Calculating Uplink Cell Load

The load placed on a cell is described in terms of load factor, which is some
fraction of the maximum theoretical load. In other words, a load factor of 0.5
equates to 50 percent cell loading. The load placed on the cell can be viewed
as the sum of the loads generated by all users of the cell. Alternatively, the
total load factor is the sum of the load factors contributed by each user as
shown in Equation 12-1:
(Equation 12-1)
where Lj is the load factor of a single user (j) and we assume N users in the
cell. Lj is simply the fraction of the total power at the base station that user
j generates. Thus,
Lj  Sj /Stotal (Equation 12-2)
Alternatively
Sj  Lj  Stotal (Equation 12-3)
The signal power (Sj) for a given user needs to be such that the Eb/No
requirement is met for the service that the user wishes to obtain. Moreover, the Eb/No is a function of the total interference in the cell. Eb/No can be
expressed as follows:
(Eb/No)j  Processing gain  [Sj /I] (Equation 12-4)
where I is the total interference and is equal to the total received power at
the base station minus Sj (the signal power from user j). This can be rewritten
as
(Eb /No)j  [C/aj  Rj][Sj /(Stotal
Sj )] (Equation 12-5)
where C is the chip rate, aj is the activity factor (such as about 65 percent
for voice including DPCCH overhead and 100 percent for data), Rj is the
user data rate, and Stotal is the total received signal power at the base station.
If we then solve for Sj, we get
Sj  Stotal /[1  C/(aj  Rj(Eb/No)j)] (Equation 12-6)
Substituting from Equation 12-2, we get
Lj  1/[1  (C/(aj  Rj)(Eb/No)j)] (Equation 12-7)
Using Equation 12-1, we now get
(Equation 12-8)
In addition to the interference generated by users on the local cell, there
will also be interference caused by transmissions from users in nearby cells.
If we define the quantity i to the ratio of nearby cell interference to the
interference in our own cell as follows:
i  [nearby cell interference]/[local cell interference] (Equation 12-9)
then the total load factor for the local cell is
(Equation 12-10)
Load factor  11  i 2 # a
N
j1
Lj  11  i 2 # a
N
j1
1> 31  1C>1aj # Rj1Eb>No2j2 2 4