Linear Transversal Filter Research Articles

Novel cat swarm optimization algorithm to enhance channel equalization

PurposeAdaptive equalization plays an important role in digital communication to reduce the distortions due to inter-symbol interference. An adaptive filter is used as an equalizer model in channel equalization. An adaptive algorithm is the heart of the adaptive filter which finds the optimum coefficients of the filter. The choice of the adaptive algorithm improves the convergence rate and minimizes the mean square error (MSE). This paper aims to propose a cat swarm optimization (CSO)-based adaptive algorithm and its modification to improve the performance of a channel equalizer.Design/methodology/approachThe input digital training data are transmitted through different channel conditions. A linear transversal filter is used as a channel and equalizer model. The equalizer coefficients are trained by the proposed simplified cat swarm optimization (SCSO) algorithm to find the estimated digital training data.FindingsThe performance of the proposed SCSO algorithm is compared with particle swarm optimization (PSO)-based channel equalization. The improvement in convergence rate and MSE is verified under linear and nonlinear channel conditions with different delay spreads. The optimum parameters of the SCSO are found using simulation-based sensitivity analysis.Originality/valueThis paper analyzes a CSO algorithm for adaptive channel equalization and proposes a SCSO algorithm to identify the optimum coefficients of a transversal equalizer. The seeking mode process is simplified in the proposed SCSO to achieve better performance in channel equalization. The proposed SCSO algorithm guarantees minimum MSE in all independent runs, whereas in PSO, few misses are possible.

Adaptive identification for hyperchaotic l system based on Weiner model

In order to be able to identify the hyper-chaotic l system with uncertain parameters effectively in real time, so that hyper-chaotic system control and synchronization tracking can be applied, this paper presents a system identification method for the hyper-chaotic system based on Wiener model. The linear part of the Wiener model consists of linear transversal filters, while the nonlinear part is represented approximately by piecewise linear filters. According to the minimum mean square error criterion, the filter parameter updated algorithm is derived, and the convergence condition is also obtained. Simulation results confirm the effectiveness of the adaptive filter for the identification of hyper-chaotic systems. The presented method not only overcomes the difficulty to identify a strongly nonlinear system only by adaptive linear filters, but also have a lower computational complexity compared with other non-linear adaptive filters.

A Linear Optimal Transversal Filter for Time-Varying Receiver Channels

Discrete linear optimal and unbiased transversal filters are proposed for onboard receiver channels to estimate continuous/discrete time-varying state-space signal models. The solutions are first found in the batch form. For optimal filtering, the mean square initial state function is determined a posteriori by the discrete algebraic Riccati equation. The unbiased filter is also represented in the iterative Kalman-like form with no requirements for noise and initial state. The filtering error bound is found in the three-sigma sense via the noise power gain (NPG). A fast iterative algorithm for NPG is also supplied. A comparison with the Kalman channel is given employing the harmonic two-state space model.

Adaptive filtering with the self-organizing map: A performance comparison

In this paper we provide an in-depth evaluation of the SOM as a feasible tool for nonlinear adaptive filtering. A comprehensive survey of existing SOM-based and related architectures for learning input–output mappings is carried out and the application of these architectures to nonlinear adaptive filtering is formulated. Then, we introduce two simple procedures for building RBF-based nonlinear filters using the Vector-Quantized Temporal Associative Memory (VQTAM), a recently proposed method for learning dynamical input–output mappings using the SOM. The aforementioned SOM-based adaptive filters are compared with standard FIR/LMS and FIR/LMS–Newton linear transversal filters, as well as with powerful MLP-based filters in nonlinear channel equalization and inverse modeling tasks. The obtained results in both tasks indicate that SOM-based filters can consistently outperform powerful MLP-based ones.

Feedforward neural network for blind equalization with PSK signals

Most of the cost functions used for blind equalization are nonconvex and nonlinear functions of tap weights, when implemented using linear transversal filter structures. Therefore, a blind equalization scheme with a nonlinear structure that can form nonconvex decision regions is desirable. The efficacy of complex-valued feedforward neural networks for blind equalization of linear and nonlinear communication channels has been confirmed by many studies. In this paper we present a complex valued neural network for blind equalization with M-ary phase shift keying (PSK) signals. The complex nonlinear activation functions used in the neural network are especially defined for handling the M-ary PSK signals. The training algorithm based on constant modulus algorithm (CMA) cost function is derived. The improved performance of the proposed neural network in both, stationary and nonstationary environments, is confirmed through computer simulations.

Complex Valued Recurrent Neural Networks for Blind Equalization

The nonlinear structure of a neural network-based blind equalizer yields a significant improvement in performance in comparison to equalizers with linear transversal filter structures. However, to reduce the burden of the feedforward neural equalizers, recurrent neural networks (RNN) are preferred for equalization. In this work two different complex valued recurrent neural structures — a fully connected RNN and a decision feedback equalizer (DFE) like multilayer perceptron (MLP)—based recurrent structure — are used for blind equalization. Their learning rules are derived using constant modulus algorithm (CMA). The activation functions used in the nodes of the networks are complex valued and suitable for quadrature amplitude modulation (QAM) signals. The performance of the MLP-based recurrent equalizer is found to be better than the fully connected RNN blind equalizer on the basis of mean square error (MSE) and symbol error rate (SER).

Achievable-SIR-based predictive closed-loop power control in a CDMA mobile system

A power control algorithm with two prediction models based on an achievable signal-to-interference power ratio (SIR) has been proposed under a multipath Rayleigh fading environment in a code-division multiple-access (CDMA) mobile system. An achievable SIR is defined as the maximum-minimum SIR among all users at a particular time step. The corresponding mobile transmission powers are denoted as the "optimum transmission powers." In the individual power predictor (IPP) model, a linear transversal filter is assigned to each user. The output of the IPP, which is a linear combination of the optimum transmission powers of the mobile during the current and previous power measurement periods, predicts the optimum transmission power of the mobile in the next time step. In the global power predictor (GPP) model, a single predictor, constructed by a linear neural network, is used to predict the optimum transmission powers of all mobiles in the next time step. In both predictor models, the weights of the predictors are updated by using the recursive least squares algorithm. To further improve the performance, a reduced power-measurement period has been studied. Simulation results show that the proposed power control algorithm can achieve a lower outage probability and a smaller dynamic range of transmission power compared with a conventional power control scheme.

Testing for the convergence of a linear decision directed equaliser

Adaptation algorithms for blind equalisation of communication channels suffer from the presence of local equilibria that may cause convergence to incorrect equaliser parameter settings. In this paper we consider an infinite impulse response (IIR) channel which is to be equalised by a linear transversal filter and a slicer connected in tandem, and use the correlation statistics of the sequence at the slicer output to determine if convergence to a desirable equilibrium has occurred. In particular, we show that if the input sequence to an IIR channel is binary, assuming values ±1, and its autocorrelation sequence is known a priori, the slicer output has the same autocorrelation sequence if, and only if, the slicer output is a possibly delayed and/or sign-inverted replica of the channel input. A Neyman-Pearson test is constructed, based on this result, to make a decision as to whether or not the equaliser has converged to an open-eye parameter setting. A method for estimating a lower bound on the equalisation delay that draws upon a classical correlation based impulse response estimation technique is discussed. Finally, simulation examples are presented to verify the theoretical results and to illustrate their application.

Cellular neural network for fast adaptive equalization

AbstractThe use of an analogue neural network in the adaptive equalization of time‐varying communication channels is proposed. the network is used to compute the coefficients of a linear transversal filter. the settling time decreases as the filter order increases and as the signal‐to‐noise ratio decreases. Owing to the real‐time processing capabilities, the network can be useful when it is of interest to track fast variations, as in radio links. the special properties of the tap input correlation matrix result in a cellular network architecture which greatly simplifies the VLSI implementation. Simulation results are presented which point out very satisfactory performance.

Analysis of the convergence behavior of adaptive distributed-arithmetic echo cancellers

Adaptive distributed-arithmetic echo cancellers are well suited for full-duplex high-speed data transmission. They allow a simpler implementation than adaptive linear transversal filters, since multiplications are replaced by table look-up and shift-and-add operations. Various tradeoffs between the number of operations and the number of memory locations of the look-up tables can be achieved by segmenting the echo canceller delay line into sections of shorter length. Adaptivity is achieved by a decision-directed stochastic gradient algorithm to adjust the contents of the look-up tables. The author adopts the mean-square error criterion to investigate the convergence behavior of adaptive distributed-arithmetic echo cancellers. Under the assumption that the look-up values are statistically independent of the symbols stored in the echo canceller delay line, he obtains an analytical expression for the mean-square error as a function of time. The maximum speed of convergence and the corresponding optimum adaptation gain are also determined. Simulation results for a full-duplex quaternary partial response class-IV system are presented and compared with theoretical results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear techniques for interference suppression in spread-spectrum systems

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. >

The optimal linear receiving filter for digital transmission over nonlinear channels

The filter minimizes the mean-square error between the sampled input to the decision device and the corresponding transmitted symbols. It is shown that the structure of this optimal receiving filter corresponds to a bank of matched filters, each followed by a linear transversal filter. Applications of this theory cover nonlinear channels with memory, linearly or nonlinearly modulated signals, and disturbances other than Gaussian noise (e.g. interference from other data sources). >

Advanced Time- and Frequency-Domain Adaptive Equalization in Multilevel QAM Digital Radio Systems

Digital radio systems employing multilevel QAM are at least optionally equipped with adaptive time- and/or frequency-domain equalizers. Their purpose is to reduce the vulnerability of these systems to linear distortion caused by multipath propagation. Linear transversal filters are prominent candidates for the realization of time-domain equalizers, especially for high-capacity applications. They are well known for their good performance and their relatively easy implementation at a high data rate. On the other hand, decision feedback equalizers are known to be very capable of eliminating linear distortion, especially of the so-called minimum-phase type. But realization problems are likely to occur in a high-speed application. A solution is proposed which merges the relative advantages of both the linear transversal and the decision feedback approaches. The goal of a frequency-domain equalizer, which is the restoration of the shape of the power density spectrum of the received signal without any recovered carrier and timing signals, can also be achieved with the aid of a transversal filter. The performance obtained with the joint utilization of the novel timeand frequency-domain equalizers is described.

Coherent radar detection in log-normal clutter

The paper deals with the problem of radar detection of a target echo embedded in log-normal clutter and white Gaussian noise. Relevant features of this article, with respect to previous papers on the same subject, refer to the coherent model assumed for the clutter and the processing chain. In more detail, the in-phase and quadrature components of clutter have been modelled to give a log-normal amplitude distribution and a near uniform distribution of the phase. Any shape of the correlation among consecutive clutter samples is also allowed in the model. At the same time, the processing chain is also coherent, i.e. it operates on the two components of the signals. Two architectures have been considered for the processor. The first, used in current practice, is formed of a linear transversal filter (for the clutter attenuation and the target echo enhancement) cascaded with a quadratic envelope detector and a comparison with a suitable threshold. The second processor considered differs from the previous one in the filter for clutter cancellation. A nonlinear homomorphic filter has been conceived to obtain a better suppression of clutter. The detection performance of the two processing chains have been evaluated, by means of computer simulation, in a number of operational cases of intrest. The paper gives a first contribution to the problem of finding better models of disturbance and of deriving more efficient processing chains.

Adaptive adjustment of receiver for distorted digital signals

The paper presents the results of an initial feasibility study into a novel technique for the adaptive adjustment of the receiver in a digital data-transmission system, operating with additive noise and severe inter-symbol interference in the received signal. The technique is an iterative process and can be used for the adjustment of the linear feedforward transversal filter that is employed ahead of a near-maximum-likelihood detector, and at the same time for the estimation of the sampled impulse response of the channel and filter, to give the information on the received signal needed by the detector. The latter two operations are equivalent to the adjustment of the feedforward and feedback transversal filters, respectively, in the corresponding nonlinear (decision-feedback)equaliser. The equaliser is, of course, a degenerate form of a near-maximum-likelihood detector, being obtained when the latter is reduced to its simplest possible form. The adaptive system operates directly on the estimate of the sampled impulse response of the channel, that must be provided at the receiver, and it requires no other input signals. It employs a root-finding algorithm that determines some of the roots (zeros) of the z-transform of the sampled impulse response of the channel. It then uses a knowledge of these roots to determine the tap gains of the linear feedforward transversal filter and to form an estimate of the sampled impulse response of the channel and filter. The technique can exploit the high tolerance to signal distortion of a near-maximum-likelihood detector in order to reduce the amount of processing of the received signal that is carried out by the adaptive filter to a level appreciably below that required by a conventional nonlinear equaliser. Thus a more cost-effective design of the receiver can be obtained. The paper describes the method of operation of two versions of the adaptive system and presents the results of computer-simulation tests over four different channels, showing both the rate and accuracy of convergence of the iterative process in each case.

Speech Band Compression Using Partial Response Codes

Using suitable partial response signalling (PRS) codes, the speech band has been compressed to a ratio of 2: 1 and is used in (i) analogue pulse-communication (PAM) through band-restricted channel and in (ii) low-bit-rate transmission using adaptive-delta-modulation (ADM). The PRS decoder consists of a novel two-stage feed-forward-cum-feed- back linear transversal filter (LTF). The performances of both the systems have been found to be satisfactory.

Simple nonlinear equalisers for binary baseband signals

Some very recent work on equalisers has led to a simple development of a conventional nonlinear (decision-feedback) equaliser, that involves only changes to the equalisation process itself and can, under certain conditions, give a useful improvement in tolerance to additive white Gaussian noise. The technique is particularly effective when binary data symbols are transmitted, at a high signal/noise ratio, and there is severe amplitude distortion in the received data signal. The paper is concerned with a further development of the technique, suitable for applications where a binary data signal is transmitted at a high rate over a linear baseband channel and where the channel introduces severe amplitude distortion. The channel may be either minimum phase or linear phase, or else it may approximate to some compromise between these two. It is shown that, under the given conditions, the linear feedforward transversal filter that forms the first part of a conventional nonlinear equaliser can often be replaced by a simple two-tap feedforward transversal filter, with either an improvement in performance or, at least, no serious degradation in performance. The paper describes both the new equaliser and a further development of this for the case where the received data signal is sampled at twice the data symbol rate. Finally, results of computer-simulation tests are presented, comparing the tolerances to additive white Gaussian noise of the two new equalisers with those of more conventional detectors, for models of various channels. Three quite different applications have been considered, one of which involves the transmission of digital data at 140 Mbit/s over a length of coaxial cable.

Linear phase analog active filters with equiripple passband responses

The theory and design of analog active filters with an approximately linear phase characteristic and equiripple passband response is presented. The filters are similar to conventional linear phase transversal filters but do not have a periodic passband response. Hence prefiltering is not required.

Linear Signal Processing by Acoustic Surface-Wave Transversal Filters

The impulse response of acoustic surface-wave (ASW) filters is determined by the configuration of an array of planar transducers tapping the acoustic signal propagated in the piezoelectric substrate. The transducer configuration is derived here by applying the generaI procedure used for the synthesis of linear transversal filters, which consists in time sampling the required impulse response and arranging the spacing and weights of the taps according to the time intervals and amplitudes of the impulse-response samples. The design of the tapping structure that synthesizes the impulse response of ASW transversal filters is based on a nonuniform sampling procedure, previously developed by the authors, that meets the particular requirements of ASW device operation. The features of this design procedure are presented, and several geometries of tapping transducers corresponding to impulse responses of different characteristics are discussed. The application of the procedure to the design of typical ASW filters is illustrated by the results of experimental models.

Design technique for nonlinear equalisers

A theoretical analysis, using the properties of linear vector spaces, is applied to the design of a nonlinear equaliser. The design minimises the probability of error in the detection of a serial digital signal, subject to the accurate equalisation of the time-invariant channel, when the signal is received in the presence of additive white Gaussian noise with a high signal/noise ratio. The equaliser contains a conventional combination of linear feedforward and nonlinear feedback transversal filters. Certain commonly used assumptions are made concerning the transmitted signal and the channel, but it is not assumed that the channel can necessarily be equalised by a linear feedforward transversal filter of limited length. A simple example shows the advantage in tolerance to additive Gaussian noise, which is achieved by the nonlinear equaliser over the corresponding linear equaliser, in a particular case where accurate equalisation of the channel is achieved by the linear equaliser.