Direction Of Arrival Estimation Error Research Articles

Robust wideband beamforming method for linear frequency modulation signals based on digital dechirp processing

This study presents a robust digital beamforming (DBF) method for wideband digital array radar, which uses linear frequency modulation (LFM) waveforms. Firstly, received signals are digitally dechirped, followed by narrowband filtering and decimation. Then the authors generate time-variant factors to compensate phase perturbations induced by the dechirp processing. It is proved that the wideband LFM signals can be treated as narrowband signals after compensation. Finally, a robust adaptive narrowband DBF method based on uncertain set constraints and interference-plus-noise matrix reconstruction is applied to suppress the interferences. The proposed method is computationally efficient and feasible for real-time applications. It behaves robustly in the presence of direction of arrival estimation errors across a wide range of signal-to-noise ratios. Simulations demonstrate the effectiveness and feasibility of the proposed method.

Weighted Incoherent Signal Subspace Method for DOA Estimation on Wideband Colored Signals

Wideband direction-of-arrival (DOA) estimation is a key part in array signal processing. The existing algorithms for the wideband DOA estimation are often studied in the situation of uniformly distributed energy. In addition, all the frequency bins are weighted equally in these algorithms. However, these algorithms perform unsatisfactorily when encountering wideband colored signals with nonuniform energy spectrum. To improve the performance of DOA estimation for wideband colored signals, we proposed two weighting methods, which are based on the perturbed subspace theory and random matrix theory, respectively. The two methods weight the space spectrum from all the frequency bins according to the mean square error of DOA estimation in each frequency bin. The numerical results show that the random matrix theory based method performs well, due to the inference premise that the dimensions of matrices increase at the same rate. The perturbed subspace-based method, which is concise in calculating the weights, shows high accuracy only at high-signal-to-noise ratio and with adequate snapshots. The effectiveness of the two algorithms are also demonstrated by comparing them to various existing algorithms and the Cramer–Rao bound.

Multi-Cell Multi-User Massive FD-MIMO: Downlink Precoding and Throughput Analysis

In this paper, downlink (DL) precoding and power allocation strategies are identified for a time-division-duplex (TDD) multi-cell multi-user massive Full-Dimension MIMO (FD-MIMO) network. Utilizing channel reciprocity, DL channel state information (CSI) feedback is eliminated and the DL multi-user MIMO precoding is linked to the uplink (UL) direction of arrival (DoA) estimation through estimation of signal parameters via rotational invariance technique (ESPRIT). Assuming non-orthogonal/non-ideal spreading sequences of the UL pilots, the performance of the UL DoA estimation is analytically characterized and the characterized DoA estimation error is incorporated into the corresponding DL precoding and power allocation strategy. Simulation results verify the accuracy of our analytical characterization of the DoA estimation and demonstrate that the introduced multi-user MIMO precoding and power allocation strategy outperforms existing zero-forcing based massive MIMO strategies.

Coherency structure exploitation in DOA estimation for non‐circular sources

This study addresses the problem of direction-of-arrival (DOA) estimation for non-circular (NC) sources in the presence of multipath propagation. Recent research reveals that the use of the association of incident signals, i.e. source association (SA), can provide a significant gain in reducing DOA estimation error, especially in the presence of multiple sources. Here, in order to make full use of both the properties of NC sources and the SA information, the multipath model with NC sources is studied, and then a simple combination algorithm is proposed to estimate the SA, based on which, the authors derive an iterative root estimator to refine a given coarse DOA estimation. Meanwhile, the stochastic Cramer-Rao bound taking these two factors into account is derived as well. The proposed method is search-free and maintains the array aperture which is up to twice of the physical array aperture. Numerical simulations have been provided to verify the effectiveness of the proposed method.

2-D Direction-of-Arrival Estimation System Using Circular Array With Mutually Coupled Reference Signal

Direction-of-arrival (DOA) systems rely on proper phase measurements acquired from receiving antennas for optimal performance. Unfortunately, imperfections in any antenna and receiver system may present false phase measurements, the major cause of DOA estimation error. This paper discusses experimental results from an actual implementation of synchronizing a DOA circular array receiver system to mitigate these imperfections. A reference signal located at the center of the DOA array was coupled to array elements such that both the coupled reference signals and signals from a target were captured simultaneously in the receiver. This coupled reference signal was used to compensate for any phase error offsets produced by receiver system imperfections on cable length, phase of local oscillators, and phase delays in active devices. Furthermore, this approach did not necessitate an off-line calibration process of each receiver channel requiring accurate measurements. We implemented a 16-element circular array DOA estimation system using the Universal Software Radio Peripheral platform operating in the $S$ - and $C$ -bands. Results show that this implementation was able to combat receiver phase offset errors and estimated the DOA angles with an rms error of 0.92°.

TDOA-Based Multiple Acoustic Source Localization Without Association Ambiguity

Multiple source localization using time-differences of arrival (TDOAs) is challenging because of the ambiguity involved in associating the TDOAs computed across microphone pairs to the sources. We show that the association ambiguity of the TDOAs can be effectively resolved using the concept of an inverse delay interval region (IDIR), which we introduce in this paper. By examining the association between a spatial domain and the TDOAs, we define IDIR as an interhyperboloidal spatial region corresponding to an interval of delays for a given pair of microphones. The proposed scheme for localizing multiple sources involves two stages. In the first stage, the given enclosure is partitioned into nonoverlapping elemental regions and the ones that contain a source are detected using a measure based on the generalized cross-correlation with phase transform and the IDIRs. In the second stage, the sources are finely localized within each of the detected elemental regions by identifying the IDIRs containing a single source and a novel region-constrained localization approach. We evaluate the performance of the proposed approach on real recordings from the AV16.3 corpus and in a simulated reverberation setting with a reverberation time RT60 of up to 500 ms, and show that the DOA estimation error with two active speakers is within 2° and the spatial localization error is less than 30 cm for each speaker.

Direction of Arrival Estimation Using Amplitude and Phase Information in Low-Profile MIMO Arrays

Accurate direction of arrival (DOA) estimation in compact terminal devices using small antenna arrays is challenging due to their limited radiating apertures. In this communication, we employ both the amplitude and the phase information to improve the estimation accuracy and eliminate phase ambiguity without increasing the size of the antenna array. The optimal amplitude ratio between the antenna patterns is theoretically studied using the theories of the Fisher information, Cramer–Rao bound, and ambiguity function. Criteria of proper amplitude ratio are summarized from the theoretical investigations. Following the guidelines, two antenna arrays are modified to build effective antenna patterns and improve the estimation accuracy. Specifically, the compact monopole-patch array and the dual-monopole array reduce the DOA estimation errors by over 60% and 20%–40%, respectively, under a medium SNR of 10 dB. The phase ambiguity has been eliminated in both arrays as well. The monopole-patch array requires phase calibration in the measurement, whereas the dual-monopole array does not. Experiments were carried out for the dual-monopole array in the anechoic chamber, achieving the estimation accuracy of 0.67° averaged over 360°.

Effect of acoustic horizontal refraction on DOA estimation with a single vector hydrophone

The effect of horizontal refraction (HR) on DOA estimation with a single vector hydrophone is studied. It has been demonstrated in a previous study that HR may bring about a significant deviation between the true bearing of the source and the direction of time-averaged sound flux at the receiver point, i.e., DOA estimation error. [J. Tang et al., 2018, 43(2), ACTA ACUSTICA (in Chinese)]. In the present work, the DOA estimation error in a more realistic scenario is studied, more precisely, source signals are considered to be wide-band instead of time-harmonic, and meanwhile ambient noise is added to the received signal. The ocean waveguide used in simulations is a 3D version of the standard ASA wedge, which implies that the HR considered in this work is raised from multiple reflections between a horizontal sea surface and a sloping sea bottom. The results of this work shall offer some reference to DOA estimation in circumstances with strong HR effects.

A Bayesian Approach to Informed Spatial Filtering With Robustness Against DOA Estimation Errors

A Bayesian approach to spatial filtering is presented, which is robust to uncertain or erroneous direction-of-arrival (DOA) information. The proposed framework aims to capture multiple sound sources at each time-frequency instant with an arbitrary direction-dependent gain, while attenuating diffuse sound and noise. For robustness, the DOA corresponding to each sound source is assumed to be a discrete random variable with a prior defined on a discrete set of candidate DOAs over the whole DOA space. With this assumption, the desired spatial filter is given as a weighted sum of spatial filters corresponding to a specific combination of probable DOA values, where the weights are given by the joint posterior probabilities of the combination of DOA values. Assuming the whole DOA space as the support for each random variable results in redundant computations and contributes to a high computational cost. To alleviate this problem, a narrowband DOA estimate-based posterior probability approximation method is proposed, which isolates regions in the DOA space with high probability of containing the actual source DOAs to compute time-adaptive supports for each random variable. Through experimental analysis, we demonstrate the robustness of the proposed framework against DOA estimation errors. Experimental evaluation with simulated and measured room impulse responses, in terms of objective performance measures, demonstrates the effectiveness of the framework to perform spatial filtering in noisy and reverberant acoustic environments.

DOA error estimation in 3D cylindrical dipole array geometries including the mutual coupling effect

The direction of arrival (DOA) error in dipole 3D arrays is estimated through Monte-Carlo simulations using the standard MUSIC algorithm. Novel 3D geometries are implemented which demonstrate better precision given the same lateral area. The mutual coupling effect is included by changing the search vector in the MUSIC DOA algorithm for the novel 3D geometries. A simple straight forward method is used which does not need complex electromagnetic computations. Simulations show that the proposed method can successfully account for the mutual coupling effects in two dimensional direction finding (both azimuth and elevation angle) with novel 3D array geometries. Reduced DOA estimation error is observed in the novel geometries which can be used as a method of mitigation for the mutual coupling effect.

Quantifying and Reducing the DOA Estimation Error Resulting from Antenna Pattern Deviation for Direction-Finding HF Radar

High-frequency (HF) radars are routinely used for remotely sensing ocean surface currents. However, the performance of the most widely used direction-finding HF radar is degraded due to the effect of the inevitable deviations of actual antenna pattern on the direction of arrival (DOA) estimation. In this paper, we quantify the DOA estimation error resulting from the deviation of the actual antenna pattern from the ideal one. Theoretical analysis and field experiment results suggest that the ratio of the deviations for the two loops dominates the DOA estimation error. Thus, eliminating the effect of the antenna pattern deviations on DOA estimation error is transformed into eliminating the effect of this ratio. From this, a calibration method based on the time-averaged local spatial coverage rate (TLSCR) is proposed to reduce the effect of the antenna pattern deviations on current extraction, which uses the ideal antenna pattern to estimate the DOA of the echoes. To validate this proposed calibration method, we assess the radar-derived radial velocities by comparing with in situ observations. The comparison results indicate that the proposed TLSCR calibration method can effectively reduce the DOA estimation error and improve the performance of the direction-finding HF radar in current observation.

Gold-MUSIC based DOA estimation using ULA antenna of DS-CDMA sources with propagation delay diversity

Direction of Arrival (DOA) estimation using gold-MUSIC is achieved for Uniform Linear Array (ULA) antenna based Direct-Sequence Code Division Multiple Access (DS-CDMA) sources having different Propagation Delay. The DOA is estimated by different MUSIC (Multiple Signal Classification) algorithms for M signal sources with Phase Shift Keying (PSK) transmission in presence of Additive White Gaussian Noise (AWGN). Spatial spectrum, computational efficiency and Root Mean Square Error (RMSE) of DOA estimation using gold-MUSIC over MUSIC and Root-MUSIC algorithms are studied meticulously. The effects of number of ULA elements, Data length and arrival angle on RMSE of DOA are also conferred here.

Analysis of Array Model Errors in GARCH-Based DOA Estimation

In this paper, we consider the theoretical performance analysis of a DOA (direction-of-arrival) estimation method using GARCH (generalized autoregressive conditional heteroscedasticity) noise model. GARCH models are feasible for heavy tailed probability density functions and time-varying variances of stochastic process and also have flexible forms. We addressed a GARCH(1,1) based noise model in the maximum likelihood approach for the estimation of DOAs of impinging sources. In this paper, by means of perturbation approach we consider error analysis of GARCH-based array processing method and derive the theoretical DOA estimation errors versus array model errors such as gain, phase and sensors positions errors. The validity of the proposed analysis is confirmed by using numerical results.

A Super-Resolution Direction of Arrival Estimation Algorithm for Coprime Array via Sparse Bayesian Learning Inference

In this paper, we address the problem of direction of arrival (DOA) estimation with coprime array in the context of sparse signal reconstruction to fully exploit the enhanced degrees of freedom (DOF) offered by the difference coarray. The proposed method is based on the framework of sparse Bayesian learning and can jointly refine the unknown DOAs and the sparse signals in a gradual and interweaved manner. Specifically, the proposed approach is constructed by iteratively decreasing a surrogate function majorizing a given objective function, which results in accelerating the speed to converge to the global minimum. Furthermore, for facilitating a noise-free sparse representation, a customized linear transformation is judiciously incorporated in our sparsity-inducing DOA estimator to eliminate the unknown noise variance, and in the mean time, the sample covariance matrix perturbation can be normalized to an identity matrix as a by-product. Extensive simulation experiments under different conditions finally demonstrate the superiority of our suggested algorithm in terms of mean-squared DOA estimation error, DOF and resolution ability over state-of-the-art techniques.

Reduced-complexity direction of arrival estimation with centro-symmetrical arrays and its performance analysis

A fast algorithm is proposed to dramatically reduce the computational complexity of the multiple signal classification (MUSIC) algorithm for direction-of-arrival (DOA) estimate using a centro-symmetrical array (CSA). The CSA is divided into two sub-arrays and a real matrix is constructed with the covariance matrices of the two sub-arrays and their cross-correlation ones. This real matrix is further regarded as the data covariance one observed by a virtual array which has a real array response, and a novel MUSIC-like cost function is derived accordingly. In the developed method, only real-valued computation is required and the spectral search is compressed into half of the total angular field-of-view. Furthermore, the dimensions of noise subspace and those of search vector are both reduced, leading to about 97% complexity reduction as compare to MUSIC. The non-asymptotic statistical performance of the new DOA estimator is analyzed and a closed-form expression is given to predict the mean square error (MSE) of DOA estimation by the new technique. The effectiveness of the presented approach as well as the theoretical analysis is verified through numerical computer simulations, and it is shown that the proposed method is able to provide good accuracy with low signal-to-noise ratio (SNR) and small numbers of snapshots.

크래머 라오 하한을 이용한 음향 표적 탐지 및 위치추정 오차 분석

본 논문에서는 배열센서에서 DOA(Direction Of Arrival)를 수행하는 경우 크래머 라오 하한을 이용하여 표적신호가 수신되는 방위오차의 최소분산을 계산하고, 탐지 방위오차 및 위치추정 거리오차를 추정하는 방안을 제시한다. 신호 대 잡음비는 DOA의 정확도 즉, 표적의 탐지 방위오차 및 위치추정 거리오차를 결정한다. 일반적으로 신호대 잡음비는 음원준위, 소음준위, 전달손실, 배열센서의 형상, 빔 조향 방위에 따라 달라진다. 표적의 공간상 상대적 위치와 소음준위가 달라지는 경우, 신호 대 잡음비의 변화에 따른 탐지 방위오차 및 위치추정 거리오차를 확률적으로 추정하는 몬테카를로 시뮬레이션을 수행함으로써, 제안된 방법을 검증하였다. In this paper, an algorithm to calculate both bearing and distance error for target detection and localization is proposed using the Cramer Rao lower bound to estimate the minium variance of their error in DOA (Direction Of Arrival) estimation. The performance of arrays in detection and localization depends on the accuracy of DOA, which is affected by a variation of SNR (Signal to Noise Ratio). The SNR is determined by sonar parameters such as a SL (Source Level), TL (Transmission Loss), NL (Noise Level), array shape and beam steering angle. For verification of the suggested method, a Monte Carlo simulation was performed to probabilistically calculate the bearing and distance error according to the SNR which varies with the relative position of the target in space and noise level.

Probe rotation effects on direction of arrival estimation in array‐type directional borehole radar

ABSTRACTThis paper discusses the relationship between feeding line delay compensation and direction of arrival estimation in an array‐type directional borehole radar. In this radar, since the space available for an array antenna is limited by the borehole diameter, direction of arrival estimation is based on small travel time differences among array elements, and an accurate compensation of feeding line delays is important. Computer simulation confirmed that the radar probe rotation in a borehole leads to errors in the direction of arrival estimation of greater than 15° if the delays associated with the feeding array antenna elements are not compensated to within 0.1 ns. This may be caused by a failure to measure the time delays of electrical circuits around the feeding points of the antenna elements. In this case, we suggest that the lengths of system components other than the coaxial cables should be kept to less than 3 cm. Based on these investigations, we developed an array‐type directional borehole radar for a geotechnical project to locate foundation piles. In a field experiment, we confirmed that direction of arrival estimation errors were below about 15°, although the radar probe rotated through more than 180° during the measurement, thanks to correct compensation of the cables. With the correct compensation, we demonstrated three‐dimensional location of a buried cylindrical conducting object, which was located at 2 m from the radar in wet soil. We were able to estimate the reflection point position with an accuracy of 34 cm, which is the averaged error of the three‐dimensional location, while allowing the radar probe to rotate.

Array geometry impact on music in the presence of spatially distributed sources

The MUltiple SIgnal Classification (MUSIC) estimator has been widely studied for a long time for its high resolution capability in the domain of the direction of arrival (DOA) estimation, with the sources assumed to be point. However, when the actual sources are spatially distributed with angular dispersion, the performance of the conventional MUSIC is degraded. In this paper, the impact of the array geometry on the DOA estimation of spatially distributed sources impinging on a sensor array is considered. Taking into account a coherently distributed source model, we establish closed-form expressions of the MUSIC-based DOA estimation error as a function of the positions of the array sensors in the presence of model errors due to the angular dispersion of the signal sources. The impact of the array geometry is studied and particular array designs are proposed to make DOA estimation more robust to source dispersion. The analytical results are validated by numerical simulations.1

Direction-of-Arrival Estimation and Sensor Array Error Calibration Based on Blind Signal Separation

We consider estimating the direction-of-arrival (DOA) in the presence of sensor array error. In the proposed method, a blind signal separation method, the joint approximation and diagonalization of eigenmatrices algorithm, is implemented to separate the signal vector and the mixing matrix consisting of the array manifold matrix and the sensor array error matrix. Based on a new mixing matrix and the reconstruction of the array output vector of each individual signal, we propose a novel DOA estimation and sensor array error calibration procedure. This method is independent of array phase errors and performs well against difference of SNR of signals. Numerical simulations verify the effectiveness of the proposed method.

DoA Estimation and Capacity Analysis for 3-D Millimeter Wave Massive-MIMO/FD-MIMO OFDM Systems

With the promise of meeting future capacity demands, 3-D massive-MIMO/full dimension multiple-input-multiple-output (FD-MIMO) systems have gained much interest in recent years. Apart from the huge spectral efficiency gain, 3-D massive-MIMO/FD-MIMO systems can also lead to significant reduction of latency, simplified multiple access layer, and robustness to interference. However, in order to completely extract the benefits of the system, accurate channel state information is critical. In this paper, a channel estimation method based on direction of arrival (DoA) estimation is presented for 3-D millimeter wave massive-MIMO orthogonal frequency division multiplexing (OFDM) systems. To be specific, the DoA is estimated using estimation of signal parameter via rotational invariance technique method, and the root mean square error of the DoA estimation is analytically characterized for the corresponding MIMO-OFDM system. An ergodic capacity analysis of the system in the presence of DoA estimation error is also conducted, and an optimum power allocation algorithm is derived. Furthermore, it is shown that the DoA-based channel estimation achieves a better performance than the traditional linear minimum mean squared error estimation in terms of ergodic throughput and minimum chordal distance between the subspaces of the downlink precoders obtained from the underlying channel and the estimated channel.