A Bivariate Index Vector to Measure Departure from Quasi-symmetry for Ordinal Square Contingency Tables

This study proposes a bivariate index vector to concurrently analyze both the degree and direction of departure from the quasi-symmetry (QS) model for ordinal square contingency tables. The QS model and extended QS (EQS) models identify the symmetry and asymmetry between the probabilities of normal circulation and reverse circulation when the order exists for arbitrary three categories. The asymmetry parameter of the EQS model implies the degree of departure from the QS model; the EQS model is equivalent to the QS model when the asymmetry parameter equals to one. The structure of the EQS model differs depending on whether the asymmetry parameter approaches zero or infinity. Thus, the asymmetry parameter of the EQS model also implies the direction of departure from the QS model. The proposed bivariate index vector is constructed by combining existing and original sub-indexes that represent the degree of departure from the QS model and its direction. These sub-indexes are expressed as functions of the asymmetry parameter under the EQS model. We construct an estimator of the proposed bivariate index vector and an approximate confidence region for the proposed bivariate index vector. Using real data, we show that the proposed bivariate index vector is important to compare degrees of departure from the QS model for plural data sets.

Angle Estimation for MIMO Radar in the Presence of Gain-Phase Errors with One Instrumental Tx/Rx Sensor: A Theoretical and Numerical Study

Ideal transmitting and receiving (Tx/Rx) array response is always desirable in multiple-input multiple-output (MIMO) radar. In practice, nevertheless, Tx/Rx arrays may be susceptible to unknown gain-phase errors (GPE) and yield seriously decreased positioning accuracy. This paper focuses on the direction-of-departure (DOD) and direction-of-arrival (DOA) problem in bistatic MIMO radar with unknown gain-phase errors (GPE). A novel parallel factor (PARAFAC) estimator is proposed. The factor matrices containing DOD and DOA are firstly obtained via PARAFAC decomposition. One DOD-DOA pair estimation is then accomplished from the spectrum searching. Thereafter, the remainder DOD and DOA are achieved by the least squares technique with the previous estimated angle pair. The proposed estimator is analyzed in detail. It only requires one instrumental Tx/Rx sensor, and it outperforms the state-of-the-art algorithms. Numerical simulations verify the theoretical advantages.

Angle Estimation and Mutual Coupling Self-Calibration in Bistatic MIMO System with Arbitrary Geometry

Ideal array responses are often desirable to a multiple-input multiple-output (MIMO) system. Unfortunately, it may not be guaranteed in practice as the mutual coupling (MC) effects always exist. Current works concerning MC in the MIMO system only account for the uniform array geometry scenario. In this paper, we generalize the issue of angle estimation and MC self-calibration in a bistatic MIMO system in the case of arbitrary sensor geometry. The MC effects corresponding to the transmit array and the receive array are modeled by two MC matrices with several distinct entities. Angle estimation is then recast to a linear constrained quadratic problem. Inspired by the MC transformation property, a multiple signal classification- (MUSIC-) like strategy is proposed, which can estimate the direction-of-departure (DOD) and direction-of-arrival (DOA) via two individual spectrum searches. Thereafter, the MC coefficients are obtained by exploiting the orthogonality between the signal subspace and the noise subspace. The proposed method is suitable for arbitrary sensor geometry. Detailed analyses with respect to computational complexity, identifiability, and Cramer-Rao bounds (CRBs) are provided. Simulation results validate the effectiveness of the proposed method.

A Propagator Method for Bistatic Coprime EMVS-MIMO Radar

In this paper, a novel two-dimensional (2D) direction-of-departure (DOD) and 2D direction-of-arrival (DOA) estimate algorithm is proposed for bistatic multiple-input multiple-output (MIMO) radar system equipped with coprime electromagnetic vector sensors (EMVS) arrays. Firstly, we construct the propagator to obtain the signal subspace. Then, the ambiguous angles are estimated by using rotation invariant technique. Based on the characteristic of coprime array, the unambiguous angles estimation is achieved. Finally, all azimuth angles estimation is followed via vector cross product. Compared to the existing uniform linear array, coprime MIMO radar is occupying large array aperture, and the proposed algorithm does not need to obtain signal subspace by eigendecomposition. In contrast to the state-of-the-art algorithms, the proposed algorithm shows better estimation performance and simpler computation performance. The proposed algorithm’s effectiveness is proved by simulation results.

A PE-MUSIC Algorithm for Sparse Array in MIMO Radar

Larger array aperture is provided by sparse arrays than uniform ones, which can improve the angle estimation resolution and reduce the cost of system evidently. However, manifold ambiguity is introduced due to the array sparsity. In this paper, a Power Estimation Multiple-Signal Classification (PE-MUSIC) algorithm is proposed to solve the manifold ambiguity of arbitrary sparse arrays for uncorrelated sources in Multiple-Input Multiple-Output (MIMO) radar. First, the paired direction of departure (DOD) and direction of arrival (DOA) are obtained for all targets by MUSIC algorithm, including the true and spurious ones; then, the well-known Davidon–Fletcher–Powell (DFP) algorithm is applied to estimate all targets’ power values, among which the value of a spurious target trends to zero. Therefore, the ambiguity of sparse array in MIMO radar can be cleared. Simulation results verify the effectiveness and feasibility of the method.

Direction-of-Departure and Direction-of-Arrival Estimation Algorithm Based on Compressive Sensing: Data Fitting

In this paper, a compressive sensing-based data fitting direction-of-departure/direction-of-arrival (DOD/DOA) estimation algorithm is proposed to apply the superior performance of compressive sensing method to the bistatic MIMO sonar systems. The algorithm proposed in this paper optimizes the output data via convex optimization-based sparse recovery, so that it is possible to estimate the DOD and the DOA for each target accurately. In order to minimize the amount of computation, the cost function with constraint condition is implemented in this paper. Furthermore, the constraint condition parameter of the cost function is analytically derived. Through various simulations, it is shown that the superior DOD and DOA estimation performance of the proposed algorithm and that the analytical derivation of the constraint condition parameter is useful for determination of regularization parameter.

2D-DOD and 2D-DOA Estimation for a Mixture of Circular and Strictly Noncircular Sources Based on L-Shaped MIMO Radar

In this paper, a joint diagonalization based two dimensional (2D) direction of departure (DOD) and 2D direction of arrival (DOA) estimation method for a mixture of circular and strictly noncircular (NC) sources is proposed based on an L-shaped bistatic multiple input multiple output (MIMO) radar. By making full use of the L-shaped MIMO array structure to obtain an extended virtual array at the receive array, we first combine the received data vector and its conjugated counterpart to construct a new data vector, and then an estimating signal parameter via rotational invariance techniques (ESPRIT)-like method is adopted to estimate the DODs and DOAs by joint diagonalization of the NC-based direction matrices, which can automatically pair the four dimensional (4D) angle parameters and solve the angle ambiguity problem with common one-dimensional (1D) DODs and DOAs. In addition, the asymptotic performance of the proposed algorithm is analyzed and the closed-form stochastic Cramer–Rao bound (CRB) expression is derived. As demonstrated by simulation results, the proposed algorithm has outperformed the existing one, with a result close to the theoretical benchmark.

Target Localization Methods Based on Iterative Super-Resolution for Bistatic MIMO Radar

The direction-of-departure (DOD) and the direction-of-arrival (DOA) are important localization parameters in bistatic MIMO radar. In this paper, we are interested in DOD/DOA estimation of both single-pulse and multiple-pulse multiple-input multiple-output (MIMO) radars. An iterative super-resolution target localization method is firstly proposed for single-pulse bistatic MIMO radar. During the iterative process, the estimated DOD and DOA can be moved from initial angles to their true values with high probability, and thus can achieve super-resolution estimation. It works well even if the number of targets is unknown. We then extend the proposed method to multiple-pulse configuration to estimate target numbers and localize targets. Compared with existing methods, both of our proposed algorithms have a higher localization accuracy and a more stable performance. Moreover, the proposed algorithms work well even with low sampling numbers and unknown target numbers. Simulation results demonstrate the effectiveness of the proposed methods.

Joint DOD and DOA Estimation Using Reduced-Capon Method in Bistatic MIMO Array

In order to resolve the problem of joint direction of departure (DOD) and direction of arrival (DOA) estimation in bistatic MIMO array, a dimensional reduced-Capon method based on Taylor series expansion and signal subspace is proposed in this paper. Firstly, the Taylor series expansion of the steering vector is used to reduce the two-dimensional (2D) spectrum peak searching of Capon method to one-dimensional searching. Then, the DOD estimator can be achieved via Lagrange multiplier by one-dimension search. Finally, the steering vector of DOA corresponding to the DOD estimator is achieved and the DOA can be estimated. Hence, the estimated DOD and DOA are obtained automatically paired. And also, the proposed method can avoid the high computational complexity of MIMO Capon method. Simulation results are presented to illustrate the effectiveness of the proposed method.