# Research on Co-Channel Interference Cancellation for Underwater Acoustic MIMO Communications
###### Abstract
In [7], a frequency-domain turbo-equalization scheme without CP or ZP was proposed for single-carrier MIMO communication. In the first iteration, a low-complexity detection was used in the frequency domain; in the second iteration, inter-block-interference and CP were applied to enable effective symbol detection. Its feasibility and effectiveness have been tested by field trial data. In [8], a three-step frequency-domain equalization scheme was described for MIMO underwater acoustic communication. The first iteration was channel estimation, the second iteration was to suppress CoI, and the final iteration was to equalize symbols. The traditional frequency domain equalizers need CP or ZP to prevent inter-block interference, which degrades the bandwidth efficiency. Some methods may not need CP or ZP [7], but serval iterations are performed for decoding, which increases the computational complexity. A common approach to decode MIMO symbols is direct adaptive decision feedback equalization (DA-DFE). Due to the serious Doppler shift in underwater acoustic channels, a phase-tracking module is usually required. For example, a second-order phase-locked loop was adopted for DA-DFE in [19]. After phase compensation, the DA-DFE approach uses adaptive algorithms, such as least mean square (LMS) and recursive least square (RLS) criteria to train the equalizer's taps or equalize received symbols. The merit of DA-DFE is not necessary to explicitly estimate the channel, but the DA-DFE approach requires long training sequences to achieve convergence, which degrades the spectral efficiency. Due to the easy implementation of DA-DFE, it was intensively used to equalize underwater acoustic single-input-multiple-output (SIMO) systems [20; 21; 22] or MIMO systems [9; 10; 11; 12; 18]. In [9], space-time trellis codes layered with space-time codes combined with low-complexity DA-DFE was proposed. The space-time trellis codes layered with space-time codes utilized the large diversity, and the ISI and the CoI were suppressed by the DA-DFE. A data rate of 48 kb/s in 23 kHz of bandwidth, and 12 kb/s in 3 kHz of bandwidth were achieved in the 2 km range. In [10], a time-reversal-based underwater acoustic MIMO communication was proposed. A parallel interference cancellation method was incorporated to suppress the CoI in the MIMO system, while the DA-DFE was used to frequently update the channel used for the time reversal process. In [11], both serial and parallel interference cancellation techniques were integrated with time reversal DA-DFE to address the CoI in underwater acoustic MIMO systems. High bandwidth efficiencies were achieved in the experiment. In [18], a joint sparsity for underwater acoustic MIMO communication was proposed, distributed compressed sensing was used to estimate the underwater acoustic channel, and then time reversal was adopted to suppress the multipath and combine multiple channels. Finally, a single-channel DA-DFE was applied to decode symbols. In [12], many kinds of sparse DA-DFEs with the proportionate-updating or the zero-attracting adaptive filtering principles were compared. To reduce the computational complexity, a partial tap update scheme via hard thresholding was introduced to sparse DA-DFEs. The results revealed that, although the improved DA-DFEs show a more improved performance, the RLS DA-DFE still achieved the best performance. The DA-DFE parameters (such as the length of feedforward filter, the iterative step, and the forgotten factor) require careful manual achieving to achieve the considerable performance. When the channel is varied, those parameters should subsequently be updated. Hence, this is not suitable for the design of a robust MIMO communication system. The turbo equalization method, which utilizes multiple iterations, was used to decode MIMO symbols [13; 14; 15]. Turbo equalization typically consists of two components: a soft-input-soft-output equalizer and a soft-input-soft-output decoder, which iteratively exchange extrinsic information to improve the detection performance.