The asymptotic mean square (steady-state) time synchronization errors are calculated from (16).
From Figure 5, the learning rate of ICMA influences the steady mean square error only a little, varying within the range of about 2 dB.
The algorithm takes average in GA run for 40 times for the influences to convergent time and steady mean square error interference (see Figure 6).
With the improved CMA, it is studied that when the learning rate is from 0.05 to 0.5, in Monte Carlo run for 43 times, the algorithm takes average of influence for convergent time and steady mean square error, as shown in Figure 5. Figure 5 Influence of learning rate to balancer.
The proposed CNFSLMS algorithm-based functional link artificial neural network (FLANN) filter, aiming to overcome the compromise between convergence speed and steady state mean square error of the NFSLMS algorithm, offers both fast convergence rate and low steady state error.
The presented algorithms have good convergence speed, low steady state mean square error (MSE), and low computational complexity features.
Also, the steady state mean square coefficient deviation (MSD) is given by mathrm{MSD}={mu}^2{sigma}_v^2{varphi}^T{left(mathbf{I}-mathbf{P}right)}^{-1}mathrm{vec}left(mathbf{I}right) (39).
The results of steady state mean square response analysis are presented in terms of the corresponding amplification factor, illustrating its dependence on excitation/system bandwidth ratios and detuning between expected excitation frequencies and the system's natural frequency.
In all these algorithms, the selected fixed step-size can change the convergence and the steady-state mean square error (MSE).
In addition, theoretical analyses are conducted on the stable range of the step size and the steady-state mean square error (MSE) under different conditions.
According to the derived matrix representation of the received signal, the analytical steady-state mean square errors (MSEs) for both receivers are also derived and compared.
