The received low frequency signals in the long range shallow water will suffer severe attenuation and modal dispersion effect, which will distort the signal and deteriorate the communication performance. In this letter, a modal dispersion compensation receiver is proposed, which exploits the de-dispersion transform to compensate intra-mode dispersion and the rake combination to combine the multi-mode components. With the proposed receiver, the waveform expansion of high order modes is compensated, and thus more modes can be distinguished from the noise and the rake combination gain is improved, which leads to high communication accuracy. Simulation results show that the proposed receiver can achieve about 3 dB gain for the 40 km range and signal with a center frequency 400 Hz.

In this study, the authors propose an l ₀ ‐norm penalised shrinkage linear least mean squares ( l ₀ ‐SH‐LMS) algorithm and an l ₀ ‐norm penalised shrinkage widely linear least mean squares ( l ₀ ‐SH‐WL‐LMS) algorithm for sparse system identification. The proposed algorithms exploit the priori and the posteriori errors to calculate the varying step‐size, thus they can adapt to the time‐varying channel. Meanwhile, in the cost function they introduce a penalty term that favours sparsity to enable the applicability for sparse condition. Moreover, the l ₀ ‐SH‐WL‐LMS algorithm also makes full use of the non‐circular properties of the signals of interest to improve the tracking capability and estimation performance. Quantitative analysis of the convergence behaviour for the l ₀ ‐SH‐WL‐LMS algorithm verifies the capabilities of the proposed algorithms. Simulation results show that compared with the existing least mean squares‐type algorithms, the proposed algorithms perform better in the sparse channels with a faster convergence rate and a lower steady‐state error. When channel changes suddenly, a filter with the proposed algorithms can adapt to the variation of the channel quickly.

To improve the identification capability of AP algorithm in time-varying sparse system, we propose a block parallel ℓ0-SWL-DCD-AP algorithm in this paper. In the proposed algorithm, we first introduce the ℓ0-norm constraint to promote its application for sparse system. Second, we use the shrinkage denoising method to improve its track ability. Third, we adopt the widely linear processing to take advantage of the non-circular properties of communication signals. Last, to reduce the high computational complexity and make it easy to implemented, we utilize the dichotomous coordinate descent (DCD) iterations and the parallel processing to deal with the tap-weight update in the proposed algorithm. To verify the convergence condition of the proposed algorithm, we also analyze its steady-state behavior. Several simulation are done and results show that the proposed algorithm can achieve a faster convergence speed and a lower steady-state misalignment than similar APA-type algorithm. When apply the proposed algorithm in the decision feedback equalizer (DFE), the bite error rate (BER) decreases obviously.