Multiple-input Multiple-output Radar Waveform Design Research Articles

Joint linear array structure and waveform design for MIMO radar under practical constraints

<abstract> <p>Optimizing the array structure or emission waveform of a multiple-input multiple-output (MIMO) radar system is an effective method to improve the performance in practical applications. In this study, the joint optimization of array structure and the corresponding emission waveform under interference and noise conditions was investigated. When compared with the waveform or array structure optimization alone, this method allowed the MIMO radar system to obtain a higher degree of freedom. By considering the practical limitations of the MIMO radar system, a waveform with good properties, such as orthogonality or pulse compression performance, was selected as the reference waveform. Subsequently, based on the similarity constraint and constant modulus constraint, a bivariate joint optimization problem of array structure and waveform was formulated, and an iterative optimization algorithm was proposed to solve it. The array composition was determined using a combinatorial search algorithm while the emission waveform was obtained by solving the similarity model. Eventually, it effectively converged to form quasi-optimal match variables after limited iterations. The proposed method can be expanded to the optimal launch of a specific target and an environment with a proper or minimum number of antennas, as well as implement array optimization with the desired waveform. The simulation results prove the effectiveness of the proposed method. This method provides an ideal choice for real-time construction, flexible launch, and signal processing of MIMO radar systems.</p> </abstract>

Integrated Waveform Design for MIMO Radar and Communication via Spatio-Spectral Modulation

This paper considers the integrated waveform design to simultaneously achieve a desired radar beampattern and multi-users communication for a dual-function Multiple-Input Multiple-Output (MIMO) system. To this end, a spatio-spectral modulation strategy via shaping the spatial waveform Energy Spectral Density (ESD) in directions of communication is proposed for the communication function, while beampattern Integrated Sidelobe Level (ISL) is minimized to enhance radar detectability. Meanwhile, Peak-to-Average Ratio (PAR) and power restrictions to comply with the current hardware technique and the mainlobe width constraint to cohere the beampattern main energy on the spatial region of interest are forced, respectively. Exploiting an equivalent reformulation of the original non-convex optimization problem, a Sequential Block Enhancement (SBE) framework that alternately updates each waveform in each emitting antenna is developed to monotonically decrease ISL. Each block involves the Dinkelbach’s procedure, sequential convex approximation and Alternating Direction Method of Multipliers (ADMM) to obtain single waveform, while the analytic proof with the converged block being a Karush-Kuhn-Tucker (KKT) point is provided. Finally, numerical results highlight the effectiveness of both the proposed dual function scheme and the waveform synthesis technique in comparison with some counterparts.

MIMO Radar Waveform Design for Simultaneous Space–Time–Doppler Domain Optimization: Framework and Implementation

Waveform design has become an attractive topic in the field of colocated multiple-input multiple-output (MIMO) radar that allows antennas to transmit different waveforms. Waveform properties of MIMO radar in space, time and Doppler domains determine the performances of resource utilization, interference suppression, and moving target detection. Therefore, simultaneous optimization of multi-domain properties through waveform design is significant to improve the performance of MIMO radar. In this paper, a novel MIMO radar waveform design framework that constrains the beampattern while maximizing the similarity between the designed and desired waveforms is proposed for simultaneous space-time-Doppler domain optimization. To solve the resulting multi-constraint non-convex problem, an efficient beampattern control and similarity maximization (BCSM) algorithm is developed and its convergence is demonstrated. Especially, the coupling problem due to the similarity constraint is handled by transforming the number domain and introducing the proximal algorithm. While reducing the target distortion in mainlobe region and interference in sidelobe region, the proposed method can also maximize the similarity of MIMO transmit waveforms. Numerical simulation results, apart from verifying that the proposed method outperforms existing methods in space-time-Doppler domain, also illustrate the robustness of proposed method in terms of mainlobe width and desired peak sidelobe level (PSL).

MIMO Radar Transmit Beampattern Shaping for Spectrally Dense Environments

Designing unimodular waveforms with a desired beampattern, spectral occupancy and orthogonality level is of vital importance in the next generation Multiple-Input Multiple-Output (MIMO) radar systems. Motivated by this fact, in this paper, we propose a framework for shaping the beampattern in MIMO radar systems under the constraints simultaneously ensuring unimodularity, desired spectral occupancy and orthogonality of the designed waveform. In this manner, the proposed framework is the most comprehensive approach for MIMO radar waveform design focusing on beampattern shaping. The problem formulation leads to a non-convex quadratic fractional programming. We propose an effective iterative to solve the problem, where each iteration is composed of a Semi-Definite Programming (SDP) followed by eigenvalue decomposition. Some numerical simulations are provided to illustrate the superior performance of our proposed over the state-of-the-art.

Spectrally compatible multiple‐input multiple‐output radar waveform design based on alternating direction method of multipliers

Multiple-input multiple-output (MIMO) radar waveform design in a spectrally crowded environment is a challenging problem. In this study, the issue of MIMO radar waveform design in coexistence with communication systems is investigated by maximising the output signal-to-interference-plus-noise ratio (SINR) of the MIMO radar under transmit energy, similarity and spectral compatibility constraints. Different from the existing alternating direction method of multipliers (ADMM) proposed in a single-antenna scenario, a novel ADMM algorithm for spectrally compatible MIMO radar waveform design is proposed to efficiently tackle the non-convex optimisation problem in both single-antenna and multi-antenna scenarios. Due to the decomposability of ADMM, only a few quadratic programming subproblems need to be solved during each iteration in the authors' algorithm, which reduces the computational complexity. In numerical simulations, the proposed ADMM algorithm is compared with the semidefinite relaxation algorithm and the existing ADMM algorithm in a single-antenna scenario and a multi-antenna scenario, respectively. It shows that the proposed ADMM algorithm can achieve almost the same performance as the two existing algorithms; however, it is computationally more efficient.

Constant modulus waveform design for MIMO radar via manifold optimization

This paper concentrates on MIMO (multiple-input multiple-output) radar waveform design to improve SINR (signal-to-interference-plus-noise ratio). Due to the constant modulus constraint, the problem is essentially an NP-hard and high dimensional problem. Many conventional methods generally transform the original problem to a convex optimization problem through relaxation. To address it more efficiently, we propose a new approach based on a Riemannian manifold, which is the product of complex circles and a Euclidean space. The original constraint problem in our proposed method is considered as unconstrained over a restricted search space. Then, the reformulated problem is solved by Riemannian conjugate gradient (RCG) algorithm efficiently. Numerical results reveal that the proposed algorithm can achieve higher SINR via different input SNR while consumes a lower computation time.

Beampattern synthesis and spectral compatibility based MIMO radar waveform design

This paper aims to design multiple-input multiple-output (MIMO) radar transmit waveform that is able to focus energy on the target space-frequency domains while avoiding specific space-frequency domains for communicational devices. Specifically, the waveform design is recast as a joint optimization problem wherein the interference-to-signal energy ratio cost function turns out to be non-convex and non-smooth. In order to solve such an optimization problem, in this paper, an iterative optimization algorithm is proposed, wherein each iteration the majorization minimization (MM) scaling is firstly performed to the logarithmic cost function, and then the best alternative performance waveform vector is analytically achieved. As a result, the proposed algorithm can form a deep radiation energy null in the space-frequency domain where the communicational devices are expected to be located, and at the same time develop a higher radiation energy gain in specific target areas. The computational complexity of the proposed approach is quadratic to the number of array elements and snapshots, which shows potential for practical applications. Finally, the performance of the proposed algorithm has been verified via simulation experiments.

MIMO Radar Waveform Design: An Overview

Waveform or code design is an important topic in many applications, which has continuously attracted attention during the past several decades. The development of waveform design has been significantly advanced since the emergence of multiple-input multiple-output (MIMO) technique. Compared to the single-waveform design for conventional radars, the multi-waveform design enables extra degrees of freedom (DOFs) for modern radars, which therefore triggers a series of relevant studies on MIMO radar. In this paper, we provide an overview on the main techniques of MIMO radar waveform designs developed in recent years, wherein the state-of-the-art methods are reviewed in terms of different designing criteria, including the minimization of auto- and cross-correlation levels (or equivalently, the integrated sidelobe level), the information theoretic, ambiguity function shaping, and signal-to-interference-plus-noise ratio maximization-based criteria, etc. Moreover, we give detailed comments on the main issues of different waveform designs, and also provide the possibly emerging directions toward the research on MIMO radar waveform design and potential challenges.

Waveform Design for Collocated MIMO Radar With High-Mix-Low-Resolution ADCs

Adopting low-resolution analog-to-digital converters (ADCs) for receive antennas of a multiple-input multiple-output (MIMO) system can remarkably reduce the hardware cost, circuit power consumption as well as amount of data to be transferred from RF components and the baseband-processing unit. However, an obvious performance loss is also expected. Towards this end, in this work we introduce a new architecture which contains both high- and low-resolution ADCs (named as high-mix-low-resolution ADCs) for collocated MIMO radar, and the associated problem of waveform design is discussed in detail. Specifically, the problem jointly optimizes the waveform, ADC switch vector and receive filter, so as to maximize the signal-to-interference-plus-quantization-error-and-noise ratio (SIQENR). To tackle the resultant nonconvex problem, an alternating optimization method (AOM) is devised. To be more specific, the ADC switch vector and waveform matrix are optimized with the block successive upper-bound minimization (BSUM) framework based on the Dinkelback method. Furthermore, a continuous and concave function is introduced to approximate the l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> norm to achieve a binary solution of the ADC switch vector. It is shown that the optimal solutions to the ADCs switch vector and waveform matrix can be efficiently attained by using the alternating direction method of multipliers (ADMM) approach and Karush-Kuhn-Tucher (KKT) conditions, respectively. Numerical simulations are provided to demonstrate the effectiveness of the proposed schemes.

Spectrally Compatible Waveform Design for MIMO Radar With ISL and PAPR Constraints

This paper deals with the waveform design to ensure the spectrum co-existence between multiple-input multiple-output (MIMO) radar and communication systems. The transmit waveform energy of MIMO radar in the prescribed spatial-frequency domain is minimized to reduce the mutual interference induced by the overlaid communication services. Additionally, the integrated sidelobes level (ISL) and peak-to-average power ratio (PAPR) constraints are forced on the probing waveform. To tackle the resulting NP-hard problem, we first introduce several auxiliary variables to convert the fourth-order ISL constraint and the PAPR constraint into several quadratic constraints. Then, the recast problem is formulated into a new alternating direction method of multipliers (ADMM) form, with small-sized tractable subproblems solved sufficiently. Numerical simulations verify that the proposed algorithm outperforms another competitive method in terms of the convergence performance and also demonstrate that the designed waveform can achieve spatial-frequency nulling under the ISL and PAPR constraints.

Spatial–temporal waveform design for MIMO radar without approximating the covariance matrix

In this study, a transmit waveform design method based on spatial-temporal optimisation for multiple-input multiple-output (MIMO) radar is proposed. The goal is not only to design the waveforms for beampattern matching, but also to minimise the autocorrelation sidelobes of the spatial synthesis signals of interested direction. Especially, to synthesise the constant envelope waveform directly, an improved sequential convex algorithm is proposed to tackle the non-convex problem in spatial optimisation. Then the autocorrelation sidelobes are reduced by using the steepest descent algorithm in temporal optimisation. Finally, the authors assess the effectiveness of the proposed technique through numerical simulations in comparison with the traditional and the alternating direction method of multipliers method.

MIMO Radar Waveform Design in the Presence of Multiple Targets and Practical Constraints

This paper deals with the joint design of Multiple-Input Multiple-Output (MIMO) radar transmit waveform and receive filter to enhance multiple targets detectability in the presence of signal-dependent (clutter) and independent disturbance. The worst-case Signal-to-Interference-Noise-Ratio (SINR) over multiple targets is explicitly maximized. To ensure hardware compatibility and the coexistence between MIMO radar and other wireless systems, constant modulus and spectral restrictions on the waveform are incorporated in our design. A max-min non-convex optimization problem emerges as a function of the transmit waveform, which we solve via a novel polynomial-time iterative procedure that involves solving a sequence of convex problems with constraints that evolve with every iteration. The overall algorithm follows an alternate optimization over the receive filter and transmit waveform. For the problem of waveform optimization (which is our central contribution), we provide analytical guarantees of monotonic cost function improvement with proof of convergence to a solution that satisfies the KarushKuhnTucker (KKT) conditions. We also develop extensions that address the well-known waveform similarity constraint. By simulating challenging practical scenarios, we evaluate the proposed algorithm against the state-of-the-art methods in terms of the achieved SINR value and the computational complexity. Overall, we show that our proposal outperforms state of the art competing methods while providing the most favorable performance-complexity balance.

Low probability of intercept‐based distributed MIMO radar waveform design against barrage jamming in signal‐dependent clutter and coloured noise

This study investigates the problem of low probability of intercept (LPI)-based distributed multiple-input multiple-output (MIMO) radar waveform design against barrage jamming in signal-dependent clutter and coloured noise. Given the priori knowledge of the extended target impulse response, signal-dependent clutter, barrage jamming signals and coloured noise, the LPI-based scheme for optimal radar waveform design is proposed to minimise the total power consumption of the MIMO radar system by optimising the transmitted waveforms of different transmitters with a predetermined mutual information (MI) constraint for target characterisation performance. Firstly, the MI between the received echoes from the target at each receiver and the target impulse response is derived as a practical metric to characterise the parameter estimation performance of a target. Then, the LPI-based distributed MIMO radar waveform design strategy is developed. The resulting radar waveform optimisation problem is convex and solved analytically, whose solutions represent the optimum power allocation for each transmitter in the MIMO radar system. With the aid of numerical simulations, it is illustrated that to minimise the total transmission power, the optimal waveform should match with the target, clutter, jamming and coloured noise. In addition, it is also demonstrated that the LPI performance of the MIMO radar system can be significantly improved by employing the proposed radar waveform design scheme.

Space-time coding waveform design for MIMO radar transmit beamforming with minimum MFL

In this paper, we utilize a space-time coding (STC) scheme to synthesize the multiple-input multiple-output (MIMO) radar transmit beampattern and meanwhile consider the matched filtering loss (MFL) of equivalent signal in waveform design. To solve the MFL optimization problem, we propose a simulated annealing based (SA-based) algorithm to effectively find the optimal solution of STC waveform matrix. Our STC method for waveform design has suppressed the fluctuation of equivalent signal so that has the advantage of achieving the minimum MFL nearly, compared to the conventional methods for constant-envelope constraint waveform design (e.g. cyclic algorithm (CA) method). Simulation results demonstrate the effectiveness of the proposed algorithm.

Spectrally Constrained MIMO Radar Waveform Design Based on Mutual Information

We address the waveform design problem for multiple-input multiple-output (MIMO) radar in spectrally crowded environments. We exploit the mutual information between the target reflections and the target responses as the design metric. To tackle the associated nonconvex optimization problem, we propose an algorithm based on first-order Taylor series approximation as well as minorization-maximization (MM) based algorithms to design the spectrally constrained waveforms. Interestingly, for some scenarios, we can synthesize the globally optimal (spectrally constrained) waveforms with the maximum mutual information. We also show that, through intelligent waveform design, MIMO radar can coexist more efficiently with other communication systems occupying the same spectrum, while suffering from insignificant mutual information losses.

A Compressive Sensing-Based Colocated MIMO Radar Power Allocation and Waveform Design

Compressive sensing (CS) is a widely used technique for (multiple) target detection in multiple input multiple output (MIMO) radars. In this paper, our goal is to enhance the quality of CS-based detection techniques for a colocated MIMO radar with given location of transmit and receive nodes. Our approach is to design the transmit waveforms based on the given antenna locations and optimally allocate the total power budget among the transmitters. The design criterion in this paper is the coherence of the resulting sensing matrix. Based on this criterion, we derive and solve a convex optimization problem for power allocation. For waveform design, however, the direct method studied is non-convex, and although iterative descent methods could be used to achieve suboptimal solutions, they might be unfeasible waveforms (e.g., waveforms with high peak to average power ratios). Here, we first show that the coherence measure depends only on the covariance matrix of the waveforms (rather than the waveforms themselves). Next, we introduce three different convex programs to achieve the covariance matrix. Finally, we transform the covariance matrix into realistic waveforms; although multiple solutions exist, a closed-form expression for all possible solutions is available. Specifically, we design the waveforms by applying practical constraints such as constant modulus. Simulation results confirm that the introduced designs improve the detection performance of a CS-MIMO radar.

OFDM MIMO radar waveform design for targets identification

In order to obtain better target identification performance, an efficient waveform design method with high range resolution and low sidelobe level for orthogonal frequency division multiplexing (OFDM) multiple-input multiple-output (MIMO) radar is proposed in this paper. First, the wideband CP-based OFDM signal is transmitted on each antenna to guarantee large bandwidth and high range resolution. Next, a complex orthogonal design (COD) is utilized to achieve code domain orthogonality among antennas, so that the spatial diversity can be obtained in MIMO radar, and only the range sidelobe on the first antenna needs suppressing. Furthermore, sidelobe suppression is expressed as an optimization problem. The integrated sidelobe level (ISL) is adopted to construct the objective function, which is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The numerical results demonstrate the superiority in performance (high resolution, strict orthogonality, and low sidelobe level) of the proposed method compared to existing algorithms.

Spectrally Compatible Waveform Design for MIMO Radar in the Presence of Multiple Targets

This paper investigates the problem of the spectrally compatible waveform design for multiple-input multiple-output (MIMO) radar in the presence of multiple targets and signal-dependent interference. Unlike the existing approaches to designing the waveform for a single target via output signal-to-interference-plus-noise ratio (SINR) maximization, a new method is proposed to deal with a more general problem, i.e., designing a spectrally compatible waveform for multiple targets, by minimizing the waveform energy of the overlayed space-frequency bands under constraints of waveform similarity and individual SINR requirements. Due to the existence of signal dependence, the formulated optimization problem is NP-hard. Toward this end, an iterative algorithm is developed. Concretely, at each iteration, the receive filter is first obtained with the aid of the minimum variance distortionless response method, then the transmit waveform is optimized by employing the dual ascent method. Both the convergence and asymptotic optimality of this algorithm are discussed. Numerical simulations are provided to demonstrate the effectiveness of the proposed approach.

Designing Sequence With Minimum PSL Using Chebyshev Distance and its Application for Chaotic MIMO Radar Waveform Design

Controlling peak side-lobe level (PSL) is of great importance in high-resolution applications of multiple-input multiple-output (MIMO) radars. In this paper, designing sequences with good autocorrelation properties are studied. The PSL of the autocorrelation is regarded as the main merit and is optimized through newly introduced cyclic algorithms, namely; PSL Minimization Quadratic Approach (PMQA), PSL Minimization Algorithm, the smallest Rectangular (PMAR), and PSL Optimization Cyclic Algorithm (POCA). It is revealed that minimizing PSL results in better sequences in terms of autocorrelation side-lobes when compared with traditional integrated side-lobe level (ISL) minimization. In order to improve the performance of these algorithms, fast-randomized Singular Value Decomposition (SVD) is utilized. To achieve waveform design for MIMO radars, this algorithm is applied to the waveform generated from a modified Bernoulli chaotic system. The numerical experiments confirm the superiority of the newly developed algorithms compared to high-performance algorithms in mono-static and MIMO radars.

Robust constrained waveform design for MIMO radar with uncertain steering vectors

This paper considers the robust waveform design of multiple-input multiple-output (MIMO) radar to enhance targets detection in the presence of signal-dependent interferences assuming the knowledge of steering vectors is imprecise. Specifically, resorting to semidefinite programming (SDP)-related technique, we first maximize the worst-case signal-to-interference-plus-noise ratio (SINR) over uncertain region to optimize waveform covariance matrix forcing a uniform elemental power requirement. Then, based on least square (LS) approach, we devise the waveform accounting for constant modulus and similarity constraints by the obtained waveform covariance matrix using cyclic algorithm (CA). Finally, we assess the effectiveness of the proposed technique through numerical simulations in terms of non-uniform point-like clutter and uniform clutter.