Sparse Learning of Higher-Order Statistics for Communications and Sensing

Signal processing based higher-order statistics (HOS) has been acting as a potential important tool on variety of target identification and information sensing fields. While a concise or compact expression of HOS is needed to ease the burden of data acquisition and computational complexity, sparse representation of HOS could be the optimum solution to this problem. In this paper, we formulate the issue of sparse representation of HOS by categorizing them into three cases according to the discriminative sparsity: strictly sparse, structure-based sparse and structure-based compressible. The corresponding algorithms of sparse representation for the three types of HOS are designed individually. For strictly sparse HOS, we mainly address on how to build the linear relationship between one-dimensional time domain samples and high-dimensional HOS and reduce the computational complexity of equivalent sensing matrix. Autocorrelation and four-order statistic are taken as examples to illustrate proposed sparse decomposing method for structure-based sparse HOS by exploiting their intra-structure properties. The sparse representation of structure-based compressible HOS are approximated with a joint decomposing algorithm using eigenvalue and single-value decomposition approaches. In addition, we have integrate our proposed sparse representation of HOS into compressive sensing framework to verify the feasibility and performance of sparse representation solutions.