Unitary ESPRIT Algorithm Research Articles

A Nyström-Based Low-Complexity Algorithm with Improved Effective Array Aperture for Coherent DOA Estimation in Monostatic MIMO Radar

In this paper, we propose a computationally efficient algorithm with improved effective aperture for coherent angle estimation in a monostatic multiple-input multiple-output (MIMO) radar. First, the direction matrix of MIMO radar is mapped into a low-dimensional matrix of virtual uniform linear array (ULA). Then, an augmented data expansion matrix with improved effective aperture is obtained by exploiting the Vandermonde-like structure of the low-dimensional direction matrix and radar cross section (RCS) matrix to enlarge the aperture of the array. Next, a unitary transformation is used to transform the augmented matrix into a real value and the approximate signal subspace of the augmented matrix is obtained by the Nyström method, which can reduce the computational complexity. The eigenvectors of the approximate signal subspace are used to reconstruct the matrix for direct decorrelation processing. Finally, direction of arrivals (DOAs) can be estimated faster by utilizing the unitary ESPRIT algorithm since the rotation invariance of the extended reconstruction matrix still exists. The proposed algorithm has a lower total computational complexity, and the estimation accuracy is improved by utilizing real values and enlarging the array aperture for estimation. Several theoretical analyses and simulation results confirm the effectiveness and advantages of the proposed method.

A novel reduced-dimensional beamspace unitary ESPRIT algorithm for monostatic MIMO radar

In this paper, a novel direction of arrival (DOA) estimation algorithm is proposed for monostatic multiple-input multiple-output (MIMO) radar. Due to redundancy of the received data of monostatic MIMO radar, the computational complexity of the inversion of the covariance matrix is increased. In order to reduce the large computational complexity of existing subspace-based algorithms, we perform two reduced-dimensional operations. First, the high-dimensional received data is transformed the low-dimensional received data through a special transformation matrix. Second, the low-dimensional received data is transformed into beamspace. The receive beamspace filter is designed using convex optimization, and it can flexibly control the bandwidth and limit the sidelobe level. To ensure that the converted noise is Gaussian white noise, the prewhitening process is performed. Based on the above precondition, the reduced-dimensional beamspace technique can be effectively combined with the unitary ESPRIT model. Finally, the Cramer-Rao bound (CRB) on angle estimation in element space and reduced-dimensional beamspace is calculated for performance analysis. Numerical simulations verify the effectiveness of the proposed algorithm.

Closed-Loop Sparse Channel Estimation for Wideband Millimeter-Wave Full-Dimensional MIMO Systems

This paper proposes a closed-loop sparse channel estimation (CE) scheme for wideband millimeter-wave hybrid full-dimensional multiple-input multiple-output and time division duplexing based systems, which exploits the channel sparsity in both angle and delay domains. At the downlink CE stage, random transmit precoding matrix is designed at base station (BS) for channel sounding, and receive combining matrices at user devices (UDs) are designed whereby the hybrid array is visualized as a low-dimensional digital array for facilitating the multi-dimensional unitary ESPRIT (MDU-ESPRIT) algorithm to estimate respective angle-of-arrivals (AoAs). At the uplink CE stage, the estimated downlink AoAs, namely, uplink angle-of-departures (AoDs), are exploited to design multi-beam transmit precoding matrices at UDs to enable BS to estimate the uplink AoAs, i.e., the downlink AoDs, and delays of different UDs, whereby the MDU-ESPRIT algorithm is used based on the designed receive combining matrix at BS. Furthermore, a maximum likelihood approach is proposed to pair the channel parameters acquired at the two stages, and the path gains are then obtained using least squares estimator. According to spectrum estimation theory, our solution can acquire the super-resolution estimations of the AoAs/AoDs and delays of sparse multipath components with low training overhead. Simulation results verify the better CE performance and lower computational complexity of our solution over state-of-the-art approaches.

Extensions of Open Box Array With Reduced Mutual Coupling

Mutual coupling effect and degree of freedom are two important factors to be considered in the planar sparse array (PSA) design. This paper presents two new planar sparse geometries, referred to as the half H array and ladder array, by introducing the effective difference co-array concept and redistributing the dense array elements of the open box array (OBA) to the outer diagonal straight line. The detection capacities of the new structures can be maintained at the same level as the OBAs. Furthermore, they possess much fewer sensor pairs closely spaced, leading to the mutual coupling between the adjacent sensors significantly reduced. Simulations of the direction-of-arrival estimation verify the superiorities of the proposed PSAs with the 2-D unitary ESPRIT algorithm.

Beam-Doppler Unitary ESPRIT for Multitarget DOA Estimation

High-resolution direction of arrival (DOA) estimation is a critical issue for mainbeam multitarget tracking in ground-based or airborne early warning radar system. A beam-Doppler unitary ESPRIT (BD-UESPRIT) algorithm is proposed to deal with this problem. Firstly, multiple snapshots without spatial aperture loss are obtained by using the technique of time-smoothing. Then the conjugate centrosymmetric discrete Fourier transform (DFT) matrix is used to transform the extracted data into beam-Doppler domain. Finally, the rotational invariance property of the space-time beam is exploited to estimate DOA of the target. The DOA estimation accuracy is improved greatly because the proposed algorithm takes full advantage of temporal information of the signal. Furthermore, the computational complexity of the presented algorithm is reduced dramatically, because the degree of freedom after beam transformation is very small and most of the operations are implemented in real-number domain. Numerical examples are given to verify the effectiveness of the proposed algorithm.

Generalized Least Squares for ESPRIT-Type Direction of Arrival Estimation

The key task in ESPRIT-based parameter estimation is finding the solution to the shift invariance equation (SIE), which is often an overdetermined, linear system of equations. Additional structure is imposed if the two selection matrices, applied to an estimate of the signal subspace, overlap such that the subspace estimation errors on both sides of the SIE are highly correlated. In this letter, we propose a novel SIE solution for Standard ESPRIT and Unitary ESPRIT based on generalized least squares (GLS), assuming a uniform linear array (ULA) and maximum subarray overlap. GLS directly incorporates the statistics of the subspace estimation error via its covariance matrix, which is found analytically by a first-order perturbation expansion. As the subspace error covariance matrix is not invertible, we introduce a regularization with a clever choice of the regularization parameter. The resulting GLS-based Standard ESPRIT and Unitary ESPRIT algorithms achieve a superior performance over existing ESPRIT-type methods and almost attain the Cramer-Rao bound (CRB).

Joint DOA and channel estimation with data detection based on 2D unitary ESPRIT in massive MIMO systems

We propose a novel method for joint two-dimensional (2D) direction-of-arrival (DOA) and channel estimation with data detection for uniform rectangular arrays (URAs) for the massive multiple-input multiple-output (MIMO) systems. The conventional DOA estimation algorithms usually assume that the channel impulse responses are known exactly. However, the large number of antennas in a massive MIMO system can lead to a challenge in estimating accurate corresponding channel impulse responses. In contrast, a joint DOA and channel estimation scheme is proposed, which first estimates the channel impulse responses for the links between the transmitters and antenna elements using training sequences. After that, the DOAs of the waves are estimated based on a unitary ESPRIT algorithm using previous channel impulse response estimates instead of accurate channel impulse responses and then, the enhanced channel impulse response estimates can be obtained. The proposed estimator enjoys closed-form expressions, and thus it bypasses the search and pairing processes. In addition, a low-complexity approach toward data detection is presented by reducing the dimension of the inversion matrix in massive MIMO systems. Different cases for the proposed method are analyzed by changing the number of antennas. Experimental results demonstrate the validity of the proposed method.

Transmit/Receive Spatial Smoothing with Improved Effective Array Aperture for Angle and Mutual Coupling Estimation in Bistatic MIMO Radar

We proposed a transmit/receive spatial smoothing with improved effective aperture approach for angle and mutual coupling estimation in bistatic MIMO radar. Firstly, the noise in each channel is restrained, by exploiting its independency, in both the spatial domain and temporal domain. Then the augmented transmit and receive spatial smoothing matrices with improved effective aperture are obtained, by exploiting the Vandermonde structure of steering vector with uniform linear array. The DOD and DOA can be estimated by utilizing the unitary ESPRIT algorithm. Finally, the mutual coupling coefficients of both the transmitter and the receiver can be figured out with the estimated angles of DOD and DOA. Numerical examples are presented to verify the effectiveness of the proposed method.

Beamspace Unitary ESPRIT Algorithm for Angle Estimation in Bistatic MIMO Radar

The beamspace unitary ESPRIT (B-UESPRIT) algorithm for estimating the joint direction of arrival (DOA) and the direction of departure (DOD) in bistatic multiple-input multiple-output (MIMO) radar is proposed. The conjugate centrosymmetrized DFT matrix is utilized to retain the rotational invariance structure in the beamspace transformation for both the receiving array and the transmitting array. Then the real-valued unitary ESPRIT algorithm is used to estimate DODs and DOAs which have been paired automatically. The proposed algorithm does not require peak searching, presents low complexity, and provides a significant better performance compared to some existing methods, such as the element-space ESPRIT (E-ESPRIT) algorithm and the beamspace ESPRIT (B-ESPRIT) algorithm for bistatic MIMO radar. Simulation results are conducted to show these conclusions.

R-dimensional esprit-type algorithms for strictly second-order non-circular sources and their performance analysis

High-resolution parameter estimation algorithms designed to exploit the prior knowledge about incident signals from strictly second-order (SO) noncircular (NC) sources allow for a lower estimation error and can resolve twice as many sources. In this paper, we derive the R \mathchar"702DD NC Standard ESPRIT and the R \mathchar"702DD NC Unitary ESPRIT algorithms that provide a significantly better performance compared to their original versions for arbitrary source signals. They are applicable to shift-invariant R \mathchar"702DD antenna arrays and do not require a centro-symmetric array structure. Moreover, we present a first-order asymptotic performance analysis of the proposed algorithms, which is based on the error in the signal subspace estimate arising from the noise perturbation. The derived expressions for the resulting parameter estimation error are explicit in the noise realizations and asymptotic in the effective signal-to-noise ratio (SNR), i.e., the results become exact for either high SNRs or a large sample size. We also provide mean squared error (MSE) expressions, where only the assumptions of a zero mean and finite SO moments of the noise are required, but no assumptions about its statistics are necessary. As a main result, we analytically prove that the asymptotic performance of both R \mathchar"702DD NC ESPRIT-type algorithms is identical in the high-effective SNR regime. Finally, a case study shows that no improvement from strictly non-circular sources can be achieved in the special case of a single source.

3-D Unitary ESPRIT: Accurate attitude estimation for unmanned aerial vehicles with a hexagon-shaped ESPAR array

Accurate estimation of the attitude of unmanned aerial vehicles (UAVs) is crucial for their control and displacement. Errors in the attitude estimate may misuse the limited battery energy of UAVs or even cause an accident. For attitude estimation, proprioceptive sensors such as inertial measurement units (IMUs) are widely applied, but they are susceptible to inertial guidance error. With antenna arrays currently being installed in UAVs for communication with ground base stations, we can take advantage of the array structure in order to improve the estimates of IMUs via data fusion. In this paper, we therefore propose an attitude estimation system based on a hexagon-shaped 7-element electronically steerable parasitic antenna radiator (ESPAR) array. The ESPAR array is well-suited for installment in the UAVs with broad wings and short bodies. Our proposed solution returns an estimation for the pitch and roll based on the inter-element phase delay estimates of the line-of-sight path of the impinging signal over the antenna array. By exploiting the parallel and centrosymmetric structure in the hexagon-shaped ESPAR array, the 3-dimensional Unitary ESPRIT algorithm is applied for phase delay estimation to achieve high accuracy as well as computational efficiency. We devise an attitude estimation algorithm by exploiting the geometrical relationship between the UAV attitude and the estimated phase delays. An analytical closed-form expression of the attitude estimates is obtained by solving the established simultaneous nonlinear equations. Simulations results show the feasibility of our proposed solution for different signal-to-noise ratio levels as well as multipath scenarios.

Unitary-ESPRIT Algorithm for Carrier Frequency Offset Estimation for Interleaved OFDMA Uplink Systems

The carrier frequency offset (CFO) estimation is an important task for orthogonal frequency-division multiple-access (OFDMA) systems. Making use of the intrinsic periodic structure of the received signal samples, an effective Unitary-ESPRIT algorithm based on unitary transformation technique is proposed for the CFO estimation problem. Compared with other recently proposed CFO estimation approaches, the proposed algorithm offers a number of advantages. Firstly, the presented approach can reduce the computation complexity considerably, since it is efficiently formulated in terms of real-valued computation except for the data preprocessing. Secondly, it can provide better CFO estimation performance by incorporating the data stacking technology and the unitary transformation, etc. Simulation results demonstrate the efficacy of the proposed algorithm.

Unitary ESPRIT algorithm for bistatic MIMO radar

A new Unitary ESPRIT algorithm for joint direction of departure (DOD) and direction of arrival (DOA) estimation in bistatic MIMO radar is proposed. The properties of centro-Hermitian matrices are utilised to transform the complex-valued data matrix into a real-valued data matrix. Then the real-valued rotational invariance equations for signal subsapce are figured out to estimate DOAs and DODs which are paired automatically in a new way. The proposed algorithm provides increased estimation accuracy with reduced computational complexity owing to real-valued processing and double the number of data samples inherently in unitary ESPRIT. Simulation results are presented to verify the effectiveness of the proposed algorithm.

DECOUPLED UNITARY ESPRIT ALGORITHM FOR 2-D DOA ESTIMATION

In this paper, a new decoupled Unitary ESPRIT algorithm for two-dimensional (2-D) direction-of-arrival (DOA) estimation is presented. By exploiting the centro-symmetric array configurations of two parallel uniform linear arrays (TP-ULAs) and utilizing the via rotational invariance techniques, the proposed algorithm has advantages as listed below. First, the algorithm enables decoupling the estimation problem into a two-step estimation problem and obtains the automatically matched 2-D DOAs. Second, employing the elements of the array fully, the algorithm can estimate 2-D DOAs up to 2(M − 1), where 2M is the sensor number of the array. Besides, the computational complexity of the proposed algorithm is lower than other representative 2-D DOA estimation methods. Simulation results are presented to show the effectiveness of the proposed method.

Layover Solution Based on Unitary ESPRIT Algorithm in Multibaseline InSAR

Layover Solution Based on Unitary ESPRIT Algorithm in Multibaseline InSAR

Conjugate unitary ESPRIT for real sources adapted to the coherent case

By virtue of real-valued property of some real sources, in this paper, we suggest a conjugate unitary ESPRIT (CU-ESPRIT) algorithm to exploit the conjugate information of partial array element outputs. To deal with correlated or coherent sources, we design a virtual centro-symmetric array and divide it into the virtual subarrays. Compared with the unitary ESPRIT for non-circular sources (NC unitary ESPRIT), CU-ESPRIT achieves a relative reduction of the computational complexity and an improved resolution for uncorrelated or coherent sources. Specifically, this algorithm can estimate as many as M - 1 coherent sources for an array of M elements. Simulation results show the validity of our approach.

A NOVEL SOURCE LOCALIZATION SCHEME BASED ON UNITARY ESPRIT AND CITY ELECTRONIC MAPS IN URBAN ENVIRONMENTS

In this paper, a novel source localization scheme is proposed based on the unitary ESPRIT algorithm with back ray tracing technique and the city electronic maps. Our scheme can be summarized into two steps. First, the unitary ESPRIT algorithm is employed to estimate the angles and delays of the arrival rays radiated from the source. Second, based on the obtained information we devise a back ray tracing technique to recover the signal propagation paths according to the Geometrical Theory of Re∞ections and the city electronic map. After these two steps the source position can be obtained by averaging all the estimated positions. In order to minimize estimated errors caused by the Unitary ESPRIT, a valid-range selection criterion for the judgment of the validity of the estimated position data is proposed. On the other hand, we introduce a path length weighting factor to reduce the estimated errors caused by the terrain data inaccuracy. This position method can locate both the line of sight (LOS) and non-line of sight (NLOS) sources e-ciently and it also can locate multi-sources simultaneously. Six simulations are carried out in three terrain scenarios. The numerical results demonstrate that our model can be applied to estimate the positions for both 2D and 3D cases. The accuracy of our model for a cell of 80m £ 45m can reach 10m when SNR is greater than 10dB.

Full Azimuth Direction-of-Arrival Estimation With Successive-Selection Technique

A method for full-azimuth direction-of-arrival (DoA) estimation of multiple signals with a hexagonal array is proposed. The DoA estimation is performed in two steps. In the first, a set of estimate candidates is constructed by gathering the estimates that are obtained from applying the low-computational-cost Unitary-ESPRIT algorithm to several translational invariances designed into a hexagonal array. In the second step, the DoA estimates are successively selected from the estimate candidate set by using a selection function. The proposed method removes the north-or-south signal membership ambiguity and the limitation on the number of estimable sources, problems common to any ESPRIT-based algorithm used with one translational invariance. Therefore, up to M-1 signal DoA estimations can be expected with an M- element hexagonal array in the full azimuth. The successive-selection approach is based on a selection function that uses an estimate of the signal's spatial correlation matrix to successively select the DoA estimates. For each DoA estimate selection, the already estimated signal components are removed from the correlation matrix. Such an approach is shown to actually allow the selection of suitable estimates from among a set of estimate candidates. Finally, the method's DoA estimation and resolution capabilities are demonstrated by computer simulation and comparison with the Cramer-Rao bound.

Introduction to the IJWIN Special Issue: ‘Physical Layer Engineering for Emerging Wireless Applications’

In 2007 we had the honor and responsibility to serve as chairs of the Technical Programme Committee (TPC) of the prestigious IEEE PIMRC (Personal Indoor and Mobile Radio Communications) conference. The conference attracted more than 1,200 participants and included several excellent contributions covering all aspects of the contemporary wireless telecommunications landscape. We personally had the chance to read almost all papers, and attend to a large number of interesting talks during the conference. Furthermore, we came directly in touch with many authors that excelled in the conference. In the scope of this special issue we extended an invitation to excellent authors, with a view to publishing the next steps of their works in this special issue. The five papers of this issue cover a number of different topics ranging from channel characterization and localization to smart antennas. Specifically, the first paper is titled ‘Analysis of Scattering in Mobile Radio Channels based on Clustered Multipath Estimates’ is co-authored by Maurice Kwakkernaat and Matti Herben from the Department of Electrical Engineering of the Eindhoven University of Technology. The paper deals with the accurate estimation of the propagation effect in smart-antenna and MIMO systems. The authors capitalize on a 3-D high-resolution channel sounder, which was developed based on a 3-D antenna array in combination with a multi-dimensional version of the Unitary ESPRIT algorithm. This system is capable of accurately measuring the angle-delay characteristics in azimuth conditions, as well as under mobile conditions. The authors also compare the results from deterministic propagation models to the clustered highresolution angle-of-arrival (AoA) estimates. Comparison results show that: (a) a significant amount of multipath components (MPCs) was missing and (b) the spreads in delay and angle are much larger in the measurements, (c) The MPCCs (MPCs clusters) tend to evolve rather slow along the trajectory, which may allow for interpolation techniques to reduce simulation time. The title of the second paper of the issue is ‘Identification of the Absence of Direct Path in ToA-Based Indoor Localization Systems’. The authors of the paper (namely Mohammad Heidari, Ferit Ozan Akgul, Nayef Alsindi and Kaveh Pahlavan from the Worcester Polytechnic Institute) introduce a methodology to identify and mitigate the undetected direct path (UDP) conditions, which can substantially improve the overall indoor positioning accuracy of Ultra-wideband (UWB) positioning systems based on time of arrival (ToA) techniques. The methodology relies on a novel UDP identification and mitigation technique that is based on analyzing the statistics of the propagation channel. The paper introduces the fundamentals of ToAbased localization and describes the metrics being used for UDP identification. Accordingly it presents results of binary likelihood ratio tests for UDP identification. In deriving these results the outcome of the hypothesis tests are compared to a certain threshold, in order to determine if a receiver is in DDP or UDP condition. The contribution is validated based on simulation results for a sample indoor environment. J. Soldatos (&) Athens Information Technology, 0.8 km Markopoulou Ave., P.O. Box 68, 19002 Peania, Athens, Greece e-mail: jsol@ait.edu.gr

High Resolution 3-D Angle of Arrival Determination for Indoor UWB Multipath Propagation

Propagation measurements using a large array are used to study the angle of arrival (AOA) across the ultrawideband (UWB) frequency range of 3.1 to 10.6 GHz. A two-dimensional Unitary ESPRIT algorithm is employed to give a high resolution estimation of AOA including both the azimuth and elevation angles of multipath components. The frequency dependence of AOA is investigated over the UWB frequency band. The multipath rays form clusters in both angular and temporal domains. Within a cluster the azimuth and elevation AOAs are determined to follow Laplacian and Gaussian distributions respectively. In the indoor environment considered, a typical cluster extends over an angular sector of approximately 14 degrees in azimuth and 9 degrees in elevation, with up to 5 clusters observed. We note that these propagation characteristics will allow UWB systems to utilise smart antennas or MIMO structures to improve overall throughput.