水声通信近似L0范数约束的BP网络均衡器*

针对稀疏水声信道的长时延扩展及梯度下降的权值迭代方案导致的神经网络均衡器收敛速度慢的问题，提出了近似L₀范数约束的BP神经网络均衡器。首先在传统BP网络均衡器基础上增加判决反馈项，然后在代价函数中对均衡器输入层到隐含层的权值增加L₀范数约束，构造新的代价函数，利用高斯族函数近似L₀范数约束，并根据不同隐层神经元节点输出权值的L₂范数设定近似参数。仿真结果表明，稀疏信道条件下，本方法相比传统的BP网络均衡器收敛速度更快，误码率更低，可以有效提升神经网络均衡器的性能。

Approximate L0 norm constrained BP neural network equalizer for underwater acoustic communication

Aiming at the problem of slow convergence speed of neural network equalizer caused by long delay spread and gradient descent weight iterative scheme of sparse underwater acoustic channel, a BP neural network equalizer with approximate L0 norm constraint is proposed. Firstly, the decision feedback term is added to the traditional BP network equalizer, and then the L0 norm constraint is added to the weight from the equalizer input layer to the hidden layer in the cost function to construct a new cost function. The Gauss family function is used to approximate the L0 norm constraint, and the approximate parameters are set according to the L2 norm of the hidden layer neurons. The simulation results show that, compared with the traditional BP network equalizer, this method has faster convergence speed and lower bit error rate in sparse channel, which can effectively improve the performance of neural network equalizer.