The Spatially Separated Polarization Sensitive FDA-MIMO Radar: A New Antenna Structure for Unambiguous Parameter Estimation

Joint DOA-range-polarization estimation with a novel radar system, i.e., spatially separated polarization sensitive random frequency diverse array based on multiple-input multiple-output (SSPSRFDA-MIMO) radar, is discussed. The proposed array can obtain not only unambiguous range estimation but also polarization parameter estimation. Firstly, the signal model of SS-PSRFDA-MIMO radar is constructed. Secondly, dimension reduction multiple signal classification (DR-MUSIC) algorithm is extended to parameter estimation with the proposed array. Last, simulations demonstrate the proposed algorithm is effective to estimate parameter, and the performance of proposed array is better than that of polarization sensitive frequency diverse array based on MIMO radar. It is worth mentioning that the Cramér–Rao lower bound (CRLB) of range estimation with the proposed array is much lower than that of PSFDA-MIMO radar.


Introduction
In reference [1], we have discussed the direction of arrival (DOA), range and polarization estimation with polarization sensitive frequency diverse array based on multiple-input multiple-output (PSFDA-MIMO) radar. Although three algorithms are proposed to obtain accurate parameter estimation in reference [1], the problem of ambiguous range estimation is not considered. So, this paper attempts to solve the problem. To solve the problem of ambiguous range estimation with linear frequency diverse array (FDA), Wang et al. propose a random frequency diverse array in reference [2]. Motivated by that idea, this paper proposes a novel array, i.e., polarization sensitive random frequency diverse array based on MIMO radar (PSRFDA-MIMO) to solve the problem of ambiguous range estimation with PSFDA-MIMO radar. In order to reduce the mutual coupling, the spatially separated crossed-dipoles is chosen to be the array element of the proposed array. Therefore, the proposed array can be abbreviated as SS-PSRFDA-MIMO radar. Then a dimension reduction multiple signal classification (DR-MUSIC) algorithm is extended to parameter estimation with the proposed array. Compared with PSFDA-MIMO radar, the proposed array has following advantages: a) it can obtain unambiguous parameter estimation; b) the Cramér-Rao lower bound (CRLB) of range estimation with the proposed array is much lower than that of PSFDA-MIMO.
where  and  denote the auxiliary polarization angle and the polarization phase difference, respectively. denotes Hadamard product. The steering vector of the proposed array can be expressed as [1,[4][5][6] ( , , , ) where  denotes Kronecker product, superscript ( ) represent transmitting and receiving steering vector, respectively. Thus the received data can be expressed as where K denotes the number of targets. The echo signal () k st is assumed to be a zero-mean, complex Gaussian, random process. ( according to the signal model of (8).

Proposed dimension reduction (DR) MUSIC algorithm
Obviously, there are four parameters to be estimated in the steering vector of (3 where N E is noise subspace, which can be computed according to the received data of (8). However, the fourdimensional searching will result in heavy calculation. So, we will propose a dimension reduction MUSIC algorithm (DR-MUSIC) with two-dimensional searching. The detail process is elaborated as follows. Utilizing , the steering vector can be converted into

Simulations
To demonstrate the perfect performance of the proposed array, PSDFDA-MIMO radar is introduced for comparison. Assume that there are 10 array elements separated by half a wavelength in the transmitting and receiving array. The space of crossed-dipoles of single vector sensor is also set to be half a wavelength. Two non-coherent narrowband signal sources are considered: , , , 20 ,30km,60 ,30 r Suppose that the probability density function (PDF) of m  is 1/2. The center frequency is set to be 3×10 9 HZ. The frequency increment is set to be 10 6 HZ. signal-tonoise-ratio (SNR) is set to be 20dB. The number of snapshots is set to be 1000. Fig. 3 (a) and (b) show the spatial spectrum of proposed array and PSFDA-MIMO array based on DR-MUSIC algorithm, respectively. As shown in Fig. 3, the proposed array can give unambiguous parameter estimation, but the range estimation with PSFDA-MIMO array is ambiguous.
(a) Spatial spectrum based on proposed array (b) Spatial spectrum based on PSFDA-MIMO radar Fig. 3. Spatial spectrum based on two kinds of arrays Next we will compare the CRLB based on proposed array with that based on PSFDA-MIMO radar to demonstrate the perfect performance of the proposed array. CRLB based on PSFDA-MIMO radar [1] has been derived. So, CRLB based on proposed array can be derived similarly. But we should substitute the joint steering vector of this paper into that of reference [1]. The number of snapshots and Monte Carlo experiment are set to be 1000 and 100, respectively. SNR varies from -10dB to 10dB with 2dB interval. Fig. 4 shows how the root mean square error (RMSE) of parameters estimation varies against SNR. From the results in Fig. 4, we can know that: (1) the proposed DR-MUSIC algorithm can give the parameter estimation effectively; (2) the performance of proposed array is better than that of PSFDA-MIMO radar, especially for the CRLB of range estimation.

Conclusions
In this paper, parameter estimation with SS-PSRFDA-MIMO radar has been investigated. The proposed DR-MUSIC algorithm for unambiguous parameter estimation with proposed array work well. Furthermore, the CRLB of range estimation with the proposed array is much lower than that of range estimation with PSFDA-MIMO radar. It is potential to improve the resolution of range.