  In this paper we describe a model for calculating the aggregate interference
encountered by primary receivers in the presence of randomly placed cognitive
radios (CRs). We show that incorporating the impact of distance attenuation and
lognormal fading on each constituent interferer in the aggregate, leads to a
composite interference that cannot be satisfactorily modeled by a lognormal.
Using the interference statistics we determine a number of key parameters
needed for the deployment of CRs. Examples of these are the exclusion zone
radius, needed to protect the primary receiver under different types of fading
environments and acceptable interference levels, and the numbers of CRs that
can be deployed. We further show that if the CRs have apriori knowledge of the
radio environment map (REM), then a much larger number of CRs can be deployed
especially in a high density environment. Given REM information, we also look
at the CR numbers achieved by two different types of techniques to process the
scheduling information.
