Beamspace Matrix Research Articles

Phase-Calibration-Based 3-D Beamspace Matrix Pencil Algorithm for Indoor Passive Positioning and Tracking

Phase-Calibration-Based 3-D Beamspace Matrix Pencil Algorithm for Indoor Passive Positioning and Tracking

A novel co-prime MIMO radar model for DOA estimation

In this paper, we propose a novel co-prime multiple-input multiple-output (MIMO) radar model based on the transmit energy focusing (TEF) technique for direction of arrival (DOA) estimation. Compared with omnidirectional radiation of the transmit energy of the traditional co-prime MIMO radar, the proposed model can focus the transmit energy in the desired spatial sector. To obtain more degrees of freedom (DOFs), we design the transmit beamspace matrix with a specific structure. Then, the sum and difference co-array (SDC) is given by vectorizing the sampling covariance matrix of the received data. Subsequently, the maximum number of consecutive lags and unique lags for SDC is derived. Besides, we also derive the Cramer–Rao bound (CRB) of our model. Moreover, the DOA estimation performance of the TEF-based co-prime MIMO radar and traditional co-prime MIMO radar is compared by using forward-backward spatial smoothing (FBSS), sparse recovery (SR), and fast iterative interpolated beamformer (FIIB) algorithms. Simulation results show the superiority of the proposed model.

Real-valued sparse Bayesian learning algorithm for off-grid DOA estimation in the beamspace

In recent years, sparse Bayesian learning (SBL) algorithms in the array element space have become very popular for off-grid direction-of-arrival (DOA) estimation. However, the SBL algorithm in beamspace has not been researched. Therefore, this paper proposes a real-valued SBL algorithm in the beamspace. First, the received data in the array element space is transformed to the beamspace using the receive beamspace matrix. Subsequently, singular value decomposition (SVD) is introduced to reduce the computational burden further. Finally, the SBL algorithm is combined to estimate the off-grid DOA. Compared with the SBL algorithms in the array element space, the proposed algorithm has less computational complexity, better robustness to grid interval, and better DOA estimation performance under certain conditions. In addition, we also show the DOA estimation performance of the proposed algorithm for correlated signals and large-scale arrays. Numerical simulations verify the effectiveness of the proposed algorithm.

DOA estimation of the coherent signals using beamspace matrix reconstruction

The matrix reconstruction technique can effectively estimate the direction-of-arrival (DOA) of coherent signals with a relatively small computational complexity. However, the existing methods are affected by the phase perturbation or the fact that the eigenvalue ratio of the signal subspace to noise subspace is linearly related to the square of input signal-to-noise ratio (SNR). This results in a significant decrease in the DOA estimation performance for the cases with a low SNR. To address these problems, we propose a new method for DOA estimation of coherent signals based on the beamspace matrix reconstruction. The array is firstly divided into multiple subarrays, and the data received is transformed from the element space into the beamspace via beamforming, which can eliminate the phase perturbation caused by the mutual impact between the coherent signals and improve the SNR. Then, we add the output covariance matrices from several beam directions to realize the beamspace matrix reconstruction, this results in the eigenvalue ratio of the signal subspace to the noise subspace is the linear transformation of the input SNR in the beamspace domain, which can enhance the eigenvalue ratio of beamspace signal to noise at low SNRs. Finally, the DOAs can be resolved by combining it with the subspace-based methods. Theoretical analysis and simulation results verify the effectiveness of the proposed method at low input SNRs due to beamspace processing, even in the cases where the DOAs between the coherent signals are closely spaced and low snapshot number, our proposed method significantly provides better performance on estimation and resolution.

Joint design of transmit beamspace and reduced‐dimension receiver filter for MIMO radar STAP

In this article, the problem of the transmit beamspace (TB) matrix design in multiple-input multiple-output (MIMO) radar is considered. To reduce the computational burden and to focus the energy within optimal spatial sector, a joint design method of the TB matrix and a reduced-dimension space-time adaptive processing (STAP) filter is proposed based on the maximum signal-to-clutter-plus-noise ratio (SCNR). Firstly, the signal model of the reduced-dimension STAP for TB-based MIMO radar is established. Then, using the maximum SCNR as the design metric, the joint design model of the TB matrix and the reduced-dimension STAP filter is presented. Furthermore, the cyclic optimisation method is exploited to deal with the non-convex joint design problem with the energy constraint. Finally, simulation experiments demonstrate the joint design method of the TB matrix and the STAP filter not only has better output SCNR performance but also owns lower computational burden when compared with the other existing methods.

A reduced-dimension RML method for transmit beamspace-based MIMO radar

In this paper, the problem of low angle estimation for multiple-input multiple-output (MIMO) radar is considered. Though the refined maximum likelihood (RML) algorithm can be directly applied to low angle estimation in MIMO radar, its computational burden is huge due to the large virtual aperture. Moreover, the conventional MIMO radar employs full waveform diversity, which actually sacrifices the emission gain. To reduce the computational burden and improve the transmit gain, a reduced-dimension RML method for transmit beamspace-based (TB-based) MIMO radar is developed. Firstly, the transmit beamspace (TB) matrix is designed to focus the transmit energy within the desired spatial sector. Then, to reduce the computational complexity and retain the estimation precision of the direct RML (D-RML) method for TB-based MIMO radar, a transmit-receive separate RML (TRS-RML) method is developed by applying the RML algorithm to the transmit and receive side respectively. Moreover, we propose to fuse the estimation results of the transmit and receive side together to improve the estimation precision. Theoretical analysis shows the TRS-RML method requires much lower computational burden than D-RML method. Numerical experiments show the proposed method has higher estimation accuracy compared with the D-RML method for the conventional MIMO radar in most angle region.

Transmit beamspace design for FDA–MIMO radar with alternating direction method of multipliers

Hybridization of a frequency diverse array (FDA) generated range-angle-time dependent beampattern with multiple input multiple output (MIMO) radar waveform diversity, namely, FDA-MIMO radar, provides more degrees-of-freedom to improve overall system performance. As the beampattern optimization needs an efficient method to approximate the desired beampattern and simultaneously minimize the cross-correlation sidelobes, we optimize the transmit beampattern over the beamspace matrix in this paper. That is, the transmit FDA antennas are divided into multiple overlapping subarrays and each subarray transmits an orthogonal waveform towards the target, whereas the weight vectors of all subarrays jointly form a beamspace matrix. Since the optimization problem turns to be a non-convex problem with a constant energy constraint, we propose an efficient algorithm based on alternating direction method of multipliers (ADMM) to solve it, which has a very fast convergence speed. The effectiveness and superiorities of the proposed method over existing methods are verified by extensive simulation results.

Cognitive FDA-MIMO With Channel Uncertainty Information for Target Tracking

In this paper, we propose a cognitive frequency diverse array multiple input multiple output (FDA-MIMO) design by utilizing channel uncertainty information. Time-variant non-uniform frequency offsets are utilized to decouple frequency diverse array (FDA) range-angle dependent beampattern and a design strategy is proposed to maximize the transmit energy toward the desired range-angle region by steering the beam to match the channel uncertainty for enhanced target detect and tracking performance. To unambiguously estimate target parameters, we divide the FDA elements into multiple fully overlapped subarrays using orthogonal waveforms. Furthermore, we adaptively update the transmit beamspace matrix with two optimization criterions, namely, signal-to-noise ratio maximization and Cramer–Rao bound minimization. All proposed approaches are verified by numerical results.

Adaptive transmit array sidelobe control using FDA-MIMO for tracking in joint radar-communications

In this paper, we present an adaptive closed–loop range-angle dependent sidelobe control using frequency diverse array (FDA) multiple-input multiple-output (MIMO) design for joint radar-communications. The system carries out tracking of the target and the communication receiver, while transmitting information bits towards the intended communication receiver using a flexible sidelobe control, i.e., controlling the power emitted at a certain angle-range position. The range-angle dependent sidelobe control utilizing an overlapped-FDA generated uncoupled beampattern with the proposed Blackman window based non-uniform frequency offsets enables the communication links to use the same radar spectrum. Moreover, we adaptively design two transmit weight vectors and finally compute a beamspace matrix that facilitates to generate the range-angle dependent beam patterns with a same radar main lobe, but distinct sidelobe levels (in accordance with the binary bit to be transmitted) for the moving target and communication receiver, respectively. Furthermore, we propose a cognitive algorithm to discriminate the target and communication receiver positions. Finally, the information bits can be efficiently detected by the intended communication receiver, merely, due to the power difference in sidelobe levels of the directed range-angle dependent radiated patterns without affecting the radar performance. The improved performance of the proposed design is verified in terms of bit error rate and inherent security for the communication functionality, while target detection, target tracking and parameter estimation are considered for the radar application.

Transmit Beamspace Design for Bistatic MIMO Radar With Improved Angle Estimation

The energy dispersion of traditional bistatic multiple-input multiple-output (MIMO) radar severely degrades the angle estimation performance. To overcome this limitation, we propose to design the transmit beamspace matrix and apply the design result to jointly estimate the target directions of departure (DOD) and directions of arrival (DOA). The essence of this method is to minimize the distance between a desired transmit steering vector and the actual one within a given angular sector. Moreover, we enforce two inequality constraints to achieve approximately uniform power distribution across the transmit array elements. In addition, we carefully devise the desired transmit steering vector to expand the virtual transmit aperture and further improve the DOD estimation performance. Furthermore, we use tensor-decomposition and a phase-searching method to estimate the target DODs and DOAs. Finally, the simulation results demonstrate the effectiveness of the proposed algorithm.

MIMO Radar Transmit Beampattern Design for DOA Estimation with Sidelobe Suppression

We address the problem of transmit beamspace design for multiple-input multiple-output (MIMO) radar with colocated antennas in direction-of-arrival (DOA) estimation application. Three transmit beampattern sidelobe suppression strategies for designing the transmit beamspace matrix are introduced. The design of transmit beamspace matrix is based on minimizing the difference between a desired transmit beampattern and the actual one while keeping the sidelobe levels under control. Uniform elemental power distribution across the transmit antenna is guaranteed; at the same time, signal rotational invariance property is considered, which enables search-free based DOA estimation algorithms to be utilized at the receiver. The proposed optimization problems are nonconvex and are solved by using semidefinite programming relaxation technique. Moreover, the DOA estimation Cramer-Rao bound with transmit beamspace matrix is discussed. Simulation results show the superiority of the proposed techniques over the existing methods.

An efficient adaptive beam-space transformation technique and its application in array processing

Beam-space transformation projects the array data into a lower space, which is not only effective in reducing computation time, improving performance, but also being capable to suppress interference. In contrast to conventional adaptive beam-space transformation method, which often requires adjusting the beam-space matrix and steering vectors online, an efficient adaptive beam-space transformation method is proposed. In the proposed method, the beam-space covariance matrix and the steering vector both have closed-forms, and do not depend on the adaptive beam-space matrix. This eliminates the online adjustment process, and, thus, improves the computational efficiency. Finally, the proposed method can also be applied to the direction of arrival (DOA) estimation. Simulation results demonstrate that it has a better DOA estimation performance than the conventional adaptive method. Furthermore, the proposed method also has another significant advantage, i.e., it is able to suppress moving interference. This can be ascribed to the proposed beam-space matrix which is independent of the historical data, and, thus, effective to avoid the mismatch between the training and application data, since this mismatch often occurs in conventional adaptive methods.

Broadband target beam-space transformation in generalized likelihood ratio test using acoustic vector sensor array

Aiming at the problem of passive detection of broadband sources in underwater acoustic vector signal processing, a novel detection algorithm based on beam-space transformation is proposed. The principle of spatial spectrum detection with human eyes is employed for reflerence, and the generalized likelihood ratio test (GLRT) is applied to the beam-space. First, the design criterion of beam-space transformation matrix is studied for the compreflensive consideration of the environment of multiple targets and the characteristic of vector ambient noise field, so that the analytical solution is obtained. Second, assuming that the number of beams not containing the target signal is given, the probability density function (PDF) model of beam-space data is constructed, and the new GLR test is made by calculating the maximum likelihood estimate of the unknown variables in PDF. Finally, the information of theoretical criterion is adopted in order to estimate the number of beams not containing target signals. The processing gain and the threshold value of this test statistics are also discussed, and the specific implement is explained in detail. Theoretical analysis and simulation results show that under the complex conditions of strong target interference and ambient noise with undulated and time-variant power spectrum, the proposed algorithm can give the processing result with higher gain and detection threshold at constant false alarm rate (CFAR); the results of lake experiment further prove the favorable and robust detection performance.

Transmit Subaperturing for Range and Angle Estimation in Frequency Diverse Array Radar

Different from conventional phased-array, which provides only angle-dependent beampattern, frequency diverse array (FDA) employs a small frequency increment across the antenna elements and results in a range-angle-dependent beampattern. This beampattern offers a potential to localize the targets in two dimensions in terms of slant ranges and azimuth angles. However, it is difficult to obtain the target location information from a standard FDA radar due to the couplings in range and angle responses. In this paper, we propose a transmit subaperturing scheme on the FDA radar for range and angle estimation of targets. The essence is to divide the FDA elements into multiple subarrays and optimize the transmit beamspace matrix with the use of convex optimization. We also discuss several practical issues for designing the FDA radar system parameters. Since the subarrays offer decoupled range and angle responses, the targets can be located using the beamspace-based multiple signal classification algorithm. The range and angle estimation performance is evaluated by comparing with the Cramer-Rao lower bound.

Robust adaptive beamforming using beam‐space steering vector estimation

To solve the problem of performance degradation owing to imprecise knowledge of the array steering vector and inaccurate estimation of the sample covariance matrix, a novel algorithm based on beam-space steering vector estimation for robust adaptive beamforming is presented. By using the complementary set of the spatial sector in which the actual steering vector lies, a beam-space transformation matrix can be constructed to remove the signal of interest from the sampling covariance matrix. The beam-space steering vector is estimated by solving a non-convex quadratically constrained quadratic optimisation problem. The effectiveness and robustness of the proposed algorithm is verified by the simulations.

Efficient Transmit Beamspace Design for Search-Free Based DOA Estimation in MIMO Radar

In this paper, we address the problem of transmit beamspace design for multiple-input multiple-output (MIMO) radar with colocated antennas in application to direction-of-arrival (DOA) estimation. A new method for designing the transmit beamspace matrix that enables the use of search-free DOA estimation techniques at the receiver is introduced. The essence of the proposed method is to design the transmit beamspace matrix based on minimizing the difference between a desired transmit beampattern and the actual one under the constraint of uniform power distribution across the transmit array elements. The desired transmit beampattern can be of arbitrary shape and is allowed to consist of one or more spatial sectors. The number of transmit waveforms is even but otherwise arbitrary. To allow for simple search-free DOA estimation algorithms at the receive array, the rotational invariance property is established at the transmit array by imposing a specific structure on the beamspace matrix. Semi-definite relaxation is used to transform the proposed formulation into a convex problem that can be solved efficiently. We also propose a spatial-division based design (SDD) by dividing the spatial domain into several subsectors and assigning a subset of the transmit beams to each subsector. The transmit beams associated with each subsector are designed separately. Simulation results demonstrate the improvement in the DOA estimation performance offered by using the proposed joint and SDD transmit beamspace design methods as compared to the traditional MIMO radar technique.

Computationally efficient 2D beamspace matrix pencil method for direction of arrival estimation

In this paper, we propose a new 2-dimensional beamspace matrix pencil (2D BMP) method for direction of arrival (DOA) estimation of plane wave signals using a uniform rectangular array (URA). Based on some a priori information about DOA, the proposed method transforms the complex signal subspace in 2D matrix pencil (2D MP) method [Y. Hua, Estimating two-dimensional frequencies by matrix enhancement and matrix pencil, IEEE Trans. Signal Process. 40 (9) (1992) 2267-2280] into a real and reduced dimensional beamspace using the discrete Fourier transform (DFT) matrix transformation. Consequently, the computational complexity is reduced (several times) in comparison with 2D MP method. Computer simulations are provided to show that 2D BMP method gives comparable performance in terms of average mean square error of the estimated DOA with lesser floating point operations as compared to the existing (MP) methods.

A Robust Adaptive Dimension Reduction Technique With Application to Array Processing

We develop a data-adaptive dimension reduction algorithm that is robust against out-of-sector sources in application to array processing. The dimension reduction is done as a linear transformation (matrix filter). The matrix filter is designed adaptively such that the signal power within a certain sector is preserved while the out-of-sector power is maximally rejected. The columns of the beamspace matrix are designed sequentially, one column at a time. This sequential implementation is carried out by imposing orthogonality constraints between beamspace matrix columns. Hence, the white noise property at the output of the beamspace preprocessor is preserved. The latter is important for subsequent data processing. The proposed algorithm is computationally less expensive as compared to the existing data-adaptive beamspace design techniques. Simulation results validate the robustness of the developed algorithm, and they show its effectiveness and superiority to the existing algorithms.

Beamspace matrix pencil method for direction of arrival estimation

In this paper, we propose DFT Beamspace Matrix pencil (BMP) method for direction of arrival estimation (DOA). The DFT beamspace approach has the advantage of reduced computational complexity due to converting complex computations (in Matrix Pencil method) into real ones along with the inherent ability to operate in a reduced beam-space in situations where some priori information is available about the DOAs. Furthermore, a novel Multiple Invariance BMP (MBMP) method is also developed and it is shown through simulations that its reduced beamspace version has comparable performance to the existing Unitary Matrix Pencil method (UMP) with lower computational cost.

Convex optimization based beam-space preprocessing with improved robustness against out-of-sector sources

Beam-space data preprocessing is a powerful tool commonly used in array processing to reduce the computational burden and improve the performance of high-resolution direction-finding algorithms. However, currently used beam-space techniques appear to lack robustness in the presence of sources that are located outside the beam-space angular sectors-of-interest. In this paper, a new approach to beam-space preprocessing with an improved robustness against such out-of-sector interfering sources is developed. Our techniques design the beam-space matrix filter based on proper tradeoffs between the in-sector (passband) source distortion and out-of-sector (stopband) source attenuation. Computationally efficient convex formulations for these beam-space matrix filter design problems are derived using second-order cone (SOC) programming.