# Blockwise Frequency Domain Active Noise Controller Over Distributed Networks
## 4 Experimental Results
In order to evaluate the performance of the different algorithms, we define the instantaneous Noise Reduction at node \(k\), \(NR_{k}(t)\), as the ratio in dB between the estimated error power with and without the application of the active noise controller:  
\[NR_{k}(t)=10\times log_{10}\left[ \begin{array}{c}\frac{c_{k}^{2}(t)}{d_{k}^ {2}(t)}\\ \end{array} \right], \tag{12}\]  
Figure 7: Photograph of the ANC prototype in the listening room at the Audio Processing Laboratory of the Polytechnic University of Valencia. where \(d_{k}^{2}(t)\) is the signal power picked up at the \(k\)th microphone when the ANC system is inactive and \(e_{k}^{2}(t)\) is the error signal power measured at the \(k\)th microphone when the ANC system works. Moreover, these signals powers have been estimated using an exponential windowing from the instantaneous signals. In the first scenario, we have evaluated the performance of both the distributed and the centralized FPBFxLMS algorithm in a network composed of four single-channel nodes with no communications constraints. Figure 8 shows the \(NR_{k}(t)\) by using Equation (12) for both algorithms. As expected, the distributed implementation exhibits the same performance than the centralized implementation for the four nodes. Both algorithms show a robust and stable performance providing an attenuation up to 11 dB for the worst node and almost 20 dB for the best node. Table 2 compares the computational complexity in terms of multiplications, additions, and FFTs per iteration of the FPBFxLMS algorithm, implemented for a centralized and a distributed ANC systems. For the centralized implementation, we consider a multichannel ANC system with one disturbance noise and the same number of microphones and loudspeakers (I:\(N\):\(N\) configuration). For the distributed implementation, we consider a network of \(N\) single-channel nodes. It is important to note that the complexity of the network as a whole is at least as high as the centralized algorithm. However, note that each node processes the algorithm simultaneously except the last addition of the global network state of the previous node (see line 11 in Algorithm 1). Therefore, in Table 2, we have only computed the operations of one single-channel node. Since we use a value of \(M=L\), and \(B=L/2\) (two partitions) the computational complexity only depends on \(L\) and \(N\). First, the third column of Table 2 shows the computational complexity of both algorithms related to values of \(L\) and \(N\). Then, this computational complexity is particularized for \(N=1\), \(N=4\) and \(N=8\). As expected, when \(N=1\), both implementations need the same number of operations. This is because both the centralized and the distributed ANC systems become a single-channel system. Moreover, for \(N=4\), we compare the operations of a centralized ANC system with a 1:4:4 configuration (16 channels) with the operations of a single-channel node of a network of four nodes. Finally, the same is done for \(N=8\). Results show that in a centralized ANC system, the computational complexity increases  
Figure 8: Noise reduction obtained by both the four-node distributed system and the centralized system with a 1:4:4 configuration. significantly with the number of channels. This fact represents a bottleneck in massive multichannel ANC systems. Otherwise, the increase of computational complexity in a distributed ANC system is not so significant. In the second scenario, the influence of a constant delay between information exchanges within a four-node network on the behavior of the distributed FPBFxLMS algorithm has been evaluated. The \(NR_{k}(t)\) curves of the best node in the network with different delay values of \(p\) are presented in Figure 9a for case 1 and Figure 9c for case 2. In both cases, as \(p\) increases, the performance of the algorithm gets worse.