Low computational complexity design over sparse channel estimator in underwater acoustic OFDM communication system

The computational complexity required in the channel estimation plays an important role in underwater acoustic communications (UAC) with orthogonal frequency duplex access (OFDM), especially when the channel is sparse. The authors develop an algorithm to carry out the orthogonal matching pursuit (OMP) for the sparse channel estimation based on the compressive sensing, where the goal is to obtain the minimum computational complexity. It is discovered that the inter-carrier interference (ICI) mainly depends on the adjacent subcarriers since the ICI interferences become more and more marginable with the increase of the distance from the other subcarriers to the current desired subcarrier in the frequency domain, which can be utilised to reduce the complexity of the design over the sparse channel estimator. By exploiting this property, the authors propose that the diagonal band of the ICI channel matrix is employed in the calculation of the objective function to minimise the required computational complexity, which develops an adaptive algorithm that is theoretically proved to be a faster algorithm. Numerical simulations are demonstrated for the typical UAC system that the proposed algorithm achieves the remarkable gain of the computational complexity compared to the existing algorithm.