# Research on Co-Channel Interference Cancellation for Underwater Acoustic MIMO Communications
###### Abstract
For example, in [13] the NLMS-algorithm-based DA-DFEs were used in a soft-input-soft-output equalizer. The DA-DFEs consisted of a feedforward filtering unit and soft interference cancellation unit; the experiment verified the effectiveness of the proposed method. In [14; 15], the IPNLMS algorithm or RLS-DCD algorithm was used for iterative channel estimation in turbo equalization, and a minimum mean-square-error equalizer was used to detect the symbols. However, the interference cancellation was not considered in channel estimation. Other methods also were proposed for underwater MIMO communications. For example, in [17], sparse learning via iterative minimization was used in the estimation channel; then linear minimum mean-square error criterion was used to detect symbols. After the 1 st iteration, the CoI was subtracted from the received signal. This process was iteratively performed. However, when the decoded symbols are incorrect, the reconstructed CoI will introduce a lot of noise, and this noise will propagate to the next iteration; hence, the detection of symbols will fail. In a single-input-multiple-output (SIMO) system, CE-DFE was demonstrated to achieve a better performance and was widely investigated. The CE-DFE directly estimates the channel using shorter training sequences, and directly calculates the equalizer's taps based on channel estimates. In [23], the CE-DFE was used for multi-band underwater acoustic channel equalization; in [24], the CE-DFE was utilized in a time-varying underwater acoustic channel. However, due to the heavy CoI, the traditional CE-DFE, which was used for SIMO communication systems, will fail when it is used in underwater acoustic communications. To date, the literature reporting on CE-DFE that is suitable for underwater acoustic MIMO communications has been very limited. In [16], we proposed a CE-DFE with CoI cancellation component for underwater acoustic MIMO communication, but the channel estimation still suffered from serious interference. The limitations of the existing methods are listed in Table 1.  
As mentioned, the CE-DFE taps were achieved via channel estimates, which provide prior information for equalizers. Some efforts have been taken to improve the performance of channel estimation under an impulsive noise environment [25; 26; 27; 28], but very limited work focuses on interference cancellation for single-carrier MIMO channel estimation. In [16], we proposed distributed compressed sensing to enhance the channel estimates with common delays, but the different delays still suffered from serious CoI. Our previous work did not fully deal with the CoI. In this paper, we propose a new framework that combines both the CoI-cancellation-based channel estimation method and CoI-cancellation-based CE-DFE. As far as we know, this is the first time that the CoI-cancellation-based channel estimation and CoI-cancellation-based channel equalization have been proposed. Specifically, in channel estimation, we use the projection method to project CoI to a specific subspace in which the CoI in this subspace is free. As a result, the CoI is cancelled. In channel equalization, we introduce CE-DFE with CoI cancellation to underwater acoustic MIMO communication. The proposed methods do not need to reconstruct the CoI, and can perfectly address the CoI, whether or not the CoI from different tranmitters is serious. In addition, to date, there has been no detailed comparison between traditional DA-DFE and CE-DFE. In this paper, the performance is compared in terms of output SNR and computational complexity between CE-DFE and DA-DFE for underwater acoustic MIMO communications. Compared to DA-DFE, the proposed receiver does not need to carefully tune parameters such as the length of taps, forgotten factor, etc. Moreover, since the CE-DFE performs block by block, the Doppler can be estimated and compensated block by block, while the DA-DFE is usually sensitive to Doppler, which has an impact on convergence.