# An improved LMS adaptive algorithm for narrowband interference suppression in direct sequence spread spectrum

01 Jul 1995-IEEE Transactions on Aerospace and Electronic Systems (IEEE)-Vol. 31, Iss: 3, pp 1198-1201

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TL;DR: The present bibliography represents a comprehensive list of references on nonlinear system identification and its applications in signal processing, communications, and biomedical engineering.

Abstract: The present bibliography represents a comprehensive list of references on nonlinear system identification and its applications in signal processing, communications, and biomedical engineering. An attempt has been made to make this bibliography complete by listing most of the existing references up to the year 2000 and by providing a detailed classification group.

235 citations

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TL;DR: A progression of techniques is described, in which successively more information about the spread-spectrum signal and interference is used to make improvements on the interference suppression capability via more advanced signal processing methods.

Abstract: Communication networks involving the overlay of spread-spectrum systems an narrower band services are of increasing interest as a means of producing greater efficiencies and flexibility in the use of the radio spectrum. Although spread-spectrum systems enjoy a natural immunity to interference from narrowband sources, their performance in the presence of such interference can be significantly enhanced by active suppression techniques. The study of this problem has elicited a very rich body of methodology, which has progressed over nearly 25 years from some of the simplest signal processing paradigms to some of the most advanced. This paper provides an overview of a number of these techniques, most of which have been developed over the past decade. In particular, a progression of techniques is described, in which successively more information about the spread-spectrum signal and interference is used to make improvements on the interference suppression capability via more advanced signal processing methods. These include linear predictive methods that make use of the spectral properties of the spread-spectrum and narrowband signals, nonlinear predictive methods that make use of the spectra and first-order probability distribution of these signals, linear code-aided methods that make use of the spreading codes of the signals of interest and the second-order statistics of the narrowband interference, and finally, a maximum-likelihood code-aided technique that makes use of essentially all that is known about the useful signals and interference. Performance comparisons show that moving up this progression of improved modeling is rewarded with performance gains that can be quite significant.

73 citations

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TL;DR: A tutorial overview of the progress made in this area over the past 15 years is provided, focusing on direct-sequence CDMA (DS/CDMA) systems and on the so-called "code-aided" techniques for NBI suppression, a term coined to indicate those strategies in which knowledge of the spreading code of a SS signal of interest is explicitly exploited in suppressing NBI.

Abstract: The push toward more efficient and flexible use of the radio spectrum has led to the consideration of the overlay of spread-spectrum (SS) communication networks on preexisting narrow-band networks. Such systems are already in widespread and rapidly expanding use in the lightly regulated spectrum where personal networking is largely centered and they are of increasing interest in the more tightly regulated spectrum due to a dearth of spectrum for new services, the desire to incorporate multi-rate (e.g., multimedia) traffic in the same network and the survival of legacy systems. Even though SS signals are inherently robust to the effects of narrower bandwidth cochannel signals, it has been shown that the use of additional processing aimed at interference suppression can result in substantial performance improvement. Motivated by this consideration, the past quarter century has seen the development of a very large body of techniques for improving the performance of SS communications systems in the presence of narrow-band interference (NBI). Early techniques (up to late 1980s) have been reviewed in the survey by Milstein (1988). Since that time, more sophisticated strategies have been developed, making use of advances from the fields of beamforming, multiuser detection (MUD), and adaptive filtering. Also, the focus of interest has shifted from techniques aimed primarily at the suppression of NBI from single-user SS systems to systems in which the SS signaling is being used to implement a code-division multiple-access (CDMA) protocol. This paper provides a tutorial overview of the progress made in this area over the past 15 years. The focus of the paper is on direct-sequence CDMA (DS/CDMA) systems and on the so-called "code-aided" techniques for NBI suppression, a term coined to indicate those strategies in which knowledge of the spreading code of a SS signal of interest is explicitly exploited in suppressing NBI. Particular attention is devoted to the case in which the CDMA signals are subject to frequency-selective fading and to the issue of blind adaptive MUD in the presence of external NBI. In particular with regard to the former issue, the effects and implications of channel-state information on system design and performance are discussed. With regard to the latter issue, it is observed that the external NBI may introduce the need for a periodically time-varying detection rule, which has significant implications in the design of blind adaptive MUD algorithms for overlaid DS/CDMA systems. The performance of the techniques discussed is compared through analysis and simulation, as well as through considerations of their relative computational complexity and required prior information. Finally, the paper is concluded by a discussion of several challenging open problems in this area.

64 citations

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TL;DR: An adaptive nonlinear predictor that consists of an (N+1)-level quantizer, four adders, and two adaptive linear filters that achieves almost the same performance even at very low signal-to-noise ratio but involves much less complexity.

Abstract: This paper presents a new nonlinear approach for narrowband interference (NBI) suppression in code-division multiple-access (CDMA) systems. The proposed scheme is an adaptive nonlinear predictor that consists of an (N+1)-level quantizer, four adders, and two adaptive linear filters, where N is the number of users in the CDMA system. Both adaptive filters have the same coefficients at each iteration: one for feedforward estimation of NBI and the other for feedback compensation for the estimated result. It could be regarded as an improved version of the nonlinear predictor with offset outputs presented recently by Wang et al. (1996). Computer simulation results support that the improved offset predictor performs much better than the original one under the same complexity. As compared with the nearly optimal approximate conditional mean filter, it achieves almost the same performance even at very low signal-to-noise ratio but involves much less complexity.

25 citations

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TL;DR: The proposed adaptive techniques for narrowband interference (NBI) suppression in DS-CDMA system are blind and provide faster convergence speed than the pure code-aided approach (without using a predictor and subtractor), but also give better BER performance.

Abstract: When overlaying spread spectrum (SS) transmission over a narrowband system, the performance of the spread spectrum system will be significantly degraded due to the interference from the narrowband signal. This paper proposes two computationally attractive and efficient adaptive techniques for narrowband interference (NBI) suppression in DS-CDMA system: adaptive linear predictor algorithm and adaptive NBI re-estimation algorithm. Unlike existing techniques in literature which use either estimator/subtracter approach or code-aided approach, the proposed methods combine these two approaches together and show that a much better performance can be achieved. In addition, the proposed algorithms are blind and do not require any training symbols and interference characteristics. The proposed methods not only provide faster convergence speed than the pure code-aided approach (without using a predictor and subtractor), but also give better BER performance

24 citations

##### References

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TL;DR: A least-mean-square adaptive filter with a variable step size, allowing the adaptive filter to track changes in the system as well as produce a small steady state error, is introduced.

Abstract: A least-mean-square (LMS) adaptive filter with a variable step size is introduced. The step size increases or decreases as the mean-square error increases or decreases, allowing the adaptive filter to track changes in the system as well as produce a small steady state error. The convergence and steady-state behavior of the algorithm are analyzed. The results reduce to well-known results when specialized to the constant-step-size case. Simulation results are presented to support the analysis and to compare the performance of the algorithm with the usual LMS algorithm and another variable-step-size algorithm. They show that its performance compares favorably with these existing algorithms. >

907 citations

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TL;DR: In this article, two approaches to the non-Gaussian filtering problem are presented, which retain the computationally attractive recursive structure of the Kalman filter and approximate well the exact minimum variance filter in cases where either the state noise is Gaussian or its variance small in comparison to the observation noise variance, or the system is one step observable.

Abstract: Two approaches to the non-Gaussian filtering problem are presented. The proposed filters retain the computationally attractive recursive structure of the Kalman filter and they approximate well the exact minimum variance filter in cases where either 1) the state noise is Gaussian or its variance small in comparison to the observation noise variance, or 2) the observation noise is Gaussian and the system is one step observable. In both cases, the state estimate is formed as a linear prediction corrected by a nonlinear function of past and present observations. Some simulation results are presented.

360 citations

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TL;DR: Simulations indicate that the nonlinear filter with LMS updates performs substantially better than the linear filter for both narrowband Gaussian and single-tone interferers, whereas the gradient algorithm gives slightly better performance for Gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer.

Abstract: The binary nature of direct-sequence signals is exploited to obtain nonlinear filters that outperform the linear filters hitherto used for this purpose. The case of a Gaussian interferer with known autoregressive parameters is considered. Using simulations, it is shown that an approximate conditional mean (ACM) filter of the Masreliez type performs significantly better than the optimum linear (Kalman-Bucy) filter. For the case of interferers with unknown parameters, the nature of the nonlinearity in the ACM filter is used to obtain an adaptive filtering algorithm that is identical to the linear transversal filter except that the previous prediction errors are transformed nonlinearly before being incorporated into the linear prediction. Two versions of this filter are considered: one in which the filter coefficients are updated using the Widrow LMS algorithm, and another in which the coefficients are updated using an approximate gradient algorithm. Simulations indicate that the nonlinear filter with LMS updates performs substantially better than the linear filter for both narrowband Gaussian and single-tone interferers, whereas the gradient algorithm gives slightly better performance for Gaussian interferers but is rather ineffective in suppressing a sinusoidal interferer. >

188 citations

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TL;DR: It is shown that the most common LLSE filter design can lead to performance inferior to that of various other filter designs, but results are also presented demonstrating that an LLSEfilter design motivated by the structure of the maximum-likelihood receiver leads to consistently superior performance.

Abstract: Linear least squares estimation (LLSE) techniques can provide an effective means of suppressing narrow-band interference in direct sequence (DS) spread-spectrum systems. In the results presented here, analytical expressions for bit error rate are derived for two DS spread-spectrum systems under the conditions of either tone or narrowband Gaussian interference. It is shown that the most common LLSE filter design can lead to performance inferior to that of various other filter designs. However, results are also presented demonstrating that an LLSE filter design motivated by the structure of the maximum-likelihood receiver leads to consistently superior performance. The performance of a system using this new design criterion is compared with that of an approximation to the maximum-likelihood (ML) receiver for the tone interference model and with that of the exact ML receiver for the Gaussian interference. Finally, it is shown that the bit error rate estimate obtained from application of a Gaussian approximation for the test statistic is overly pessimistic for the systems studied here.

127 citations

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TL;DR: The performance of PN spread-spectrum communication systems in the presence of narrow-band interference is studied when linear interpolation filters are employed for the estimation and subsequent suppression of the interference.

Abstract: The performance of PN spread-spectrum communication systems in the presence of narrow-band interference is studied when linear interpolation filters are employed for the estimation and subsequent suppression of the interference. Closed-form analytical expressions for the system's performance are established for a broad class of interference processes. The advantages of linear interpolation filters over predictive filters with identical number of taps are examined analytically and some unexpected results are obtained. The analytical results are illustrated by examples.

96 citations

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