Ambiguity Function Analysis for Orthogonal-LFM Waveform Based Multistatic Radar

Recent progress in bistatic radar techniques can be used to improve performances of classical monostatic radar. A prominent limitation of coherent radar is its inability to measure the complete velocity vector (magnitude and direction) of a detected target. A single coherent detection can provide range-rate only. At least two detections, separated in time, are needed to estimate the target's velocity vector. This study discusses how the velocity vector can be determined by two simultaneous detections spaced in distance. The second detection is obtained by an auxiliary distant bistatic coherent receiver; an approach proposed in the 1990s to enhance meteorological radar. Being a very simple case of a distributed radar system allows for a simple demonstration of how to calculate the target's position and velocity vector and how to analyse the estimation accuracy, including geometric dilution of precision plots of the velocity error. Also discussed are two methods to identify correct data association when more than one target is detected.

This article addresses the problem of radar waveform design for imaging targets in a cluttered environment. A multistatic radar scenario is considered for sparse and random sensor positions. The target impulse response is modeled using the simulated frequency response of a buried metallic mine, and the clutter is modeled using the compound Gaussian (CG) distribution. We explore novel waveform design techniques with respect to the mutual information (MI) criterion based on the CG clutter. The first method presents a waveform that exploits the CG distribution of the scene reflectivity function when projected onto a sparse basis. This is compared to the second method, called the target-specific approach that uses knowledge of the target and clutter frequency responses to optimize a matched illumination waveform. In both cases, the Taguchi and particle swarm optimization solvers are employed for MI-based waveform design optimization. To validate and compare the effectiveness of the optimized waveforms, the resulting scene reflectivity function is estimated using the sparsity-driven regularization radar imaging method. Our experimental results demonstrate that both waveform optimization techniques result in significantly better image reconstruction performance than the traditional linear-frequency-modulated waveform, and that the target-specific approach additionally suppresses clutter information in the scene.

Multiple-input multiple-output radar waveform diversity design has received much attention, but many of existing waveforms are lack of a large time-bandwidth product. This paper proposes an orthogonal frequency division multiplexing (OFDM) chirp waveform diversity design scheme to generate four waveforms with good correlation properties, ambiguity performance and Doppler tolerance. The method jointly utilizes classic chirp waveform and OFDM to conduct multi-carrier modulation. This scheme enables us to exploit full bandwidth for each waveform and thus has an high frequency utilization efficiency. The modulation and demodulation of the four OFDM chirp waveforms are presented. The performance of the designed waveforms is analyzed by the correlation and ambiguity functions. Simulation results validate that our proposal can generate more orthogonal waveforms without significant performance degradation.

We consider waveform design for colocated multiple-input, multiple-output (MIMO) radar systems where the signal phase is subject to random phase perturbations during propagation. We formulate an iterative algorithm to obtain both waveform parameters and the space-time adaptive weights to maximize the signal-to-interference-plus-noise ratio (SINR). We ensure that the impact of the chosen waveforms on the interference signal is accounted for when modeling the second-order interference statistics. The waveform design technique is then extended to include peak-to-average power constraints. An example of a clutter and target model is provided to show how the optimal waveform design improves radar detection performance in the presence of the signal phase randomization.

We develop new fast and efficient algorithms for designing single or multiple unimodular waveforms with good auto- and cross-correlation or weighted correlation properties, which are highly desired in radar and communication systems. The waveform design is based on the minimization of the integrated sidelobe level (ISL) and weighted ISL (WISL) of waveforms. As the corresponding problems can quickly grow to a large scale with increasing the code length and the number of waveforms, the main issue turns to be the development of fast large-scale optimization techniques. The difficulty is also that the corresponding optimization problems are nonconvex, but the required accuracy is high. Therefore, we formulate the ISL and WISL minimization problems as nonconvex quartic optimization problems in frequency domain, and then simplify them into quadratic problems via majorization-minimization technique, which is one of the basic techniques for addressing large-scale and/or nonconvex optimization problems. While designing our fast algorithms, we explore and use the inherent algebraic structures in objective functions to rewrite them into quartic forms, and in the case of WISL minimization, to derive additionally an alternative quartic form that allows us to apply the quartic-quadratic transformation. Our algorithms are applicable to large-scale unimodular waveform design problems as they are proved to have lower or comparable computational burden (analyzed theoretically) and faster convergence speed (confirmed by comprehensive simulations) than the state-of-the-art algorithms. In addition, the waveforms designed by our algorithms demonstrate better correlation properties compared to their counterparts.

In the field of target detection and tracking, the resolvability of multiple closely located targets is a significant criterion for measuring the sensing ability of radar and other sensing systems. This paper considers the problem of adaptive radar waveform design to maximize the practical resolvability of closely located targets. Conventional ambiguity function (AF)-based radar resolution considers only the waveform, regardless of the influence of noise. However, noise grreatly influences the achievable resolution as well as radar detection and tracking performance. As a result of this deficiency in conventional radar resolution, Kullback-Leibler Divergence (KLD) is introduced in this paper in order to quantify the “distance” between two probability density functions (PDFs) of radar measurements, and thus to represent practical radar resolution, which includes not only the effect of the waveform but also the signal-to-noise ratio (SNR) and measurement model. Consequently, a new adaptive radar waveform design criterion is proposed, which aims to maximize the practical radar resolution. Simulation results show the effectiveness of the proposed adaptive waveform design method.

Integrated sidelobe level(ISL) criterion and the maximal sidelobe level(MSL) criterion are used to design frequency-hopping waveforms based on ambiguity functions respectively in this paper. Some simulation results are given and analyzed. The performance of the proposed algorithm is validated by numerical simulations. Frequency-hopping coding is a kind of orthogonal signals which can be used in radar and sonar systems. And frequency- hopping coding such as Costas arrays (1, 2) has good autocorrelation property. However, for radar and sonar systems, their properties of ambiguity function are mainly considered. In this paper, frequency-hopping waveforms are designed based on ambiguity functions. The results are achieved by minimizing two cost functions which measure the integrated sidelobe level(ISL) and the maximal sidelobe level(MSL) of the autocorrelation function respectively. In this paper, cost functions are defined based on ISL criterion and MSL criterion respectively, and some results are achieved based on genetic algorithm. The remainder of this paper is organized as follows. Section Ⅱ presents the ambiguity function of frequency-hopping waveforms and cost functions designed in this paper, and formulates the problem of designing frequency-hopping waveforms. In section Ⅲ, we introduce the genetic algorithm to optimize frequency-hopping waveforms sets. And design results and their curves of ambiguity functions are presented in Section Ⅳ. Finally, some conclusions are drawn in section Ⅴ.

Match filter is one of the important parts of radar receiver. By using of Match Filter, the signal to noise ratio can be maximized so that the probability of detection is increased. Match Filter can be used as a pulse compression filter in radar receiver. Binary phase code is one of the pulse compression methods that, the compression can be down with a Match Filter in the receiver. Doppler effect is one of the problems that degrade the performance of Match Filter. In this paper, two methods “Mixer Array” and “Segmented Match Filter” are proposed for Doppler compensation. The operation of these two methods as Doppler compensation techniques are considered theoretically. The simulation is used to demonstrate the Doppler compensation performance of new techniques compared to conventional methods.

Target vibration introduces unexpected vibration phases in the echo signal of inverse synthetic aperture LADAR (ISAL). The vibration phases cause the imaging results to be defocused. How to estimate the vibration phases has always been one of the difficulties in ISAL imaging, and there has not been an effective solution. In this paper, two methods are proposed to estimate the vibration phases in different situations. The method based on multi-channel along-track interferometry (MCATI method) is for some cases that the target velocity vector is parallel to some baselines of ISAL. The method based on orthogonal interferometry (OI method) is for other cases that the target velocity vector is not parallel to any baseline of ISAL. In addition, a high signal to noise ratio (SNR) is essential for the MCATI and OI methods to get high estimation accuracy. Therefore, a large power-aperture product should be carefully considered in the ISAL system design. Furthermore, on the condition of low SNR, range cell accumulation is also helpful to reduce the influence of noise. Take the ISAL, which is utilized to image the satellite in 500km orbit, as an example, the estimation accuracy can satisfy the demand of synthetic aperture imaging with 0dB single-pulse SNR and 300 range cell accumulation. The proposed methods are verified with simulation and experiment.

In this paper a multi-static ambiguity function (AF) based on the Kullback directed divergence (KDD) and a distributed multiple-input and multiple-output radar system (DMRS) framework is introduced. Additionally a mathematical analysis is used to derive the AF in terms of signal-to-noise ratios (SNRs) and matched filter outputs. This method manages to extract an upper bound and properly define an AF bounded from 0 to 1. Moreover, this method leads in avoidance of large matrices inversions allowing less complex and more accurate computations. Finally the performance of the proposed method in localisation problems is assessed by comparing the proposed AF with the squared summation of the matched filter outputs at each receiver at different SNR scenarios.

In this paper, a method for combining wideband and narrowband waveforms is proposed to improve target detection in shallow water environments. In this regard, a sonar waveform design suitable for target speed has been proposed too. The method uses a wideband frequency-modulated waveform for high range resolution in a reverberation environment and the Doppler-sensitive (DS) waveform to improve the detection of moving targets. The proposed combined waveform is mathematically modeled, and the Calculating of ambiguity function (AF) is performed. The AF and autocorrelation function (ACF) of the designed waveform indicate both DS and fair range resolution features simultaneously exist. So the initial range resolution for target detection is preserved. The Peak to Sidelobe level (PSL) ratio of the proposed waveform is at least 25 dB more than the previous state of the art waveforms. Calculating the Q-function criterion for the designed waveform reveals the superior reverberation suppression and detection performance with respect to the state of the art waveforms. After calculating the reverberation channel model, waveform echo, and detection of the target, the probability of detection (Pd) versus signal-to-reverberation ratio (SRR) was simulated by the Monte Carlo method. It was shown that the proposed waveform improved the probability of target detection by 20 dB, comparing to the base waveforms.

We deal with the waveform design problem for the radar-communications coexistence (RCC) that ensures low levels of waveform correlations and meanwhile implements efficient information embedding (IE) via the fast-time waveform transmission. To tackle the problem, we propose two unimodular waveform designs, in which the integrated sidelobe level (ISL) is evaluated to find the optimal waveform correlations for the radar transmission and the attributes of waveform phases with large degrees of freedom are exploited to embed communication symbols. The first design is an offline strategy simply using the phase initialization for waveform generation to embed communication symbols. It requires only a predefined database that maps the waveform initialization to the emitted version of it, which gives the lowest ISL of the waveform. The second design serves as an online strategy employing the phase difference between any two waveform elements for the implementation of IE, and its accuracy to approaching desirable phases is elaborately transformed into a quadratic form and jointly designed with the minimization of ISL. We formulate this design as a nonconvex optimization problem, whose compound objective involves the outer product of the waveform vector that is to be designed. Moreover, we apply the majorization-minimization technique to solve the formulated problem, based on which we also devise an efficient algorithm that iterates with a closed-form solution. Simulation results verify the effectiveness of the proposed designs for the RCC.

An important tool for assessing a radar's performance is the ambiguity function. On the other hand, many different schemes have been designed for the transmit waveforms of a MIMO radar. For each one, a criterion has been chosen to improve the performace, e.g. achieving better missed detection. In this paper, considering the ambiguity function as the benchmark, we propose a waveform design scheme, which optimizes the ambiguity function of the MIMO radar system.

Due to high frequency and large time bandwidth product; photonic generation and processing of arbitrary microwave waveforms has been an interesting topic in recent time. Here, a relatively new photonic technique has been proposed for the generation of a dual linear chirp microwave waveform in Ku-band. In this method two single drive Mach–Zehnder Modulators are cascaded at minimum transmission point and in push–pull mode. Theoretical analysis and simulation are developed by giving a complete mathematical model. As the result of this methodology, a dual linear chirp microwave waveform in Ku-band with relatively large bandwidth is generated. Comparative analysis is done in the present cascading technique with dual parallel Mach–Zehnder Modulator (DPMZM) technique. Range-Doppler coupling of the radar system has been investigated with the help of an ambiguity function diagram of the generated waveform. Results have analyzed through MATLAB simulation and verified by experimental results.

OF THE DISSERTATION Adaptive OFDM Radar for Target Detection and Tracking by Satyabrata Sen Doctor of Philosophy in Electrical Engineering Washington University in St. Louis, December 2010 Research Advisor: Dr. Arye Nehorai We develop algorithms to detect and track targets by employing a wideband orthogonal frequency division multiplexing (OFDM) radar signal. The frequency diversity of the OFDM signal improves the sensing performance since the scattering centers of a target resonate variably at different frequencies. In addition, being a wideband signal, OFDM improves the range resolution and provides spectral efficiency. We first design the spectrum of the OFDM signal to improve the radar’s wideband ambiguity function. Our designed waveform enhances the range resolution and motivates us to use adaptive OFDM waveform in specific problems, such as the detection and tracking of targets. We develop methods for detecting a moving target in the presence of multipath, which exist, for example, in urban environments. We exploit the multipath reflections by utilizing different Doppler shifts. We analytically evaluate the asymptotic performance of the detector and adaptively design the OFDM waveform, by maximizing the noncentrality-parameter expression, to further improve the detection performance. ii Next, we transform the detection problem into the task of a sparse-signal estimation by making use of the sparsity of multiple paths. We propose an efficient sparse-recovery algorithm by employing a collection of multiple small Dantzig selectors, and analytically compute the reconstruction performance in terms of the `1-constrained minimal singular value. We solve a constrained multi-objective optimization algorithm to design the OFDM waveform and infer that the resultant signal-energy distribution is in proportion to the distribution of the target energy across different subcarriers. Then, we develop tracking methods for both a single and multiple targets. We propose a tracking method for a low-grazing angle target by realistically modeling different physical and statistical effects, such as the meteorological conditions in the troposphere, curved surface of the earth, and roughness of the sea-surface. To further enhance the tracking performance, we integrate a maximum mutual information based waveform design technique into the tracker. To track multiple targets, we exploit the inherent sparsity on the delay-Doppler plane to develop an computationally efficient procedure. For computational efficiency, we use more prior information to dynamically partition a small portion of the delay-Doppler plane. We utilize the block-sparsity property to propose a block version of the CoSaMP algorithm in the tracking filter.