WAVES: weighted average of signal subspaces for robust widebanddirection finding

Existing algorithms for wideband direction finding are mainly based on local approximations of the Gaussian log-likelihood around the true directions of arrival (DOAs), assuming negligible array calibration errors. Suboptimal and costly algorithms, such as classical or sequential beamforming, are required to initialize a local search that eventually furnishes DOA estimates. This multistage process may be nonrobust in the presence of even small errors in prior guesses about angles and number of sources generated by inherent limitations of the preprocessing and may lead to catastrophic errors in practical applications. A new approach to wideband direction finding is introduced and described. The proposed strategy combines a robust near-optimal data-adaptive statistic, called the weighted average of signal subspaces (WAVES), with an enhanced design of focusing matrices to ensure a statistically robust preprocessing of wideband data. The overall sensitivity of WAVES to various error sources, such as imperfect array focusing, is also reduced with respect to traditional CSSM algorithms, as demonstrated by extensive Monte Carlo simulations     

FSF MUSIC for Joint DOA and Frequency Estimation and Its Performance Analysis

In this paper, we present a tree-structured frequency-space-frequency (FSF) multiple signal classification (MUSIC)-based algorithm for joint estimation of the directions of arrival (DOAs) and frequencies in wireless communication systems. The proposed approach is a novel twist of parameter estimation and filtering processes, in which two one-dimensional (1-D) frequency (F)- and one 1-D space (S)-MUSIC algorithms are employed-in a tree structure-to estimate the DOAs and frequencies, respectively. In between every other MUSIC algorithm, a temporal filtering process or a spatial beamforming process, implemented by a set of complementary projection matrices, is incorporated to partition the incoming rays to enhance the estimation accuracy, so that the incoming rays can be well resolved even with very close DOAs or frequencies, using the 1-D MUSIC algorithms. Also, with such a tree-structured estimation scheme, the estimated DOAs and frequencies are automatically paired without extra computational overhead. Furthermore, some statistical analyses of the undesired residue signals propagating between the 1-D MUSIC algorithms and the mean square errors of the parameter estimates are derived to provide further insights into the proposed approach. Simulations show that the new approach can provide comparable performance, but with reduced complexity compared with previous works, and that there is a close match between the derived analytic expressions and simulation results     

FPGA Based Implementation and Comparison of Beamformers for CDMA2000

For the integration of smart antennas into third generation code division multiple access (CDMA) base stations, it still remains as a challenging task to implement smart antenna algorithms on programmable processors. In this paper, we study implementations of some CDMA compatible beamforming algorithms, namely least mean square (LMS), constant modulus (CM), and space code correlator (SCC) algorithms, using Xilinx??s Virtex family FPGAs. This study exhibits feasibility of implementing even simple, practical, and computationally small algorithms based on today??s most powerful FPGA technologies. 16 and 32 bits floating point implementations of the algorithms are investigated using both Virtex II and Virtex IV FPGAs. CDMA2000 reverse link baseband signal format is used in the signal modeling. Randomly changing fading and Direction-of-arrivals (DOAs) of multipaths are considered as a channel condition. The implementation results in terms of beamforming accuracy, FPGA resource utilization, weight vector computation time, and DOA estimation error are presented. Beamformer weight vectors using LMS and CM can be computed within less than 20 ??s on Virtex II FPGA and 10 ??s on Virtex IV FPGA, and using SCC it can be achieved within less than 22 ??s on Virtex IV FPGA. These results show that FPGAs provide approximately 500 times faster speed in implementations than our previous work with DSPs.     

TST-MUSIC for joint DOA-delay estimation

A multiple signal classification (MUSIC)-based approach known as the time-space-time MUSIC (TST-MUSIC) is proposed to jointly estimate the directions of arrival (DOAs) and the propagation delays of a wireless multiray channel. The MUSIC algorithm for the DOA estimation is referred to as the spatial-MUSIC (S-MUSIC) algorithm. On the other hand, the temporal-MUSIC (T-MUSIC), which estimates the propagation delays, is introduced as well. Making use of the space-time characteristics of the multiray channel, the proposed algorithm-in a tree structure-combines the techniques of temporal filtering and of spatial beamforming with three one-dimensional (1-D) MUSIC algorithms, i.e., one S-MUSIC and two T-MUSIC algorithms. The incoming rays are thus grouped, isolated, and estimated. At the same time, the pairing of the estimated DOAs and delays is automatically determined. Furthermore, the proposed approach can resolve the incoming rays with very close DOAs or delays, and the number of antennas required by the TST-MUSIC algorithm can be made less than that of the incoming rays     

Fast adaptive blind beamforming algorithm for antenna array in CDMA systems

In this paper, the maximum signal-to-interference-plus-noise ratio (MSINR) beamforming problem in antenna-array CDMA systems is considered. In this paper, a modified MSINR criterion presented in a previous paper is interpreted as an unconstrained scalar cost function. By applying recursive least squares (RLS) to minimize the cost function, a novel blind adaptive beamforming algorithm to estimate the beamforming vector, which optimally combines the desired signal contributions from different antenna elements while suppressing noise and interference, is derived. Neither the knowledge of the channel conditions (fading coefficients, signature sequences and timing of interferers, statistics of other noises, etc.) nor training sequence is required. Compared with previously published adaptive beamforming algorithms based on the stochastic-gradient method, it has faster convergence and better tracking capability in the time-varying environment. Simulation results in various signal environments are presented to show the performance of the proposed algorithm.     

A set of algorithms linking NLMS and block RLS algorithms

This paper describes a set of block processing algorithms which contains as extremal cases the normalized least mean squares (NLMS) and the block recursive least squares (BRLS) algorithms. All these algorithms use small block lengths, thus allowing easy implementation and small input-output delay. It is shown that these algorithms require a lower number of arithmetic operations than the classical least mean squares (LMS) algorithm, while converging much faster. A precise evaluation of the arithmetic complexity is provided, and the adaptive behavior of the algorithm is analyzed. Simulations illustrate that the tracking characteristics of the new algorithm are also improved compared to those of the NLMS algorithm. The conclusions of the theoretical analysis are checked by simulations, illustrating that, even in the case where noise is added to the reference signal, the proposed algorithm allows altogether a faster convergence and a lower residual error than the NLMS algorithm. Finally, a sample-by-sample version of this algorithm is outlined, which is the link between the NLMS and recursive least squares (RLS) algorithms     

Robust antenna array calibration and accurate angle estimation based on least trimmed squares

A robust antenna array calibration and single target angle estimation algorithm is proposed. The proposed algorithm is based on the least trimmed squares algorithm and operates in two steps. First, the conventional least squares algorithm is used to estimate the intermediate phases (or angle) and the residual values at each element are calculated. In the second step, it excludes large residual elements and uses only the smallest of them, which prevents large errors during the angle estimation. The least trimmed-based phase difference approximation algorithm is simple to implement and is a practical way of mitigating errors at the antenna elements that are due to hardware and imperfect calibration. The results demonstrate that our proposed algorithm is robust and outperforms other algorithms in three scenarios.     

Robust adaptive beamforming using worst-case performance optimization: a solution to the signal mismatch problem

Adaptive beamforming methods are known to degrade if some of underlying assumptions on the environment, sources, or sensor array become violated. In particular, if the desired signal is present in training snapshots, the adaptive array performance may be quite sensitive even to slight mismatches between the presumed and actual signal steering vectors (spatial signatures). Such mismatches can occur as a result of environmental nonstationarities, look direction errors, imperfect array calibration, distorted antenna shape, as well as distortions caused by medium inhomogeneities, near-far mismatch, source spreading, and local scattering. The similar type of performance degradation can occur when the signal steering vector is known exactly but the training sample size is small. In this paper, we develop a new approach to robust adaptive beamforming in the presence of an arbitrary unknown signal steering vector mismatch. Our approach is based on the optimization of worst-case performance. It turns out that the natural formulation of this adaptive beamforming problem involves minimization of a quadratic function subject to infinitely many nonconvex quadratic constraints. We show that this (originally intractable) problem can be reformulated in a convex form as the so-called second-order cone (SOC) program and solved efficiently (in polynomial time) using the well-established interior point method. It is also shown that the proposed technique can be interpreted in terms of diagonal loading where the optimal value of the diagonal loading factor is computed based on the known level of uncertainty of the signal steering vector. Computer simulations with several frequently encountered types of signal steering vector mismatches show better performance of our robust beamformer as compared with existing adaptive beamforming algorithms.     

Adaptive Complex-Coefficient 2D FIR Trapezoidal Filters for Broadband Beamforming in Cognitive Radio Systems

A novel design method is proposed for an adaptive discrete-domain beamformer for the beamforming of temporally broadband-bandpass signals in cognitive radio (CR) systems. The method is based on a complex-coefficient 2D finite impulse response (FIR) filter having a trapezoidal-shaped passband. The temporally broadband-bandpass signals are received by a 1D uniformly distributed antenna array (1D UDAA), where the outputs of the antennas are complex-quadrature sampled by the front end of the CR system. This CR system is based on a software defined radio (SDR) architecture and can be instantly reconfigured by the control system to select the appropriate frequency band and the required sampling rate. The subsequent beamforming enhances the spectral components of the desired temporally broadband-bandpass signals by arranging for the asymmetric trapezoidal-shaped passband of the 2D filter transfer function to closely enclose the region of support (ROS) of the spectrum of the desired signal, whereas the ROSs of the spectral components of the interfering signals are enclosed by the stopband. The proposed novel closed-form design method facilitates instant adaptation of the shape and orientation of the passband of the beamforming 2D FIR trapezoidal filter in order to match the time-varying frequency band and the time-varying bandwidth of the signal, as well as to track and enhance received signals with time-varying directions of arrival (DOAs). Simulated results confirm that, compared with previously reported methods, the proposed method achieves the best overall tradeoff with respect to the instantaneous adaptations of the operating frequency band, the bandwidth, and the time-varying DOAs, the distortion of the desired passband signal, and the stopband attenuation of interfering signals.     

Array Calibration for CDMA Smart Antenna Systems

In this paper, we investigate array calibration algorithms to derive a further improved version for correcting antenna array errors and RF transceiver errors in CDMA smart antenna systems. The structure of a multi‐channel RF transceiver with a digital calibration apparatus and its calibration techniques are presented, where we propose a new RF receiver calibration scheme to minimize interference of the calibration signal on the user signals. The calibration signal is injected into a multichannel receiver through a calibration signal injector whose array response vector is controlled in order to have a low correlation with the antenna response vector of the receive signals. We suggest a model‐based antenna array calibration to remove the antenna array errors including mutual coupling errors or to predict the element patterns from the array manifold measured at a small number of angles. Computer simulations and experiment results are shown to verify the calibration algorithms.     

Blind beamforming on a randomly distributed sensor array system

We consider a digital signal processing sensor array system, based on randomly distributed sensor nodes, for surveillance and source localization applications. In most array processing the sensor array geometry is fixed and known and the steering array vector/manifold information is used in beamformation. In this system, array calibration may be impractical due to unknown placement and orientation of the sensors with unknown frequency/spatial responses. This paper proposes a blind beamforming technique, using only the measured sensor data, to form either a sample data or a sample correlation matrix. The maximum power collection criterion is used to obtain array weights from the dominant eigenvector associated with the largest eigenvalue of a matrix eigenvalue problem. Theoretical justification of this approach uses a generalization of Szego's (1958) theory of the asymptotic distribution of eigenvalues of the Toeplitz form. An efficient blind beamforming time delay estimate of the dominant source is proposed. Source localization based on a least squares (LS) method for time delay estimation is also given. Results based on analysis, simulation, and measured acoustical sensor data show the effectiveness of this beamforming technique for signal enhancement and space-time filtering     

用于波束形成的最小二乘广义模值算法研究

对用于波束形成的最小二乘广义模值算法(LSGMA)在多种信号环境下的收敛性能进行了分析;在此基础上提出一种新的多用户盲波束形成算法--迭代最小二乘广义模投影(ILSP-GMA)算法,克服LSGMA算法当恒模干扰信号强于所需信号时会错误收敛的缺陷.仿真结果表明该算法可有效适用于多用户情况,并可获得较原迭代最小二乘投影算法(ILSP)更快的收敛速度.     

A class of square root and division free algorithms andarchitectures for QRD-based adaptive signal processing

The least squares (LS) minimization problem constitutes the core of many real-time signal processing problems, such as adaptive filtering, system identification and adaptive beamforming. Recently efficient implementations of the recursive least squares (RLS) algorithm and the constrained recursive least squares (CRLS) algorithm based on the numerically stable QR decomposition (QRD) have been of great interest. Several papers have proposed modifications to the rotation algorithm that circumvent the square root operations and minimize the number of divisions that are involved in the Givens rotation. It has also been shown that all the known square root free algorithms are instances of one parametric algorithm. Recently, a square root free and division free algorithm has also been proposed. In this paper, we propose a family of square root and division free algorithms and examine its relationship with the square root free parametric family. We choose a specific instance for each one of the two parametric algorithms and make a comparative study of the systolic structures based on these two instances, as well as the standard Givens rotation. We consider the architectures for both the optimal residual computation and the optimal weight vector extraction. The dynamic range of the newly proposed algorithm for QRD-RLS optimal residual computation and the wordlength lower bounds that guarantee no overflow are presented. The numerical stability of the algorithm is also considered. A number of obscure points relevant to the realization of the QRD-RLS and the QRD-CRLS algorithms are clarified. Some systolic structures that are described in this paper are very promising, since they require less computational complexity (in various aspects) than the structures known to date and they make the VLSI implementation easier     

基于加权最小二乘的宽带波束形成算法

宽带波束形成技术是阵列信号处理研究的一个重要方向。基阵对信号的响应特性随频率而改变导致通过基阵的宽带信号产生波形畸变。恒定束宽波束形成可以实现在信号带宽内基阵波束图主瓣宽度保持恒定。主要研究基于加权最小二乘的恒定束宽宽带数字波束形成方法及其实现,MATLAB仿真实验表明算法的正确性和有效性。     

基于可变对角载入的鲁棒自适应波束形成算法

针对传统算法对方向向量偏差敏感的缺点,提出了一种基于可变对角载入的鲁棒自适应波束形成算法.为了提高算法的鲁棒性,采用非线性约束条件下的最优化阵列输出功率对信号方向向量进行优化求解,且优化解中的参量能够准确求出.为了减少计算量,采用递推算法求逆矩阵并利用泰勒级数展开,推导出基于可变对角载入的权重向量公式.该算法可有效地抑制方向向量偏差所带来的影响,降低了计算量易于实时实现,提高了系统的鲁棒性,改善了阵列输出的信干噪比,使其更接近最优值.仿真结果表明,该算法相对传统算法可以获得更好的性能.     

A Class of Adaptive Cyclostationary Beamforming Algorithms

One of the main benefits of the cyclostationary beamforming algorithms is their ability to extract signals from co-channel interference with only a knowledge of the cycle frequency. In this paper, we study the popular cyclostationary beamformers, and propose five new algorithms, namely, the adaptive cyclic adaptive beamforming (ACAB), adaptive cross-SCORE (ACS), constrained least-squares (CLS), adaptive phase-SCORE (APS), and maximal constrained autocorrelation (MCA) algorithms. All these algorithms are adaptive and have a computational complexity of O(n ²) complex multiplications, where n is the number of array elements. A comparative study of these algorithms is made based on numerical simulations. Each of these algorithms has specific application scenarios. The ACS and the APS algorithms are particularly suited for very adverse signal environments. The ACAB, MCA and cyclic adaptive beamforming (CAB, from the work of Wu and Wong) algorithms can provide good performance in the case of medium or weak interference, while the CLS algorithm is especially suitable for weak interference. The CAB algorithm is shown to be a special case of the least-square self-coherent restoral (LS-SCORE) algorithm. Some insights as to how one can assign carrier frequency and symbol rate during digital modulation are also suggested. The proposed adaptive algorithms are easy to implement, and thus are very promising for applications in wireless and mobile communications. This work was supported by the NSERC of Canada.     

Adaptive Beamforming and Recursive DOA Estimation Using Frequency-Invariant Uniform Concentric Spherical Arrays

This paper proposes recursive adaptive beamforming and broadband 2-D direction-of-arrival (DOA) estimation algorithms for uniform concentric spherical arrays (UCSAs) having nearly frequency-invariant (FI) characteristics. The basic principle of the FI-UCSA is to transform the received signals to the phase mode and remove the frequency dependency of individual phase modes through a digital beamforming network. Hence, the far-field pattern of the array is determined by a set of weights. Thanks to the FI characteristic, traditional narrowband adaptive beamforming algorithms such as minimum variance beamforming and the generalized sidelobe canceller method can be applied to the FI-UCSA. Simulation results show that the proposed adaptive FI-UCSA beamformer achieves a lower steady-state error and converges faster than the conventional tapped-delay line approach while requiring fewer adaptive coefficients. A new broadband 2-D DOA estimation algorithm using ESPRIT techniques for FI-UCSA is proposed to recursively estimate the DOAs of the moving targets. Simulation results show that the proposed DOA estimation algorithm achieves a satisfactory performance for slowly varying sources at low arithmetic complexity.      

高信噪比低信干比环境下盲自适应波束形成

本文针对通信双方是合作方这一特点，利用信号的周期平稳性，提出了一种能够适应于高信噪比、低信干比环境的盲自适应波束形成算法，采用了特征向量识别的方法，较好地解决了CAB、CCAB等方法存在的主特征向量误判的问题。该方法不需要系统提供波束指向和估计目标信号方向、具有对系统误差的稳健性，能够较好地抑制干扰。模拟实验验证了本文的方法。     

Finite word-length effects in recursive least squares algorithms with application to adaptive equalization

In this paper we provide a summary of recent and new results on finite word length effects in recursive least squares adaptive algorithms. We define the numerical accuracy and numerical stability of adaptive recursive least squares algorithms and show that these two properties are related to each other, but are not equivalent. The numerical stability of adaptive recursive least squares algorithms is analyzed theoretically and the numerical accuracy with finite word length is investigated by computer simulation. It is shown that the conventional recursive least squares algorithm gives poor numerical accuracy when a short word length is used. A new form of a recursive least squares lattice algorithm is presented which is more robust to round-off errors compared to the conventional form. Optimum scaling of recursive least squares algorithms for fixedpoint implementation is also considered.