## 4 Simulation Results  
We evaluate the performance of the proposed algorithm by considering a 1:2:2 multichannel ANC system. The tap length of the primary path, the secondary path, and the adaptive filter was of 256, 128 and 100 coefficients, respectively. These values were defined previously by considering a typical case (\(M=128\), \(N=100\), \(L=5\), \(I=1\) and \(J=K=2\)). Therefore, the computational cost of the proposed algorithm is defined in Tables 1 and 2. The impulse response of the acoustics paths was obtained from [14]. In order to evaluate the behavior of the proposal, we performed 50 independent trials each with 50,000 iterations. Furthermore, to test the tracking capabilities, we caused an abrupt change to the impulse response of the acoustic primary path at the middle of the iterations. As the reference signal, we used white Gaussian noise with unit variance and we also added white Gaussian noise to the error microphones with SNR 30 dB. Figure 2 shows a comparison of the mean square error (MSE) at the error microphone 1, for the filtered-x affine projection-like-I (FXAPI-I) algorithm, the conventional FXECAP-L algorithm and the proposed algorithm. For this experiment, the projection order was \(L=5\)  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Number of Multiplications** & **Typical Case** \\ \hline FXAPL-I algorithm & \([((2N+1)L+2N+M+1)IJK+(N)IJ]\) & 5536 \\ Conventional FXECAP-L algorithm & \([((3N+1)L+2N+2+M)IJK+(N)IJ+L(K)]\) & 7550 \\ Proposed method & \([((3N+1)L+5N+3+M)IJK+(N)IJ+L(K)]\) & 8754 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Number of multiplications per iteration of the FXAPI-I algorithm, the conventional FXECAP-L algorithm and the proposed algorithm. Typical case \(M=128\), \(N=100\), \(L=5\), \(I=1\) and \(J=K=2\).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Number of Multiplications** & **Typical Case** \\ \hline FXAPL-I algorithm & \([((2N+1)L+2N+M+1)IJK+(N)IJ]\) & 5536 \\ Conventional FXECAP-L algorithm & \([((3N+1)L+2N+2+M)IJK+(N)IJ+L(K)]\) & 7550 \\ Proposed method & \([((3N+1)L+5N+3+M)IJK+(N)IJ+L(K)]\) & 8754 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Number of additions per iteration of the FXAPL-I algorithm, conventional FXECAP-L algorithm and the proposed algorithm. Typical case \(M=128\), \(N=100\), \(L=5\), \(I=1\) and \(J=K=2\).  
for all the algorithms and the error was encoded with \(b\) = 6 bits in the FXECAP-L algorithm and the proposed algorithm. The scaling factor for the FXAPL-I algorithm and the FXECAP-L algorithm was \(sf\) = 0.008, and \(sf\) = 0.015, respectively. As can be observed from Figure 2, the convergence speed for all the algorithms is almost identical.  
Figure 3 shows the number of bits that are used to encode the error of the proposed algorithm. As can be seen, the number of bits decreases as the process advances. This allows the algorithm to stay within the update threshold, avoiding the computation of the algorithm in each iteration. In this way, the average number of updates performed by the proposed algorithm was 19,966 (39.93%), while the FXECAP-L algorithm updated its coefficients 49,610 times (99.2%).  
Figure 4 shows the number of input vectors for the proposed algorithm. As can be seen, the proposed strategy does not affect the evolving behavior; therefore, the computational burden is reduced.  
Figure 4: Number of input vectors of the proposed algorithm.  
Figure 3: Number of bits used to encode the error in the proposed algorithm.  
Figure 2: Comparison of the MSE curves for the FXAPL-I, FXECAP-L and the proposed algorithm.