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Direction dispersion and space selectivity in the mobile radio channel

We present analytical results relating to first- and second-moment characterization of direction dispersion and spatial selectivity in the radio channel as well as to the duality between these two effects. The natural figure characterizing the extent of direction dispersion is introduced. This parameter called the direction spread shares the same features as the delay and Doppler spreads, two parameters commonly employed to describe the extent of dispersion in delay and Doppler frequency respectively. It is shown that the direction spread and the coherence distance are related by an uncertainty relation as are the components of the pairs delay spread-coherence bandwidth and Doppler spread-coherence time. An application of this uncertainty relation to the design of antenna arrays is sketched.