Consequently, taking the expectation on both sides of (14), under A.1-A.3, the mean weight-error vector of the proposed algorithm evolves as E [ v n + 1 ] = E [ v n ] + μ α ̄ n E e n x n ∥ x n ∥ 2 + ( 1 - α ̄ n ) E e n 3 x n ∥ x n ∥ 2. (15).
The study investigates the MSE error, mean weight behavior, stationary points, misadjustment error, and stability conditions.
Specifically, for the general case, in terms of the mean performance, we show that the mean value of the weight error vector approaches zero as iteration numbers go to infinity, which implies the asymptotical convergence of the proposed algorithms; from the perspective of mean square performance, we derive the mathematical expressions for the steady-state MSD and EMSE values.
Third, the error is different for players with different weights; players with weight closer to the mean weight have a lower error than those with weight further away.
Both the mean and the mean-square behaviors of the weight error vector are presented in the ensuing analysis.
The first part examines the proposed algorithms in the mean square error and mean weight context.
Here we give analytical expressions for the mean squared error (MSE), explore the stationary points of the algorithm, evaluate the misadjustment error due to weight fluctuations, and derive recursions for the mean weight transient behavior during the learning process.
For trials that did not report mean weight change, but reported mean group weight (and either SE or SD) at baseline and follow up, standard errors of weight change were calculated assuming an intra-correlation coefficient of ρ = 0.5.
Weight loss was observed in the SXB-treated groups, with a mean (standard error) weight change from baseline of −1.19 (0.22) kg in the SXB 6 g/night group and −0.43 (0.20) kg in the SXB 4.5 g/night group compared with a mean weight gain of 0.43 (0.16) kg in the placebo group.
To suppress noise and to enhance signal reception after the fuzzy MOE detector, a signal subspace projection and minimum mean square error weight combiner is proposed to enhance signal-to-interference-plus-noise ratio and bit error rate performances.
