Large system transient analysis of adaptive least squares filtering

Weimin Xiao*, Michael L. Honig

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

The performance of adaptive least squares (LS) filtering is analyzed for the suppression of multiple-access interference. Both full-rank LS filters and reduced-rank LS filters, which reside in a lower dimensional Krylov space, are considered with training, and without training but with known signature for the desired user. We compute the large system limit of output signal-to-interference-plus-noise ratio (SINR) as a function of normalized observations, load, and noise level. Specifically, the number of users K, the degrees of freedom N, and the number of training symbols or observations i all tend to infinity with fixed ratios K/N and i/N. Our results account for an arbitrary power distribution over the users, data windowing (e.g., recursive LS (RLS) with exponential windowing), and initial diagonal loading of the covariance matrix to prevent ill-conditioning. Numerical results show that the large system analysis accurately predicts the simulated convergence performance of the algorithms considered with moderate degrees of freedom (typically N = 32). Given a fixed, short training length, the relative performance of full- and reduced-rank filters depends on the selected rank and diagonal loading. With an optimized diagonal loading factor, the performance of full- and reduced-rank filters are similar. However, full-rank performance is generally much more sensitive to the choice of diagonal loading factor than reduced-rank performance.

Original languageEnglish (US)
Pages (from-to)2447-2474
Number of pages28
JournalIEEE Transactions on Information Theory
Volume51
Issue number7
DOIs
StatePublished - Jul 2005

Funding

Manuscript received July 12, 2002; revised March 14, 2005. This work was supported in part by the Army Research Office under Grant DAAD19-99-1-0288 and by the National Science Foundation under Grant CCR-0073686. The material in this paper was presented in part at the Conference on Information Sciences and Systems, Princeton, NJ, March 2000 and at the 39th Annual Allerton Conference on Communication, Control, and Computing, Monticello, IL, October 2001.

Keywords

  • Adaptive filter
  • Large system analysis
  • Least squares (LS)
  • Reduced-rank filters

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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