On the second order power spectral statistics of wideband indoor microwave channels

We derive closed form expressions for the second-order statistics of the spectral power gain of wide-band microwave indoor channels. We obtain our results within a framework general enough to be compatible with several popular channel models, such as those proposed by the IEEE 802.15.3a task group, as well as the Saleh-Valenzuela channel model. As all these models, our channel description is based upon clusters and rays with Poisson arrivals and random amplitudes. Our results consist of closed form expressions for the second-order statistics of the channel power frequency response, where statistical averages involve expectations over ray amplitudes and arrival times. We first express the auto-covariance of this frequency response in closed-form. We then use this result to obtain an analytical expression for the variance and second-order moment of the channel power within any given interval of frequencies. This allows us to express the channel spectral diversity as a function of model parameters and bandwidth. From this function, we determine the range within which diversity scales approximately linearly with bandwidth and its upper limit.