In multiple-input multiple-output–orthogonal frequency-division multiplexing underwater acoustic communication systems, the correlation of the sampling matrix is the key of the channel estimation algorithm based on compressed sensing. To reduce the cross-correlation of the sampling matrix and improve the channel estimation performance, a pilot design algorithm for co-sparse channel estimation based on compressed sensing is proposed in this article. Based on the time-domain correlation of the channel, the channel estimation is modeled as a common sparse signal reconstruction problem. When replacing each pilot indices position, the algorithm selects multiple pilot indices with the least cross-correlation from the alternative positions to replace the current pilot indices position, and it uses the inner and outer two-layer loops to realize the bit-by-bit optimal replacement of the pilot. The simulation results show that the channel estimation mean squared error of pilot design algorithm for co-sparse channel estimation based on compressed sensing can be reduced by approximately 18 dB compared with the least square algorithm. Compared with the genetic algorithm and search space size methods, the structural sequence search proposed by pilot design algorithm for co-sparse channel estimation based on compressed sensing is used to design the pilot to complete the channel estimation. Thus, the mean squared error of the channel estimation can be reduced by 2 dB. At the same bit error rate of 0.03, the signal-to-noise ratio can be decreased by approximately 7 dB.

在多输入多输出正交频分复用水声通信系统中，采样矩阵的相关性是基于压缩感知的信道估计算法的关键。为了减少采样矩阵的互相关，提高信道估计性能，本文提出了一种基于压缩感知的协同稀疏信道估计导频设计算法。基于信道的时域相关性，信道估计被建模为一个常见的稀疏信号重建问题。当替换每个导频索引位置时，算法从替代位置中选择互相关最小的多个导频索引来替换当前的导频索引位置，并利用内外两层环路实现导频的逐位优化替换。仿真结果表明，与最小二乘算法相比，基于压缩感知的协同稀疏信道估计导频设计算法的信道估计均方误差可降低约18 dB。与遗传算法和搜索空间大小方法相比，采用导频设计算法提出的基于压缩感知的协同稀疏信道估计的结构序列搜索设计导频完成信道估计。因此，信道估计的均方误差可以减少2dB。在 0.03 的相同误码率下，信噪比可降低约 7 dB。仿真结果表明，与最小二乘算法相比，基于压缩感知的协同稀疏信道估计导频设计算法的信道估计均方误差可降低约18 dB。与遗传算法和搜索空间大小方法相比，采用导频设计算法提出的基于压缩感知的协同稀疏信道估计的结构序列搜索设计导频完成信道估计。因此，信道估计的均方误差可以减少2dB。在 0.03 的相同误码率下，信噪比可降低约 7 dB。仿真结果表明，与最小二乘算法相比，基于压缩感知的协同稀疏信道估计导频设计算法的信道估计均方误差可降低约18 dB。与遗传算法和搜索空间大小方法相比，采用导频设计算法提出的基于压缩感知的协同稀疏信道估计的结构序列搜索设计导频完成信道估计。因此，信道估计的均方误差可以减少2dB。在 0.03 的相同误码率下，信噪比可降低约 7 dB。