Blind signal separation (BSS) and independent component analysis (ICA) are emerging techniques of array processing and data analysis, aiming at recovering unobserved signals or `sources' from observed mixtures (typically, the output of an array of sensors), exploiting only the assumption of mutual independence between the signals. The weakness of the assumptions makes it a powerful approach but requires to venture beyond familiar second order statistics. The objective of this paper is to review some of the approaches that have been recently developed to address this exciting problem, to show how they stem from basic principles and how they relate to each other.

Separation of sources consists in recovering a set of signals of which only instantaneous linear mixtures are observed. In many situations, no a priori information on the mixing matrix is available: the linear mixture should be `blindly' processed. This typically occurs in narrow-band array processing applications when the array manifold is unknown or distorted. This paper introduces a new source separation technique exploiting the time coherence of the source signals. In contrast to other previously reported techniques, the proposed approach relies only on stationary second-order statistics, being based on a joint diagonalization of a set of covariance matrices. Asymptotic performance analysis of this method is carried out; some numerical simulations are provided to illustrate the effectiveness of the proposed method. I. Introduction I N many situations of practical interest, one has to process multidimensional observations of the form: x(t) = y(t) + n(t) = As(t) + n(t); (1) i.e. x...

Iterative constant modulus algorithms such as Godard and CMA have been used to blindly separate a superposition of co-channel constant modulus (CM) signals impinging on an antenna array. These algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual CM signals that are present in the channel. In this paper, we show that the underlying constant modulus factorization problem is, in fact, a generalized eigenvalue problem, and may be solved via a simultaneous diagonalization of a set of matrices. With this new, analytical approach, it is possible to detect the number of CM signals present in the channel, and to retrieve all of them exactly, rejecting other, non-CM signals. Only a modest amount of samples are required. The algorithm is robust in the presence of noise, and is tested on measured data, collected from an experimental set-up. I. INTRODUCTION A. Blind signal separation An elementary problem in the area of spatial si...

The demand for wireless mobile... This paper is the first of a two-part study. It provides a comprehensive treatment, at a level appropriate to nonspecialists, of the use of an antenna array to enhance the efficiency of mobile communications systems. It presents an overview of mobile communications as well as details of how an array may be used in various mobile communications systems, including land-mobile, indoor-radio, and satellite-based systems. It discusses advantages of an array of antennas in a mobile communications system, highlights improvements that are possible by using multiple antennas compared to a single antenna in a system, and provides details on the feasibility of antenna arrays for mobile communications applications.

A general tool for multichannel and multipath problems is given in FIR matrix algebra. With Finite Impulse Response (FIR) filters (or polynomials) assuming the role played by complex scalars in traditional matrix algebra, we adapt standard eigenvalue routines, factorizations, decompositions, and matrix algorithms for use in multichannel /multipath problems. Using abstract algebra/group theoretic concepts, information theoretic principles, and the Bussgang property, methods of single channel filtering and source separation of multipath mixtures are merged into a general FIR matrix framework. Techniques developed for equalization may be applied to source separation and vice versa. Potential applications of these results lie in neural networks with feed-forward memory connections, wideband array processing, and in problems with a multi-input, multi-output network having channels between each source and sensor, such as source separation. Particular applications of FIR polynomial matrix alg...

We propose a novel approach for separating and estimating multiple co-channel digital signals using an antenna array. The spatial response of the array is unknown. We exploit the temporal structure of the digital signals to simultaneously determine the array response and the bit sequence for each signal. Uniqueness of the estimates is established for signals with BPSK modulation format. This new approach is applicable to an unknown array geometry and propagation environment, which is particularly useful in digital mobile communications. Simulation results demonstrate its promising performance.

We propose a maximum-likelihood approach for separating and estimating multiple synchronous digital signals arriving at an antenna array. The spatial response of the array is assumed to be known imprecisely or unknown. We exploit the finite alphabet (FA) property of digital signals to simultaneously determine the array response and the symbol sequence for each signal. Uniqueness of the estimates is established for signals with linear modulation formats. We introduce a signal detection technique based on the FA property which is different from a standard linear combiner. Computationally efficient algorithms for both block and recursive estimation of the signals are presented. This new approach is applicable to an unknown array geometry and propagation environment, which is particularly useful in wireless communication systems. Simulation results demonstrate its promising performance. Email: talwar@sccm.stanford.edu, Ph: (415) 723-0061, Fax: (415) 723-2411. This work was suppor...

This paper links the direct-sequence code-division multiple access (DS-CDMA) multiuser separation-equalization-detection problem to the parallel factor (PARAFAC) model, which is an analysis tool rooted in psychometrics and chemometrics. Exploiting this link, it derives a deterministic blind PARAFAC DS-CDMA receiver with performance close to nonblind minimum mean-squared error (MMSE). The proposed PARAFAC receiver capitalizes on code, spatial, and temporal diversity-combining, thereby supporting small sample sizes, more users than sensors, and/or less spreading than users. Interestingly, PARAFAC does not require knowledge of spreading codes, the specifics of multipath (interchip interference), DOA-calibration information, finite alphabet/constant modulus, or statistical independence/whiteness to recover the information-bearing signals. Instead, PARAFAC relies on a fundamental result regarding the uniqueness of low-rank three-way array decomposition due to Kruskal (and generalized herein to the complex-valued case) that guarantees identifiability of all relevant signals and propagation parameters. These and other issues are also demonstrated in pertinent simulation experiments.

Deterministic blind beamforming algorithms try to separate superpositions of source signals impinging on a phased antenna array by using 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, and generic algorithms that exploit them.

By equipping the base stations of a wireless network with antenna arrays, it is possible to more fully exploit the spatial dimension in a wireless communication system. Multiple antennas can provide a processing gain to increase the base station range and improve coverage. Also, by exploiting the spatial selectivity of an antenna array, interference may be reduced which in turn can be traded for increased capacity of the system. A wide range of wireless communication systems may benefit from spatial processing including high mobility cellular systems, low mobility short range systems, wireless local loop applications, satellite communications and wireless LAN. By employing an array of antennas, it is possible to multiplex channels in the spatial dimension just as in the frequency and time dimensions. This is often referred to as Spatial Division Multiple Access (SDMA). To increase system capacity, spatially selective reception as well as spatially selective transmission must be achieve...