##
Properties
of PN Sequence:

In CDMA user signal is
multiplied by pseudo random sequence. This sequence must be known by the
transmitter and also by the receiver to be able to realize synchronisation and
despreading. To be used in real systems the sequence should be able to be
constructed from a finite number of randomly pre-selected parameters. On the
other hand the PN sequence should look like noise

A PN sequence has three following properties:

·
The number of ‘1’s and the number of
‘0’s in a PN sequence are only different by one.

·
Run lengths of zeroes or ones are the
same as in a coin flipping experiment. Half of the run lengths are unity,
one-quarter are of length two, one-eighth are of length three and a fraction
1/2^{n} of all runs are of length *n*.

·
If the sequence is shifted by any
non-zero number of elements, the resulting sequence will have an equal number
of agreements and disagreements with the original sequence.

A
deterministic generated sequence that nearly satisfies these three
requirements, within extremely small difference, will be a pseudorandom
sequence.

A
PN sequence can be generated by a linear shift register. Fig 3.2 shows a linear
shift register sequence generator.

In each clock cycle the
register shifts all its contents to the right. The sequence a_{n}
can be written as

a_{n}
= c_{1 }a_{n-1} + c_{2 }a_{n-1}
+ ^{...} + c_{r }a_{n-r}

where c_{1} to c_{r}
are the connection variables (0 for no connection and 1 for connection ).