UWB Sparse/Diffuse Channels, Part II: Estimator Analysis and Practical Channels

In this two-part paper, the problem of channel estimation in Ultra Wide-Band (UWB) systems is investigated. In Part I, a novel Hybrid Sparse/Diffuse (HSD) model is proposed for the UWB channel, and new channel estimation strategies are designed for this model. In this paper (Part II), a Mean-Squared Error (MSE) analysis of the Generalized MMSE and Generalized Thresholding Estimators developed in Part I is performed, for the asymptotic regimes of low and high SNR. The analysis quantifies the achievable MSE performance of these schemes over unstructured estimators. Specifically, we prove that it is beneficial to be conservative in the estimation of the sparse component, i.e., to assume that the sparse component is sparser than it actually is. Moreover, we analyze the scenario with a non-orthogonal pilot sequence, and establish a connection between the Generalized Thresholding estimator and conventional sparse approximation algorithms proposed in the literature. In addition to the theoretical analysis, these channel estimation schemes are evaluated in a more realistic geometry-based channel emulator, for which the HSD model developed in Part I is an approximation. The numerical results are shown to match the expected asymptotic MSE behavior. Moreover, the proposed estimation techniques are shown to outperform conventional unstructured and purely sparse estimators, from both an MSE and a bit error rate perspectives, even for the realistic geometry-based channel model.