Elsevier

Signal Processing

Volume 183, June 2021, 108006
Signal Processing

Cognitive FDA radar transmit power allocation for target tracking in spectrally dense scenario

https://doi.org/10.1016/j.sigpro.2021.108006Get rights and content

Abstract

In this paper, we propose a cognitive radar paradigm based on frequency diverse array (FDA), which allows flexible spectrum control via element-wise transmit power allocation. As an emerging array technique, FDA differs from conventional phased array (PA) in that it imposes an additional frequency increment across the array elements. The use of frequency increment provides the FDA radar with the ability of flexible spectrum adjustment. We propose the cognitive FDA radar for target tracking in spectrally dense scenarios. Two optimization criteria, i.e., signal-to-interference-plus-noise ratio (SINR) maximization and Cramér-Rao bound (CRB) minimization, are employed to adaptively update the array weight vector for power allocation at each transmission. Numerical results show that the proposed cognitive FDA radar can adjust the signal spectrum to avoid the interfered frequencies for better output SINR. The resulting tracking errors of FDA radar with adaptive power allocation are lower than that for fixed power allocation. Moreover, the CRB criterion further improves the tracking performance.

Introduction

Cognitive radar [1] differs from conventional radar in that it is capable of learning experience from interaction with the surrounding environment, and then adaptively updates its transmit parameters to match current environment for improved performance of target detection and tracking [2], [3], [4]. In spectrally dense scenarios due to the interferences from non-cooperative or hostile illuminators [5], cognitive radar can adjust the transmit parameters according to its spectrum sensing result to avoid potential interferences. Conventional approaches for single-antenna and phased array (PA) radars to realize flexible spectrum adjustment are enabled by spectrum-notched sequences, which were designed by optimization techniques and then synthesized by waveform generators [6], [7]. As an emerging array technique, frequency diverse array (FDA) [8] imposes an additional frequency increment across the elements of conventional PA [9]. The use of frequency increment renders the FDA signal with multiple carrier frequencies across the elements, which opens a door for flexible adjustment of the FDA signal spectrum via element-wise transmit power allocation. This leads to a promising paradigm of cognitive FDA radar especially suitable for target detection and tracking in spectrally dense environment, which enjoys the advantage of requiring no extra waveform optimization. Therefore, this paper proposes the use of FDA for cognitive target tracking in spectrally dense environment.

In fact, cognitive target tracking approaches have extensively been investigated for traditional radars [10], [11], [12], [13], [14], [15], spanning from the early attempts made by Kershaw and Evans [10] that minimizes the tracking error in clutters via adaptive waveform selection to the general framework of cognitive target tracking summarized by Bell et al. [15]. However, limited works have been conducted for cognitive target tracking using FDA radar. In recent years, FDA has attracted considerable attention mainly due to its jointly range-angle-dependent beampattern [8]. This joint dependency finds promising applications in radar systems, such as range-dependent beampattern synthesis [16], [17], range-angle localization of targets [18], [19], [20], suppression of deceptive jamming [21] and range-ambiguous clutters [22], [23]. The concept of cognitive FDA radar was initially applied in range-angle transmit beamforming with low probability of interception (LPI) [24], [25], [26]. Although moving target tracking approaches were subsequently proposed for cognitive FDA radar with LPI and energy-focused beamforming functions in [27] and [28], respectively, they are only applied to the interference-free environment. Different from Wang [27], Gui et al. [28], this work focuses on the application of cognitive FDA radar in target tracking under spectral interference, which has not been investigated in the literature. Note that the target tracking in spectrally dense environment is expected to be fairly realistic for future development of radar systems. It is because the increasing scarcity in radio spectrum would inevitably push part of the civil radar and communication systems to co-exist with each other over the same frequency band [5], thereby leading to mutual interferences. On the other hand, intentional jamming from hostile transmitters would also cause spectral interference to the desired radar signal.

In this paper, we propose an adaptive transmit element-wise power allocation approach for cognitive FDA radar to achieve adaptive avoidance for spectral interferences. To this end, we first derive a spectral interference model for the FDA radar with a focus on the structure of interference covariance matrix (ICM). Since the actual measurement data are highly non-linearly dependent on the target state, we exploit a particle filter-based tracking approach to deal with the high non-linearity problem. Moreover, inspired by the cognitive target tracking framework in [15], we propose two optimization criteria with predictive-average signal-to-interference-plus-noise ratio (SINR) maximization and Cramér-Rao bound (CRB) minimization, respectively, to update the array weight vector for power allocation during each transmission. Since the spectrum sensing result is absorbed as a prior knowledge, the proposed approach enables the cognitive FDA radar to flexibly adjust the transmit spectrum to avoid potential interferences. Our main contributions are summarized as follows.

  • We derive a novel structured covariance matrix model of spectral interference signals for FDA radar, enabling the subsequent cognitive FDA target tracking paradigm with dynamic transmit power allocation.

  • We propose a particle filter-based tracking approach to deal with the high non-linearity of FDA radar measurement data model. Moreover, two optimization criteria including the predictive average SINR maximization and CRB minimization together with their low-complexity approximations are derived to update the transmit power allocating weight vector of FDA radar for each probing.

  • We show through the numerical results that the proposed cognitive FDA radar can adjust the transmit spectrum flexibly to avoid potential spectral interferences. As a result, the output SINR and mean tracking error are higher and lower than those of FDA radar without transmit power allocation, respectively. Moreover, the CRB-based power allocation yields slightly better tracking performance than the SINR-based counterpart, at the cost of increased complexity.

The remainder of this paper is organized as follows. Section 2 describes the echo signal model of FDA radar first and then derives the corresponding covariance matrix structure under spectral interferences. Section 3 presents the particle filter-based implementation for target tracking in spectrally dense environment. Next, the SINR and CRB criteria for transmit power allocation together with their low-complexity approximations are proposed in Section 4, followed by numerical results in Section 5. The conclusions are drawn in Section 6.

Section snippets

Signal model for FDA radar

We consider an FDA transmitter with M-element uniform linear array (ULA), as shown in Fig. 1(a), where the carrier frequency of the mth transmit element is expressed asfm=f0+(m1)Δf,m=1,2,,Mwith f0 and Δf denoting the common carrier frequency and frequency increment, respectively. The radio frequency signal emitted from the mth element issm(t)cT,ms(t)ej2πfmtwhere cT,m is the mth transmit weight used for power allocation (PA) and s(t) denotes the baseband waveform, assumed to consist of total L

Particle filtering-based target tracking

Assume that a target with horizontal coordinate xk and vertical coordinate yk on 2-D plane is moving with a horizontal velocity x˙k and a vertical velocity y˙k. Note that the target state is updated every CPI, and the discrete time k means the kth CPI. The target is firstly detected and then tracked by the proposed FDA radar in spectrally dense scenarios.

Adaptive transmit power allocation

According to the cognitive target tracking approach [15], [28], the transmit weight vector cT,k can be designed via minimizing the predictive average of a given cost function J(x^k,xk), i.e.,cT,kopt=argmincT,kEp(Zk,xk|Z1:k1;cT,k){J(x^k,xk)}s.t.cT,k=1where the 2-norm · is used to constrain the transmit power, and p(Zk,xk|Z1:k1;cT,k), dependent on the weight vector cT,k, denotes the predictive joint PDF of Zk and xk, given previous measurement data Z1:k1. The predictive joint PDF can

Numerical results

Numerical examples are provided to investigate the performance of the proposed cognitive FDA radar-based target tracking approach with adaptive transmit power allocation.

Conclusion

In this paper, we developed an FDA-based cognitive radar paradigm with flexible spectrum control and then applied the cognitive FDA radar for target tracking in spectrally dense scenarios. To suppress potential interfered frequencies, we firstly established the receiver data model for spectral interfering signals with a focus on the covariance matrix structure and then proposed two optimization criteria including the predictive average SINR maximization and CRB minimization to adaptively update

CRediT authorship contribution statement

Ronghua Gui: Conceptualization, Methodology, Software, Investigation, Writing - review & editing. Zhi Zheng: Writing - review & editing. Wen-Qin Wang: Conceptualization, Methodology, Writing - review & editing, Supervision.

Declaration of Competing Interest

The authors declared that they have no conflicts of interest to this work entitled Cognitive FDA Radar Transmit Power Allocation for Target Tracking in Spectrally Dense Scenario authored by authored by Ronghua Gui, Zhi Zheng, Wen-Qin Wang for possible publication in Signal Processing. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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