ESPRIT-like angle estimation for bistatic MIMO radar with gain and phase uncertainties

Abstract

Gain and phase uncertainties would destroy the invariance property of both the transmit array and the receive array in bistatic MIMO radar, so the computationally efficient ESPRIT algorithm cannot be applied directly. Proposed is a novel ESPRIT-like algorithm, which uses the instrumental sensors method (ISM), to estimate the direction of departures and direction of arrivals. The ESPRIT-like algorithm is able to achieve favourable and unambiguous angle estimation without any information of the gain and phase uncertainties. The effectiveness of the proposed algorithm is verified by simulation results.Introduction: Multiple-input multiple-output (MIMO) radar is characterised by using multiple antennas to simultaneously transmit orthogonal waveforms and multiple antennas to receive the reflected signals [1]. Direction of departure (DOD) and direction of arrival (DOA) have been recently investigated in [2][3][4]. All of them are based on the assumption that the transmit array and receive array steering vector are exactly known corresponding to the array geometry. But the transmit array and receive array steering vector cannot be obtained precisely when there exist gain and phase uncertainties. Therefore, the performance of the algorithms proposed in [2 -4] will seriously degrade. To deal with the problem of gain and phase uncertainties of the transmit array and the receive array, a novel ESPRIT-like angle estimation algorithm is proposed in this Letter. As there is not requirement of space searching or iterative procedure, the computational complexity is low.

Joint DOA and DOD Estimation Based on Tensor Subspace with Partially Calibrated Bistatic MIMO Radar

“…In Figure 2, the RMSEs of the conventional ESPRIT algorithm, tensor-based ESPRIT algorithm, method in [16] (denoted as Guo's method), and the proposed algorithm are compared with different SNRs. Due to the partially calibrated arrays, the conventional ESPRIT algorithm and the tensorbased ESPRIT algorithm fail to achieve accurate angle estimations.…”

“…Due to the partially calibrated arrays, the conventional ESPRIT algorithm and the tensorbased ESPRIT algorithm fail to achieve accurate angle estimations. The Guo's method [16] is robust under the partially calibrated array case, however, it has a worse RMSE performance. On the other hand, the proposed method achieves the best estimation among the existing algorithms especially for the case of low SNR.…”

“…Therefore, the above algorithms will suffer from performance degradation or even fail to achieve accurate DOD and DOA estimation in many scenarios. A number of algorithms have been proposed to deal with the array calibration problem [13][14][15][16][17]. An iterative algorithm based on the MUSIC technique is proposed in [13], which can simultaneously achieve the angle and gain-phase uncertainties estimation.…”

“…In addition, this method is based on the assumption that the gain-phase uncertainties are small, otherwise it will suffer from suboptimal convergence. The algorithms proposed in [15,16] do not require iteration and exploit the ESPRIT-like technique to achieve accurate angle estimations. To achieve higher DOFs, the method proposed in [17] utilizes the property of the quasistationary signals to solve the underdetermined DOA estimation problem with partly calibrated arrays.…”

Underdetermined DOA Estimation of Quasi-Stationary Signals Using a Partly-Calibrated Array

“…As shown in (11), $\mathsf{\Pi }$ can be calculated based on the least squares method as $\mathrm{sans-serif\Pi }={\left({\mathbf{E}}_{s1}^H{\mathbf{E}}_{s1}\right)}^{-1}{\mathbf{E}}_{s1}^H\mathrm{sans-serif\Gamma }\left(\mathit{Y}\right){\mathbf{E}}_{s2}.$Substituting (A1) back to (14) results in $\begin{array}{cc}\hfill \underset{\mathrm{bold-italicY}}{falseprefixmin}& \parallel \mathrm{boldP}\mathrm{sans-serif\Gamma }(\mathit{Y}){\mathbf{E}}_{s2}{\parallel }_F^2\hfill \\ \hfill \mathrm{normals}.\mathrm{normalt}.& \mathbf{W}\mathit{Y}={\mathrm{bold1}}_{(N_c-1)N},\hfill \end{array}$ where $\mathrm{boldP}={\mathrm{boldI}}_{N(N-1)}-{\mathrm{boldE}}_{s1}{({\mathrm{boldE}}_{s1}^H{\mathrm{boldE}}_{s1})}^{-1}{\mathrm{boldE}}_{s1}^H$.To simplify the objective function in (A2), the following properties of matrix trace are applied [42,43], i.e., ${\parallel \mathrm{boldM}\parallel }_F^2=\mathrm{trace}[{\mathbf{M}}^H\mathbf{M}]$, $\mathrm{trace}false[\mathrm{boldMN}false]=\mathrm{trace}false[\mathrm{boldNM}false]$ and $\mathrm{trace}[\mathbf{M}\mathsf{\Gamma }false(\mathrm{boldd}false)\mathbf{N}\mathsf{\Gamma }false(\mathrm{boldd}false)]={\mathrm{boldd}}^H$…”