Elsevier

Signal Processing

Volume 176, November 2020, 107650
Signal Processing

Joint time-space resource allocation and waveform selection for the collocated MIMO radar in multiple targets tracking

https://doi.org/10.1016/j.sigpro.2020.107650Get rights and content

Highlights

  • Resource management for the collocated MIMO radar in multiple targets tracking.

  • The ability of simultaneous multiple targets illumination by a wide beam in the collocated MIMO radar and sub-array number’s influence on beam width.

  • Joint adjustment of sub-array number, system sampling period, transmitting energy, illuminated targets set, and transmitting waveform parameters.

  • Simulation results demonstrate that the validity and effectiveness of the proposed algorithm.

Abstract

Compared with conventional phased array radar, the collocated MIMO radar can effectively control the transmitting beam width by means of sub-array division. Therefore, different targets may be illuminated simultaneously with one beam in the collocated MIMO radar, providing greater freedom degree in resource management. The joint time-space resource allocation and waveform selection optimization model for the collocated MIMO radar is proposed in this paper, where the objective function that takes both the system resource and tracking precision into consideration is minimized under the guarantee of effective targets detection. Through solving the proposed optimization model, the corresponding joint optimization algorithm is obtained. The optimal sampling period, sub-array number, illuminated targets set, transmitting energy and transmitting waveform parameters combination is chosen adaptively, where the former four realize the time-space resource allocation and the last one realizes the waveform selection. Simulation results demonstrate that the validity and effectiveness of the proposed algorithm.

Introduction

The multiple-input multiple-output (MIMO) radar system receives considerable attention recently [1]. It has advantages in the aspects of location accuracy, detection of low speed targets, space distinguishing, dealing with invisible targets and low probability of interception etc [1]. In general, MIMO radar can be divided into two types, including the one with separated antennas [2] and the collocated MIMO radar [3]. In the former, the transmitting antennas are located far apart from each other relative to their distance to the target [2]. However, there are many actual difficulties that prevent the distributed MIMO radar from being applied in practice. The latter is a promotion of conventional phased array radar, which is a more practical MIMO radar system [4].

The orthogonal waveforms are transmitted via its array elements in the collocated MIMO radar. Compared with conventional phased array radar, the collocated MIMO radar can effectively control the transmitting beam width by the number of transmitted orthogonal waveforms. Therefore, different targets may be illuminated simultaneously with one wide beam. Due to unique structure of the collocated MIMO radar, it can transmit a high gain narrow beam to illuminate multiple targets one by one or a low gain wide beam to illuminate multiple targets simultaneously [5], [6], [7]. For the collocated MIMO radar, its degree of freedom in resource management is increased, therefore, in order to make full use of it, the corresponding radar resource management strategy should be designed.

The radar resource management problem arises from conventional phased array radar. For adaptive time resource management, an adaptive sampling period algorithm named the formula method is proposed in [8], which is based on the Singer model. In [9], an adaptive sampling period algorithm based on the residual is proposed, where the residual is from the α-β filter. The predicted error covariance threshold method is proposed in [10], which is based on the interactive multiple model (IMM) algorithm [11]. For the transmitting waveform parameters, the connection between the transmitting waveform and the filter based on the Cramér-Rao lower bound (CRLB) is established in [12]. Furthermore, above conclusion is extended to the clutter environment [13], [14]. One step ahead as well as two steps ahead methods for the waveform scheduling are proposed in [14], [15], and the superiority of the latter algorithm is demonstrated. A general frequency-modulated (FM) waveform library is established and the multiple sensors’ dynamic waveform configuration is studied in clutter in [16], [17]. There are also many applications related to waveform in other domains such as biomedical and medical domains. A joint time-frequency localized three-band biorthogonal wavelet filter bank to compress electrocardiogram (ECG) signals is proposed in [18]. A joint algorithm based on biorthogonal wavelet transform and run-length encoding (RLE) is proposed in [19], detecting QRS of the ECG signal and compressing the detected ECG data. In [20], biorthogonal wavelet transform is used to detect ECG signal’s QRS complex and lempel ziv markov chain algorithm (LZMA) based on ECG data compression technique is proposed. A joint approach for denoising, detection, compression, and wireless transmission of ECG signal is proposed in [21], where the modified biorthogonal wavelet transform is used.

For multiple targets tracking, an algorithm for beam scheduling is proposed in [22], where radar resource management of multiple targets tracking is formulated as a hidden Markov chain multi-arm bandit problem. Above algorithms are only for conventional phased array radar. For the resource management in the collocated MIMO radar, optimal joint power and bandwidth allocation algorithm is proposed for best target localization performance in [23]. In [24], a resource management algorithm in multiple targets tracking is proposed, where the limited system resource is entirely consumed to improve the tracking precision of worst target. Similar work that considers clutter environment is given in [25]. A joint beam, power and waveform selection strategy for the MIMO radar target tracking is proposed in [26], where the posterior estimation error of multiple targets in worst case is minimized. A resource management algorithm for multiple targets tracking is proposed in [27] to guarantee the desired tracking precision. An adaptive resource allocation strategy for multiple targets tracking with different performance requirements is brought forward in [28]. While the aforementioned works have made definite contributions to the collocated MIMO radar resource management, there are still some issues to be addressed.

  • The time resource allocation is not considered in the existing resource management strategies for the collocated MIMO radar [23], [24], [26], [27], [28], [32], [33], which is an important topic in resource management. Furthermore, the dynamic waveform design and resource allocation are always considered separately, where the relationship between them is ignored. The joint optimization is seldom investigated. However, both the allocated resource and waveform parameters have effect on the tracking precision and the tracking precision will affect subsequent resource allocation.

  • Moreover, resource awareness is of crucial importance in the implementation of a radar system because of the contradiction between resource utilization and performance requirement. Most of the existing resource management algorithms aim to consume entire limited system resource to improve the tracking precision [23], [24], [25]. However, in actual systems, it is not necessary to maximize the tracking precision. How to minimize the system resource consumption under the guarantee of normal tracking has more practical value.

  • More importantly, in the existing resource management strategies for the collocated MIMO radar, the realization form of orthogonal waveforms is not considered. In general, the orthogonal waveforms are transmitted via each sub-array by means of sub-array division. In this case, the beam is much wider than that in In practice, the theoretical optimal tracking precision can’t be obtained. phased array radar. Therefore, the collocated MIMO radar has the ability to illuminate multiple targets simultaneously. However, most of the existing resource management algorithms only consider one beam corresponds to one target [24], [26], [27], [28], [32].

  • Besides, the CRLB is often adopted to evaluate the tracking performance in resource management algorithms [23], [24], [25], [26]. However, it only quantifies the theoretically achievable performance. For adaptive resource management, it is more reasonable to optimize resource allocation based on the actual tracking precision instead of the theoretical one. Furthermore, particle filter (PF) is always used in resource management algorithms in order to deal with the nonlinear measurements [24], [25], [32], which has large computational complexity.

Based on above, a joint time-space resource allocation and waveform selection optimization model for the collocated MIMO radar is proposed in this paper, where the objective function that firstly takes both the system resource and tracking precision into consideration is minimized under the guarantee of effective targets detection. Through solving the proposed optimization model, the corresponding joint optimization algorithm is obtained. The optimal sampling period, sub-array number, illuminated targets set, transmitting energy and transmitting waveform parameters combination is chosen adaptively, where the former four realize the time-space resource allocation and the last one realizes the waveform selection. The main contributions are summarized as follows.

  • The joint time-space resource allocation and waveform selection problem is firstly considered, in which the sampling period determines the time resource allocation, the sub-array number, the transmitting energy and the illuminated targets set determine the space allocation. The transmitting waveform parameters achieve the selection of the transmitting waveform.

  • A joint time-space resource allocation and waveform selection optimization model is established, where the objective function that firstly takes both the system resource and tracking precision into consideration is minimized under the guarantee of effective targets detection. Moreover, the allocated resource, including the sampling period, the sub-array number and the transmitting energy, has effect on the tracking precision by influencing signal-to-noise (SNR).

  • The ability of simultaneous multiple targets illumination by a wide beam in the collocated MIMO radar is fully considered. The orthogonal waveforms are transmitted by sub-arrays, and the beam width can be flexibly changed by means of sub-array division.

  • The estimation error covariance is used to evaluate the tracking performance instead of CRLB, which can reflect the actual tracking precision during tracking. The predicted sequential unbiased converted measurement filtering (PRE-SQU) algorithm is used to deal with the nonlinear measurements [36]. The estimation error covariance is predicted in the PRE-SQU to guide the resource management. Thereby, the finite resource can be utilized more reasonably and efficiently.

The rest of this work is organized as follows. In Section 2, the problem formulation is given. In Section 3, the system model is introduced, and the joint time-space resource allocation and waveform selection optimization model for the collocated MIMO radar is established in Section 4, the corresponding algorithm is given in Section 5. Section 6 shows the simulation results, and the conclusion is given in Section 7.

Section snippets

Problem formulation

It is assumed that there are M array elements in the collocated MIMO radar transceiver array. The array can be divided into several sub-arrays, whose transmitting waveforms are orthogonal to each other. The sub-array number can be changed flexibly in the system, so is the elements number in each sub-array. Because the transmitting beam width is proportional to the elements number in each sub-array, a wider transmitting beam can be obtained compared with conventional phased array radar.

System model

In this section, we introduce the target dynamic model, measurement model, and the structure of PRE-SQU, which is used to deal with nonlinear measurement.

Successful illumination constraint

To obtain the measurements in multiple targets tracking, the targets whose states are to be updated should be illuminated by the transmitting beam firstly. The illumination means the targets should be located in the coverage of the transmitting beam. For example, if the illuminated targets set is { 1, 3}, Target 1 and Target 3 should be in the coverage of the transmitting beam. Thereforeuϕ(K)/2<ui<u+ϕ(K)/2iqIt means that only when the predicted position of target is in the range of the

Joint time-space resource allocation and waveform selection algorithm for the collocated MIMO radar

As shown in (18), the joint time-space resource allocation and waveform selection optimization problem involves six working parameters of the collocated MIMO radar, namely the sub-array number, the sampling period, the illuminated targets set, the transmitting energy and the transmitting waveform parameters. Assume the previous update moment is tk1, after filtering the state of each target is {tk1(i),x^i(tk1(i)),Pi(tk1(i))}i=1,2,,D, where tk1(i) is the latest update moment for Target i.

Simulation

Assume that there are two targets moving in the scene. They move with constant velocity from 0 to 200 s. The initial position of Target 1 and Target 2 are [120000 m 120400 m] and [120800 m 120800 m], and the velocity of them are [20 m/s, 4 m/s] and [15 m/s, 0 m/s]. The trajectories of the two targets are shown in Fig. 3. For Target 1, the process noise is zero mean with variance of 5m2/s4. For Target 2, the process noise is zero mean with variance of 15m2/s4. For the collocated MIMO system, the

Conclusion

For the collocated MIMO radar in multiple targets tracking, how to minimize the resource consumption with preferable tracking precision has important practical value. The joint time-space resource allocation and waveform selection optimization model is proposed in this paper. The optimal sampling period, sub-array number, illuminated targets set, transmitting energy and transmitting waveform parameters combination is chosen adaptively, where the former four realize the time-space resource

CRediT authorship contribution statement

Xi Li: Conceptualization, Writing - original draft, Writing - review & editing, Methodology, Software. Ting Cheng: Conceptualization, Methodology, Resources, Supervision, Writing - review & editing. Yang Su: Investigation, Validation, Data curation, Writing - review & editing. Han Peng: Investigation, Validation, Data curation, Writing - review & editing.

Declaration of Competing Interest

We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.

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