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3.3.2 The OVSF Code Tree
The UMTS air interface uses a constant chip rate of 3.84 Mchips/s. If the spreading
factor was also constant, all users of a cell would have to communicate with the network
at the same speed. This is not desirable, as a single cell has to support many users with
many different applications simultaneously. While some users may want to simply make
voice calls, which require only a small bandwidth, other users might want to place video
calls, watch some mobile TV (video streaming) or start a web‐surfing session. All these
services require much higher bandwidths, and thus using the same spreading factor for
all connections is not practicable.
The solution to this problem is called Orthogonal Variable Spreading Factors, or
OVSF for short. While in the previous mathematical representation the spreading
factors of both users were of the same length, it is possible to assign different code
lengths to different users at the same time with the approach described below.
As the codes of different lengths also have to be orthogonal to each other, the codes need
to fulfill the condition shown in Figure 3.7. In the simplest case (C1, 1), the vector is one
dimensional. On the next level, with two chips, four vectors are possible of which two are
orthogonal to each other (C2, 1 and C2, 2). On the third level, with four chips, there are 16
possible vector combinations and four that are orthogonal to each other. The tree, which
continues to grow for SF 8, 16, 32, 64, and so on shows that the higher the spreading factor
the greater the number of subscribers who can communicate with a cell at the same time.
If a mobile device, for example, uses a spreading factor of eight, all longer codes of the
same branch cannot be used anymore. This is due to the codes below not being orthog-
onal to the code on the higher level. As the tree offers seven other SF 8 spreading factors,
it is still possible for other users to have codes with higher spreading factors from one of
the other vertical branches of the code tree. It is up to the network to decide how many
codes are used from each level of the tree. Thus, the network has the ability to react
dynamically to different usage scenarios.

C = (1)
1,1
C = (1,1) C = (1,−1)
2,2
2,1
SF = 2
C = (1,1,1,1) C = (1,1,−1,−1) C = (1,−1,1,−1) C = (1,−1,−1,1)
4,2
4,3
4,1
4,4
SF = 4
C = …
8,2

SF = 8
Subtree cannot be used if
the code above has been
SF = 16 allocated to a subscriber.
…
SF = 512
Figure 3.7 The OVSF code tree.