Tensor-Based Reduced-Dimension MUSIC Method for Parameter Estimation in Monostatic FDA-MIMO Radar

Frequency diverse array (FDA) radar has attracted much attention due to the angle and range dependence of the beam pattern. Multiple-input-multiple-output (MIMO) radar has high degrees of freedom (DOF) and spatial resolution. The FDA-MIMO radar, a hybrid of FDA and MIMO radar, can be used for target parameter estimation. This paper investigates a tensor-based reduced-dimension multiple signal classification (MUSIC) method, which is used for target parameter estimation in the FDA-MIMO radar. The existing subspace methods deteriorate quickly in performance with small samples and a low signal-to-noise ratio (SNR). To deal with the deterioration difficulty, the sparse estimation method is then proposed. However, the sparse algorithm has high computation complexity and poor stability, making it difficult to apply in practice. Therefore, we use tensor to capture the multi-dimensional structure of the received signal, which can optimize the effectiveness and stability of parameter estimation, reduce computation complexity and overcome performance degradation in small samples or low SNR simultaneously. In our work, we first obtain the tensor-based subspace by the high-order-singular value decomposition (HOSVD) and establish a two-dimensional spectrum function. Then the Lagrange multiplier method is applied to realize a one-dimensional spectrum function, estimate the direction of arrival (DOA) and reduce computation complexity. The transmitting steering vector is obtained by the partial derivative of the Lagrange function, and automatic pairing of target parameters is then realized. Finally, the range can be obtained by using the least square method to process the phase of transmitting steering vector. Method analysis and simulation results prove the superiority and reliability of the proposed method.

TOA and DOA Estimation for IR-UWB Signals: An Efficient Algorithm by Improved Root-MUSIC

The automatically paired time of arrival (TOA) and direction of arrival (DOA) can be jointly estimated via a high-precision multidimensional spectral peak search- (SPS-) based multiple signal classification (MUSIC) algorithm in the impulse radio ultrawideband (IR-UWB) positioning system, while heavy computational burden is required. To tackle this issue, we propose an improved root-MUSIC algorithm for joint TOA and DOA estimation. After modelling the frequency domain form of the received signal, the algorithm first uses the signal subspace to establish the relationship between the two antennas. Then, the MUSIC spatial spectrum function is reconstructed with this relation, which enables it to offer a spectrum function in regard to the one-dimensional (1D) parameter of time delay. For further reducing the complexity, the TOA estimates of one antenna are obtained via 1D polynomial root finding instead of SPS, and the TOA estimates of the other antenna can be calculated by the established relationship. Finally, the DOA estimation can be achieved with the estimated TOAs. Due to the relationship between two antennas with signal subspace, the parameters estimated by the proposed algorithm are autopaired. Numerical simulations substantiate the superiority of the proposed algorithm.

Blind Joint DOA and Polarization Estimation for Polarization-Sensitive Coprime Arrays Via Reduced-Dimensional Root Finding Approach

In this paper, we investigate the problem of blind joint multi-parameter estimation for polarization-sensitive coprime linear arrays (PS-CLAs). We propose a reduced-dimensional polynomial root finding approach, which first utilizes the relation between the two subarrays to reconstruct the spectrum function and then converts three-dimensional (3D) total spectral search (TSS) to one-dimensional (1D) TSS. Furthermore, 1D polynomial root finding technique is employed to obtain the ambiguous direction of arrival (DOA) estimates, for further saving the computational cost. Finally, the true DOA estimates can be obtained based on the arrangements with coprime property, and subsequently the polarization parameters can be estimated through pairing. In addition, the matching error of false targets can be avoided due to the relation between the two subarrays. The proposed approach only requires about 0.01% computational complexity of the 1D TSS method to achieve the same estimation performance and behaves better in resolution. Simulations are provided to validate the superiority of the proposed approach.

Marked length rigidity for Fuchsian buildings

We consider finite $2$-complexes $X$ that arise as quotients of Fuchsian buildings by subgroups of the combinatorial automorphism group, which we assume act freely and cocompactly. We show that locally CAT($-1$) metrics on $X$, which are piecewise hyperbolic and satisfy a natural non-singularity condition at vertices, are marked length spectrum rigid within certain classes of negatively curved, piecewise Riemannian metrics on $X$. As a key step in our proof, we show that the marked length spectrum function for such metrics determines the volume of $X$.

Cyclic Relation Method for DOA and Polarization Parameters Estimation of Arbitrary Polarized Array

Focus on the estimation for DOA and polarization parameters of electromagnetic sensor array, this paper proposes the method that uses cyclic relation function to substitute for covariance matrix. Because cyclic statistic is less sensitive to stable noise and any cyclic stable noise with different cyclic frequency, the method proposed is immune to any stable color noise. This method use minimum norm method to solve the spectrum function. So this method can restrict the effect of the cyclic relation matrix estimating error. Computer simulation experiments prove the performance of this method.