A Lower Bound for the Coherence Block Length in Mobile Radio Channels

Abstract

A lower bound for the coherence block (ChB) length in mobile radio channels is derived in this paper. The ChB length, associated with a certain mobile radio channel, is of great practical importance in future wireless systems, mainly those based on massive multiple input and multiple output (M-MIMO) technology. In fact, it is one of the factors that determines the achievable spectral efficiency. Firstly, theoretical aspects regarding the mobile radio channels are summarized, focusing on the rigorous definition of coherence bandwidth (BC) and coherence time (TC) parameters. Secondly, the uncertainty relations developed by B. H. Fleury, involving both BC and TC, are presented. Afterwards, a lower bound for the product BCTC is derived, i.e., the ChB length. The obtained bound is an explicit function of easily measurable parameters, such as the delay spread, mobile speed and carrier frequency. Furthermore, and especially important, this bound is also a function of the degree of coherence with which we define both BC and TC. Finally, an application example that illustrates the practical possibilities of the bound obtained is presented. As a further conclusion, the need to determine what degree of correlation is required to consider mobile channels as effectively flat-fading and stationary is highlighted.