMO radar can exploit the spatial diversity of target scatterers opening the way to a variety of new techniques that can improve radar performance. This paper focuses on the application of the target spatial diversity to improve detection performance. The optimal detector in the Neyman-Pearson sense is developed and analyzed for the statistical MIMO radar. It is shown that the optimal detector consists of noncoherent processing of the receiver sensors' outputs and that for cases of practical interest, detection performance is superior to that obtained through coherent processing. An optimal detector invariant to the signal and noise levels is also developed and analyzed. In this case as well, statistical MIMO radar provides great improvements over other types of array radars.     

非完备杂波先验知识场景下MIMO-STAP稳健波形设计

本文考虑了色高斯干扰条件下MIMO STAP稳健波形优化问题以提高非完备杂波先验知识条件下多输入多输出（MIMO）雷达体制下空时自适应处理（STAP）最坏情况下探测性能。由于高斯干扰（包括杂波、干扰以及热噪声）场景下最大化系统输出信干噪比（SINR）等价于最大化MIMO STAP检测性能,因而在本文所建立杂波协方差估计误差的模型基础上,总功率发射以及参数不确定凸集约束下,经推导可得稳健波形优化问题。为求解得到的复杂非线性问题,本文提出了一种迭代算法以优化发射波形相关阵（WCM）从而最大化凸不确定集上最差情况下的输出SINR进而改善最差情况下MIMO STAP的检测性能。通过利用对角加载（DL）方法,所提算法中的每个迭代步骤皆可表示为能获得高效求解的半定规划（SDP）问题。与非稳健方法及非相关波形相比,数值实验验证了本文所提方法的有效性。      

MIMO天波雷达波形综合分析与改进

针对天波雷达应用背景及实际需求,详细分析了多输入-多输出(Multiple-Input Multiple-Output,MIMO)天波雷达波形设计问题,对典型MIMO天波雷达波形的优缺点和适用探测任务进行了综合比较,并得出了部分波形之间的关系。为改善已有波形在多普勒容限、速度模糊和频率限制,提出了一种慢时间随机相位编码波形。相关结论和改进措施为MIMO天波超视距雷达信号理论研究、工程实现提供了参考。     

MIMO雷达相位编码波形集相关函数下界综述

MIMO雷达波形集的互相关函数峰值越低，则正交性越好，波形分集增益越高。非循环互相关函数下界的研究有助于确定波形分集增益的极限值，对MIMO雷达波形设计与应用有重要意义。相位编码波形集是目前被研究最多的MIMO雷达波形集，对其相关函数下界的研究较为深入。本文对目前相位编码波形集相关函数各类下界的研究进行归纳总结，包括相关函数峰值旁瓣下界、相关函数积分旁瓣下界、互相关内积下界、互补序列相关函数下界四大类。相关函数峰值旁瓣下界是影响MIMO雷达波形分集增益的关键指标，其他类型的下界与相关函数峰值旁瓣下界之间存在潜在联系，这可能有助于相关函数峰值旁瓣下界的确定。不同波形数，不同码长的典型相位编码波形相关函数指标与下界的对比结果表明，目前已有下界都不够紧，尤其在波形数较多时。因此，MIMO雷达相位编码波形集相关函数下界仍是一个值得研究的开放问题。      

基于线性调频时宽的MIMO雷达正交波形设计

线性调频(LFM)信号是一种被广泛应用的大时宽带宽积信号,利用LFM信号的多样性可设计多输入多输出(MIMO)雷达的正交波形。该文针对现有波形相关函数存在的问题,以理论分析为基础,提出一种基于LFM时宽的发射波形,并给出了一种相应的正交波形设计方法。该方法以峰值旁瓣电平为准则,利用序列二次规划对各子脉冲LFM信号的时宽进行优化设计。仿真结果表明,与现有方法相比,所设计波形具有较低的自相关旁瓣电平和互相关电平。此外,通过数值实验分析了相关性能随波形个数及子脉冲个数的变化关系。