Code division multiple access

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Code division multiple access (CDMA) is a multiplexing technique found in the context of wireless systems. It is also known as spread spectrum.

CDMA Defined

Any discussion of spread spectrum must begin with a note about its inventors; Hedy Markey (aka Hedy Lamarr), and George Antheil. Ms. Lamarr, an electrical engineer by education, is better known as an actor and Mr. Antheil, also an engineer, is better know as the “bad boy of music” for his antics as a composer in Paris. Both had escaped the Nazi regime and emigrated to the U.S. before the Second World War. Using their engineering talents they created what is called today frequency hopping spread spectrum (FHSS). To them the challenge was to create an anti-jamming scheme for radio-controlled torpedoes. In the original patent document, they discuss using 88 frequencies (the same as the number of keys on a piano) that are synchronized as they hop by using a type of player piano roll at the transmitter and receiver. They were granted U.S. patent #2,292,387. To close the story, Lamarr and Antheil gave the patent rights to the U.S. government, but the jam-proof torpedo was never created. In the 1950’s, spread spectrum began to be used in satellite communications by Loral Space Systems, which was later acquired by Qualcomm.

The basic premise of spread spectrum is to make the signal look like noise and thereby render the transmission to be secure. When done correctly, the actual signal looks like a small blip in the noise floor. It is often called noise modulation. While Lamarr and Antheil invented the frequency hopping version, the more popular version is direct sequence spread spectrum.

The scheme is quite simple. Make each user look like a unique component of the noise on the channel. The limiting factor then becomes the amount of interference created by each user and the magnitude of the noise floor. The whole process also relies on precise power control because power is a source of interference. This should be obvious as a shouting person creates more noise than a whispering person. Finally, lower power operation yields better battery life.

Both of the spread spectrum techniques are lumped under the access method called code division multiple access (CDMA). The code comes from the fact that each user’s uniqueness is accomplished by the unique code they are assigned. These codes are usually based on binary polynomials.

It is often difficult to grasp how spread spectrum works without doing the mathematics. However, the equations that govern spread spectrum are beyond the scope of this discussion. Instead, we will look an example that actually puts the math into a more understandable format.

CDMA Without the Math

Imagine that you are an English speaking person in the transit lounge at Heathrow International Airport in London. Your code in this scenario is English. When you tune your ears to that code you can hear the English speaking conversations in the room, the other conversations are just background noise. As more people enter the lounge, the noise level increases to a point at which you can no longer hear the English speaking conversation—the maximum number of users has been reached. An increase in the noise floor (background noise) from a jet taking off will also disrupt your ability to hear the English speaking conversations even though you know the code. Finally, low power is better than high power because shouting people create an excessive amount of noise and also limit the total number of users.

The Mathematics of CDMA

The Mathematics of CDMA

The visual contains a simplified view of CDMA system operation. First, the RAKE structure leads to processing gains over a single antenna structure since a significant amount of interference can be tolerated before the combined signals do not yield a definitive result. Second, the signal-to-noise ratio for a user can be easily expressed as the energy per bit divided by the noise plus interference. The interference is from external sources whereas the noise is from the energy of all the other bits being transmitted at the same time. Raising the energy per bit helps on the one hand but increases the noise on the other. So, if everything is kept in balance and outside interference is minimized, the system works very well.

The last item concerns the classic near/far problem of CDMA. The math is difficult but the concept is easy if we remember that CDMA originated in the satellite communications industry. Basically, a satellite is so far away that we have to shout at it to get the signal to travel 22,300 miles. Since the probability is low that two shouting users on the Earth will be close to each other, a shouting user typically does not bother other users. Now, put the users in a one-mile diameter cell (i.e., close together). In this case, shouting is not good because it interferes with other users. One solution is to increase the bandwidth and hence the separation between the users—not practical because of limited bandwidth and low bandwidth efficiency. The ideal solution is to control the output power (i.e., no shouting allowed) as a function of the distance between the mobile user and the base station. Power controlled CDMA, as it is called, minimizes the noise from adjacent users.


A CDMA call starts with a 9600 bps encoded voice signal. This signal is spread to a rate of 1.23 Mbps, which means that each bit in the original bit stream is replicated 128 times in the spread data signal.

The spread data bits are transmitted along with all of the data bits from other users in the same channel. At the receiving end, the RAKES gather in the spread signals, and the digital signal processors sort the signals by the appropriate spreading code. When the receiver pairs up a spreading code with a received bit that was spread by that same code, a slight increase in power occurs. In this way it is somewhat easy to pair up the spreading codes with the correct bits at the receiver and recreate the 9600 bps voice signal.

External Links


<mp3></mp3> | Code division multiple access (CDMA)

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