Why Is Shadow Fading Lognormal?

Received signal power in mobile wireless communications is often modelled as a product of three factors: distance-dependent average path loss, lognormal variation in the local mean power level (shadow fading), and small-scale fading due to movement in the order of a wavelength. Of these three factors, the least well understood is the shadow fading, the lognormality of which is usually explained as a result of multiplication of large number of random attenuating factors in the radio channel. This model is not credible from physical propagation point of view, and is also partly contradicted by measurements. In this paper, we propose an additive clusterbased model for shadow fading. We assume that the received signal is a superposition from several scattering clusters. It is shown that if the distribution of the local mean cluster powers satisfy certain mild statistical conditions, the shadow fading of the received signal will be approximately lognormal. We also present measurement results that support the theory.