AKL
et al.: MULTICELL CDMA NETWORK DESIGN
715
For the general case where the capacity in each cell may be
different, the derivative of
with respect to
is
if
if
.
(18)
The above derivatives will be used in the solution to the opti-
mization problems (31) and (34).
B. Sensitivity with Respect to Transmitted Pilot-Signal Power
In a CDMA network, it is important to control the intercell
interference. Increasing the pilot-signal power of a base sta-
tion expands the coverage area of that cell, thereby increasing
the number of users in that cell and thus the intracell interfer-
ence. On the other hand, it will decrease the number of users in
the adjacent cells, thus decreasing the intercell interference on
this base station. The opposite effect takes place in the adjacent
cells. The intercell interference into these cells increases and
the intracell interference decreases. Therefore, we wish to find
the optimal values of the transmitted pilot-signal powers that
will maximize the capacity of the entire network. Let
and
be the coordinates of base station and
the transmitted
pilot-signal power of base station . For brevity, we use the no-
tation
,
. Let
denote the set of base stations
adjacent to base station . Given a path-loss model, the region of
cell ,
, is completely determined by
,
,
,
,
, and
for
.
For example, consider two adjacent cells
and . Let
be
the point on the straight line connecting
and
, where the
received pilot power from base station equals the received pilot
power from base station . Then, using the COST-231 model for
path loss [25]
(19)
where
is the distance between base stations
and
and
is a constant that depends on the average base-station antenna
height and the average mobile antenna height.
is the region
enclosed in the polygon whose sides pass through
and are
perpendicular to the line connecting
to
for
(ig-
noring edge effects).
To find the optimal values of the transmitted pilot-signal
powers that will maximize the capacity of the entire network,
we calculate the derivatives of the network capacity with
respect to
s and use them in an optimization algorithm. They
capture the effect of increases in the transmitted pilot-signal
power of one base station on the capacity of the entire network.
The derivative of
with respect to the intercell interference
factor
is
(20)
if
and
, and zero otherwise. From (4)
(21)
where
(22)
The region of cell ,
, is a function of the independent vari-
ables
,
,
, and
, where
. Thus the partial deriva-
tive of
with respect to
is given by
(23)
if
or
, and zero otherwise. The intercell interference
factors
for
, are a function of
.
Also, the intercell interference factors
for
and
, are a function of
. Thus, the derivative
of
with respect to the transmitted pilot-signal power
is
(24)
For the general case, the derivative of
with respect to
is
if
and
otherwise.
(25)
The derivative of
with respect to
is
(26)
The above derivatives will be used in the solution to the opti-
mization problems (32) and (34).
