FIR Equalizer Research Articles

Blind equalization in antenna array CDMA systems

Multipath induced interchip-interference (ICI) alters waveforms of transmitted signals and presents a major obstacle to direct-sequence (DS) code-division-multiple-access (CDMA) communications. For systems with aperiodic pseudorandom (PN) spreading sequences, the primary way to counter fading is through employing RAKE receivers that enhance the signal-to-interference ratio (SIR) by combining multipath signals from the desired user. In this paper, we formulate a discrete-time model for antenna array CDMA systems and study the 2-D RAKE receiver problem by casting it into an optimum vector FIR equalizer design and estimation framework. A novel aspect of the present work is the full exploitation of the potential of 2-D RAKE receivers without requiring any detailed knowledge of the multipath channels.

Analog complex graphic equalizer for EPR4 channels

A continuous-time analog adaptive equalizer for use in EPR4 channels in magnetic recording is presented. The equalizer is implemented as the summation of several bandpass filters covering different frequency bands as in a graphic equalizer. The outputs from each filter are weighted by a complex coefficient and summed, which results in a linear combiner structure guaranteed to minimize MSE under LMS adaptation. System-level simulations of our 'Complex Graphic Equalizer (CGE)' shows that its performance is comparable to that of a 10-tap FIR equalizer on an EPR4 channel.

Blind equalization of constant modulus signals using an adaptive observer approach

The paper addresses the problem of blind equalization of constant modulus signals which are degraded by frequency selective multipath propagation and additive white noise. An adaptive observer is used to update the weights of an FIR equalizer in order to restore the signal's constant modulus property. The observer gain is selected using fake algebraic Riccati methods in order to guarantee local stability. The performance of this method is compared to the constant modulus algorithm for simulated FM-FDM signals and exhibits significantly better convergence properties, particularly for heavy-tailed noise.

A low-power analog sampled-data VLSI architecture for equalization and FDTS/DF detection

The design philosophy behind a low-power integrated circuit architecture for implementing an FDTS/DF magnetic recording channel is presented. The goal of this philosophy is to achieve high clock speed, moderate power consumption, and relatively small die area. The principle components that are considered are a programmable FIR sampled-data analog equalizer and an analog sampled-data FDTS/DF detector. These blocks are implemented using sampled-data analog signal processing circuitry to avoid the need for a high-speed high-power analog-to-digital converter. Novel features of the FIR equalizer architecture include sampling of current rather than voltage, which allows extremely high sampling bandwidth; and, analog multiplication using MOS devices in their linear region which achieves a power dissipation on the order of 5 mW/tap at 100 MS/s. >

Adaptive continuous-time equalization followed by FDTS/DF sequence detection

Employing an adaptive continuous-time forward equalizer with a Fixed Delay Tree Search with Decision Feedback (FDTS/DF) detector provides several advantages to a magnetic recording system. Although an adaptive continuous-time filter of modest complexity cannot achieve the degree of pulse shape control provided by a long FIR filter, its power consumption may be dramatically lower. An FDTS/DP detector can be easily adapted to widely varying equalized pulses. By combining the two, we can achieve channel performance comparable to that of a system including an FDTS/DF detector and a long FIR equalizer-but with a power dissipation that is potentially much less than conventional sequence detection channels. Simulation results are presented that compare this new approach with a finite length FIR equalizer followed by an FDTS/DP detector. We present and compare several architectures for the adaptive continuous-time equalizer that offer improved convergence when using the least-mean-squares (LMS) adaptation algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Convex cost functions in blind equalization

Existing blind adaptive equalizers that use nonconvex cost functions and stochastic gradient descent suffer from lack of global convergence to an equalizer setup that removes sufficient ISI when an FIR equalizer is used. The authors impose convexity on the cost function and anchoring of the equalizer away from the all-zero setup. They establish that there exists a globally convergent blind equalization strategy for 1D pulse amplitude modulation (PAM) systems with bounded input data (discrete or continuous) even when the equalizer is truncated. The resulting cost function is a constrained l/sub 1/ norm of the joint impulse response of the channel and the equalizer. The results apply to arbitrary linear channels (provided there are no unit circle zeros) and apply regardless of the initial ISI (that is whether the eye is initially open or closed). They also show a globally convergent stochastic gradient scheme based on an implementable approximation of the l/sub 1/ cost function. >

On the nonvanishing stability of undesirable equilibria for FIR Godard blind equalizers

The existence of undesirable equilibria of Godard (1980) or constant modulus algorithms (CMA) is demonstrated for all finite-dimensional FIR equalizers. Sufficient stability conditions are presented for these equilibria. It is shown that for the Godard-2 algorithm, these undesirable equilibria are locally stable as long as the equalizer length remains finite. Results indicate that merely increasing the equalizer length does not necessarily nullify the potential for local convergence by Godard algorithms. >

An l/sub 1/-approximation based method for synthesizing FIR filters

A method is proposed for the synthesis of digital filters having approximately the desired linear phase frequency responses. A mathematical optimization problem is formulated from the synthesis objective, and a theorem from the theory of l/sub 2/-approximation is used to convert the optimization problem such that it can be solved by the linear programming technique. The method is successfully applied to the synthesis of a digital FIR equalizer for a given analog antialiasing filter.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reduced complexity decision feedback equalization for digital subscriber loops

Decision feedback equalizers (DFEs) are widely used in modern local network digital transmission systems to remove the intersymbol interference caused by slowly decaying pulse tails. A gradient descent algorithm for adapting a coefficient to model the slowly decaying portion of the tail is described. An equalization strategy is described that exploits prior knowledge of the nature of the subscriber loop channel, together with the new adaptation algorithm, to give reduced complexity DFE structures. The use of this algorithm in FIR and IIR equalizer structures is described. The use of this algorithm in FIR and IIR equalizers is quantitatively compared to a conventional DFE in terms of performance and implementation complexity. An analysis is presented describing the operation of the adaptation algorithm in the presence of noise. Simulation results illustrate the training of the algorithm and its stability in the presence of near-end crosstalk noise. >

A Modified Adaptive FIR Equalizer for Multipath Echo Cancellation in FM Transmission

Multipath propagation is a severe problem in conventional FM broadcasting since this phenomenon causes nonlinear distortions after demodulation. Several proposals for the correction of multipath corrupted FM signals were given in some recent papers, but up to now there exist no satisfactory solutions with sufficiently low hardware complexity for commercial application. The main idea of the present paper is to take advantage of some a priori knowledge of the multipath transfer function with the goal to develop a nonrecursive equalizer structure with minimum hardware expense. For adaptive adjustment of the equalizer, we use a recently introduced constant modulus algorithm (CMA) in a modified form. Instead of direct coefficient adjustment, we regard the parameters of the transmission channel as unknowns which are updated adaptively. The equalizer coefficients are uniquely defined by the channel parameters and can be determined in one step. The advantage of this method is a large improvement of the convergence behavior in comparison to existing solutions. The methods presented here are tested by means of an FM hardware system including FM transmitter, multipath simulation, FM demodulator, and an FIR multipath equalizer, which allows real-time investigations of the equalizer performance under well-defined multipath conditions.