Code Division Multiple Access

David Chamberlain

December 10, 2010

EE235, Autumn 2010

1 Introduction

A multiple access system allows multiple signals to be transmitted over a mediumwithout harmfully interfering with each other. As demand for wireless devicescontinues to grow, more and more signals need to be transmitted through theatmosphere as radio waves, necessitating advanced multiple access systems.

Traditional multiple access systems require that different users transmitwithin unique segments of the frequency spectrum, a system know as FrequencyDivision Multiple Access (FDMA), or that they transmit at different times, asystem known as Time Division Multiple Access (TDMA). In contrast, CodeDivision Multiple Access (CDMA) allows multiple users to share the same fre-quency band at the same time without harmful interference [3]. At first glance,this may seem to be impossible, but the rest of this document will provide asimplified explanation of how CDMA works.

2 Spread Spectrum

A major difference between CDMA and FDMA is that CDMA signals are in-tentionally spread out in frequency, so they occupy a bandwidth much largerthan would normally be required to send the same data. The power needed tocommunicate over a given distance remains the same, but because the poweris spread over a large bandwidth, the spectral power density is much lower[3]. This means that to a traditional FDMA receiver, the CDMA signal wouldappear to be background noise as shown in Figure 1.

CDMA increases the bandwidth (spreading in frequency) by multiplying thebaseband signal by a signal with a much higher data-rate (called a chip code),before modulating it for transmission [3]. Each bit of the higher frequency signalis called a chip, and there are many chips for each data bit, as shown in Figure2. Note that for the purpose of transmission, the zeros in the binary data andchip code are converted to -1s.

1

Figure 1: Spectral power density of FDMA vs CDMA

Data Signal

Chip Code

Spread signal

T

T

b

c

Figure 2: Data signal multiplied by chip code. Adapted from [1].

3 Synchronous CDMA

If multiple signals are being spread over the same frequency band as explainedin the previous section, how can the receivers extract the desired signal? Thekey is the selection of chip codes which are used for the spreading. Consider thattwo vectors are said to be orthogonal if their dot product is zero. This conceptcan be extended to signals by viewing them as very long vectors. Then the dotproduct of two signals is just the sum of the products of the corresponding bitsin each signal.

For synchronous CDMA, the chip codes for each signal are mutually orthog-onal [4]. If two data signals a and b are to be transmitted using synchronousCDMA, then they are multiplied by two orthogonal chip codes x and y, respec-tively. The signal heard by a receiver would be the sum ax+ by. To recover thesignal a, the receiver de-spreads the signal, that is it multiplies by the associated

2

chip code x:

x (ax + by) = a|x|2 + bx y = a|x|2

because x and y are orthogonal. |x|2 is a positive constant, so the original datafrom a is recovered by mapping positive values to a binary 1 and negative valuesto a binary 0, while zero values are interpreted as no data at all. Note that thisis a greatly simplified version of what actually happens, but it demonstrates thebasic principle. For more detailed examples, see [4].

4 Asynchronous CDMA

Because we cant guarantee that the chip codes will remain orthogonal if they areshifted in time relative to each other, synchronous CDMA requires careful timingsynchronization between the circuits that spread the different signals. Thissynchronization is not practical in the case of many mobile transmitters, suchas in a Personal Communication System (PCS) [3]. In this case, Pseudo-Noise(PN) (also called pseudo-random) chip codes are used instead of orthogonal chipcodes, in a system called Asynchronous CDMA.

Because the PN codes are not orthogonal, their dot product will not be zero.However, the statistical correlation between different PN codes will be very low,so the dot product of two different codes x and y would be small compared to|x|2. Thus the de-spread signal in the receiver contains both the desired signalplus some background noise created by the small amount of correlation betweenthe correct PN code and the other codes.

The more signals that are present, the more PN codes would be needed andthe higher the probability that two PN codes would correlate over any givendata bit. Thus the background noise in the de-spread signal becomes strongeras the number of signals increases. This places a practical limit on the numberof signals in a given frequency band, because the background noise eventuallyovertakes the desired signal. Although it is beyond the scope of this document,it can be shown that the number of signals that can be transmitted in a givenfrequency band is much greater with asynchronous CDMA than with eitherFDMA or TDMA, which is the primary advantage of CDMA [2].

References

[1] Vicente, Marcos, File:Generation of CDMA.svg, Jan 12 2010. [Online,accessed 9-Dec-2010]. Available: http://en.wikipedia.org/wiki/File:Generation_of_CDMA.svg

[2] Viterbi, Andrew J., Introduction, in CDMA: Principles of Spread Spec-trum Communication. New York: Addison-Wesley, 1995, pp. 4-8.

[3] Buehrer, R. Michael, Multi-user Communications, in Code DivisionMultiple Access [Online; accessed 09-Dec-2010]. Available: http://www.morganclaypool.com/doi/pdf/10.2200/S00017ED1V01Y200508COM002

3

[4] Wikipedia, Code Dividion Multiple Access, Wikipedia: The Free En-cyclopedia, Dec 9, 2010. [Online; accessed 9-Dec-2010]. Available: http://en.wikipedia.org/wiki/Cdma

4

IntroductionSpread SpectrumSynchronous CDMAAsynchronous CDMA