# Blockwise Frequency Domain Active Noise Controller Over Distributed Networks
## 1 Introduction  
Active Noise Control (ANC) systems try to cancel, or at least minimize, some undesired noise by generating some sound signals specifically designed to cancel the first [1]. The global noise reduction is virtually impossible in an entire enclosure. Alternatively, we can attempt to control the noise field within a certain area to create local zones of quiet [2]. In particular, the system is intended to reduce the disturbance signal, called primary noise, at specific spatial points monitored by microphones, called error sensors. Generally speaking, the use of a large number of microphones strategically located produces larger zones of quiet. Similarly, multiple transducers are commonly used to improve the system performance, resulting in a multichannel ANC system. Typically, multichannel ANC systems use a single centralized processor managed by a control algorithm that has access to all the signals involved in the system. However, distributed systems offer a good solution to satisfy both high computational requirements and multiple signals capture, management and generation. Distributed systems are characterized by their flexibility, versatility and scalability. Flexibility allows the system to select the suitable strategy depending on the objective application. In addition, they have the versatility to adapt quickly and easily to different situations. Moreover, these systems can increase the number of controllers without redesigning the system. Therefore, a distributed system can be understood as a set of centralized systems that distribute the computational burden as well as the acquisition and signal generation to reach a common target. For example, a multichannel centralized controller can be distributed into several single-channel controllers (see Figure 1). In bothsystems, the error signals \(e_{k}(t)\) are the signals recorded at the \(N\) microphones, the anti-noise signals \(y_{j}(t)\) are the filter output signals reproduced by the \(N\) loudspeakers, the acoustic channels \(h_{j,k}\) are the impulse responses between the \(j\)th loudspeaker and the \(k\)th microphone, and the reference signal \(x(t)\) is the noise signal recorded at the reference sensor used by the adaptive controller to design the output signals \(y_{j}(t)\) (where \(k=1,2,\ \ldots\,N\) and \(j=1,2,\ \ldots\,N\)). While centralized systems work with all the signals generated by the loudspeakers and captured by the microphones, distributed systems employ independent processors which control a subset of loudspeakers from the signals picked up by a subset of microphones. The concept of distributed ANC systems for sound control applications was first introduced in [3], which considers processors that work independently and do not interchange local information. Thus, the computational burden is distributed among the processors and, in the case that there was no acoustic interaction among loudspeakers and microphones, it is possible to reach the centralized cancelation solution. As Figure 1b shows and it is stated in [3], each error signal \(e_{k}(t)\) is used only for its corresponding controller, and the reference signal \(x(t)\) is common to all of them. Therefore, the use of a network that allows communication among the controllers would be beneficial for the distributed ANC system to achieve results equivalent to those of the centralized method. Recently, the miniaturization of electronic components is enabling a low-cost implementation of many types of electronic devices with a high performance as well. These devices are usually equipped with sensors and actuators, and they also contain increasingly powerful and efficient processors with communication capability. Moreover, despite their small size, they allow for a great autonomy as a result of the low power requirements. In the last decade, the cooperation and communications among these kind of devices to perform a specific task through the so-called Wireless Sensor Networks (WSN) has been addressed [4].