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of UMTS network equipment.
CDMA is part of a general ¬eld of communications known as spread spectrum. Spread
spectrum describes any system in which a signal is modulated so that its energy is spread
across a frequency range that is greater than that of the original signal. In CDMA, it is the
codes that perform this spreading function, and also allow multiple users to be separated
at the receiver. The two most common forms of CDMA are:

• Frequency hopping (FH): with FH, the transmitted signal on a certain carrier frequency
is changed after a certain time interval, known as the hopping rate. This has the effect
of ˜hopping™ the signal around different frequencies across a certain wide frequency
range. At a particular instant in time, the signal is transmitted on a certain frequency,
and the code de¬nes this frequency. This system is used for many communications
systems, including the 802.11b wireless LAN standard and Bluetooth. These systems
both use the unlicensed 2.4 GHz band, which is inherently subject to interference due
to the large number of radio systems sharing that band, not to mention the effects of
microwave ovens. By using a large number of frequencies, the effect of interference on
the signal is substantially reduced, since the interference will tend to be concentrated in
a particular narrow frequency range. FH is also employed in military communications,
where the secrecy of the code and the rejection of interference in the form of a jamming
signal make it extremely effective.

• Direct sequence (DS): with DS, a binary modulated signal is ˜directly™ multiplied by
a code. The code is a pseudo-random sequence of ±1, where the bit rate of the code
is higher than the rate of the signal, usually considerably higher. This has the effect of
spreading the signal to a wideband. At the receiver, the same code is used to extract
the original signal from the incoming wideband signal. A bit of the code is referred to
as a chip, and the de¬ning parameter for such a system is the chip rate.

DS-CDMA is the form used for the air interface in UMTS, known as wideband CDMA
(WCDMA), with a chip rate of 3.84 Mchip/s.
The origin of the spread spectrum and CDMA concept is generally accredited to the
1930s Austrian-born Hollywood actress Hedy Lamarr, and her pianist George Antheil,
who ¬led a US patent for a ˜Secret Communications System™ in 1942 at the height
of the Second World War. The system used a piano type system to perform frequency
hopping on a signal. Neither of the two ever made any money from the patent, which
subsequently expired.

2.7.1 DS-CDMA signal spreading
According to information theory, as the frequency spectrum a signal occupies is expanded,
the overall power level decreases. In CDMA, the user signals are spread up to a wideband
by multiplication by a code. Consider a narrowband signal, say, for example, a voice call.
When viewed in the frequency spectrum, it occupies some frequency and has some power
level, as illustrated in Figure 2.10(a). Once the frequency is spread across a wideband,
the total power of this signal is substantially reduced.
Now consider that another user has the same procedure performed on it and is also
spread to the same wideband. The total system power is increased by a small amount
as the two users are transmitted at the same time. Therefore, each new user entering
the system will cause the power of the wideband to increase. The idea is shown in
Figure 2.10(b).




freq freq
wideband wideband
(a) (b)

Figure 2.10 Signal spreading

At the receiver, the process of extracting one user is performed; the mechanism of how
this can be implemented is described in the next section. The regenerated signal needs to
be retrieved with enough power that it can be perceived above the level of the remaining
spread signals. That is, it needs to be of a suf¬cient strength, or margin, above the rest of
the signals so that the signal can be accurately interpreted. Considering this as a signal
to interference ratio (SIR), or carrier to interference (C/I) ratio, the noise affecting one
signal is the remaining spread signals that are transmitting at that frequency. This SIR is
classi¬ed in CDMA as Eb /N0 . Literally, this means the energy per bit, Eb , divided by
the noise spectral density, N0 . However, it is really a measure of the minimum required
level the signal should be above the noise which is contributed by the other transmitting
users. For mobile device measurements of the quality of the signals from the network, it
uses a pilot channel, which is broadcast by each cell. The mobile device measures Ec /I0 ,
the energy level of this pilot channel, Ec , compared to the total energy received, I0 .
Another important characteristic is the rejection of unwanted narrowband noise signals.
If a wideband signal is affected by a narrowband noise signal, then since the spreading
function is commutative, the despreading operation while extracting the wanted signal
will in turn spread the narrowband noise to the wideband, and reduce its power level.
The rejection of the interference effects of wideband noise from other users is the role of
convolution coding, which is described in Section 2.9.1.
This implies that the important factor that will affect how easily signals can be inter-
preted after they are despread is the power level in the system. The lower the power that
the original signals are transmitted with, the lower the noise in the system. It is therefore
essential that each user in the system transmits with an optimum power level to reach
the receiver with its required power level. If the power level is too high, then that user
will generate noise, which in turn affects the performance of all the other users. If there
is too little power, then the signal which reaches the receiver is of too low quality, and it
cannot be accurately ˜heard™.
An analogy to this idea is a party at which all the guests are talking at the same time.
At some point, with too many guests, the overall noise level rises to a point where none
of the guests™ individual conversations can be heard clearly.
There are two solutions to the problem of noise levels. First, an admission control
policy is required that monitors the number of users and the noise level, and once it
reaches some maximum tolerable level, refuses admission of further users. In a cellular
system, such admission control needs to be considered not only for one cell, but also
for the effects that noise levels within that cell have on neighbouring cells. In the party
analogy, the effect on the neighbours should be considered. In conjunction with admission
control, load control should also be implemented to try to encourage some users to leave
a cell which has too many users, and consequently in which the noise level is too high.
The second solution is to implement power control. Each user needs to transmit with
just enough power to provide a clear signal at the receiver above the noise ¬‚oor. This
should be maintained regardless of where the users are located with respect to the receiver,
and how fast they are moving. Power control needs to be performed frequently to ensure
that each user is transmitting at an optimum level. For more details, please refer to
Section 2.8.2.
In direct sequence spread spectrum the signal is spread over a large frequency range.
For example, a telephone speech conversation which has a bandwidth of 3.1 kHz would

be spread over 5 MHz when transferred over the UMTS WCDMA system. The bandwidth
has increased but the information transfer rate has remained constant. This is achieved by
using a technique which introduces a code to represent a symbol of the transmitted mes-
sage. A code is made up of a number of binary digits (bits), each one of which is referred
to as a chip. The whole code consisting of all of the chips representing a symbol takes
up the same time span as the original symbol. Thus if a single symbol is represented by
a code of 8 chips, the chip rate must be 8 — the symbol rate. For example, if the symbol
rate were 16 kbps then the chip rate (assuming 8 chips per symbol) would be 128 kbps.
This higher data rate requires a larger frequency range (bandwidth). Figure 2.11(a) illus-
trates the data (symbols) to be spread (1001). Figure 2.11(b) indicates the 8-chip code
˜10010110™. Figure 2.11(c) combines parts (a) and (b) into a single waveform which
represents the original data but which has been spread over a number of chips. This
combining is achieved through the use of an exclusive-OR function.
The ratio of the original signal to the spread signal is referred to as the spreading factor
and is de¬ned as:

Spreading factor (SF) = chip rate/symbol rate

Thus in the above example, the SF is 8. Hence, variable data rates can be supported
by using variable length codes and variable SF to spread the data to a common chip rate.
When considering CDMA systems, it is useful to de¬ne how the different signals
interact with each other. Correlation is de¬ned as the relationship or similarity between
signals. For pulse-type waveforms, such as CDMA codes, the cross-correlation between
two signals is de¬ned as:

R12 („ ) = …1 (t)…2 (t + „ ) dt

where R12 is the correlation between two signals …1 and …2 , and „ is their relative
time offset.
For the code to be effective, the receiver must know the speci¬c code (in this case
10010110) which is being used for transmission and it must also be synchronized with
this transmission. On reception the receiver can then simply reintroduce the correct code
which is multiplied with the incoming signal and reproduce the actual symbol sent by the
transmitter. The receiver also needs to know the actual number of chips that represent a

1 symbol 1 symbol 1 symbol 1 symbol

(a) 1 chip



Figure 2.11 Spreading of data

symbol (spreading factor) so that the chips can be regenerated to the sent symbol through
averaging the value of the chips over the symbol time. This is achieved through integration,
where the chips are summed over the total time period of the symbol they represent.
The principle of correlation is used at the receiver to retrieve the original signal out of
the noise generated by all the other users™ wideband signal. Consider Figure 2.12. Notice
that the logic levels of 0 and 1 have been replaced by the binary coded real values 1 and
’1, respectively. The original data is coded and the resulting signal is transmitted. At the
receiver, the received signal is multiplied by the code and the result is integrated over the
period of each baseband bit to extract the original data. Since the receiver has four chips
over which to integrate, the procedure yields a strong result at the output.
However, consider now that the receiver does not know the correct code. Then the
integration process will result in a signal which averages to around zero (see Figure 2.13).
For both of these, the relative strength of the desired signal and the rejection of other
signals is proportionate to the number of chips over which the receiver has to integrate,
which is the SF. Large SFs result in more processing gain and hence the original signals
do not need so much transmission power to achieve a target quality level.
As can be seen, the longer the symbol time (i.e. lower data rate and higher chip rate),
the longer the integration process, thus the higher the amplitude of the summed signal.
This is referred to as processing gain (Gp ) and is directly proportional to the SF used.
For example, if the symbols were spread over 8 chips then the Gp will be 8; if spread
over 16 chips, Gp would be 16. This means that the processing gain is higher for lower
data rates than for higher data rates, i.e. lower data rates can be sent with reduced power
since it is easier to detect them at the receiver. The processing gain can be used for link

data 1 -1 1 1 -1
code 1 -1 -1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1
data x code 1 -1 -1 1 1 1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1
transmission across air interface
known code
1 -1 -1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1
at receiver



Figure 2.12 Correlation at a CDMA receiver

data 1 -1 1 1 -1
code 1 -1 -1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1
data x code 1 -1 -1 1 1 1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1
transmission across air interface
use of
incorrect -1 1 -1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 1 -1 -1 1



Figure 2.13 Correlation with incorrect code

budget calculations as follows:

Gp = 10 log10 chip rate/data rate

Here, the data rate of the application can be used instead of the symbol rate, since it
may be considered that what is lost in terms of bandwidth by the process of convolution
coding and rate matching is gained again in terms of signal quality improvement.
As an example, consider that for voice, 12.2 kbps are required. The processing gain
for this may be calculated as follows:

Gp = 10 log10 3.84 Mbps/12.2 kbps = 25 dB


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