TY - JOUR
T1 - Adaptive Filtering Based on Time-Averaged MSE for Cyclostationary Signals
AU - Shlezinger, Nir
AU - Todros, Koby
AU - Dabora, Ron
N1 - Funding Information:
This work was supported in part by the Ministry of Economy of Israel through the Israeli Smart Grid Consortium and in part by the Israel Science Foundation under Grant 1685/16.
Publisher Copyright:
© 1972-2012 IEEE.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - Adaptive filters are commonly used in many signal processing and communications systems. In many practical digital communications scenarios, including, for example, interference-limited wireless and wireline communications, as well as narrowband power line communications, the considered signals are jointly cyclostationary. Yet, most works on adaptive filtering of cyclostationary signals used ad hoc application of adaptive algorithms designed for stationary signals, e.g., the least-mean-squares (LMS). It is known that these algorithms may not converge for jointly cyclostationary signals. In this paper, we rigorously study the optimal adaptive filtering of jointly cyclostationary signals. We first identify the relevant objective as the time-averaged mean-squared error criterion (TA-MSE), and obtain an adaptive algorithm as the stochastic approximation of the TA-MSE minimizer. When the considered signals are jointly stationary, the algorithm specializes to the standard LMS algorithm. We provide a comprehensive transient and steady-state performance analysis without imposing a specific distribution on the considered signals, and derive conditions for convergence and stability. The algorithm, which we call time-averaged LMS, is applied to practical scenarios in a simulations study, and an excellent agreement between the theoretical and the empirical performance is observed.
AB - Adaptive filters are commonly used in many signal processing and communications systems. In many practical digital communications scenarios, including, for example, interference-limited wireless and wireline communications, as well as narrowband power line communications, the considered signals are jointly cyclostationary. Yet, most works on adaptive filtering of cyclostationary signals used ad hoc application of adaptive algorithms designed for stationary signals, e.g., the least-mean-squares (LMS). It is known that these algorithms may not converge for jointly cyclostationary signals. In this paper, we rigorously study the optimal adaptive filtering of jointly cyclostationary signals. We first identify the relevant objective as the time-averaged mean-squared error criterion (TA-MSE), and obtain an adaptive algorithm as the stochastic approximation of the TA-MSE minimizer. When the considered signals are jointly stationary, the algorithm specializes to the standard LMS algorithm. We provide a comprehensive transient and steady-state performance analysis without imposing a specific distribution on the considered signals, and derive conditions for convergence and stability. The algorithm, which we call time-averaged LMS, is applied to practical scenarios in a simulations study, and an excellent agreement between the theoretical and the empirical performance is observed.
KW - Adaptive estimation
KW - cyclostationary signals
KW - power line communications
UR - http://www.scopus.com/inward/record.url?scp=85019136206&partnerID=8YFLogxK
U2 - 10.1109/TCOMM.2017.2655526
DO - 10.1109/TCOMM.2017.2655526
M3 - Article
AN - SCOPUS:85019136206
SN - 1558-0857
VL - 65
SP - 1746
EP - 1761
JO - IEEE Transactions on Communications
JF - IEEE Transactions on Communications
IS - 4
M1 - 7828023
ER -