Robust adaptive array for wireless communications

In the application of a receiver antenna array to wireless communications, a known signal preamble is used for estimating the propagation vector at the beginning of each data frame. The estimated propagation vector is then used in linear combining of array inputs for interference suppression and demodulation of a desired user's information data stream. Since the training preamble is usually very short, conventional training methods, which estimate the propagation vector based solely on the training preamble, may incur large estimation errors. In many wireless channels, the ambient noise is known to be decidedly non-Gaussian, due to impulsive phenomena. The conventional training methods may suffer further from such impulsive noise. Moreover, performance of linear combining techniques can degrade substantially in the presence of impulsive noise. We first propose a new technique for propagation vector estimation which exploits the whole frame of the received signal. It is shown that as the length of the signal frame tends to infinity, in the absence of noise, this method can recover the propagation vector of the desired user exactly, given a small number of training symbols for that user. We then develop robust techniques for propagation vector estimation and array combining in the presence of impulsive noise. These techniques are nonlinear in nature and are based on the M-estimation method. It is seen that the proposed robust methods offer performance improvement over linear techniques in non-Gaussian noise, with little attendant increase in computational complexity. Finally, we address the extension of the proposed techniques to dispersive channels with intersymbol interference     

Robust adaptive beamforming for general-rank signal models

The performance of adaptive beamforming methods is known to degrade severely in the presence of even small mismatches between the actual and presumed array responses to the desired signal. Such mismatches may frequently occur in practical situations because of violation of underlying assumptions on the environment, sources, or sensor array. This is especially true when the desired signal components are present in the beamformer "training" data snapshots because in this case, the adaptive array performance is very sensitive to array and model imperfections. The similar phenomenon of performance degradation can occur even when the array response to the desired signal is known exactly, but the training sample size is small. We propose a new powerful approach to robust adaptive beamforming in the presence of unknown arbitrary-type mismatches of the desired signal array response. Our approach is developed for the most general case of an arbitrary dimension of the desired signal subspace and is applicable to both the rank-one (point source) and higher rank (scattered source/fluctuating wavefront) desired signal models. The proposed robust adaptive beamformers are based on explicit modeling of uncertainties in the desired signal array response and data covariance matrix as well as worst-case performance optimization. Simple closed-form solutions to the considered robust adaptive beamforming problems are derived. Our new beamformers have a computational complexity comparable with that of the traditional adaptive beamforming algorithms, while, at the same time, offer a significantly improved robustness and faster convergence rates.     

Noise cancellation with improved residuals

An effective adaptive scheme for noise cancellation when the signal to be recovered has known autocorrelation is presented. Two algorithms that exploit a special form of prior information are investigated. In this approach the desired signal is removed from the output feedback by linear prediction: the prior information used is the desired signal's autocorrelation. Knowing this, one can find a filter that whitens the desired signal. Screening the error feedback through this filter removes most of the desired signal energy, reducing its interference with the coefficient update. This is the basis for the first algorithm discussed, namely, the least-mean-square algorithm with augmented predictor (LMS-AP) proposed by Orgren et al. (1986). In many applications the whitening filter may not be strictly positive real (SPR). In such cases a different algorithm is needed; one which is assuredly convergent regardless of the satisfaction of the SPR condition. A modified LMS algorithm with augmented predictor (MLMS-AP) which provides such an alternative is proposed     

Competitive Randomized Nonlinear Prediction Under Additive Noise

We consider sequential nonlinear prediction of a bounded, real-valued and deterministic signal from its noise-corrupted past samples in a competitive algorithm framework. We introduce a randomized algorithm based on context-trees . The introduced algorithm asymptotically achieves the performance of the best piecewise affine model that can both select the best partition of the past observations space (from a doubly exponential number of possible partitions) and the affine model parameters based on the desired clean signal in hindsight. Although the performance measure including the loss function is defined with respect to the noise-free clean signal, the clean signal, its past samples or prediction errors are not available for training or constructing predictions. We demonstrate the performance of the introduced algorithm when applied to certain chaotic signals.      

Iterative and sequential algorithms for multisensor signalenhancement

In problems of enhancing a desired signal in the presence of noise, multiple sensor measurements will typically have components from both the signal and the noise sources. When the systems that couple the signal and the noise to the sensors are unknown, the problem becomes one of joint signal estimation and system identification. The authors specifically consider the two-sensor signal enhancement problem in which the desired signal is modeled as a Gaussian autoregressive (AR) process, the noise is modeled as a white Gaussian process, and the coupling systems are modeled as linear time-invariant finite impulse response (FIR) filters. The main approach consists of modeling the observed signals as outputs of a stochastic dynamic linear system, and the authors apply the estimate-maximize (EM) algorithm for jointly estimating the desired signal, the coupling systems, and the unknown signal and noise spectral parameters. The resulting algorithm can be viewed as the time-domain version of the frequency-domain approach of Feder et al. (1989), where instead of the noncausal frequency-domain Wiener filter, the Kalman smoother is used. This approach leads naturally to a sequential/adaptive algorithm by replacing the Kalman smoother with the Kalman filter, and in place of successive iterations on each data block, the algorithm proceeds sequentially through the data with exponential weighting applied to allow adaption to nonstationary changes in the structure of the data. A computationally efficient implementation of the algorithm is developed. An expression for the log-likelihood gradient based on the Kalman smoother/filter output is also developed and used to incorporate efficient gradient-based algorithms in the estimation process     

Subspace blind adaptive detection for multiuser CDMA

Direct adaptive realizations of the linear minimum mean-square error (MMSE) receiver for direct-sequence code-division multiple access possess the attractive feature of not requiring any explicit information of interference parameters such as timing, amplitudes, or spreading sequences; however, they need a training sequence for the desired user. Previously, a new blind adaptive receiver was proposed based on an anchored least mean-squared (LMS) algorithm that requires only the spreading code and symbol timing of the desired user but obviates the need for a training sequence. In this work, it is analytically demonstrated that the blind LMS algorithm always provides (nominally) faster convergence than the training driven LMS-MMSE receiver of but at the cost of increased tap-weight fluctuations or misadjustment. Second, the property that the optimal MMSE or minimum-output energy filter coefficients lies in the signal subspace is exploited to propose a new efficient blind adaptive receiver requiring fewer adaptive coefficients. Improved detector characteristics (superior convergence rates and steady-state signal-to-interference-plus-noise ratios) is indicated by analysis and supported by simulation     

An interference-tolerant algorithm for localization ofcyclostationary-signal sources

A method for detecting the number of cyclostationary signals radiated by remote sources and for estimating their directions of arrival by a linear and uniform array is presented. Whereas the traditional techniques exploit the spatial coherent properties, the new method locates the signal sources using the spectral coherence properties as well. This approach eliminates the need to know the characteristics of the noise and the interference, regardless of the extent of their spectral overlap. Moreover, the method applied equally well to environments containing more interferers than sensors. The conditions of applicability of the method are the existence and the knowledge of a cycle frequency at which all the signal sources exhibit spectral correlation but the noise and interference signals do not, and the existence and the knowledge of a value of the lag parameter such that the cyclic cross-correlation matrix of the desired signals has full rank     

Adaptive MMSE receiver with beamforming for DS/CDMA systems

The minimum mean-squared error (MMSE) receiver is a linear filter which can suppress multiple access interference (MAI) effectively in direct-sequence code-division multiple-access (CDMA) communications. An antenna array is also an efficient scheme for suppressing MAI and improving the system performance. In this letter, we consider an adaptive MMSE receiver in conjunction with beamforming in CDMA systems employing an antenna array. The proposed structure is featured as a low complexity receiver, which adapts the MMSE filter coefficients and the beamforming weights simultaneously. However, it does require the channel state information and the direction of arrival (DOA) of the desired user signal. As a result, we propose two adaptation methods to perform joint channel estimation and signal detection without any training sequence. It is demonstrated that the two proposed methods achieve similar bit-error-rate performance. More importantly, their performance degradation compared with the case with perfect channel information is small.     

Stability analyses of information-theoretic blind separationalgorithms in the case where the sources are nonlinear processes

A basic approach to blind source separation is to define an index representing the statistical dependency among the output signals of the separator and minimize it with respect to the separator's parameters. The most natural index might be mutual information among the output signals of the separator. In the case of a convolutive mixture, however, since the signals must be treated as a time series, it becomes very complicated to concretely express the mutual information as a function of the parameters. To cope with this difficulty, in most of the conventional methods, the source signals are assumed to be independent identically distributed (i.i.d.) or linear. Based on this assumption, some simpler indices are defined, and their minimization is made by such an iterative calculation as the gradient method. In actual applications, however, the sources are often not linear processes. This paper discusses what will happen when those algorithms postulating the linearity of the sources are applied to the case of nonlinear sources. An analysis of local stability derives a couple of conditions guaranteeing that the separator stably tends toward a desired one with iteration. The obtained results reveal that those methods, which are based on the minimization of some indices related to the mutual information, do not work well when the sources signals are far from linear     

Walsh coded training signal aided time domain channel estimation for MIMO-OFDM systems

This letter proposes a novel Walsh coded training signal design and decoding method to estimate the channel response in MIMO-OFDM systems. The Walsh coded training signals, designed to be orthogonal in the time domain, facilitate the separation of the desired training signal from the received mixed signal and the estimation of the channel response. The proposed channel estimation method is directly applicable to practical MIMO-OFDM systems with null subcarriers and exhibits nearly the same performance as Li?s original channel estimator [5] at a much reduced computational complexity.     

Robust H2 filtering for uncertain systems withmeasurable inputs

This paper deals with the robust minimum variance filtering problem for linear time-varying systems subject to a measurable input and to norm bounded parameter uncertainty in the state and/or the output matrices of the state-space model. The problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty and any input of bounded energy. Three types of input signals are considered: a signal that is a priori known for the whole time interval, an unknown signal of very large bandwidth that is perfectly measured on-line, and a large bandwidth signal that is measured ahead of time in a fixed preview time interval. Both the time-varying finite-horizon and stationary infinite-horizon cases are treated     

Robust filtering under randomly varying sensor delay with variance constraints

This paper deals with a new filtering problem for linear uncertain discrete-time stochastic systems with randomly varying sensor delay. The norm-bounded parameter uncertainties enter into the system matrix of the state space model. The system measurements are subject to randomly varying sensor delays, which often occur in information transmissions through networks. The problem addressed is the design of a linear filter such that, for all admissible parameter uncertainties and all probabilistic sensor delays, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error for each state is not more than the individual prescribed upper bound. We show that the filtering problem under consideration can effectively be solved if there are positive definite solutions to a couple of algebraic Riccati-like inequalities or linear matrix inequalities. We also characterize the set of desired robust filters in terms of some free parameters. An illustrative numerical example is used to demonstrate the usefulness and flexibility of the proposed design approach.     

High-resolution direction finding of non-stationary signals using matching pursuit

One of the main goals of time–frequency (TF) signal representations in non-stationary array processing is to equip multi-antenna receivers with the ability to separate sources in the TF domain prior to direction finding. This permits high-resolution direction-of-arrival (DOA) estimation of individual sources and of more sources than sensors. In this paper, we use linear decomposition of sensor data based on matching pursuit (MP). The leading atoms of the MP, which capture most of the source TF signatures, can be different for different sources and, as such, provide the desired source discrimination. The MP coefficients with high signal-to-noise ratio (SNR) and corresponding to the leading decomposition atoms are used to develop the MP-MUSIC DOA estimation for non-stationary source signals. We demonstrate the source discriminatory capability of the proposed technique using linear FM, nonlinear FM, and other non-stationary signals. Further, we compare MP-MUSIC performance with conventional MUSIC and the time–frequency MUSIC, which incorporates bilinear transforms.     

Blind adaptive noncoherent multiuser detection for nonlinear modulation

Noncoherent multiuser detection for nonlinear modulation was previously studied and the idea of phase-independent noncoherent decorrelation was introduced and three post-decorrelative detectors were obtained and analyzed. However, their implementation requires the knowledge of the signature waveforms of all the users, which may be available only for centralized implementation. In this paper, we obtain a blind adaptive noncoherent decorrelative detector for nonlinear modulation that is suitable for distributed implementation with the knowledge of only the normalized signals of the desired user and the additive noise variance. This detector is based on the stochastic approximation method and does not require the overhead of any kind of "training." Two adaptive algorithms are developed, one guided by every signal in the desired user's signal set individually, and the other by the user's entire signal space. While this paper focuses on the particular problem of blind adaptive noncoherent decorrelative detection, it addresses a more general adaptation issue, namely, that of improving the convergence properties of an adaptive scheme by effectively using all the information that is known, and adapting only to the part of the desired solution that is truly unknown. Convergence is shown in the mean squared error sense for both the fixed step-size and time-varying step-size versions of the two algorithms.     

Robust and efficient recovery of a signal passed through a filterand then contaminated by non-Gaussian noise

Consider a channel where a continuous periodic input signal is passed through a linear filter and then is contaminated by an additive noise. The problem is to recover this signal when we observe n repeated realizations of the output signal. Adaptive efficient procedures, that are asymptotically minimax over all possible procedures, are known for channels with Gaussian noise and no filter (the case of direct observation). Efficient procedures, based on the smoothness of a recovered signal, are known for the case of Gaussian noise. Robust rate-optimal procedures are known as well. However, there are no results on robust and efficient data-driven procedures; moreover, the known results for the case of direct observation indicate that even a small deviation from Gaussian noise may lead to a drastic change. We show that for the considered case of indirect data and a particular class of so-called supersmooth filters there exists a procedure of recovery of an input signal that possesses the desired properties; namely, it is: adaptive to the smoothness of the input signal; robust to the distribution of the noise; globally and pointwise-efficient, that is, its minimax global and pointwise risks converge with the best constant and rate over all possible estimators as n→∞; and universal in the sense that for a wide class of linear (not necessarily bounded) operators the efficient estimator is a plug-in one. Furthermore, we explain how to employ the obtained asymptotic results for the practically important case of small n (large noise)     

MMSE interference suppression for timing acquisition anddemodulation in direct-sequence CDMA systems

It has been shown that minimum-mean-squared-error (MMSE) demodulators are effective means of interference suppression in code division multiple-access (CDMA) systems. The MMSE demodulator can be implemented adaptively using an initial training sequence, followed by decision-directed adaptation. This requires that the symbol-level timing of the desired user be known prior to training. We remove this requirement by providing a method for timing acquisition in which the output of the acquisition process is a near-far-resistant demodulator which automatically accounts for the delays and amplitudes of both the desired signal and the interference without explicitly estimating these parameters. The only requirements are a training sequence for the desired user and a finite uncertainty regarding the symbol timing. The latter condition can be realized by using a periodic training sequence even if the absolute timing uncertainty is arbitrarily large     

Two-stage interference-resistant adaptive periodically time-varyingCMA blind equalization

We consider the problem of blindly equalizing a digital communication signal distorted by a linear time-invariant channel and contaminated by severe co-channel or adjacent-channel digital interference under the assumption that the latter exhibits a different symbol rate from the desired signal. The proposed equalizer is composed of two stages that are both periodically time-varying (PTV) in order to better match the periodical statistics of the received signal. The first stage employs linear PTV filtering to mitigate interference, thus allowing the second stage, based on the constant modulus algorithm (CMA), to reliably recover the transmitted information symbols. Computer simulations confirm the effectiveness of the new approach, and comparisons with existing blind methods show that a significant performance gain can be attained     

Antenna spacing considerations in an interference canceller

It is possible to remove an interfering signal from a receiver by injecting a sample of the interference in equal amplitude but opposite phase into the receive line. In the case of a remotely located source of interference, an auxiliary antenna is used to obtain the interfering-signal sample. When the angle of arrival of an interfering signal relative to the desired signal is small, or when other system requirements dictate omnidirectional antennas, the desired signal can either be enhanced or reduced in amplitude depending upon the spacing between the auxiliary and receive antennas. The author discusses the effect of antenna spacing on the desired signal and provides quantitative guidelines for such spacing. Placement of antennas relative to the direction of the signal sources is also considered. Experimental data are presented to verify the calculated results     

Blind space-time multiuser channel estimation in time-varying DS-CDMA systems

A multistep linear prediction (MSLP) approach is presented for blind channel estimation for short-code direct sequence code division multiple access signals in time-varying multipath channels using a receiver antenna array. The time-varying channel is assumed to be described by a complex exponential basis expansion model. First, a recently proposed MSLP approach to blind channel estimation for time-varying single-input multiple-output (SIMO) systems is extended to time-varying multiple-input multiple-output (MIMO) systems to define a "signal" subspace. Second, the knowledge of the spreading code of a desired user is exploited in conjunction with the signal subspace to estimate the time-varying channel of the desired user up to an unknown time-invariant scale factor. Equalization/detection for the desired user can be then carried out if the information sequence is differentially encoded/decoded. Sufficient conditions for channel identifiability are investigated. Three illustrative simulation examples are provided.     

A unified approach to the design of linear constraints in minimumvariance adaptive beamformers

A simple, systematic procedure for designing linear constraints in minimum-variance beamformers which allows an arbitrary specification of the quiescent response (the beamformer response when only white noise is present) is described. In this approach, the first constraint is dedicated to the imposition of a desired quiescent response, and additional constraints are included to assure proper reception of the desired signal. These additional constraints make the overall beamformer response equal to the quiescent response in the desired signal region so that the signal is not cancelled when it is present. Optionally, the response can be fixed in other regions of interest by adding more constraints. This design procedure demonstrates that the key to designing efficient constraints is finding the weighting coefficients which specify the desired quiescent response, a problem identical to the synthesis of desired beam patterns for nonadaptive arrays. The effectiveness of the procedure is illustrated by examples in both narrowband and broadband arrays