压缩感知OFDM稀疏信道估计导频设计

为提高稀疏信道估计性能，基于压缩感知（CS）理论，研究了正交频分复用（OFDM）系统中的导频设计问题。由于已有方法不能准确衡量采样矩阵重建性能，从而导致根据已有方法设计的导频具有较差的信道估计性能，因此提出以互相关矩阵元素的立方和为准则准确评价采样矩阵的重建性能。针对OFDM系统信道估计导频设计为离散组合优化问题，提出了一种并行完全树分组替换搜索算法用于搜索最优的导频。在算法的每次循环中，先将导频索引集合分组，再根据每一组替换的结果更新导频，提出的方法扩大了导频搜索空间，避免了导频搜索的局部最优问题。仿真结果表明，提出的评价方法相比现有方法能够准确评价采样矩阵重建性能，使用提出的准则设计的导频与现有互相关准则相比信道估计均方误差可减小约3 dB。同时，所提出的导频搜索算法具有更快的收敛速度和最优的导频搜索性能。

Pilot design for compressed sensing based OFDM sparse channel estimation

In order to improve channel estimation performance, the pilot design problem in orthogonal frequency division multiplexing (OFDM) is investigated from the perspective of compressed sensing (CS). Since the reconstruction performance of the sampling matrix cannot be accurately measured by the existing methods, the pilot designed by the existing methods has poor channel estimation performance. Therefore, the cubic sum criterion which computes the cubic summation of entries of correlation matrix is proposed to measure the reconstruction performance of sampling matrix. Besides, for the pilot design of OFDM channel estimation which is a discrete combinatorial optimization problem, a novel pilot search method named grouped substitution with concurrent full trees is also proposed to search optimal pilot. At each iteration of the proposed algorithm, the pilot pattern set is divided into groups. Then, the pilot patterns are successively updated by obtained pilot sets. The proposed method enlarges the search space and avoids getting in local optimum in searching pilot pattern. The simulation results show that, the proposed evaluation method can accurately evaluate the reconstruction performance of the sampling matrix in comparison to the existing evaluation methods and compared with mutual coherence criterion, the proposed criterion can gain 3 dB improvement in mean square error. Furthermore, the proposed pilot search method has faster convergence speed and the best searching performance.