跳频压缩采样的快速重构研究

Research on Fast Reconstruction of Frequency Hopping Using Compressive Sampling

摘要: 受奈奎斯特采样定理的限制，对跳频信号进行传统采集需要很高的采样率，带来高昂的处理代价，压缩采样理论突破了奈奎斯特采样定理的限制，可大幅度降低信息采样率。本文以每个跳频频点最近的连续三个原子基作为该跳频频点的稀疏表示块进行迭代，削弱了相邻跳信号频率突变引起的瞬间频率展宽和数据符号调制带来的频偏影响，使之更适合实际跳频信号场合。仿真结果验证了修正的稀疏度自适应匹配追踪算法的有效性，提高了重构算法的性能。并且本文将修正的算法在不同M值下的重构概率与原算法进行了对比。

Abstract: Limited by the Nyquist sampling theorem, for traditional frequency hopping signals acquisition which needs very high sampling rate and high processing cost, compression sampling theory breaks through the limitation of the Nyquist sampling theorem, and the sampling rate can be significantly reduced. The paper proposes an iteration that takes three continuous atomic bases, which have got the nearest hopping point, as the sparse representation block of this hopping point. This algorithm weakens instantaneous frequency bandwidth caused by the adjacent signal frequency mutation and the modulated data symbol brings frequency deviation effect, and makes it more suitable for the actual frequency hopping signal. The simulation results verify the correction of the effectiveness of the sparse degree of adaptive matching pursuit algorithm, which improves the performance of reconstruction algorithm. Moreover, the paper compares the correction algorithm’s reconstruction probability with the original algorithm under different M value.