01-10-2012, 04:31 PM
Code Division Multiple Access (CDMA) - The Concept of signal spreading and its uses in communications
CDMA.pdf (Size: 123 KB / Downloads: 42)
Properties of spreading codes
Multiplication with the code sequence which is of a higher bit rate, results in a much
wider spectrum. The ratio of the code rate to the information bit rate is called both the
spreading factor and the processing gain of the CDMA system. In IS-95, the chipping
rate is 1.2288 and the spreading factor is 64. Processing gain is usually given in dBs.
To distinguish the information bit rate from the code rate, we call the code rate, chipping
rate. In effect, we take each data bit and convert it into k chips, which is the code
sequence. We call it the chipping rate because the code sequence applied to each bit is as
you can imagine it chipping the original bit into many smaller bits.
Gold sequences
Combining two m-sequences creates Gold codes. These codes are used in asynchronous
CDMA systems. Gold sequences are an important class of sequences that allow construction of long
sequences with three valued Auto Correlation Function ACFs. Gold sequences are
constructed from pairs of preferred m-sequences by modulo-2 addition of two maximal
sequences of the same length.
Gold sequences are in useful in non-orthogonal CDMA. (CDMA 2000 is mostly an
orthogonal CDMA system) Gold sequences have only three cross-correlation peaks,
which tend to get less important as the length of the code increases. They also have a
single auto-correlation peak at zero, just like ordinary PN sequences.
The use of Gold sequences permits the transmission to be asynchronous. The receiver can
synchronize using the auto-correlation property of the Gold sequence.
More codes
IS-95 and IS-2000 use two particular codes that are really m-sequences but have special
names and uses. These are called long codes and short codes.
Long code
The Long Codes are 242 bits (created from a LFSR of 42 registers) long and run at 1.2288
Mb/s. The time it takes to recycle this length of code at this speed is 41.2 days. It is used
to both spread the signal and to encrypt it. A cyclically shifted version of the long code is
generated by the cell phone during call setup. The shift is called the Long Code Mask
and is unique to each phone call. CDMA networks have a security protocol called CAVE
that requires a 64-bit authentication key, called A-key and the unique ESN (Electronic
Serial Number, assigned to mobile based on the phone number). The network uses both
of these to create a random number that is then used to create a mask for the long code
used to encrypt and spread each phone call. This number, the long code mask is not fixed
but changes each time a connection is created.
Short code
The short code used in CDMA system is based on a m-sequence (created from a LFSR of
15 registers) of length 215 – 1 = 32,767 codes. These codes are used for synchronization in
the forward and reverse links and for cell/base station identification in the forward link
The short code repeats every 26.666 milliseconds. The sequences repeat exactly 75 times
in every 2 seconds. We want this sequence to be fairly short because during call setup,
the mobile is looking for a short code and needs to be able find it fairly quickly. Two
seconds is the maximum time that a mobile will need to find a base station, if one is
present because in 2 seconds the mobile has checked each of the allowed base stations in
its database against the network signal it is receiving.
Each base station is assigned one of these codes. Since short code is only one sequence,
how do we assign it to all the stations? We cyclically shift it. Each station gets the same
sequence but it is shifted.
From properties of the m-sequences, the shifted version of a m-sequences has a very
small cross correlation and so each shifted code is an independent code. For CDMA this
shift is 512 chips for each adjacent station. Different cells and cell sectors all use the
same short code, but use different phases or shifts, which is how the mobile
differentiates one base station from another. The phase shift is known as the PN Offset.
The moment when the Short code wraps around and begins again is called a PN Roll.
If I call the word “please” a short code, then I can assign, “leasep” to one user, “easepl”
to another and so on. The shift by one letter would be my PN Offset. So if I say your ID
is 3, then you would use the code “aseple”.
Pilot Channel
Let’s start with how the base station establishes contact with the mobiles within its cell. It
is continually transmitting an all zero signal, which is covered by a Walsh code 0, a all
0’s code. So what we have here is a one very long bit of all zeros. For this reason, the
pilot channel has very good SNR making it easy for mobiles to find it. This all zero signal
is then multiplied by the base stations’ short code, which if you recall is the same short
code that all base station use, but each with different PN offset. Pilot PN Offsets are
always assigned to stations in multiples of 64 chips, giving a total of 512 possible
assignments. The 9-bit number that identifies the pilot phase assignment is called the
Pilot Offset.