Power bandwidth trade-off for sensory and ad-hoc wireless networks

We look at the power bandwidth trade-off in random sensory and ad-hoc wireless networks with n users and r/spl les/n/sup 1/2/ simultaneous source/destination pairs. Under a specific protocol, we show that the minimum power required for maintaining an achievable scaling law of R/sub sum/=/spl Theta/(f(n)) for the sum-rate in the network, scales like /spl Theta/(f(n)/n/sup 1/2/). The required bandwidth B in this case is of order /spl Theta/(f(n)/r). It is also proved that the minimum achievable energy per information bit (E/sub b//N/sub 0/)/sub min/ for this protocol, scales as /spl Theta/(1/n/sup 1/2/) and in this case the spectral efficiency is nonzero and is of constant order.