Wireless Network Design: Optimization Models and Solution ...

108 Eli Olinick
levels (possibly less than P target) as long as the SIR for each connection is at least
SIRmin. Allowing mobiles to reduce transmission power can lead to more efficient
use of system resources, however the resulting mathematical programming model
is a nonlinear integer program that is extremely difficult to solve to provable optimality.
In Sections 5.3.2 and 5.3.3 we build up to the comprehensive planning
model depicted in Figures 5.1 and 5.2. The model presented in Section 5.3.2 extends
ACMIP to maximize profit subject to government-imposed minimum-service
requirements. This model is then extended in Section 5.3.3 to include network infrastructure
(i.e, MTSOs, PSTN gateways, and the backbone links). We discuss the
trade-off between profit and power in Section 5.3.4 and conclude by outlining other
design considerations that researchers have incorporated into the these models in
Section 5.3.5.
5.3.1 SIR-Based Power Control
In their computational study Amaldi et al. observed that SIR values often exceed
SIRmin in solutions to ACMIP [7]. That is, after the tower location and subscriber
assignment decisions have been made it may turn out that an acceptable SIR can be
achieved even if signals from certain test points are received at their assigned towers
at power levels less than P target. This means that system resources can be used more efficiently
by allowing mobiles at appropriate test points to transmit at reduced power
levels. This improves the total transmission power term in the objective function
(5.4) and reduces interference systemwide thereby increasing capacity. For a given
solution to ACMIP, an iterative power-control algorithm given by Yates [57] can
determine transmission powers at the test points to minimize total transmit power
under minimum SIR constraints. While this approach cannot be directly embedded
in ACMIP, it can be approximated by using a more sophisticated SIR-Based Power
Control model. As an alternative to assuming that each connection is received at
P target, Amaldi et al. [7] propose a model in which the transmission power of a mobile
at test point m is a decision variable, pm. In this model, the signal from test point
m is received by tower ℓ at power level pmgmℓ, and the total strength of all signals
received at tower ℓ (assuming all test points are covered) is ∑i∈M di pigiℓ. The model
assumes that there is a thermal or background noise of η (typically -130 dB) at each
tower location. If test point m is assigned to tower ℓ, then the SIR for the connection
is
pmgmℓ
∑i∈M dipigiℓ + η − pmgmℓ
. (5.14)
Thus, the model imposes the following set of constraints for each allowable test
point assignment:
xmℓ(∑ di pigiℓ + η − pmgmℓ) ≤
i∈M
pmgmℓ
SIRmin
∀m ∈ M,ℓ ∈ Lm. (5.15)