Combinatorial Approach to the Performance Analysis of Signal Demodulation in Mobile Telecommunications


We shall consider the physical layer of mobile communications, i.e. one link between
a Base Station (in GSM, Node-B in UMTS) and a mobile station (User Equipment UE)
in UMTS. An important measure for the analysis of this link's performance is the probability 
that a bit is decoded incorrectly at reception, otherwise called Bit Error Rate (BER).

A classical formula due to Barrett ('87) giving a closed form of this probability is
computationaly unstable in some cases that reflect some real-life situations. Rewriting
it in a such a way that it becomes stable, one obtains an expression containing certain
symmetric functions.

Their decomposition in the base of Schur functions gives rise to a set  of interesting combinatorial 
objects (combinations of Young tableaux). Those in turn can be bijectively mapped to sets of 0-1matrices 
that yield easier to analysis and allow to obtain stable closed form expressions for the probability in 
question in several cases where Barrett's formula fails to do so.