Joint compressed sensing and enhanced whale optimization algorithm for pilot allocation in underwater acoustic OFDM systems

In underwater acoustic-orthogonal frequency division multiplexing (UWA-OFDM) systems, the performance of channel estimation is significantly affected by pilot allocation in the framework of compressed sensing (CS). However, for optimizing the pilot allocation, an exhaustive search method over all possible allocations is computationally prohibitive and random search method may not ensure convergence accuracy. In this paper, the meta-heuristic algorithm of the whale optimization algorithm (WOA) is employed to address this issue. For reinforcing the capability of balancing exploration and exploitation, an enhanced variant of WOA termed EWOA is presented with four optimization strategies. After that, a joint algorithm combining CS with EWOA (CS-EWOA) is proposed for pilot allocation in UWA-OFDM systems. Through extensive simulations, the improvement of EWOA is demonstrated on the majority of benchmark functions over other well-known meta-heuristic algorithms. With regard to bit error rate (BER) and mean square error (MSE) for channel estimation, the proposed CS-EWOA algorithm outperforms the equispaced, random, genetic algorithm (GA), particle swarm optimization (PSO), and WOA-based pilot allocation methods. Moreover, it is robust with varying system subcarriers and channel models. Furthermore, the CS-EWOA exhibits superior convergence performance without increasing the computational complexity compared with the GA-, PSO-, and WOA-based methods in the iteration process of pilot allocation optimization. It can be concluded from the simulation results that the proposed CS-EWOA algorithm is competitive to optimize pilot allocation for channel estimation in UWA-OFDM systems.