Multidimensional multirate DOA estimation in beamspace

This paper presents a beamspace version of ESPRIT for uniform rectangular arrays that supports closed-form 2-D angle estimation, automatically couples the two components of the source directions, and works with any front end beamformer. The proposed algorithm is based on the observation that beamspace noise eigenvectors can be transformed to vectors that are bandpass and have spectral nulls at the inband source locations. This facilitates multirate processing (involving modulation to baseband, filtering, and decimation) and yields a space with dimensionality equal to the number of beams used to probe the subband rather than the number of elements in the sensor array. The MUSIC algorithm can be applied to this noise subspace. Alternatively, a transformation matrix can be computed a priori, which maps the beamspace signal eigenvectors to the corresponding signal subspace that has the ESPRIT structure. The TLS-ESPRIT algorithm is then modified to obtain the two directions for each source from a single eigenvalue-eigenvector pair. Hence, they are automatically coupled     

波束空间的双基地MIMO雷达定位方法

提出了一种基于波束空间的双基地多输入多输出(MIMO)雷达目标定位方法——B-ESPRIT算法。该算法可重构受波束空间变换破坏的发射和接收阵列旋转不变特性,从而可利用ESPRIT方法来得到对目标收发方位角的估计值。由于降低了处理数据的维数,所提的B-ESPRIT算法相比常规的阵元空间ESPRIT(E-ESPRIT)算法具有更小的运算量。此外,还详细分析讨论了算法的波束增益与目标角度的关系,并通过计算机仿真证明了分析的正确性。     

Beamspace ESPRIT

Most high-resolution algorithms for sensor array processing require an eigendecomposition, which is a computation that is difficult to implement in parallel and requires O(M³) multiplications for an M×M matrix, corresponding to M sensors. Beamspace transformation is one way of reducing computation and sometimes improving the estimation accuracy. As a consequence of the beamspace transformation performed, however, arrays such as uniform linear arrays commonly used in direction finding lose their displacement invariance structure. As a result, computational complexity may actually increase since the computationally efficient ESPRIT algorithm cannot be applied directly. In this paper, a method for restoring the invariance structure resulting in a beamspace ESPRIT algorithm is described. Asymptotic performance analysis of beamspace ESPRIT and simulation results are presented as well     

任意几何结构阵列下的空间信号频率估计

该文论述了一种基于波束空间ESPRIT并适用于任意几何结构阵列的空间信号频率估计算法。在把阵元空间数据映射到DFT空间后,提取出不依赖于阵列几何结构的频率矢量,然后运用BeamspaceESPRIT的概念并通过一个间接的方法估计出信号频率。计算机模拟结果证实了该算法对不同阵列获取的信号的测频有效性并显示出良好的高分辨、高精度性能。     

基于降维波束空间的实值ESPRIT单基地MIMO雷达测角算法

单基地多输入多输出(MIMO)雷达的波达方向(DOA)估计问题是近年来研究的热点。高维度的MIMO雷达数据,导致传统旋转不变性参数估计技术(ESPRIT)算法需要付出较大的运算代价。在低信噪比、低快拍数的条件下,传统ESPRIT算法性能会严重下降。为了克服传统ESPRIT算法的以上缺点,该文提出一种降维波束空间的实值ESPRIT算法。该算法通过转换矩阵,将高维度MIMO雷达数据转换到低维度的数据,从而去除数据中的冗余。然后再将低维数据变换到波束空间,构造实值旋转不变性等式,用以估计目标的角度。仿真结果表明,在低信噪比和低快拍数时,相比于传统ESPRIT算法,该文所提方法具有更好的角度估计性能和更少的运算量。     

Beamspace Root-MUSIC Algorithm for Joint DOD DOA Estimation in Bistatic MIMO Radar

The computational complexity for the direction of departure (DOD) and direction of arrival (DOA) estimation in bistatic MIMO radar increases very rapidly with the number of sensors. To reduced computational complexity, a beamspace Root-MUSIC algorithm for joint DOD and DOA is proposed in this paper. Ingenuous mathematical manipulations utilizing the properties of common out-of-band nulls offered by discrete Fourier transform matrix beamformer are proposed to restore the Vandermonde structure with a reduced degree, which is lost in beamspace transformation for both the transmit array and the receive array. Then the DOD and DOA can be estimated via polynomials root finding procedure. The proposed algorithm can work in reduced dimension beamspace data and reduced degree polynomial root finding procedure in the final stage of Root-MUSIC. Moreover, automatic paring between the DODs and DOAs can be obtained. Simulation results demonstrate that the effectiveness of the proposed algorithm.     

A method for solving DOA estimation ambiguity in esprit algorithm

This paper introduces a method for solving DOA estimation ambiguity in ESPRIT algorithm with the conventional beamformer. With the help of it, for any space of two subarrays, the signal DOA in [-π/2 ,π/2] can be estimated effectively by using ESPRIT algorithm. Finally, some simulation results to verify the theoretical analyses are presented.     

Conjugate ESPRIT (C-SPRIT)

In this paper, we present an algorithm to estimate the direction of the arrival angles (DOAs) from noncoherent one-dimensional (1-D) signal sources such as binary phase shift keying (BPSK) and M-ary amplitude shift keying (MASK). The proposed algorithm can provide a more precise DOA estimation and can detect more signals than well-known classical subspace-methods MUSIC and ESPRIT for the 1-D signals. The complexity is the same as that of ESPRIT since the proposed algorithm uses the same array geometry and subarray processing that ESPRIT does. The main differences between the proposed algorithm and the ESPRIT algorithm are as follows: 1) the number of overlapping array elements between two subarrays is equal to M in the proposed algorithm, while in ESPRIT the maximum number of overlapping elements is M-1, where M denotes the total number of array elements, and 2) the proposed algorithm employs the conjugate of rotation matrix (CRM) /spl Phi//sup */ while ESPRIT uses /spl Phi/ with no conjugate for the second subarray geometry.     

Closed-form 2-D angle estimation with rectangular arrays in elementspace or beamspace via unitary ESPRIT

The UCA-ESPRIT is a closed-form algorithm developed for use in conjunction with a uniform circular array (UCA) that provides automatically paired source azimuth and elevation angle estimates. The 2-D unitary ESPRIT is presented as an algorithm providing the same capabilities for a uniform rectangular array (URA). In the final stage of the algorithm, the real and imaginary parts of the ith eigenvalue of a matrix are one-to-one related to the respective direction cosines of the ith source relative to the two major array axes. The 2-D unitary ESPRIT offers a number of advantages over other proposed ESPRIT based closed-form 2-D angle estimation techniques. First, except for the final eigenvalue decomposition of a dimension equal to the number of sources, it is efficiently formulated in terms of real-valued computation throughout. Second, it is amenable to efficient beamspace implementations that are presented. Third, it is applicable to array configurations that do not exhibit identical subarrays, e.g., two orthogonal linear arrays. Finally, the 2-D unitary ESPRIT easily handles sources having one member of the spatial frequency coordinate pair in common. Simulation results are presented verifying the efficacy of the method     

均匀线列阵下的快速TLS-ESPRIT算法

ＴＬＳ－ＥＳＰＲＩＴ算法是一种方位估计算法,由于采用了全局最小二乘估计,其在低信噪比下的估计性能较ＥＳＰＲＩＴ算法有所提高,但算法略显复杂。本文针对均匀线列阵,构成了ＴＬＳ－ＥＳＰＲＩＴ的简化算法,使其运算量明显减少,同时还可给出源功率的估计。文中给出了算法的结构及计算机仿真结果。     

A novel wavelet-based generalized sidelobe canceller

This paper presents a novel narrow-band adaptive beamformer with the generalized sidelobe canceller (GSC) as the underlying structure. The new beamformer employs a wavelet-based approach for the design of the blocking matrix of the GSC, which is now constituted by a set of regular M-band wavelet filters. Such a construction of the blocking matrix can not only block the desired signals from the lower path as required provided the wavelet filters have sufficiently high regularity, but it also encompasses the widely used one with ones and minus ones along the diagonals as a special case. In addition, it possesses two advantageous features. First, the eigenvalue spreads of the covariance matrices of the blocking matrix outputs, as demonstrated in various scenarios, are decreased as compared with those of previous approaches. Since the popular least mean squares (LMS) algorithm has been notorious for its slow convergence rate, the reduction of the eigenvalue spreads can, in general, accelerate the convergence speed of the succeeding LMS algorithm. Second, the new beamformer belongs to a specific type of partially adaptive beamformers, wherein only a portion of the available degree of freedom is utilized in the adaptive processing. As such, the overall computational complexity is substantially reduced when compared to previous works. The issues of choosing the parameters involved for superior performance are also addressed. Simulation results are furnished as well to justify this new approach     

用均匀中心对称阵二维西ESPRIT方法实现闭环形式二维角估计

本文提出了适用于一类均匀中心对称阵的二维西ESPRIT方法,它是一种闭环形式的高分辨算法,对信号源方位角和仰角估计实现自动配对.在算法最后阶段构造一个矩阵,其第I个特征值的实部和虚部分别与第I个信号源相对X轴和Y轴的方向余波一一对应.该算法除了初始变换和最后矩阵特征分解外,整个过程都采用高效的实值计算.并推广应用于DFT波束空间,可在较小的空间维数上处理,从而减小计算复杂性.最后对算法做了一阶近似渐进性能分析.仿真结果说明了算法是有效的.     

共轭增强ESPRIT算法

提出了共轭增强ESPRIT（CA-ESPRIT）算法，利用阵列输出的延迟相关函数及其共轭形成伪阵列输出，从而得到伪协方差矩阵，对其进行特征分解，用ESPRIT算法得到波迭方向。仿真实验表明，新算法可对多于阵元数的信号进行测向，其测角精度和分辨能力优于ESPRIT算法，运行时间小于有相同阵列扩展能力的MUSIC—like算法。     

Performance analysis of MUSIC employing conjugate symmetricbeamformers

If one incorporates a beamformer composed of conjugate centro-symmetric weight vectors as a preprocessor to an eigenstructure direction finding algorithm, a real-valued decomposition can be employed to estimate the noise and signal subspaces from the sample covariance matrix. The effect of employing the real processing methodology on the angle estimation performance of beamspace MUSIC is explored. Specifically, the distribution of the real-valued signal subspace eigenvectors is derived and used in an asymptotic analysis of the bias and variance of the MUSIC estimator. The theoretical analysis shows that processing the real part of the beamspace sample covariance matrix offers significant performance gains, in addition to the obvious computational benefit, relative to the conventional complex-valued procedure, particularly in the case of correlated sources. Monte Carlo simulations are included to verify the theoretical expressions. A trade-off study of the estimation accuracy versus the desire to provide adequate rejection of unwanted signals in a sector-based interrogation scheme for various beamforming architectures is also presented     

基于ESPRIT宽带信号测向技术研究

研究了基于ESPRIT宽带信号测向技术,采用信号子空间变换方法分别对2个平移矩阵聚焦处理,并利用窄带ESPRIT测向方法计算出来波方向,提出利用ESPRIT与聚焦处理相结合测向的方法,解决了ESPRIT宽带信号测向精度差问题。通过聚焦处理有效抑制噪声,提高信噪比,从而获得高精度、高分辨率的渐进无偏估计信号方向。计算机仿真验证了算法的有效性。     

Uniform Concentric Circular Arrays With Frequency-Invariant Characteristics—Theory, Design, Adaptive Beamforming and DOA Estimation

This paper proposes a new digital beamformer for uniform concentric circular arrays (UCCAs) having nearly frequency-invariant (FI) characteristics. The basic principle is to transform the received signals to the phase mode and remove the frequency dependency of the individual phase mode through the use of a digital beamforming or compensation network. As a result, the far-field pattern of the array, which is governed by a set of variable beamformer weights, is electronically steerable, and it is approximately invariant over a wider range of frequencies than conventional uniform circular arrays (UCAs). This also makes it possible to design the compensation network and the beamformer weights separately. The design of the compensation network is formulated as a second order cone programming (SOCP) problem and is solved optimally for minimax criterion. By employing the beamspace approach using the outputs of a set of fixed UCCA frequency-invariant beamformers (FIBs), a new beamspace MUSIC algorithm is proposed for estimating the direction-of-arrivals (DOAs) of broadband sources. Since the beampatterns of the UCCA-FIB is approximately invariant with frequency and is governed by a small set of weights, a very efficient adaptive beamformer using the minimum variance beamforming (MVB) approach can be developed. Simulation results using broadband Gaussian and multisinusoidal inputs show that the proposed adaptive UCCA-FIB is numerically better conditioned than the conventional broadband tapped-delay-line-based adaptive beamformers, due to the FI property and significantly fewer numbers of adaptive parameters. Consequently, a higher output signal-to-inference-plus-noise ratio over the conventional tapped-delay-line approach is observed. The usefulness of the proposed UCCA-FIB in broadband DOA estimation is also verified by computer simulation     

波束-多普勒酉ESPRIT多目标DOA估计

高分辨波达方向(DOA)估计是地基/空基预警雷达实现主波束内多目标精细跟踪需要解决的关键问题。针对上述问题,该文提出一种波束-多普勒酉ESPRIT多目标DOA估计算法。该方法首先通过时域平滑技术构造多个快拍。然后采用中心共轭对称傅里叶变换矩阵将数据变换至波束-多普勒域,同时保留旋转不变结构。最后采用实值ESPRIT算法估计目标的DOA。所提方法充分利用了信号的时域信息来改善空域参数估计性能,同时具有较低的计算复杂度。实验结果证明了所提方法的有效性。     

基于任意阵列形式的LFM信号参数估计

基于任意阵列形式的LFM信号参数估计算法，利用分段解线调建立频域波束空间数据模型，通过Beamspace—ESPRIT算法和线性调频波束形成器算法(CBF)实现了调频斜率和初始频率的高精度估计。针对多信号交叉项的影响，提出了逐次滤波和迭代滤波的解决办法。算法对线性调频参数无模糊估计的条件进行了研究，并给出了欠采样条件下初始频率估计解模糊的方法。仿真实验证明了算法的有效性。     

An adaptive generalized sidelobe canceller with derivative constraints

An adaptive broad-band beamforming structure is presented which employs a gradient-based weight adjustment algorithm to minimize output variance subject to a set ofJlinear constraints on broadband directional derivatives in the desired look direction. A generalized sidelobe-cancelling structure is employed in which a nonadaptive (conventional) beamformer operates in parallel with an adaptive beamformer. The conventional portion has a broad-band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped-delay line filters. Blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped-delay lines. As a result, an unconstrained least mean square (LMS) power minimization algorithm is employed to adapt the delay line weights. It is shown that with the addition of the directional derivative constraints, the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints. A design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented.