Transmit Beampattern Synthesis Research Articles

MIMO radar partially correlated waveform design based on chirp rate diversity

Waveform design is a significant topic in multiple-input-multiple-output (MIMO) radar. In this paper, we address the problem of waveform design for colocated narrowband MIMO radar transmit beampattern synthesis. The existing methods have not comprehensively considered the transmit beampattern synthesis under multiple practical constraints, such as constant modulus constraint, Doppler tolerance, high range resolution and low auto-correlation sidelobe. We consider these practical constraints and propose a novel chirp rate diversity-based linear frequency modulated (CRD-LFM) waveform design for approximating the desired MIMO radar transmit beampattern. To tackle the problem, we improve the classical two-step approach. Firstly we design the covariance matrix using the existing closed-form solution. Then we model the problem of obtaining the waveforms from the covariance matrix as a nonlinear optimization problem, and we utilize the Sequential Quadratic Programming (SQP) algorithm to solve it. The simulations demonstrate that the waveforms obtained by this method can well approximate the desired transmit beampattern and have higher range resolution. Furthermore, we verify that the suppression of auto-correlation sidelobe can be achieved using amplitude weighting, which is easily realizable in practical engineering.

Phase-Only Transmit Beampattern Synthesis With Maximum Mainlobe Gain via Manifold ADMM

Phase-Only Transmit Beampattern Synthesis With Maximum Mainlobe Gain via Manifold ADMM

Wideband MIMO Radar Transmit Beampattern Synthesis in a Spectrally Crowded Environment

Wideband MIMO Radar Transmit Beampattern Synthesis in a Spectrally Crowded Environment

Beampattern synthesis for active RIS-assisted radar with sidelobe level minimization

To enhance the performance, reconfigurable intelligent surface (RIS) is now employed in monostatic radars since it creates a new path between the radar and the target by artificially reflecting radar signals and thus provides novel degrees of freedom. This correspondence studies the transmit beampattern synthesis for an active RIS-assisted monostatic radar via minimizing the sidelobe levels. The proposed beampattern synthesis is coined as a nonconvex and nonlinear optimization problem which is solved by jointly optimizing the beamforming weights of the transmitter and the phase shift and amplification matrix of the active RIS. The auxiliary variables are first introduced to simplify the nonconvex constraints, and two variables are then alternatively optimized by the alternating direction method of multipliers (ADMM) where their close-form optimal solutions are derived. Numerical results show that the active RIS-assisted radar has a significantly lower sidelobe level than conventional monostatic radars.

A Modified Method for Beam-Forming Using Covariance Matrix in MIMO Radar System

A MIMO radar provides solution for beamforming, since transmit beampattern synthesis is well proven method for stimulating the antenna array to develop the beampattern. It is close to the desired one which can give minimum error between these two. A covariance matrix in beamforming contains the direction of invariable data and magnitude distribution in multidimensional space which decides the closeness with the desired beampattern. Here, selection of an optimal covariance matrix is constrained optimization problem with minimization of cost function. In high directivity radar systems, the antenna beam is needed to be steered to cover a large area for detection. In this proposed work, minimization of convex function and transmit beampattern synthesis is carried out with modifications of the covariance matrix ‘Rcov’ for minimum and maximum transmission power utilization constraints. The beampattern design problem is reformulated here, as semi-definite programming optimization problem and solved using convex optimization, with MATLAB simulation platform. The results show that the beampattern generated using this modified covariance matrix is optimally close to desired pattern.

Min-Max Optimization for MIMO Radar Waveform Design With Improved Power Efficiency

Transmit waveform design with power efficiency constraint is a prominent problem for colocated multiple-input-multiple-output (MIMO) radar. Though there are extensive relevant works in the literature, the existing peak-to-average-power ratio (PAR) constraint is insufficient in controlling the transmit power uniformity and the conventional constant modulus (CM) is imposed on both waveform temporal and spatial dimensions, resulting in an unnecessary loss of degrees of freedom. Thereby, we introduce an individual antenna power control (IAPC) scheme with a new peak-to-valley-power-ratio (PVR) constraint to flexibly control the transmit power uniformity along the spatial dimension. We then devise two min-max waveform designs for shaped transmit beampattern synthesis. To tackle the resultant non-convex problems, we propose a surrogate primal alternating direction method of multipliers (SP-ADMM) to approximately solve a surrogate primal subproblem for PVR projection since the standard ADMM is unable to tackle the intricate primal problems directly. We theoretically prove the convergence behavior of the SP-ADMM. Finally, experiments verify the effectiveness and improved performance of the developed methods against their counterparts, especially in the metric of sidelobe level.

Transmit beampattern synthesis for MIMO radar with one-bit digital-to-analog converters

This paper considers the problem of transmit beampattern synthesis (i.e., transmit beamforming) in multiple-input multiple-output (MIMO) radar which deploys one-bit digital-to-analog converts (DACs). By appropriately designing the transmitted signal waveforms quantized by one-bit DACs, the majority of radiated energy can be focused into the mainlobe(s) region to enhance the intensity of backscattered signals from targets. Meanwhile, the amount of energy inevitably leaked into the sidelobe region is minimized to suppress the interferences. More specifically, the essence of the proposed design can be regarded as optimizing the one-bit signal waveforms such that the synthesized transmit beampattern has a minimum integrated-sidelobe-to-mainlobe ratio (ISMR). In order to tackle the nonconvex discrete constraint in the resulting optimization problem, we propose to introduce auxiliary variables to reformulate the discrete constraint into continuous constraints. On this basis, the alternating direction multiplier method (ADMM) framework is applied to deal with the reformulated problem. The proposed method can approximately solve the sub-problems with closed-form solutions in each iteration, and hence, it is computationally efficient. Simulation results indicate that the proposed method is able to provide promising performance.

Wideband MIMO Radar Transmit Beampattern Synthesis via Majorization–Minimization

We consider the design of constant-modulus waveforms for wideband multiple-input multiple-output radar. The aim is to match a desired transmit beampattern. To tackle the non-convex design problem, we develop an iterative algorithm, which is based on cyclic optimization and majorization–minimization. We prove that the sequence of the objective values of the proposed algorithm has guaranteed convergence. Moreover, we can obtain closed-form solutions for the associated optimization problems at every iteration. Furthermore, the proposed method can be implemented without matrix inversion and hence is computationally efficient. Simulation results demonstrate that the performance of the proposed algorithm is better than existing methods.

A unified sparse array design framework for beampattern synthesis

A smaller number of transmit antennas can reduce the array system cost, while sparse antenna design can provide additional degrees of freedom to beampattern synthesis. It is also known that the min-max beampattern matching design criterion can synthesize beampattern with small mainlobe ripple, low peak sidelobe level, and specified null/notch. Based on this design metric, we formulate a unified sparse array design framework for beampattern synthesis. Our framework includes the colocated multiple-input multiple-output (MIMO) radar transmit beampattern synthesis, phase-only beampattern synthesis, and phased-array beampattern synthesis as special cases. In the design formulation, the antenna positions and phase-only waveforms (for MIMO radar beampattern) or array weight vector (for phase-only and traditional phased-array beampattern) are jointly determined. The resultant problem is challenging because the nonconvex nonsmooth min-max objective function, and phase-only/unimodular requirements make it become typically NP-hard, and the antenna position selection results in a difficult Boolean constraint. Nevertheless, we are able to find a local optimal solution efficiently by applying the Lawson approximation and majorization-minimization. Numerical examples show that the devised approach can achieve the desired transmit beampattern by jointly optimizing the phase-only waveforms/weight vector and antenna locations.

Spectrally-Agile Waveform Design for Wideband MIMO Radar Transmit Beampattern Synthesis via Majorization-ADMM

This paper investigates the problem of wideband multiple-input multiple-output radar transmit beampattern synthesis in a spectrally dense environment, and two optimization problems are formulated according to practical consideration. The first one is beampattern matching design under the scenario of known interference spectral band while the second addresses minimum peak sidelobe beampattern design given both interference spectral band and interference direction. In addition, to improve transmission efficiency, other than the peak-to-average power ratio constraint, a useful modulus constraint, namely, dynamic range ratio, is adopted in our development. The resultant problems are nonconvex and nonsmooth, together with multiple constraints. The advantages of the majorization-minimization and alternating direction method of multipliers (ADMM) are combined to handle them. We first use the majorization technique to handle the nonconvex and nonsmooth issues and then utilize the ADMM to solve the multi-constrained problem. Two variants of the ADMM, called majorization-ADMM and proximal-ADMM, are devised, and their convergence is also studied. Finally, numerical examples are provided to verify the effectiveness of the proposed algorithms.

Transmit beampattern synthesis for chirp space-time coding array by time delay design

In a multiple-input multiple-output (MIMO) radar, it is desired to maximize the power radiation in an angular region of interest, which, however, is hardly achievable because a set of orthogonal waveforms is employed at the engineering. Different from traditional colocated MIMO radar, space-time coding array (STCA) transmits an identical waveform with a tiny time delay circulating across array elements. It can provide a simple way to achieve the full angular coverage with a stable gain. In this paper, a new scheme referred to as chirp-STCA is proposed to synthesize the desired beampattern flexibly. With the quantitative relationship between the time delay and the span of beam spreading, the transmit beampattern synthesis issue is converted to the design of time delay value which can be readily realized based on the framework of chirp-STCA. As a result, the desired angular sector coverage of the radiation power can be realized by setting a proper time delay. The proposed chirp-STCA can provide many desired features including low range sidelobe level, low computational complexity, and constant modulus. In addition, the range-angle properties are examined by analyzing the transmit beampattern response and the ambiguity function. Numerical results are presented to demonstrate the effectiveness and simplicity of the chirp-STCA scheme for the transmit beampattern synthesis.

Transmit Beampattern Synthesis for Frequency Diverse Array With Particle Swarm Frequency Offset Optimization

Different from the conventional phased array radar, a frequency diverse array (FDA) applies additional frequency shift across the array elements, yielding a range-angle-dependent transmit beampattern that provides a huge potential opportunity for target estimation and range-dependent clutter and interference suppression. Generally, the conventional FDA employs a linear small frequency increment, forming a time-varying “S”-shape range-angle beampattern, which is range-angle coupled. In this article, a range-angle transmit beampattern synthesis method for FDA based on frequency offset optimization is proposed. Particle swarm optimization (PSO) is adopted in the FDA element frequency increment design to achieve a dot-shaped transmit beampattern. Meanwhile, matched weights are designed for time-modulation compensation. Numerical simulation results demonstrate that the proposed approach achieves better time-invariant performance over other FDA frameworks.

ADMM-based transmit beampattern synthesis for antenna arrays under a constant modulus constraint

Transmit beampattern synthesis for antenna arrays is addressed in this paper. In pursuit of high radiation efficiency, most phased array radar systems utilize nonlinear power amplifiers, which leads to a constant modulus constraint for transmit weight vector optimization. Existing methods to solve this hard nonconvex problem (unit-modulus quadratic program) generally have high computational cost and large memory burden, which may increase dramatically as the array size increases. To that end, we propose a low-complexity algorithm based on the alternating direction method of multipliers (ADMM) framework. By introducing auxiliary variables, the original problem is decomposed into several subproblems with closed-form solutions. The transmit weight vector and the phase response of the desired beampattern is updated alternately so that the cost function value can be monotonically reduced. With bounded penalty parameters, the proposed ADMM-based algorithm can guarantee to converge. We further prove that the converged solution satisfies the Karush-Kuhn-Tucker conditions of the nonconvex optimization problem. Numerical simulation results confirm the effectiveness of the proposed method.

Waveform Analytic Design Method for Transmit Beampattern Synthesis of Circulating Coded MIMO Radar

The transmit beampattern of multiple-input and multiple-output (MIMO) radar can be controlled by transmitting properly designed correlated waveforms. However, most of the correlated waveform design methods proposed in recent years are computational complex. For real time application, the low computational complex waveform design technique has become the interest of research. In this article, we present a waveform analytic design method for the transmit beampattern synthesis of circulating coded MIMO radar. The relationship between the parameters of linear frequency modulated (LFM) waveform and the instantaneous beam pointing angle of circulating coded MIMO radar is developed. Based on such a relationship, the analytic solutions to the parameters of LFM waveform are derived for arbitrary transmit beampattern synthesis. The computational burden of this method is negligible. Numerical simulation results demonstrate the performance of the proposed method.

Statistical Analysis for Time Modulation-Based Frequency Diverse Array Beampattern

Frequency diverse array (FDA) has received much attention due to its both range- and angle-dependent beampatterns. However, the range–angle coupling and time-variant beampattern in FDA may affect its applicability. In order to address the beampattern range–angle coupling problem and time variance, many existing algorithms, by using the time-modulated optimized frequency offset (TMOFO) scheme, are presented to obtain the spatial-focusing time-invariant transmit beampattern synthesis for the FDA. To discuss their irrationality, we first give a time-modulated optimized weight vector (TMOWV) scheme with frequency offset optimization, which is a more general time-modulated scheme for the FDA beampattern synthesis and more convenient for the statistical analysis of the designed FDA transmit beampattern characteristics. Then, the statistical analysis of the designed FDA transmit beampattern is investigated through both theoretical derivations and numerical examples. The extensive simulation results demonstrate that the time-modulated approach for the time-invariant FDA transmit beampattern is invalid.

Transmit beampattern synthesis for MIMO radar using extended circulating code

In multiple-input multiple-output (MIMO) radar settings, it is often desired to transmit power only to a given location or sets of locations defined by the beampattern. Some previous works achieve transmit beampattern synthesis by developing new MIMO radar architectures. In these radar architectures, orthogonal waveforms must be utilised. In fact, the perfect orthogonal waveforms are hardly achievable so that the radar performance loss is inevitable. On the other hand, some waveform design methods, which show superior performance, are proposed. However, the modulus variation and high computational complexity impede their applications in reality. In this study, a simple method for transmit beampattern synthesis is proposed. Based on the circulating code principle, the beampattern synthesis problem has been simplified as a single waveform spectral shaping issue. To solve the spectral shaping issue, an extended circulating code (ECC) with constant modulus is provided. The proposed ECC can achieve an arbitrary beampattern with a single constant modulus waveform while the computational complexity is relatively low. Due to these properties, ECC is simple to apply in practice. The method is evaluated by simulated data and the results can verify its effectiveness.

A Short-Range Range-Angle Dependent Beampattern Synthesis by Frequency Diverse Array

In this paper, we propose a new technique to generate a range-angle dependent transmit beampattern by introducing a nonlinear frequency modulation scheme based on arctangent function in the frequency diverse array (FDA) system. The propagation process of the transmitted signals is usually neglected in most of the existing range-angle dependent transmit beampattern synthesis schemes. More specifically, the time variable is considered to be a constant value or defined from 0 to ${T}$ , where ${T}$ is the pulse duration for pulsed FDA. As a result, such schemes cease to focus the signal power at a desired position for a period of time when this practical constraint is taken into account. The proposed methodology incorporates the propagation process of the transmitted signal and simultaneously focuses the signal power at a desired position and lasting for a period of time. We investigate the consequences of this constraint briefly and also explain the corrected model. Numerical simulations are implemented to validate the theoretical analysis of the proposed methodology.

Robust transmit beampattern matching synthesis for MIMO radar

A robust transmit beampattern matching synthesis approach is described for a multiple-input and multiple-output radar with manifold vectors perturbation. This synthesis technique minimises the worst-case matching performance between the transmit beampattern and the desired beampattern (in a least absolute deviations sense), through designing the waveform covariance matrix. Also, the resulting minimax problem can be translated into a convex problem is showed. Finally, simulation results verify good performance of the proposed robust transmit beampattern synthesis approach.

Time-Invariant Range-Angle-Dependent Beampattern Synthesis for FDA Radar Targets Tracking

The frequency-diverse array (FDA) radar has drawn substantial attention in recent years because of its particular range-angle-dependent beampattern. However, with the linear incremental frequency offset, the basic FDA radar's beampattern is time-variant, range-periodic, and coupled in range and angle dimensions, which limits FDA radar's practical application seriously. In this letter, we propose a novel transmit beampattern synthesis method using the multicarrier FDA architecture and nonlinear time-dependent frequency offset. As a result, a pencil-shaped time-invariant and range-angle-dependent beampattern can be synthesized for target tracking. Furthermore, a time division method is utilized to form multiple narrow pencil-shaped beampatterns for tracking multiple targets within one pulse duration. Simulation results show the effectiveness of the proposed scheme and demonstrate its outperformance via comparison to other existing methods.

Convex optimisation based transmit beampattern synthesis for MIMO radar

A multiple input multiple output (MIMO) radar allows its antenna elements to transmit multiple signal waveforms. This waveform diversity offers enhanced flexibility in transmit beampattern synthesis and signal design. Two algorithms where the transmit is synthesised beampattern by optimising transmitted signal covariance matrix is proposed. In the first algorithm, a method to achieve a desired beampattern by reformulating the design problem as an unconstrained semi-definite programming problem is proposed. Second, a method for beampattern synthesis such that the cross correlation beampattern, which is the correlation between the signals at different target locations, is minimised and at the same time the sidelobe levels are constrained to be lower than a threshold value proposed. These design problems are modelled as convex optimisation problem and are solved using Matlab based toolbox CVX.