Training analysis of adaptive interference suppression fordirect-sequence code-division multiple-access systems

This paper studies the transient behavior of an adaptive near-far resistant receiver for direct-sequence (DS) code-division multiple-access (CDMA) known as the minimum mean-squared error (MMSE) receiver. This receiver structure is known to be near-far resistant and yet does not require the large amounts of side information that are typically required for other near-far resistant receivers. In fact, this receiver only requires code timing on the one desired signal. The MMSE receiver uses an adaptive filter which is operated in a manner similar to adaptive equalizers. Initially there is a training period where the filter locks onto the signal that is sending a known training sequence. After training, the system can then switch to a decision-directed mode and send actual data. This work examines the length of the training period needed as a function of the number of interfering users and the severity of the near-far problem. A standard least mean-square (LMS) algorithm is used to adapt the filter and so the trade-off between convergence and excess mean-squared error is studied. It is found that in almost all cases a step size near 1.0/(total input power) gives the best speed of convergence with a reasonable excess mean-squared error. Also, it is shown that the MMSE receiver can tolerate a 30-40 dB near-far problem without excessively long convergence time     

Suppression of Narrow-Band Interference in a PN Spread-Spectrum Receiver Using a CTD-Based Adaptive Filter

Analytical results have shown that adaptive filtering can be a powerful tool for the rejection of narrow-band interference in a spreadspectrum receiver. However, the complexity of adaptive filtering hardware has hindered the experimental verification of these results. This paper describes a new adaptive filter architecture for implementing the Widrow-Hoff LMS algorithm while using only two multipliers regardless of filter order. This hardware simplification is achieved through the use of a burst processing technique. A 16-tap version of this adaptive filter constructed using charge-transfer devices (CTD's) is used to suppress a single tone jammer in a direct sequence spread-spectrum receiver. Probability of error measurements demonstrating the effectiveness of the adaptive filter for suppressing the single tone jammer along with simulation results for the optimal Weiner-Hopf filter are presented and discussed.     

Stochastic analysis of the LMS algorithm with a saturationnonlinearity following the adaptive filter output

This paper presents a statistical analysis of the least mean square (LMS) algorithm with a zero-memory scaled error function nonlinearity following the adaptive filter output. This structure models saturation effects in active noise and active vibration control systems when the acoustic transducers are driven by large amplitude signals. The problem is first defined as a nonlinear signal estimation problem and the mean-square error (MSE) performance surface is studied. Analytical expressions are obtained for the optimum weight vector and the minimum achievable MSE as functions of the saturation. These results are useful for adaptive algorithm design and evaluation. The LMS algorithm behavior with saturation is analyzed for Gaussian inputs and slow adaptation. Deterministic nonlinear recursions are obtained for the time-varying mean weight and MSE behavior. Simplified results are derived for white inputs and small step sizes. Monte Carlo simulations display excellent agreement with the theoretical predictions, even for relatively large step sizes. The new analytical results accurately predict the effect of saturation on the LMS adaptive filter behavior     

DFT/LMS算法在DSSS中的应用及性能分析

本文分析了直接序列扩频(DSSS)系统中最小错误概率(MPE)意义下的最优滤波器,并依据矩阵求逆引理证明最小均方误差(MMSE)意义下的最优滤波——维纳滤波也是MPE意义下的最优滤波。在DSSS中应用自适应滤波,无须先验已知扩频码的码型和干扰的统计特性,就能一并完成解扩以及有效抑制干扰。离散傅立叶变换/最小均方(DFT/LMS)算法的收敛速度远快于LMS算法,而运算量、稳健性与LMS算法基本相同。基于DFT/LMS算法的自适应滤波大大简化DSSS系统接收机的设计,显著增强系统抗干扰能力,具有很强的实用性。     

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     

A HYBRID INTERFERENCE CANCELLATION SCHEME FOR BLIND MULTIUSER DETECTION IN MULTIPATH FADING CHANNELS

This paper introduces and analyzes a detection scheme for adaptive suppressionof Multiuser Access Interference (MAI) and MultiPath Distortion (MPD) for mobile station ofDS/CDMA system. The proposed detection scheme may amount to a RAKE receiver structure,wherein each branch is considered as a linear multiuser filter designed under a Linear ConstrainedMinimum Variance (LCMV) optimization strategy to suppress MAI, followed by a proper combin-     

A HYBRID INTERFERENCE CANCELLATION SCHEME FOR BLIND MULTIUSER DETECTION IN MULTIPATH FADING CHANNELS

This paper introduces and analyzes a detection scheme for adaptive suppression of Multiuser Access Interference(MAI) and Multipath Distortion(MPD) for mobile station of DS/CDMA system.The proposed detection scheme may amount to a RAKE receiver structure, wherein each branch is considered as a linear multiuser filter designed under a Linear Constrained Minimum Variance(LCMV) optimization strategy to suppress MAI, followed by a proper combin-ing rule to suppress MPD.The adaptive blind multiuser detecting and optimum combining of the proposed receiver are realized, based on the Least-Mean-Square(LMS) algorithm and an adap-tive vector tracking algorithm respectively.Finally,the feasibility of the above two algorithms is proved by the numerical results provided by computer simulation.     

Acquisition performance of an adaptive receiver for DS-CDMA

This paper presents a single-user code timing estimation algorithm for direct-sequence code-division multiple access that is based on processing the weight vector of an adaptive filter. The filter weight vector can be shown to adapt in the mean to a scaled time-shifted version of the spreading code of the desired user. Therefore, our algorithm requires very little side information in order to form its estimate. The acquisition performance of the algorithm is investigated when the filter is adapted using the least mean square (LMS) or the recursive least square (RLS) algorithm. The proposed algorithm is shown through experimental results to be resistant to the near-far problem when the RLS adaptation algorithm is used, but not when the LMS algorithm is used. However, the performance of this code-acquisition technique is still substantially better than the traditional correlator-based approach, even when the computationally simple LMS algorithm is used. As an extension to the basic timing estimator algorithm, we consider the effect of frequency synchronization error on the performance of the timing estimate. As expected, frequency-offset error degrades the performance of the timing estimate. However, a modified version of the adaptive filter is presented to combat this effect     

Steady-state analysis of the adaptive successive interferencecanceler for DS/CDMA signals

The adaptive successive interference canceler (ASIC) is a multistage receiver that sequentially detects and removes cochannel users from the received signal impinging on a single antenna element. Each stage of the ASIC consists of a conventional matched filter (MF) detector and an adaptive interference canceler (AIC) that employs the least-mean-square (LMS) algorithm to recursively estimate the received amplitude of the detected signal. In this paper, we investigate the performance of the ASIC using a Wiener model of convergence for the LMS algorithm, deriving expressions for the asymptotic mean and variance of the amplitude estimate and the steady-state bit error rate (BER). The analyses and computer simulations demonstrate that the performance of the ASIC exceeds that of the conventional SIC (CSIC), which utilizes the MF output as the received amplitude estimate     

A variable step size LMS algorithm

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     

Performance evaluation of LMS-based adaptive suppression schemes in asynchronous CDMA

The objective of this paper is to evaluate the bit-error-rate performance of various adaptive structures in combating multi-user interference in an asynchronous code division multiple access (CDMA) system. In particular, two adaptive schemes, known as the N-tap filter and D-tap cyclical shifted bank filter, are considered. The least mean square (LMS) and predictive LMS (PLMS) algorithms are employed for the adaptation of tap weights. An analytical expression is developed for the numerical evaluation of the bit error probability. In addition, the bit error rate performances of the adaptive schemes are compared with those of the matched filter receiver. Results attest to the pratical usefulness of the LMS-based adaptive suppression schemes in combating multi-user interference in an asynchronous CDMA system.     

Performance of coded DS‐CDMA system using reduced rank MMSE receiver in Rayleigh fading channels

This paper examines the performance of a reduced rank minimum mean square error (MMSE) receiver‐based direct sequence code division multiple access (DS‐CDMA) system. For such system, when a large processing gain is employed, substantial time is consumed in computing the filter tap weights. Many schemes for reducing the complexity of the MMSE have been proposed in recent years. In this paper, computational complexity reduction of the MMSE receiver is achieved by using the K‐mean classification algorithm. The performance of the uncoded and coded systems are investigated for the full rank MMSE receiver and reduced rank MMSE receiver and results are compared in terms of bit error rate at different loading levels in both AWGN and fading channels. A system with the matched filter (MF) receiver is also presented for the purpose of comparison and an analytical pair‐wise error bound for the coded system is derived. In the adaptive implementation of the receivers, results show that good performance is achieved for the reduced rank receiver when compared to the full rank receiver in both coded and uncoded systems, while in the optimum implementation of the tap weights, the reduced dimension receiver performance experiences degradation when compared to the full rank scheme. Over the band‐limited channels considered, results for the reduced rank receiver also reiterate the fact that higher code rates tend to yield lower BER than that of low rate codes. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance Analysis of Narrow-Band Interference Rejection Techniques in DS Spread-Spectrum Systems

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.     

Analysis of Convergence of a Frequency-Domain LMS Adaptive Filter Implemented as a Multi-Stage Adaptive Filter

We present an analysis of the convergence of the frequency-domain LMS adaptive filter when the DFT is computed using the LMS steepest descent algorithm. In this case, the frequency-domain adaptive filter is implemented with a cascade of two sections, each updated using the LMS algorithm. The structure requires less computations compared to using the FFT and is modular suitable for VLSI implementations. Since the structure contains two adaptive algorithms updating in parallel, an analysis of the overall system convergence needs to consider the effect of the two adaptive algorithms on each other, in addition to their individual convergence. Analysis was based on the expected mean-square coefficient error for each of the two LMS adaptive algorithms, with some simplifying approximations for the second algorithm, to describe the convergence behavior of the overall system. Simulations were used to verify the results.     

Leaky LMS algorithm: MSE analysis for Gaussian data

Despite the widespread usage of the leaky LMS algorithm, there has been no detailed study of its performance. This paper presents an analytical treatment of the mean-square error (MSE) performance for the leaky LMS adaptive algorithm for Gaussian input data. The common independence assumption regarding W(n) and X(n) is also used. Exact expressions that completely characterize the second moment of the coefficient vector and algorithm steady-state excess MSE are developed. Rigorous conditions for MSE convergence are also established. Analytical results are compared with simulation and are shown to agree well     

Virtex FPGA implementation of a pipelined adaptive LMS predictor for electronic support measures receivers

High-speed field-programmable gate array (FPGA) implementations of an adaptive least mean square (LMS) filter with application in an electronic support measures (ESM) digital receiver, are presented. They employ "fine-grained" pipelining, i.e., pipelining within the processor and result in an increased output latency when used in the LMS recursive system. Therefore, the major challenge is to maintain a low latency output whilst increasing the pipeline stage in the filter for higher speeds. Using the delayed LMS (DLMS) algorithm, fine-grained pipelined FPGA implementations using both the direct form (DF) and the transposed form (TF) are considered and compared. It is shown that the direct form LMS filter utilizes the FPGA resources more efficiently thereby allowing a 120 MHz sampling rate.     

LMS algorithms for tracking slow Markov chains with applications to hidden Markov estimation and adaptive multiuser detection

This paper analyzes the tracking properties of the least mean squares (LMS) algorithm when the underlying parameter evolves according to a finite-state Markov chain with infrequent jumps. First, using perturbed Liapunov function methods, mean-square error estimates are obtained for the tracking error. Then using recent results on two-time-scale Markov chains, mean ordinary differential equation and diffusion approximation results are obtained. It is shown that a sequence of the centered tracking errors converges to an ordinary differential equation. Moreover, a suitably scaled sequence of the tracking errors converges weakly to a diffusion process. It is also shown that iterate averaging of the tracking algorithm results in optimal asymptotic convergence rate in an appropriate sense. Two application examples, analysis of the performance of an adaptive multiuser detection algorithm in a direct-sequence code-division multiple-access (DS/CDMA) system, and tracking analysis of the state of a hidden Markov model (HMM) with infrequent jumps, are presented.     

Adaptive DFE Multiuser Receiver for CDMA Systems using Two-Step LMS-Type Algorithm: An Equalization Approach

This paper presents an adaptive decision feedback equalizer (DFE) based multiuser receiver for code division multiple access (CDMA) systems over smoothly time-varying multipath fading channels using the two-step LMS-type algorithm. The frequency-selective fading channel is modeled as a tapped-delay-line filter with smoothly time-varying Rayleigh-distributed tap coefficients. The receiver uses an adaptive minimum mean square error (MMSE) multiuser channel estimator based on the reduced Kalman least mean square (RK-LMS) algorithm to predict these tap coefficients (Kohli and Mehra, Wireless Personal Communication 46:507–521, 2008). We propose the design of adaptive MMSE feedforward and feedback filters by using the estimated channel response. Unlike the previously available Kalman filtering algorithm based approach (Chen and Chen, IEEE Transactions on Signal Processing 49:1523–1532, 2001), the incorporation of RK-LMS algorithm reduces the computational complexity of multiuser receiver. The computer simulation results are presented to show the substantial improvement in its bit error rate performance over the conventional LMS algorithm based receiver. It can be inferred that the proposed multiuser receiver proves to be robust against the nonstationarity introduced due to channel variations, and it is also beneficial for the multiuser interference cancellation and data detection in CDMA systems.     

MIMO DFE equalization for multitone DS/SS systems over multipathchannels

The combination of multitone modulation with direct sequence spectrum spreading (DS/SS) has been introduced in the past. The performance of a correlation receiver has been evaluated for a multipath channel and in the presence of an additional multiple access interference. We analyze the problem of decision feedback equalization (DFE) for such a system. In order to understand the potential of the system with equalization, we first study the steady-state behavior of the equalizer for a minimum mean square error (MMSE) criterion. The investigation is carried out for a receiver made of a bank of filters matched to both the symbol shape and the channel, and for a two path channel. Assuming transmission of binary phase shift keying (BPSK) symbols, an exact expression of the bit error probability is obtained in the form of an integral. Then adaptive least mean square (LMS) and recursive least square (RLS) structures are derived. The performance of the adaptive RLS algorithm is demonstrated by means of computer simulations     

Convergence analysis of adaptive filtering algorithms with singulardata covariance matrix

The paper provides a rigorous analysis of the behavior of adaptive filtering algorithms when the covariance matrix of the filter input is singular. The analysis is done in the context of adaptive plant identification. The considered algorithms are LMS, RLS, sign (SA), and signed regressor (SRA) algorithms. Both the signal and weight behavior of the algorithms are considered. The signal behavior is evaluated in terms of the moments of the excess output error of the filter. The weight behavior is evaluated in terms of the moments of the filter weight misalignment vector. It is found that the RLS and SRA diverge when the input covariance matrix is singular. The steady-state signal behavior of the LMS and SA can be made arbitrarily fine by using sufficiently small step sizes of the algorithms. Indeed, the long-term average of the mean square excess error of the LMS is proportional to the algorithm step size. The long-term average of the mean absolute excess error of the SA is proportional to the square root of the algorithm step size. On the other hand, the steady-state weight behavior of both the LMS and SA have biases that depend on the weight initialization. The analytical results of the paper are supported by simulations