Colocated Multiple-input Multiple-output Radar Research Articles

Direction finding in MIMO radar with large antenna arrays and nonorthogonal waveforms

As an important research branch in multiple-input multiple-output (MIMO) radar, orthogonal waveforms are always desirable. In practice, however, the orthogonality may not be always guaranteed. In this paper, a computationally efficient parallel factor (PARAFAC) estimator is proposed, which is suitable for direction-of-arrival (DOA) estimation in colocated MIMO radar with large antenna arrays as well as nonorthogonal waveforms. Firstly, the spatially colored noise caused by the nonorthogonal waveforms is eliminated via temporal cross-correlation of the measurement. Thereafter, a third-order PARAFAC (or called trilinear decomposition) model is established by exploiting the multidimensional structure as well as the low rank property of the cross covariance matrix. The DOA estimation problem is then linked to PARAFAC decomposition and finally obtained via least squares technique. Compared with the existing matrix completion-based algorithm, the proposed estimator is attractive from the perspective of computational complexity and estimation accuracy, especially with large antenna arrays scenario. In addition, the stochastic Cramér-Rao bound on DOA estimation with waveform imperfectly is derived. Numerical simulations are provided to verify the effectiveness of the proposed estimator.

Computationally Efficient DOA Estimation Algorithm for MIMO Radar With Imperfect Waveforms

Orthogonal waveforms are often desirable to multiple-input multiple-output (MIMO) radar systems. Unfortunately, the orthogonality may not be always guaranteed in practice. In this letter, we consider the direction-of-arrival (DOA) estimation problem in colocated MIMO radar with imperfect waveforms, and a new methodology is presented. The noiseless cross-covariance matrix is obtained by utilizing the spatial cross-correlation technique. DOAs are obtained via reduced-dimension multiple signal classification (RD-MUSIC). In contrast to the state-of-the-art matrix completion (MC) algorithm, the proposed RD-MUSIC method is computationally more efficient and may have an estimation performance more accurate than the existing MC approach. The numerical results show the improvement in the proposed scheme.

Toeplitz covariance matrix of colocated MIMO radar waveforms for SINR maximization

Abstract Focusing on the signal to interference-plus-noise ratio (SINR) maximization in colocated multiple-input multiple-output (MIMO) radars, using the transmit covariance matrix (TCM) design of transmit waveforms, we have proposed a TCM Rpm with the form of symmetrical Toeplitz matrix, where m is the control parameter to generate different TCM. The main features include (a) full rank, to exploit the waveform diversity advantage of MIMO radar and to further suppress the maximum number of interfering sources, (b) positive semi-definition of sin ((π/2)Rpm) to guarantee that Rpm can be synthesized with binary phase shift keying (BPSK) waveforms in closed form, (c) higher output SINR level using the Rpm with smaller m in the receiver, with the prior knowledge of target and interference locations, (d) lower receive sidelobe levels (SLLs) using the Rpm with certain larger m (e.g. m = 1.5 or 2) for the unwanted and unknown sidelobe interference suppression. Simulation results validate the better performance of our proposed TCM compared to the phased-array, omnidirectional MIMO radar, phased-MIMO radar and the recently proposed TCMs.

Off-Grid DOA Estimation for Colocated MIMO Radar via Reduced-Complexity Sparse Bayesian Learning

Recent advance on signal processing has witnessed increasing interest in machine learning. In this paper, we revisit the problem of direction-of-arrival (DOA) estimation for colocated multiple-input multiple-output (MIMO) radar from the perspective of machine learning. The reduced-complexity transformation is first applied on the array data from matched filters, thus eliminating the redundancy of the array data for the relief of calculational burden. Furthermore, the pre-whitening is followed to obtain a simplified noise model. Finally, the DOA estimation is linked to off-grid sparse Bayesian learning (OGSBL), which does not require to update the noise hyper-parameter, and a block hyper-parameter is utilized to accelerate the convergence of the OGSBL algorithm. The proposed estimator provides better DOA estimation accuracy than the existing peak searching algorithm. The effectiveness of the proposed algorithm is verified via numerical simulation.

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.

Joint Design of Space-Time Transmit and Receive Weights for Colocated MIMO Radar.

Compared with single-input multiple-output (SIMO) radar, colocated multiple-input multiple-output (MIMO) radar can detect moving targets better by adopting waveform diversity. When the colocated MIMO radar transmits a set of orthogonal waveforms, the transmit weights are usually set equal to one, and the receive weights are adaptively adjusted to suppress clutter based on space-time adaptive processing technology. This paper proposes the joint design of space-time transmit and receive weights for colocated MIMO radar. The approach is based on the premise that all possible moving targets are detected by setting a lower threshold. In each direction where there may be moving targets, the space-time transmit and receive weights can be iteratively updated by using the proposed approach to improve the output signal-to-interference-plus-noise ratio (SINR), which is helpful to improve the precision of target detection. Simulation results demonstrate that the proposed method improves the output SINR by greater than 13 dB.

Adaptive resource management in multiple targets tracking for co‐located multiple input multiple output radar

Co-located multiple input multiple output (MIMO) radar is one kind of new style radar, whose transmitting waveforms of each sub-array are orthogonal to each other. Compared with phased array radar, its beam width is wider. Therefore, different targets may be illuminated simultaneously with one beam in co-located MIMO radar. An adaptive resource management in tracking for co-located MIMO radar is proposed, where the sub-array number, the illuminated targets set and the transmitting waveform of the system can be controlled. The optimal parameters are chosen according to a cost function that takes both the desired tracking precision and consumed energy into consideration. Simulation results demonstrate the effectiveness of the algorithm. Using the algorithm, co-located MIMO radar can achieve the desired tracking precision with less cost compared with phased array radar.

Waveform covariance matrix design for robust signal-dependent interference suppression in colocated MIMO radars

Abstract In multiple-input multiple-output (MIMO) radars, interference can be properly suppressed by designing transmit waveforms. However, having an error in initial estimation of interferers’ locations can result in degradation of signal-to-interference-plus-noise ratio (SINR), significantly. In this paper we consider the problem of robust interference suppression and SINR increment in collocated MIMO radars, in the presence of signal-dependent interference resources. We propose an efficient method to generate transmit waveform covariance matrix with the following properties: (a) robustness in interference suppression, (b) high SINR at the receiver, c) using the same power level for all transmit antennas and (d) suitable for generating BPSK waveforms in a closed-form. We solve the resulted optimization problems with numerical approaches in a short period of time. The proposed covariance matrix, by exploiting the correlated MIMO radar concept and a technique we use in the transmitter, yields to a better SINR level compared to conventional MIMO radars, phased array method and the recent introduced schemes. Simulation results validate our claims and show the advantages of our work .

Sparse Antenna and Pulse Placement for Colocated MIMO Radar

Multiple-input multiple-output (MIMO) radar is known for its superiority over conventional radar due to its antenna and waveform diversity. Although higher angular resolution, improved parameter identifiability, and better target detection are achieved, the hardware costs (due to multiple transmitters and multiple receivers) and high-energy consumption (multiple pulses) limit the usage of MIMO radars in large scale networks. On one hand, higher angle and velocity estimation accuracy is required, but on the other hand, a lower number of antennas/pulses is desirable. To achieve such a compromise, in this paper, the Cramér-Rao lower bound (CRLB) for the angle and velocity estimator is employed as a performance metric to design the antenna and the pulse placement. It is shown that the CRLB derived for two targets is a more appropriate criterion in comparison with the single-target CRLB since the two-target CRLB takes into account both the mainlobe width and the sidelobe level of the ambiguity function. In this paper, several algorithms for antenna and pulse selection based on convex and submodular optimization are proposed. Numerical experiments are provided to illustrate the developed theory.

Colocated MIMO Radar SINR Maximization Under ISL and PSL Constraints

This letter considers joint design of transmit waveform and receive filter in colocated multiple-input multiple-output (MIMO) radars in order to enhance target detection performance in the presence of signal-dependent interference. Here, signal-to-interference-plus-noise ratio (SINR) is maximized under the practical constraints of integrated sidelobe level (ISL) and peak sidelobe level (PSL) at the pulse compression output. We have also shown that the joint transmit signal and receive filter design can be formulated as a convex optimization problem, which can be efficiently solved using optimization toolbox (CVX). Simulation results show that our proposed algorithm is able to suppress interference efficiently under ISL and PSL constraints and get close to the SINR efficiency of unconstrained methods.

On the Statistical Resolution Limit (SRL) for Time-Reversal based MIMO radar

In the single-input multiple-output radar, the system transmits scaled (coherent) versions of a single waveform. The multiple-input multiple-output (MIMO) radar uses multiple antennas to simultaneously transmit several non-coherent waveforms and exploits multiple antennas to receive the reflected signals (echoes). This diversity in term of waveform coding allows to transmit orthogonal waveforms which enables the MIMO radar superiority in several fundamental aspects, including: improved parameter identifiability and estimation and much enhanced flexibility for transmit beam-pattern design. The context of this work is the co-located MIMO radar where the transmit and the receive arrays are close in space. In this paper, we provide a theoretical performance analysis to compare two configurations of MIMO radar: Conventional configuration and Time Reversal (TR) configuration in term of Statistical Resolution Limit (SRL). This study provides new insights on the performance gain of the TR scheme which is discussed and illustrated by appropriate simulation results depending on the receive noise level.

Constrained transmit beampattern design for colocated MIMO radar

This paper considers the constrained waveform design for Multiple-Input Multiple-Output (MIMO) radar to synthesize a desired beampattern. Specifically, resorting to SemiDefinite Programming (SDP) related technique, we first minimize Integration Sidelobe Level (ISL) to optimize the waveform covariance matrix enforcing a uniform elemental power restriction as well as a 3dB bandwidth constraint. Then, based on Least Square (LS) approach, we present the existing Cyclic Algorithm (CA) and a new Sequential Iterative Algorithm (SIA) to devise the waveform under a constant modulus constraint, and a similarity constraint to allow the designed waveform sharing the similarity feature with a given reference waveform. In particular, the proposed SIA directly optimizes the objective function and its each iteration turns the multidimensional optimization problem into multiple one-dimensional optimization problems with closed-form solutions. Finally, we assess the effectiveness of the proposed technique through numerical simulations in comparison with CA.

Transmit Signal Design in Colocated MIMO Radar Without Covariance Matrix Optimization

In this paper, the problem of the waveform design for colocated multiple-input multiple-output (MIMO) radars is considered in two parts. In the first part, we design transmit waveform in order to approximate the desired beampattern with low number of samples in the transmitter. Unlike the traditional waveform design methods, in our solution, waveforms are designed for a specific number of samples. Also, the constant envelope constraint that is an important practical constraint is considered. In the second part, we jointly design the transmit waveform and receive filter by a sequential algorithm, considering a priori information of target and interference angle locations. We have evaluated the performance of the proposed algorithms via numerical simulations and shown that the proposed algorithm in the first part is able to approximate the desired beampattern with low number of samples. Also, our method in the second part achieves better signal-to-interference-plus-noise ratio performance compared with the existing active sensing array methods (e.g., phased-array and correlated MIMO radars).

Design of multiple‐input–multiple‐output radar waveforms for Rician target detection

This study addresses the waveform design problem of multiple-input–multiple-output (MIMO) radar. The goal is to improve the detection performance for the Rician targets. The authors first establish a general signal model, which can describe the returns by both statistical and colocated MIMO radar systems. Then they derive the associated optimal Neyman–Pearson detector and find the difficulty of optimising the waveforms that maximise the probability of detection (for a fixed probability of false alarm). Alternatively, they employ the relative entropy associated with the detection problem as the design metric. In order to tackle the non-convex waveform optimisation problem, they propose a minorisation-maximisation-based design method. They prove that the proposed method can increase the relative entropy (of the devised waveforms) at each iteration and guarantees convergence. Finally, they include several numerical examples to demonstrate the effectiveness of the proposed method.

Doppler sensitivity of MIMO radar waveforms

Doppler sensitivity of multiple-input multiple-output (MIMO) radar waveforms is complicated but rarely is of concern in most existing MIMO waveform designs. For both distributed and colocated MIMO radar, this paper studies the impact of Doppler sensitivity on both autocorrelation and mutual correlation sidelobes of both constant-modulus MIMO transmit waveforms and angular waveforms in theory and via numerical results, finding that Doppler sensitivity deserves consideration in future MIMO radar waveform designs.

Robust Design of Transmit Waveform and Receive Filter For Colocated MIMO Radar

We consider the problem of angle-robust joint transmit waveform and receive filter design for colocated multiple-input multiple-output (MIMO) radar, in the presence of signal-dependent interferences. The design problem is cast as a max-min optimization problem to maximize the worst-case output signal-to-interference-plus-noise-ratio (SINR) with respect to the unknown angle of the target of interest. Based on rank-one relaxation and semi-definite programming (SDP) representation of a nonnegative trigonometric polynomial, a cyclic optimization algorithm is proposed to tackle this problem. The effectiveness of the proposed method is illustrated via numerical examples.

Transmit Signal and Receive Filter Design in Co-located MIMO Radar Using a Transmit Weighting Matrix

In this letter, we jointly design the transmit signals and the receive combining filter based on exact information on the locations of target and interferences in co-located multiple-input multiple-output (MIMO) radars. The idea behind the proposed method is to maximize the signal-to-interference-plus-noise ratio (SINR) without designing the waveform covariance matrix and exploit the advantages of MIMO radar. Each transmit element sends linear combinations of the orthogonal waveforms by a weighting matrix. Numerical results show the improvement in the SINR performance offered by using the proposed algorithm compared to the phased array and existing MIMO radar techniques.

SINR maximization in colocated MIMO radars using transmit covariance matrix

The main waveform design features in multiple-input multiple-output (MIMO) radars include (a) signal transmission with full rank covariance matrix in order to use the maximum waveform diversity and to suppress more number of interferers, (b) constant envelope in order to have simplicity in deployment and to reduce the destructive effect of nonlinear amplifiers and (c) small side lobe level (SLL) in order to reduce the effect of interferers with unknown location. Therefore, in order to maximize the signal-to-interference-plus-noise ratio (SINR) and to exploit the advantages of MIMO radars, in this paper we have proposed two full rank transmit covariance matrices and maximum achievable SINR is calculated analytically for both. We have shown that the two proposed covariance matrices can be used to generate BPSK waveforms which satisfy constant modulus constraint. Simulation results show that when the angle location of interferences is known, the first proposed matrix achieves a higher level of SINR compared to the second one, while the second proposed matrix has a lower SLL compared with the first one. Also we have shown that the two proposed covariance matrices can handle more interferences compared to phased-array and the recently proposed methods in MIMO radars.

Adaptive detection without training data in colocated MIMO radar

For colocated multiple-input multiple-output (MIMO) radar target detection in colored noise, we propose two adaptive detectors according to the Rao andWald test criteria. These detectors do not need training data and possess constant false alarm rate properties. We investigate the manner in which they work. From a detection viewpoint, we show that there is no need for matched filtering for colocated MIMO radar.We derive the statistical distributions of the proposed detectors and then obtain the analytical expressions for the probabilities of false alarm and detection for both deterministic and random signals. Numerical examples are provided to compare the detection performance of the Rao andWald tests with an existing detector.

Relative Entropy-Based Waveform Design for MIMO Radar Detection in the Presence of Clutter and Interference

This paper considers the waveform design problem for multiple-input multiple-output (MIMO) radars in order to improve the detection performance of the systems. We assume that target echoes are embedded in (signal-dependent) clutter as well as (colored) interference. Considering the optimal (Neyman-Pearson) detector, obtaining waveforms which maximize the detection probability for a fixed value of the probability of false alarm is intractable. Therefore, we employ relative entropy associated with the detection problem as the figure of merit for the waveform design. We devise an iterative method based on minorization-maximization (MM) technique to tackle the nonconvex design problem. This method also includes a novel trick for replacing a nonconvex constraint set (associated with an equivalent form of the design problem) with a convex one iteratively. The proposed method increases the design metric monotonically and is guaranteed to converge. We extend the devised method for using in design with peak-to-average power ratio (PAR) and similarity constraints. The method can be applied to both statistical and colocated MIMO radars. Several numerical examples are included to demonstrate the effectiveness of the proposed method.