Distribution of signal-to-interference ratio in wireless networks

Keith Briggs keith.briggs@bt.com keithbriggs.info
BT Technology, Services, and Operations
Second supervisor: Samuel Johnson

Scenario: a system of small cells (home LTE femtocells, nodes), with their positions modelled by a Poisson point process in the plane:

λ average points per unit area
μ(A) is the area of a region A
Pr [k points in region A] = exp(−λμ(A))*(λμ(A))/k!

System model: a UE (user equipment: phone, tablet, etc.) is placed at random,
and connects to the nearest node. All other nodes become interferers. Pathloss
is r^−γ (2<γ<4), and there is Rayleigh fading. What is the distribution of SIR?

Signal-to-interference ratio (SIR) is the critical parameter determining
overall system performance.  Haenggi and others have shown that an exact
formula for the distrubution of SIR can be written in terms of a Gauss
hypergeometric function.  In this project we want to see how this exact result
can be extended.

Project outline

In this project we will extend these exact results in several ways:
- Situations in which the PPP is not homogeneous: the node density varies with position
- Situations where the nodes transmit with varying powers
- Situations where there are two sets of nodes of different types (femto and macro cells)
- Extension to three dimensions, for modelling multi-storey buildings
- (Hard) non-independence of node positions

Potential outcomes:
- Construct generalized PPP models of node distribution in dense deployment of small 4G cells
- Obtain analytic results useful to engineers and validate these against simulations