To efficiently cancel the self-interference (SI) caused by the simultaneous transmission and reception in in-band full-duplex (IBFD) underwater acoustic (UWA) communication system, we propose a novel channel estimation approach to estimate the sparse SI channel, the proposed channel estimation algorithm has a better estimation performance than the traditional channel estimator. In the IRED radio communication system, the SI and intended channels are estimated through using training symbols in different time slots, and therefore, the effect of intended signal can be avoided in SI channel estimation. Because of the time variable and longtime delay in the UWA channel, we cannot estimate the SI and intended channel in different time slots. The intended signal is treated as additive noise when estimating SI channel in the IBFD-UWA communication system, and thus, the SI channel estimation is affected by non-Gaussian noise and the traditional algorithms designed for Gaussian noise typically perform poor. In view of this situation, we propose a maximum likelihood (ML) with sparse constraint to estimate the sparse SI channel. The ML with sparse constraint is derived via combining a sparse constraint into conventional ML cost function and using stochastic gradient algorithm to get the iterative formula, thereby resulting in a better performance. Extensive simulations and experimental results show that the proposed algorithm has faster convergence and better cancelation performance compared with traditional ML and least square. We also present the convergence and steady-state mean-squared error analysis of the proposed algorithm.
