Blind Beamforming Research Articles

Identifiability results for blind beamforming in incoherent multipath with small delay spread

Several explicit identifiability results are derived for deterministic blind beamforming in incoherent multipath with small delay spread. For example, it is shown that if the sum of spatial and fractional sampling diversities exceeds two times the total number of paths, then identifiability can be guaranteed even for one symbol snapshot. The tools come from the theory of low-rank three-way array decomposition (commonly referred to as parallel factor analysis (PARAFAC) and data smoothing in one and two dimensions. New results regarding the Kruskal-rank of certain structured matrices are also included, and they are of interest in their own right.

Analysis of the Multistage CM Array/Signal Canceler for Digital Communication Signals

The multistage constant modulus (CM) array is a blind adaptive beamformer that can separate cochannel digital communication signals. It consists of several identical stages connected in a cascade structure. Each stage is composed of a multichannel linear equalizer (MCLE) and a multichannel signal canceler (MCSC). The MCLE generates a linear estimate of one cochannel signal impinging on the antenna array. This captured source is removed from the input by the MCSC, which is a parallel connection of adaptive FIR filters, one for each antenna element. In this paper, we describe the architecture of the multistage CM array/signal canceler, and derive the Wiener weights for the MCLE and the MCSC. A discrete-time channel model with fractional sampling at the antenna array is employed. It is demonstrated that the power of the source captured by the first stage is reduced to the noise floor at the input of the next stage, whereas the other sources pass through essentially unchanged. Computer simulations are presented to illustrate the capture behavior of the multistage system.

Comments on blind beamforming for multiple non-Gaussian signals and the constant-modulus algorithm

For original paper see Sheinvald (IEEE Trans. Signal Processing, vol.46, p.1878-85 July 1998). Sheinvald compared a cumulant matching criterion to three simplified criteria that he claimed to be equivalent. We show that two simplified criteria can be viewed as direct consequences of a result already published and that their equivalence must be revised. We also give additional references of closely related works that have been omitted, some of them presenting Jacobi-like source separation algorithms, presented as original by Sheinvald.

Doubly spread DS-CDMA for efficient blind interference cancellation

A new spreading scheme, which consists of two stages of spreading, is considered for DS-CDMA systems. The data of a user is spread first with a long signature sequence and then with a short signature sequence. The scheme combines the advantages of the two types of spreading techniques and allows the suppression of MAI by performing both beamforming and multiuser detection efficiently. A joint receiver with blind multiuser detection and blind beamforming is proposed for the new spreading scheme. Simulations show that the joint receiver performs better than either beamforming or multiuser detection alone. To speed up convergence, an iterative version of the joint receiver is considered. A simple adaptive sequence design method is also included.

Robust blind beamforming using neural network

Many blind beamforming algorithms, such as C-CAB, use cyclostationarity to estimate the steering vector and adaptively obtain the LCMV optimum solution. However, LCMV methods are sensitive to the mismatch caused by the uncalibration array or estimate error. After discussion of this mismatch, a robust blind beamforming algorithm is presented in the paper. Implemented as a neural network, this algorithm reduces computational complexity for real-time use. Computer simulations verify the analysis.

RLS adaptive blind beamforming algorithmfor cyclostationary signals

A new cost function, which is a modification of the cost function of Castedo and Figugiras-Vidal for the adaptive blind beamforming of cyclostationary signals, is proposed. The proposed cost function enables the well-known recursive least-squares technique to be applied. Simulations demonstrate that the resulting algorithm has a faster convergence speed than the stochastic gradient-based algorithm of Castedo and Figugiras-Vidal.

Fast adaptive super-exponential multistage beamforming for cellular base-station transceivers with antenna arrays

A new blind adaptive beamforming algorithm is introduced. We show how cumulants of the received signals can be used to obtain the weights of the beamformer that perform blind extraction. The method is based on a spatial interpretation of a deconvolution procedure known as the super-exponential algorithm. The basic block processing algorithm is attractive because it can be transformed in an efficient adaptive algorithm which exhibits good tracking capability. To prove the effectiveness of the idea, we show results for a typical mobile communications scenario where several cochannel interferers corrupt the signals of interest.

A two-sensor array blind beamformer for direct sequence spread spectrum communications

We present an efficient blind beamformer dedicated to the problem of interference mitigation in direct sequence spread spectrum (DSSS) communication systems using a two-sensor array. A closed-form solution for the blind identification of the communication channel is derived by exploiting the temporal properties of the desired signal and the interference. The optimal beamformer is derived from the maximization of the signal-to-interference and noise ratio (SINR) at the output of the receiver in terms of the blindly estimated channel coefficients. Three structures of the DSSS receiver are presented. One structure consists of the blind beamformer followed by the spread spectrum demodulator. The other two structures consist of the spread spectrum demodulator followed by the blind beamformer. The performance of these structures is discussed in terms of the achieved SINR and the computational cost. Simulation results are provided to illustrate the effectiveness of the proposed blind beamformers in interference excision.

A least squares approach to blind beamforming

We present a least squares approach to blind beamforming. Two estimation criteria are derived. One turns out to coincide with the Comon (1990, 1994) criterion, whereas the other is a computationally simpler criterion similar in nature to the joint approximate diagonalization of eigenmatrices (JADE) criterion.

Adaptive multistage beamforming using cyclic higher order statistics (CHOS)

A new blind beamforming algorithm for signals that exhibit higher order cyclostationarity is presented. Exploiting some previous theoretical developments, we show how cyclic cumulants of the received signals can be used to obtain the weights of the beamformer that perform blind extraction. The method is based on a spatial interpretation of a deconvolution procedure known as the super-exponential algorithm. The basic block processing algorithm is made fully adaptive using an adaptive URV scheme and applied to a typical mobile communications scenario where several cochannel interferers corrupt the signals of interest.

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.

Misadjustment and tracking analysis of the constant modulus array

The constant modulus (CM) array is a blind adaptive beamformer that can separate cochannel signals. A follow-on adaptive signal canceler may be used to perform direction finding of the source captured by the array. In this paper, we analyze the convergence and tracking properties of the CM array using a least-mean-square approximation. Expressions are derived for the misadjustment of the adaptive algorithms, and a tracking model is developed that accurately predicts the behavior of the system during fades. It is demonstrated that the adaptive canceler contributes more to the overall misadjustment than does the adaptive CM beamformer. Computer simulations are presented to illustrate the transient properties of the system and to verify the analytical results.

Algebraic methods for deterministic blind beamforming

Deterministic blind beamforming algorithms try to separate superpositions of source signals impinging on a phased antenna array by using the deterministic properties of the signals or the channels such as their constant modulus or directions-of-arrival. Progress in this area has been abundant over the past ten years and has resulted in several powerful algorithms. Unlike optimal or adaptive methods, the algebraic methods discussed in this review act on a fixed block of data and give closed-form expressions for beamformers by focusing on algebraic structures. This typically leads to subspace estimation and generalized eigenvalue problems. After introducing a simple and widely used multipath channel model, the paper provides an anthology of properties that are available, as well as generic algorithms that exploit them.

A least-squares approach to joint diagonalization

We present a new least-squares-based approach for the joint diagonalization problem arising in blind beamforming. The resulting estimation criterion turns out to coincide with that proposed by Cardoso and Souloumaic (see IEE Proc. F, Radar Signal Process., vol.140, no.6, p.362-70, Dec. 1993) on intuitive grounds, thus establishing the optimality of their criterion in the least-squares (LS) sense.

Applications of cumulants to array processing. III. Blind beamforming for coherent signals

For pt.II see ibid., vol.43, no.7, p.1663-7, 1995. We provide a cumulant-based blind beamforming method for recovery of statistically independent narrowband source signals in the presence of coherent (or perfectly correlated) multipath propagation. Our method is based on the fact that for a blind beamformer, the presence of coherent multipaths is equivalent to the case of independent sources with a different steering matrix. Our approach is applicable to any array configuration having unknown response. Signal sources must have nonzero fourth-order cumulants. There is no need to estimate the directions of arrival. Our method maximizes signal-to-interference plus noise ratio (SINR). A comparable result does not exist using just second-order statistics.

A subarray manifold revealing projection for partially blind identification and beamforming

We consider the problem of locating and extracting sources received by an array of sensors in two significant cases. In one case, sensor positions are partially unknown. In the other one, the propagation to a subset of sensors is unknown. The core of the algorithm is partially blind identification of steering vectors. It relies on a tracking procedure with low computational complexity. We apply it to the calibration of maneuvering and towed arrays receiving multiple and correlated sources.

Higher-Order Statistics Applied to Some Array Signal Processing Problems

Array signal processing is a very rich area for applications of higher-order statistics. This paper provides a short overview of: cumulant-based blind beamforming, virtual cross-correlation computer, the virtual ESPRIT algorithm (VESPA), waveform recovery, and suppression of non-Gaussian noise, all of which represent novel applications of higher-order statistics, and in all cases provide solutions to problems that either could not be solved before or can now be solved better than before.

Blind beamforming for non-gaussian signals

The paper considers an application of blind identification to beamforming. The key point is to use estimates of directional vectors rather than resort to their hypothesised value. By using estimates of the directional vectors obtained via blind identification, i.e. without knowing the array manifold, beamforming is made robust with respect to array deformations, distortion of the wave front, pointing errors etc., so that neither array calibration nor physical modelling is necessary. Rather suprisingly, ‘blind beamformers’ may outperform ‘informed beamformers’ in a plausible range of parameters, even when the array is perfectly known to the informed beamformer. The key assumption on which blind identification relies is the statistical independence of the sources, which is exploited using fourth-order cumulants. A computationally efficient technique is presented for the blind estimation of directional vectors, based on joint diagonalisation of fourth-order cumulant matrices; its implementation is described, and its performance is investigated by numerical experiments.