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This chapter is from the book

CDMA Explained

Spread Spectrum

Signal and Noise Spectrums

CDMA technology either does or will play an important role in current and future cellular systems, so I figured it might be nice to understand how it works.

To understand how CDMA works, you will need to understand how spread spectrum works. Before you can understand how spread spectrum works though, you will need to be able to visualize what the spectrum of a signal and the spectrum of noise look like. Figure 7–9a is a graphical depiction of a signal's spectrum. The horizontal axis represents the frequency and the vertical axis is the signal's strength or power. Where the signal comes to its peak is the location of the carrier frequency (on the horizontal axis, represented by the fc). This is representative of a single conversation in the old analog cellular systems. In such a case, the signal is about 30 kHz wide and the location of the carrier is in the 900 MHz range.

Figure 7–9 Signal spectrum and noise spectrum.

Did You Know

Spread spectrum technology has really been around since World War II, where it was used to avoid signal detection and jamming by the enemy. The reason it is just now beginning to appear in the commercial arena is more a result of the improvements in and cost reduction of integrated circuits.

Figure 7–9b is the spectrum of noise. In this case there is no signal present and all you see is a low-level, fairly flat but randomly varying noise signal. This low-level, random signal exists everywhere and is the result of all the various RF and non-RF signals floating around in the air. The way an RF engineer views a signal or noise spectrum is with a piece of equipment called a spectrum analyzer.

Think back to the analogy of wireless communications being like mailing a letter. In this analogy, the letter is the information signal and the envelope is the RF carrier signal. Modulation is used to combine the letter (information) and the envelope (the carrier). In the previous discussions of wireless communications, I assumed that only one party could transmit and receive at a given frequency within a given geographical location. In that version of the analogy, there was no need to address the envelope because there was only one party who could receive it. (Maybe there was only one other house in the neighborhood.) This is not the case with spread spectrum. With spread spectrum, many parties can transmit and receive at a given frequency within a given geographical location. (There are a lot of houses in the neighborhood and they can all mail letters to each other.)

Direct Sequence

Spread spectrum is analogous to imprinting an address onto the wireless signal. How does spread spectrum pull off this little magic trick? It modulates the signal again. The type of spread spectrum used in CDMA is called direct sequence spread spectrum or DSSS. In DSSS, the spread spectrum modulation takes place before the "RF modulation" (that is the one that puts the information signal onto the RF carrier). By the way, did I neglect to mention that spread spectrum only works with a digital information signal?

Did You Know

There are other types of spread spectrum in addition to DSSS. There is frequency hopping spread spectrum or FHSS (which you will learn more about shortly), and time hopping spread spectrum or THSS. So far nobody's invented bunny hopping spread spectrum (BHSS?), but give them time.

DSSS imprints the address by logically multiplying the digital information signal by another, higher frequency digital signal. This other digital signal is known as a pseudo random noise or PN signal. The reason it is called random is that the 1s and 0s appear to have no discernible pattern. More importantly, if the PN signal were modulated onto an RF carrier, its signal spectrum would look just like that of noise (Figure 7–9b). The reason the PN signal is called pseudo is because as random as the bit stream appears, in reality it repeats itself over and over. Of course quite a few random-appearing 1s and 0s go by before the pattern repeats itself. The 1s and 0s in the PN signal are called chips and the frequency of the PN signal is called the chipping rate. This PN code is generated thanks to the magic of digital signal processing.

The other aspect mentioned above is that the PN signal is at a much higher frequency than the information signal. For instance, in the case of voice over CDMA, the digital bit stream for voice is on the order of 64 Kbps and the chipping rate of the PN signal is on the order of 1.25 million chips (bits) per second.


Figure 7–10 depicts graphically the result of logically multiplying a digital voice signal by a PN signal. The top of Figure 7–10 is just the digital bit sequence 101101, which is part of a digital signal that represents a telephone conversation.

Figure 7–10 Spreading of an information signal by a PN signal.

The middle of Figure 7–10 is the PN signal. Notice that the 1s and 0s appear to be random and that the frequency is much higher (in this case about six times) than the voice signal. The bottom of Figure 7–10 is the result of "multiplying" the top two signals. In fact this multiplying is really just an exclusive OR function, which is very easy to understand because there are only two rules. In places where both of the signals above it are the same (either both high or both low), the bottom signal is high. In places where both of the signals above it are different (one high, one low), the bottom signal is low.

There are three very important things about this new "spread" signal. First, it is at a much higher frequency than the original voice signal. Second, it is random-like, which means that in a plot of its spectrum, it would look just like noise. And third, all of the information contained in the original voice signal (101101) is still contained within it.

Why is this new signal considered a spread signal? Because the original signal occupied perhaps only 30 kHz of bandwidth. This new signal occupies on the order of 1.25 MHz of bandwidth (it is at a much higher frequency). The signal has been spread over a larger bandwidth. The real trick, however, is not this spreading of the original signal over a wider bandwidth. The real trick is that as the signal is spread over a wider bandwidth, its power level drops.

The top of Figure 7–11 is a graphical simplification of this phenomenon. Figure 7–11a shows a signal 30 kHz wide, located somewhere in the 900 MHz range with some amount of energy represented by the gray area under the rectangle. (This is representative of the signal shown in Figure 7–9a.) Since spreading the signal does not add any energy to the signal (only an amplifier can do that), the gray area under the spread signal must be the same, and therefore, as the signal gets wider, the power drops lower as shown in Figure 7–11b.

Figure 7–11 Spreading and de-spreading of signals.

In reality, this new lower spread signal appears to be noise, just like that in Figure 7–9b. In fact this new signal is noise, with one notable exception. It still contains the original voice information. And because it is noise, up to a certain limit, a whole bunch of these noise signals can be piled on top of one another. The result is just more noise, and noise is noise, assuming you can still retrieve the original information signal. How does one retrieve the original voice information? I'm glad you asked.


The original signal is retrieved from the noise the same exact way it was spread: by logically multiplying it by the same exact PN signal. This restoring of the information signal is referred to as de-spreading.

The top of Figure 7–12 is the same exact spread signal as the one at the bottom of Figure 7–10 (take my word for it). The only difference is that the signal in Figure 7–10 is coming out of the sending transmitter and the one in Figure 7–12 is going into the receiving receiver. Assuming for the moment that the same exact PN signal that was used to spread the signal in the transmitter also exists in the receiver, it can be used to de-spread the signal.

The middle of Figure 7–12 is the same exact PN signal as the one in Figure 7–10. By applying the same exclusive OR function to the top two signals in Figure 7–12 a miracle happens: the original voice signal (101101) reappears. Isn't this stuff amazing?

This may be all well and good, but since all of the signals in a CDMA system occupy the same bandwidth at the same time, what happens to the other, unwanted signals that just happen to make their way into our handset?

Figure 7–12 De-spreading of an information signal.

Unwanted Signals

Let us see what happens when someone else's signal makes it into our handset. There are two possibilities here. We can receive someone else's CDMA (spread) signal or we can receive someone else's narrowband (unspread) signal from a non-CDMA system. In either case, we will attempt to de-spread it with our PN signal.

The top of Figure 7–13 shows a CDMA voice signal spread with someone else's PN signal. When we attempt to de-spread this signal with our PN signal (middle of Figure 7–13), what results is the signal at the bottom of Figure 7–13. While it may not be totally evident from the figure, the bottom signal is still a high-frequency, random signal, which means it is not de-spread. This signal appears as noise to our receiver and so it gets ignored.

When a narrow band signal enters our mobile unit, the attempt to de-spread it just ends up spreading it because the two processes are identical. Once again this spread signal appears as noise and is ignored by our receiver. This phenomenon is depicted in Figure 7–11c and Figure 7–11d. Figure 7–11c shows two signals entering our receiver: the wanted spread signal (in gray) and the unwanted narrowband signal (clear). After the de-spreading (Figure 7–11d), the wanted signal becomes narrow band and the unwanted signal become spread. The bottom line is that any unwanted signal that enters our receiver, spread or not, will ultimately be ignored by our receiver.

For a CDMA system to work properly, everybody has to use a different PN signal. But in reality, everybody uses the same PN signal (which just repeats itself over and over). How is that possible? Everyone uses the same PN signal but they all start at a different bit (chip). Refer back to the middle of Figure 7–13. Suppose that very first bit (a high) is labeled bit number 1. The second bit (a low) is bit number 2 and so on. Would you believe me if I told you that two, otherwise identical PN signals that start at different bits are completely different PN signals? I'll prove it.

Figure 7–13 Attempting to de-spread someone else's signal.

The top of Figure 7–14 is our original spread signal, which was spread with our very own PN signal. The middle of Figure 7–14 is our PN signal shifted by one bit. It now starts at bit number two rather than bit number one. Attempting to de-spread our signal with this one-bit shifted PN signal results in the signal shown at the bottom of Figure 7–14, which clearly is not our original 101101 bit stream. This signal is still a high-frequency, random noise-like signal, which is ignored by our receiver. In fact, this noise signal is just the result of our spread signal entering someone else's receiver and being multiplied by their PN signal (one-bit shifted from ours). And their receiver ignores this "noise" signal.

So in a CDMA system, there is just one long, continuously looping PN signal, which is used by all the basestations and all the mobile phones and the only difference is that each conversation starts at a different bit. It follows that all of the basestations need to have their PN signals synchronized to a master clock. What facilitates the synchronization of all basestations to a master clock? Go back and read the section on GPS.

Not only do all the basestations need to be synchronized, but the sender and receiver in a particular call need to be synchronized to each other. How is this accomplished? Through the use of a synchronization channel.

Figure 7–14 De-spreading a signal by a one-bit shifted PN signal.


When a conversation is sent wirelessly in a CDMA system, more than just the voice data is sent wirelessly. In fact, the wireless information sent is broken up into different channels, or packets of information. From the basestation to the mobile unit there are four of these unique packets of information. From the mobile to the basestation, there are two.

The top of Figure 7–15 shows how the information sent from the basestation to the mobile unit in a CDMA system is broken down into channels. The pilot channel, which is continuously transmitted by the basestation, is used for several things including power management and to aid in handoff. As mentioned previously, all cellular telephony requires power management. It is even more important in CDMA because for the system to work properly, the received power level from every cellular phone must be the same. (If not, signals received from close-in phones will swamp out those received from far away ones by raising the combined noise level too high.) The pilot signal from each basestation has a different time offset (from the master clock), which uniquely identifies each base-station and therefore helps the mobile switching center know where each mobile unit is located.

The sync (or synchronization) channel helps synchronize the basestation's PN signal to that of the mobile unit, among other things. The paging channel is used to page the mobile unit. Recall that when a cellular phone first turns on, it listens for a signal from the basestation. The paging channel is what it listens for and it contains overhead and subscriber-specific information. Finally, the downstream information contains one or more traffic channels, which contain the voice signal.

The bottom of Figure 7–15 shows how information is sent from the mobile unit to the basestation. The access channel is used by the mobile to initiate a call, respond to a paging channel, and to update location information. Just like the downstream, there are also traffic channels to carry the voice and data information.

Figure 7–15 Downstream and upstream CDMA channels.

There you have it. A general understanding of direct sequence spread spectrum and a specific understanding of how CDMA systems uses it to cram a lot of users into a fixed amount of bandwidth.

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