Higher-Order Statistics in Co-Prime Sampling With Application to Channel Estimation

This paper studies higher-order statistics of non-Gaussian signal using temporal co-prime sampling. We extend co-prime sampling to pairwise co-prime sequence (PCS) in order to derive higher-order statistics (HOS). We also examine the computational complexity of PCS-HOS algorithm for both parametric and nonparametric methods. Compared to the existing HOS algorithms, the proposed approach vastly reduces the complexity by several orders in terms of the length of segmentation window. Besides, we apply PCS-HOS to estimate both the orders and coefficients of fading channels, which are modeled as autoregressive moving average (ARMA) processes. In particular, we analyze the variance of third-order cumulants as the output of the model, and use it to determine the orders of autoregressive and moving average processes. In simulations, the proposed algorithm decreases the computational complexity to 17% of the existing HOS algorithms with negligible performance loss in high noise-to-signal ratio (SNR) environment. In low SNR scenario, it is more sensitive to order mismatch in terms of the variances of expectations, which makes it a more reliable indicator to confirm the correct order. Furthermore, we also develop the overdetermined matrix representation for moving average (MA) system, and apply PCS-HOS algorithm to calculate its parameters only based on the outputs. The results of our simulations show that 3rd-order PCS-HOS achieves 80% performance gain versus the existing HOS with the same computational complexity, or it has 12% performance loss with 85% reduction in complexity compared to the counterpart processing the same length of signal.