Space-frequency second-order statistics of the power gain of wideband indoor channels

This paper presents closed-form expressions for the space-frequency (SF) second-order statistics for the power gain of indoor wideband channels. These expressions hold for channel models in which multi-path components are clustered, both in their arrival angles and their arrival times. Assuming that the arrival times are independent of the angles of arrival, we derive a closed-form expression for the covariance between the channel power gains at two receiving antenna positions d meters apart, at any pair of frequencies ω₁ and ω₂. This expression reveals that increasing d yields the same SF covariance asymptotic reduction attainable by increasing |ω₁ - ω₂|, only if |ω₁ - ω₂|≠0, and that the covariance is symmetric in its dependence with ω₁ - ω₂ and with ω₁ + ω₂. Thus, the channel power gain at higher frequency bands has less variation than at lower frequencies. Finally, we show that the variable part of the SF covariance decays approximately as 1/d.