TY - JOUR
T1 - Large system transient analysis of adaptive least squares filtering
AU - Xiao, Weimin
AU - Honig, Michael L.
N1 - Funding Information:
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.
PY - 2005/7
Y1 - 2005/7
N2 - 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.
AB - 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.
KW - Adaptive filter
KW - Large system analysis
KW - Least squares (LS)
KW - Reduced-rank filters
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U2 - 10.1109/TIT.2005.850081
DO - 10.1109/TIT.2005.850081
M3 - Article
AN - SCOPUS:23744450508
SN - 0018-9448
VL - 51
SP - 2447
EP - 2474
JO - IRE Professional Group on Information Theory
JF - IRE Professional Group on Information Theory
IS - 7
ER -