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). po w er freq freq po w er (a) (b) wideband narrowband signal wideband margin spread signals

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 sufficient 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 classified 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 measuresEc/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 floor. 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 thespreading factor

and is defined 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 define how the different signals interact with each other. Correlation is defined as the relationship or similarity between signals. For pulse-type waveforms, such as CDMA codes, thecross-correlation between two signals is defined as:

R12(τ)=

υ1(t)υ2(t+τ)dt

where R12 is the correlation between two signals υ1 and υ2, and τ is their relative

time offset.

For the code to be effective, the receiver must know the specific 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 1 chip

(a)

(b)

(c)

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 theGp 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

1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1 1 -1 1 -1 4 -4 integration known code at receiver data x code code data

transmission across air interface

1 -1 -1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1

1 -1 1 -1 -1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 1 -1 1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 -1 -1 1 1 -1 -1 1 -1 1 1 1 -1 -1 1 4 -4 integration use of incorrect code data x code code data

transmission across air interface

Figure 2.13 Correlation with incorrect code

budget calculations as follows:

Gp=10 log10chip 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 log103.84 Mbps/12.2 kbps=25 dB

Thus higher data rates require more power and the limiting factor here is that the mobile devices can only supply of the order of 200–300 mW. Therefore to achieve higher data rates, the mobile device must be situated physically closer to the base station.