Wireless Network Design: Optimization Models and Solution ...

2 Introduction to Wireless Communications 21
Similar to the discrete time channel, for a continuous time additive white Gaussian
noise channel with bandwidth W the capacity can be calculated as
CAWGN = W log(1 + P/N0W)bits/sec (2.12)
Further, the capacity of wireless fading channels has been well investigated under
several conditions [10]. The concept of channel capacity has also been extended to
multiuser channels. We illustrate the idea in 2 different settings.
1. Uplink Channel: Consider a simple uplink channel in which multiple users are
communicating with a single base station. Again, consider the simple Gaussian
noise channel in which the received signal ybs(n) at the base station is given by
ybs(n) =
K
∑
i=1
xi(n) + zbs(n) (2.13)
where xi(n) is the signal transmitted by user i and zbs is the effective noise at the
base station receiver, which is modeled as having a Gaussian pdf. Similar to the
capacity of a single user channel, in this case, the capacity region is defined as
the set of all K−tuples of achievable rates for the various users.
Fig. 2.7 Capacity of AWGN channel and maximum possible transmission rates with various modulation
schemes.