APPLICATIONS OF ADAPTIVE INFINITE IMPULSE RESPONSE FILTERS TO ECHO CANCELLATION AND EQUALIZATION

Abstract

In recent years there has been an increase in the demand for high speed data transmission over the telephone network. The increased processing power and decreasing cost of the VLSI has led to the development of new digital subscriber line (DSL) technologies for the application in the metallic copper loop plant. Over the last decade, the achievable data rates have increased from basic rate access @ 160 Kbps for ISDN to 1.544 Mbps for HDSL and upto 9 Mbps for ADSL. At present very-high-bit rate DSL (VHDSL) supporting data rates upto 155.52 Mbps is being proposed for short-range ATM-LAN applications. Adaptive signal processing techniques are being extensively used in these technologies to achieve the data transmission rates. In a typical HDSL environment, the received data is usually corrupted by the echo signal, the inter-symbol interference (ISI) and the near-end crosstalk (NEXT). Thus a transceiver used in the HDSL system consists of an echo canceller to suppress the echo and an equalizer to mitigate the effect of the ISI. Echo cancellation is used to achieve full duplex data transmission over the twisted pair subscriber loops. Due to the severe amplitude distortion of subscriber loops and the fact that the ISI is mostly trailing type, a decision feedback equalizer (DFE) is a natural part of the HDSL transceiver design. Adaptive filtering techniques are being used for the above applications because of the wide variations in the loop characteristics encountered in the HDSL environment. The adaptive echo cancellers and the adaptive DFEs reported in the literature, have been mostly implemented using the adaptive FIR techniques. However a study of the impulse responses of the typical echo path and the channel impulse responses shows that, it mainly consists of a slowly decaying tail portion spanning a few hundred bauds at the HDSL rate. A conventional adaptive FIR implementation ofthe echo canceller and the DFE will require a few hundred taps each at the above rate. This amounts to a large computational complexity for the echo canceller and the DFE, making their implementation difficult in practice. Alternative methods which will result in lower computational complexity and better asymptotic accuracy are thus required to be investigated. Another potential impairment in the HDSL systems is the presence of the crosstalk i.e. NEXT. There has been a little study towards the cancellation/suppression of the NEXTin the HDSL systems. This work encompasses the application of the adaptive IIR filtering techniques to the echo cancellation and decision feedback equalization of the HDSL channels and investigates the convergence performance of various algorithms and structures. We also compare the performance of the adaptive IIR echo cancellers and the adaptive IIR DFE with their FIR counterparts. Using the adaptive IIR techniques, a generalized IIR DFE (GDFE) structure suitable for the combined NEXT cancellation and equalization of HDSL channels, also has been presented. We consider first, the performance of adaptive FIR echo cancellers using the stabilized fast transversal filter (SFTF) algorithm and the recursive least squares (RLS) lattice-ladder algorithm using simulation techniques. It is found that the SFTF and the RLS-lattice-ladder algorithms behave in a stable manner and achieve the target echo return loss enhancement (ERLE) of 60 dB. The convergence performance of both the algorithms is found to be comparable. However the FIR echo canceller employing the SFTF algorithm requires almost half the computational complexity compared to the RLS-lattice-ladder algorithm. The large computational saving and better asymptotic accuracy that can be achieved by the adaptive IIR filters, has prompted us to investigate its performance and consider its application to the problems ofecho cancellation and equalization at the HDSL rate. We first review the adaptive IIR techniques and present the equation error generalized FTF (PZ-GFTF) algorithm for the adaptive echo cancellation. We also present the SM-PZ-GFTF algorithm based onthe Steiglitz-McBride identification technique. We investigate the effect of the bias in the equation error formulation and propose its removal using the bias removal technique. We then present the RLS and the GFTF formulations of the bias removal technique for the adaptive IIR filtering. Using computer simulation techniques, the convergence performance of the adaptive IIR echo cancellers using these algorithms has been presented. It has been found that the adaptive IIR echo cancellers employing bias-removal technique offer a better ERLE performance compared to the equation error and the SM-identification based formulations in the presence of the NEXT interference. A computational saving of almost 90% has been realized by the adaptive IIR echo cancellers compared to the adaptive FIR echo cancellers for the echo cancellation application at the HDSL rate. We have next considered the application of the adaptive FIR and the adaptive IIR algorithms for the decision feedback equalization at the HDSL rate. We first present the conventional FIR-DFE and then present the LMS and GFTF algorithms for its adaptive implementation. Considering the nature of the ISI, its span and pole-zero representation of the channel impulse response and to reduce the computational complexity of the equalizer, we propose a DFE that has a pole-zero filter in the feedback path. The adaptive implementation of the proposed pole-zero DFE has been realized using the SM-RLS algorithm, a new version of the multichannel SM-PZ-GFTF algorithm and the SM-lattice-LMS algorithm based on the SM-identification technique. The convergence characteristics ofthe adaptive FIR-DFE and the pole-zero DFE has been studied using the above mentioned respective adaptive algorithms through computer simulation techniques. Even though a slower convergence of the adaptive pole-zero DFE compared to the adaptive FIR-DFE has been observed, it may not be a serious limitation considering the high transmission rate of the HDSL A comparison of the

computational complexity of the adaptive pole-zero DFE with the adaptive FIR-DFE shows that a large saving of the order of 40 can be achieved using the proposed adaptive pole-zero DFE. In the HDSL environment besides the echo and the ISI, the NEXT is a major source of interference and is modeled as a colored noise process. The suppression/cancellation of NEXT in the HDSL environment has received less attention of the researchers and it is usually achieved with the help of a fractionally spaced equalizer (FSE), which operate at a 2/3 times the symbol rate thereby increasing the complexity of the transceiver design. Instead we propose the GDFE structure for the combined equalization and NEXT cancellation in the HDSL channels which operates at a symbol rate. We then present the steps involved in the design of a GDFE and a few number of examples have been presented to show that the GDFE is able to spectrally eliminate the colored noise entering the receiver. For a typical HDSL channel, it has been shown that the GDFE offers an improvement in the MSE of 3 dB compared to the FIR DFE We then present the adaptive implementation of the GDFE using the modified versions of the SM-RLS and the SM-lattice-LMS algorithms. The performance of the proposed adaptive GDFE is evaluated using the simulation techniques which shows that the convergence takes place in approximately 200 milliseconds for all loops under consideration. We also present the bit-error-rate performance, which shows that the adaptive GDFE offers 2 dB improvement in the MSE compared to the adaptive pole-zero DFE. The improvement in the MSE shows that the adaptive GDFE is able to suppress the NEXT as well as cancel the ISI in the HDSL environment.