# Adaptive Noise Cancellation Based on Time Delay Estimation for Low Frequency Communication
## 1 Introduction
The noises from different sources have different and time-varying delays between the primary channel and reference channels, resulting in poor noise cancellation performance. To solve this problem, we can estimate the time-varying delays and compensate them by nonlinear processing [24; 25]. But the time delay estimation algorithms based on correlation have poor performance in the impulsive noise environment. To suppress the influence of impulsive noise, the explicit time delay estimation (ETDE) algorithm based on MCC (MCC-ETDE) is proposed in [26], and has better performance in indoor near-field electromagnetic ranging system. In the near-field electromagnetic ranging system, the ETDE algorithm is used to estimate the time delay between the electric filed and magnetic field of transmitted signal. The electric and magnetic fields of the signal are correlated. Therefore, the ETDE algorithm can converge to true time delay, which is used to measure the distance between receiver and transmitter. In the TTE communication systems, some reference inputs are not correlated with the noise in the primary input, which leads to non-convergence of the ETDE algorithm. Therefore, the convergence performance of the ETDE algorithm can be used to measure the correlationship between the reference inputs and the primary input. The reference input will be selected as the reference noise only when the time delay estimation value of this input has the smallest variance. Then the time delay is compensated to improve the noise cancellation performance. In this paper, an adaptive noise cancellation algorithm based on time delay estimation (ANC-TDE) is proposed and implemented on field programmable gate array (FPGA). The ETDE algorithm not only estimates the time-varying delay but also evaluates the noise correlationship between the primary channel and reference channels. The reference input will be selected as the reference noise only when the time delay value of this input has the smallest variance. Then the time delay is compensated to make sure that the delay between primary input and inference input is almost half the time delay of the adaptive filter. At last, the noise is removed from primary input by adaptive noise canceller based on MCC. The performance of the proposed adaptive noise cancellation algorithm is evaluated by simulation and experiment. As shown in the results, the MCC-ETDE algorithm can converge to the true time delay with small variance in the impulsive noise when the reference noise is correlated to the noise in the primary input. With the time delay compensated, the proposed ANC-TDE algorithm can reduce the impulsive noise, and provide better performance. With the filter length shortened, the proposed ANC-TDE algorithm can reduce the complexity of the ANC filter and is suitable for real-time systems. In summary, our main contributions are as follows:  
* An adaptive noise cancellation algorithm is proposed based on time delay estimation. The convergence performance of the ETDE algorithm is used to measure the correlationhip between the reference inputs and the primary input. The reference input will be selected as the reference noise only when the time delay estimation value of this input has the smallest variance. * When the reference noise is determined, the time delay between primary input and inference noise is compensated according to the time delay estimation results. After compensation, the value of delay \(\Delta\) is equal to about half time delay of the adaptive filter and the adaptive filter can obtain best noise cancellation performance. * The adaptive filter is designed based on MCC, which can improve the noise cancellation performance in the impulsive noise environment. * In order to filter out the correlated noise in real time, the proposed algorithm is implemented on FPGA, which includes three modules: time delay estimation module, delay and channel control module, and noise cancellation module. The remainder of this paper is organized as follows.