Asymptotic performance of ZF and MMSE crosstalk cancelers for DSL systems

S. M. Zafaruddin*, Itsik Bergel, Amir Leshem

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We present asymptotic expressions for user throughput in a multi-user digital subscriber line system (DSL) with a linear decoder, in increasingly large system sizes. This analysis can be seen as a generalization of results obtained for wireless communication. The features of the diagonal elements of the wireline DSL channel matrices make wireless asymptotic analyses inapplicable for wireline systems. Further, direct application of results from random matrix theory (RMT) yields a trivial lower bound. This paper presents a novel approach to asymptotic analysis, where an alternative sequence of systems is constructed that includes the system of interest in order to approximate the spectral efficiency of the linear zero-forcing (ZF) and minimum mean squared error (MMSE) crosstalk cancelers. Using works in the field of large dimensional random matrices, we show that the user rate in this sequence converges to a non-zero rate. The approximation of the user rate for both the ZF and MMSE cancelers are very simple to evaluate and does not need to take specific channel realizations into account. The analysis reveals the intricate behavior of the throughput as a function of the transmission power and the channel crosstalk. This unique behavior has not been observed for linear decoders in other systems. The approximation presented here is much more useful for the next generation wireline system than earlier DSL systems as previously computed performance bounds, which are strictly larger than zero only at low frequencies. We also provide a numerical performance analysis over measured and simulated DSL channels which show that the approximation is accurate even for relatively low dimensional systems and is useful for many scenarios in practical DSL systems.

Original languageAmerican English
Pages (from-to)182-196
Number of pages15
JournalDigital Signal Processing: A Review Journal
StatePublished - May 2019
Externally publishedYes

Bibliographical note

Funding Information:
S.M. Zafaruddin ( ) received his Ph.D. degree in electrical engineering from the Indian Institute of Technology Delhi in 2013. His Ph.D. degree research was on crosstalk cancellation for vectored digital subscriber line (DSL) systems. From 2012 to 2015, he was with Ikanos Communications (now part of Qualcomm), Bangalore, India, working directly with the CTO Office, Red Bank, New Jersey, where he was involved in research and development for xDSL systems. From 2015 to 2018, he was with the faculty of engineering at Bar-Ilan University, Ramat Gan, Israel, as a post-doctoral researcher working on signal processing for wireline and wireless communications. The Council for Higher Education, Israel, awarded him the Planning and Budgeting Commission Fellowship for Outstanding Post-Doctoral Researchers from China and India (2016–2018). He is currently a faculty member in the Department of Electrical and Electronics Engineering, BITS-Pilani, Pilani campus, India. His current research interests include signal processing for wireless and wireline communications, distributed signal processing, resource allocation, machine learning, wireless sensor networks, 5G, and DSL. He is an Associate Editor of IEEE Access.

Funding Information:
S.M. Zafaruddin was partially funded by the Planning and Budgeting Committee (PBC), Council for Higher Education, Israel, Fellowship Program for Outstanding Post-Doctoral Researchers from China and India awarded in 2016 for two years (2016–2018).

Publisher Copyright:
© 2019 Elsevier Inc.


  • Asymptotic Analysis
  • Digital Subscriber Lines
  • MMSE
  • Random Matrix Theory
  • Wireline Channels
  • Zero Forcing


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