Elsevier

Signal Processing

Volume 101, August 2014, Pages 42-51
Signal Processing

Transmit beamforming for DOA estimation based on Cramer–Rao bound optimization in subarray MIMO radar

https://doi.org/10.1016/j.sigpro.2014.01.033Get rights and content

Highlights

  • The CRBs for DOA estimation of subarray MIMO radar are derived.

  • A new transmit beamforming algorithm for subarray MIMO radar is proposed.

  • Our method can obtain better tradeoff between array aperture and coherent gain.

  • A better DOA estimation performance is obtained while fewer waveforms are emitted.

  • The computational cost of MIMO radar is also reduced in our method.

Abstract

Compared to conventional phased-array radar, MIMO radar benefiting from its extra degrees of freedom brought by waveform diversity allows to optimize the Cramer–Rao Bound (CRB) for Direction-of-arrival (DOA) estimation more freely. In this paper, under the premise that the general angular directions of targets are known as priori, a new transmit beamforming method for subarray MIMO radar is proposed with the application to improve the performance of DOA estimator for multiple targets. The CRB expression for DOA estimation of subarray MIMO radar is derived firstly. Then, the correlation matrix of the transmitted waveforms is optimized to minimize the CRB for DOA estimation. Once the optimized correlation matrix is determined, eigendecomposition method is applied to calculate the subarray beamforming weights. Meanwhile, fewer orthogonal waveforms are transmitted in the proposed method compared to conventional MIMO radar, which means that less number of subarrays will be used. The reduction in the number of transmitted orthogonal waveforms can effectively reduce the computational complexity. The proposed method obtains the optimized tradeoff between the effective aperture of virtual array and coherent gain, and consequently improves the performance of DOA estimator. Simulation results show that the proposed method has a superior performance compared with the existing methods.

Introduction

In recent years, MIMO radar as an emerging field of radar research has attracted more and more attentions of scientific researchers [1], [2]. Depending on the array element configuration, MIMO radar can be classified into two categories: separated distributed MIMO radar [3] and co-located distributed MIMO radar [4], [5]. Compared with conventional phased-array radar, MIMO radar may have a similar array structure, whereas the transmitted waveforms may be quite different from each other. Due to the extra degrees of freedom offered by waveform diversity, MIMO radar obtains superior capabilities compared with conventional phased-array radar, such as higher resolution and better parameter identifiability[ [6], [7], [8].

Estimating DOAs of multiple targets is one of the most important applications of radar system in practice. Some classic DOA estimation algorithms have been applied to MIMO radar, such as ESPRIT and MUSIC [9], [10], [11], [12], [13]. The methods proposed in [9], [10] both take full advantage of the rotational invariance property of the uniform linear array to estimate the DOA of target. The ESPRIT-like algorithm for non-uniform array MIMO radar is also proposed in [12]. As we all know, spatial angular resolution of radar is inversely proportional to the effective aperture of array. For the reason that larger virtual effective aperture can be obtained in MIMO radar, in some scenarios, these algorithms applied by MIMO radar will have better performance than that applied by conventional phased-array radar. However, the performance of DOA estimation algorithms is still affected by other factors. For example, ESPRIT algorithm is also subject to SNR [14]. MIMO radar transmitting orthogonal waveforms is faced with the problem of SNR gain loss, which is unfavorable for DOA estimation.

In order to mitigate the effects of the SNR gain loss, there are many energy focus methods proposed for MIMO radar recently. These methods can be generally classified into two categories.

One is utilizing partially correlated signals as the transmitted waveforms [15], [16], [17], [18], which we refer to as Partially Correlated Waveforms (PCW) MIMO radar for convenience. The basic idea of PCW MIMO radar is to optimize the correlation matrix of transmitted waveforms firstly, and then to design the partially correlated signals according to the optimized correlation matrix. By focusing the transmit energy within the interested regions, this method will achieve better parameter identifiability. Meanwhile, some partially correlated signals design methods are developed for PCW MIMO radar [19], [20], [21]. The BPSK and polyphase coded signals which have the approximately correlation matrix to a desired one can be obtained respectively by the methods proposed in [19], [20] with high computational cost.

The other category is subarray MIMO radar. The transmit array of the subarray MIMO radar is divided into several subarrays, and the transmit waveforms are coherent within each subarray while orthogonal among the subarrays. Actually, subarray MIMO radar can be regarded as a tradeoff between phased-array and MIMO radar, and thus it is also called as phased-MIMO radar in [22]. Overlapped and non-overlapped subarray configurations are discussed in [22], [23] and [24] respectively. However, one of the disadvantages in subarray MIMO radar is that the transmit beam-pattern optimization with respect to the beamforming weights of the subarrays is often hard to be resolved by convex optimization algorithms directly. Besides, there is no adaptive principle for the division of subarrays so far. In essence, PCW MIMO radar and subarray MIMO radar both sacrifice partial effective aperture of virtual array for coherent transmit gain. The signal models of them are equivalent mathematically.

In this paper, a new transmit beamforming algorithm based on the optimization of CRB for DOA estimation is proposed for subarray MIMO radar, under the premise that the general angular directions of targets are known as priori. Firstly, the correlation matrix of transmitted waveforms is optimized to minimize the CRB for DOA estimation. It is worth noting that the optimized correlation matrix of transmit waveforms is obtained without considering the configurations of the subarrays. Secondly, eigendecomposition method is applied in the optimized correlation matrix to determine the configurations of the subarrays. Generally, the correlation matrix of transmitted waveforms is not always full rank, which makes it possible to transmit less number of orthogonal waveforms in the proposed method. Although less number of orthogonal waveforms will result in the reductions of the effective aperture of virtual array and the number of DOAs that can be estimated, the SNR gain of each virtual array will be increased and the huge amount of computational complexity of MIMO radar at the receiver will be reduced. In fact, part of the extra degrees of freedom are converted into transmit coherent gain, which will improve the DOA estimation performance. Therefore, the proposed method develops a way to achieve the optimized tradeoff between the effective aperture of virtual array and coherent gain, which obtains the optimized DOA estimation performance.

Actually, the optimization method based on CRB is proposed in [18], but it cannot be applied in subarray MIMO radar directly because the algorithm is based on PCW MIMO radar. The concept of subarray MIMO radar is first proposed in [22] and the further researches can be found in [26]. Nevertheless, the methods of optimization for subarray beamforming weights or the subarry division are not investigated by them. The particular contributions of this paper are as follows. Firstly, the CRB for DOA estimation of subarray MIMO radar are derived, and the CRB based optimization method for PCW MIMO radar is extended to subarray MIMO radar. Then, the method we proposed provides an effective principle for the division of subarrays and determining the minimum number of transmitted orthogonal waveforms. Meanwhile, the proposed method also enables us to design the correlation matrix more freely without consideration of the partially correlated signals design. Due to the optimized tradeoff between the effective aperture of virtual array and coherent gain, the proposed method can achieve a better DOA estimation performance with less computational complexity compared to the existing algorithms.

The paper is organized as follows. In Section 2, we briefly introduce the signal models of conventional MIMO radar, PCW MIMO radar and subarray MIMO radar respectively. In Section 3, a new transmit beamforming algorithm based on CRB optimization is proposed for subarray MIMO radar. The performance of the proposed algorithm is analyzed in Section 4. The simulations results that show the advantages of the proposed method are presented in Section 5 which is followed by the conclusions in Section 6.

Section snippets

Conventional MIMO radar

Consider a MIMO radar equipped with a transmit array of Mt antennas and a receive array of Mr antennas. The transmit and receive arrays are both uniform linearly array (ULA), and they are assumed to be closely located so that both of them can see a target located in the far-field at the same spatial angle. In conventional MIMO radar, the Mt antennas of transmit array are used to transmit Mt orthogonal waveforms. Assume that there are K targets existing in the far-field, then the complex envelop

Transmit beamforming based on CRB optimization for DOA estimation

The CRB for DOA of the unknown target represents the best performance of any unbiased estimator. The stochastic and deterministic CRB matrixes for DOA estimation have been given in [26]. However, according to Stoica and Moses [28], the deterministic CRB matrix for DOA estimation of the subarray MIMO radar assumed in Section 2 can be calculated as follows (The derivation can be found in Appendix A.):CRBDOA(θ)=σ22L{Re(DHΠVDP^)}1whereD[d(θ1),,d(θK)]d(θ)v(θ)θ=(CHa(θ)θ)b(θ)+(CHa(θ))b(θ)

Performance analysis

In this section, the performance of the proposed transmit beamforming method for subarray MIMO radar is analyzed in terms of the power transmitted by each subarray, subarray transmit beamforming gain, maximum effective aperture of the virtual array, and the computational complexity associated with eigendecomposition based DOA estimation techniques.

In the proposed method, the number and configurations of the subarrays can be adjusted adaptively to the priori information of targets. However,

Simulation results

In all of the simulation experiments in this section, a MIMO radar system is assumed to have a transmit array of Mt=10 omni-directional antennas spaced half a wavelength apart, which is also used as the receive array. The additive noise is Gaussian zero-mean σ2-variance spatially and temporally white. To compare the performance of the proposed method with other existing methods, five beamforming methods are considered: (a) the proposed transmit beamforming method, (b) the beamforming method

Conclusion

In this paper, the proposed transmit beamforming for subarray MIMO radar can achieve a superior performance of DOA estimation with the minimum number of subarrays owing to the following two reasons. First, the proposed method can achieve the theoretical minimum CRB for DOA estimation by optimizing the correlation matrix of transmitted waveforms. Then, fewer orthogonal waveforms transmitted in our method makes the transmit energy further concentrated at the region of interest, which also reduces

Acknowledgments

This work is supported in part by the National Natural Science Foundation of China under grant 11273017.

References (28)

  • Z. Shenghua et al.

    Adaptive MIMO radar target parameter estimation with Kronecker-product structured interference covariance matrix

    Signal Process.

    (2012)
  • I. Bekkerman et al.

    Target detection and localization using MIMO radars and sonars

    IEEE Trans. Signal Process.

    (2006)
  • C. Duofang et al.

    Angle estimation using ESPRIT in MIMO radar

    Electron. Lett.

    (2008)
  • C. Jinli et al.

    Angle estimation using ESPRIT without pairing in MIMO radar

    Electron. Lett.

    (2008)
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