Wireless Channel Sparsity: Measurement, Analysis, and Exploitation in Estimation

Sparse channel arises in a number of applications in wireless communications such as channel estimation and signal processing. There is growing evidence that physical wireless channels exhibit a sparse structure, and channel sparsity has been even considered as a nature of channels in many recent research works. However, there still lacks a good measure of channel sparsity, and mostly the assumptions that channel is sparse or non-sparse are based on intuitive analysis without measurement validation, which leads to some contradictions. In this article, based on channel measurement data, it is pointed out that a widely-used assumption, that wireless channels can be considered to be sparse, has pitfalls. Without loss of generality, the measurements are conducted in an urban scenario with different degrees of channel multipath richness. The channel degrees of freedom, diversity measure, and the Ricean K factor are used to evaluate channel sparsity, and they are found to have fairly high accuracy of measuring degrees of channel sparsity. It is also observed from measurements that the degree of channel sparsity is not steady and a sparse channel may change to non-sparse within a short time/distance observation window. Moreover, sparse and non-sparse based channel estimators are evaluated based on the measurements and the performances are analyzed. The results show that a sparse channel estimator cannot guarantee stable estimation accuracy even in channels with a high degree of sparsity, and considerable performance degradation will occur if a channel changes to non-sparse, which actually often happens in realistic communication scenarios and should be carefully considered in performance analysis. Some sparse channel related technical issues are also discussed in the article.