Wireless Network Design: Optimization Models and Solution ...

40 Dinesh Rajan
the transmission of user m. For instance, in a CDMA network using non-orthogonal
codes and a frequency reuse of 1, Km = M − m ∀m ∈ M. In a GSM system, Km will
only include mobiles from cells other than bm and which use the same frequency
as m.
The average channel attenuation between mobile m ∈ M and base station b ∈
B is given by hmb. Let the transmit power of mobile m equal Pm and the receiver
noise at base station b be denoted by Nb. Thus, the received signal-to-interference
ratio SIRmb for mobile m at base station b is given by,
SIRmb =
Pm|hmb| 2
∑i∈Km Pi|hib| 2 + Nb
(2.28)
As noted before, the obtained average SIR is proportional to a variety of performance
metrics including throughput, and bit error rate. Thus, a typical performance
requirement might be to ensure a desired minimum level of signal-to-interference
ratio, SIR ¯ is achieved for each user. There is clearly a conflicting requirement for
each user. For instance, increasing Pm results in an increase in the ratio SIRmb but
also decreases the ratio SIR jk for all users j such that m ∈ Kj. Thus, if each user
employed a greedy approach of increasing their power when their received SIR is
Fig. 2.18 Basic block diagram of an OFDM system.