denote the set of M SUs contending for access. When jth SU
is allocated a particular channel i in a networkm, it is assumed
that SU creates a unit interference denoted by hjm with
the PUs. The amount of interference depends on the channel
condition. It is desired to limit the maximum interference
to the PUs of mth network below a specied threshold m.
Assume that a cost fm is associated with every mth network;
this means if a jth SU joins an mth primary network the cost fjm
will be charged. The objective is to minimize the overall cost
and the interference caused by assigning SUs to different
networks, subject to the constraints of each network. Thus,
the objective function for the optimization is expressed as:
Minimize V Q(x) D
XM
jD1
XN
mD1
(hjm C fjm)xjm;
Subject to:
XN
mD1
xjm D 1; 8 j D 1; 2; : : :M;
XM
jD1
hjmxjm m; 8 j D 1; 2; : : :N;
jxjm Cim; 8 i; j; and m;
pjxjm fm; 8 j and m;
xjm 2 f0; 1g; (1)
where Q(X) is the objective function