Wireless Network Design: Optimization Models and Solution ...

5 Mathematical Programming Models for Third Generation Wireless Network Design 105
of the number of mobile users who simultaneously request service at that location.
The attenuation factors are assumed to be measured empirically or derived from an
appropriate propagation model for the planning region (e.g., the Hata model [31]).
Note that throughout this presentation the terms “subscriber” and “mobile user” are
used synonymously to refer to users of the CDMA network (i.e., customers who
subscribe to the service provided by the network owner). We also use the terms
“subscriber assignment” and “test point assignment” interchangeably since demand
is modeled using test points.
The tower location and subscriber assignment decisions are represented in the
model by binary indicator variables. The variable yℓ is equal to one if tower ℓ is
selected for the design and zero, otherwise. Likewise xmℓ is equal to one if, and only
if, subscribers at test point m are assigned to tower ℓ.
The core model in [7] assumes a power-control mechanism by which connections
from mobile handsets to towers must be received at a guaranteed power level
of P target. Thus, a handset at test point m will transmit with power level P target/gmℓ in
order to send a signal to tower ℓ that is received at power level gmℓ Ptarget
g mℓ = P target. The
model further assumes that the maximum transmission power of a mobile handset
is P max, and so test point m may only be assigned to tower ℓ if P target/gmℓ ≤ P max. The
subset of towers to which test point m may be assigned is denoted by Lm = {ℓ ∈
L : P target/gmℓ ≤ P max}, and the set of test points that could be assigned to (covered
by) tower ℓ is denoted by Mℓ = {m ∈ M : P target/gmℓ ≤ P max}. In a CDMA-based network
every mobile-to-tower connection can, in theory, interfere with every other
mobile-to-tower connection. Consequently, the total strength of all signals received
at tower location ℓ from all mobile users in the system is P target ∑m∈M ∑ j∈Lm dm g mℓ
gm j xm j
and the interference with respect to a given connection assigned to the tower is
P target ∑m∈M ∑ j∈Lm dm g mℓ
gm j xm j − P target [7]. The SIR for a connection to tower ℓ, denoted
by SIRℓ, is thus given by
SIRℓ =
Ptarget Ptarget ∑m∈M ∑ j∈Lm dm gmℓ gm j xm j − Ptarget 1
=
∑m∈M ∑ j∈Lm dm gmℓ gm j xm
. (5.1)
j − 1
To ensure a minimum acceptable SIR of SIRmin for each session assigned to tower
ℓ, test points must be assigned to towers in such a way that SIRℓ ≥ SIRmin. That is,
a feasible solution that uses tower ℓ must satisfy the constraint
which is equivalent to the linear constraint
where s denotes 1 + 1
SIR min .
1
∑m∈M ∑ j∈Lm dm gmℓ gm j xm j − 1 ≥ SIRmin, (5.2)
gmℓ
∑ ∑ dm
m∈M
gm j∈Lm j
xm j ≤ s. (5.3)