Pilot-assisted linear turbo equaliser over doubly selective channels

The underwater acoustic channel is considered as one of the most challenging channels for reliable communications. Long delay spread and Doppler effect bring a great challenge to directly apply the algorithms in radio communications to underwater communications, which calls for modification and enhancement. In this study, a pilot-assisted linear turbo equalisation algorithm termed P-TE is proposed. Unlike the existing pilot methods that insert pilot into the modulated symbols to facilitate the channel estimation, the authors insert the known bits into the uncoded binary sequence to assist equalisation as well as decoding with the careful design of the bit positions. A second-order least mean square adaptive algorithm as well as adaptive step size method is introduced for weights update. Furthermore, a modified low-density parity-check decoding algorithm is presented to describe the pilot-assisted decoding algorithm, which does not increase the complexity. Moreover, pilot extraction from error-free blocks is proposed for enhanced performance. Experimental results have indicated that P-TE can significantly improve the performance and reduce the required number of the iterations, leading to lower complexity. Furthermore, experiments show that the effective throughput of P-TE can be higher than the method without pilot at a signal-to-noise ratio of 10 dB.