Nested sampling for higher-order statistics with application to LTE channel estimation

This paper studies higher-order statistics based on nested sampling. We propose multilevel nested sampling (MNS) algorithm to obtain higher-order statistics (HOS), and analyze the computational complexity of the MNS-HOS algorithm for both parametric and nonparametric methods. Compared to the existing HOS algorithms, the proposed algorithm vastly reduces the complexity by several orders in terms of the length of segmentation window. We also apply MNS-HOS algorithm to estimate the coefficients of a simplified LTE spatial channel model blindly without using any training sequences. Our simulations show that compared with pairwise coprime sampling HOS algorithm, MNS-HOS produces less variance and converges faster in estimating higher-order cumulants, and achieves 17% performance gain for channel estimation. The proposed MNS-HOS algorithm is also able to reduce computational complexity by 98% with a tradeoff of 22% performance loss in contrast with the HOS algorithm without sparse sampling.