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Spread Spectrum

Spread spectrum is probably today’s most important wireless networking protocol.  As unlikely as it might seem, a 26-year-old Hollywood movie star, a screen siren named Miss Hedy Lamarr, invented spread spectrum.  In 1942 during World War II, she and a partner (who was a music composer and producer) received a US patent (#2,292,387) for inventing spread spectrum.  The essential insight is to spread a signal across many channels over a much wider bandwidth than would normally be used and therefore to make jamming or intercepting that signal much more difficult.  This idea has military significance because assuring reliable communications during a battle has high priority.  Almost immediately, the US government realizing the import of her ideas snapped up the patent and classified it as ‘top secret.’  After her film career when the scientific community began to discover her contributions, she received several prestigious awards as a premiere inventor.

Every telecommunications protocol standard has its own language and terminology, and this is no exception.  The concept of spread spectrum is based upon a sequence of digits known as a ‘spreading code.’  At the source, this code is used to spread a single stream of signals across a range of frequencies; the same code is used at reception to ‘de-spread’ the signals back into the original form.  Spreading the signal in this manner uses a lot more bandwidth for each transmission.  Therefore, on the surface, this approach would appear to waste a critical resource.  But there are very significant advantages here.  Spread spectrum does prevent military opponents from jamming battlefield communications or torpedo guidance systems.  And these same characteristics provide commercial networks with effective immunity from various forms of interference, noise, and distortion.  Spread spectrum protocols can also be used to help secure signals, because a receiver cannot decode the incoming signal without the original spreading code.  Most importantly, several users can use overlapping ranges of high bandwidth frequencies at the same time with very little effective operational interference.  These properties make spread spectrum especially desirable for cellular telephony applications.

User Code

There are three forms of spread spectrum, frequency hopping spread spectrum, direct sequence spread spectrum, and code division multiple access.  The last of these is the newest, and most important, and is used in modern cellular telephony.  Essentially, CDMA systems mix a long binary spreading code called a ‘user code’ with a small amount of communications data to produce a combined signal that is then spread over a very wide range of frequencies.  The same user code is also used at the destination to reconstruct the original digital signal.  In this approach, every device that connects to the system (such as a digital mobile cell phone) is dynamically assigned a unique user code when a connection is established.  This code is typically more than a hundred digits in length.  The number of digits used in the code is called the ‘spreading factor.’  The code uses binary digits with each digit being interpreted as plus or minus one.  So, each active device in the system has associated with it a unique code made up of a long sequence of intermixed plus ones and minus ones.

When a digital cellular device communicates with a cellular tower, the user code is transmitted across multiple channels to indicate a ONE, and its complement is transmitted to indicate a ZERO.  (The complement of the user code is the same code with all the bits flipped; that is, with all the pluses and minuses reversed.)  Both the device and the tower use the user code and its complement to communicate with one another in this fashion.  The number of channels used for transmission is the same as the spreading factor, which is the number of digits in the user code, so the entire pattern of plus and minus ones arrives at the destination for each transmission, in unison each on a different frequency.  The receiver then decodes the incoming signal to get back the original bit.  A stream of these transmissions effectively sends a bit stream of information between the cellular device and the tower, as required.

However, the cellular airways can be jammed full of traffic.  Using spread spectrum means that channels are shared and allocated bandwidths overlap.  So, how does a receiver figure out if a message it hears in the air is meant for it, and also what is being sent, a zero or a one?  This is the ingenious part of CDMA.  All it requires is a bit of mathematics.  The computer in the cellular tower knows the user codes for all active devices in its area because it assigned those codes originally.  The codes are just long sequences of plus or minus ones.  And they can be treated as vectors, and manipulated using vector algebra.  When a transmission is received, the computer can quickly calculate a dot-product between the received code pattern and each of the active user codes for all the devices in its area to get answers to these questions.[1]

Historically, one of the greatest problems with cellular telephony has been finding a way to share bandwidth efficiently.  Failure to share dramatically limits the capacity of a cellular system and severely restricts the number of devices that an individual cell tower can support at any one time.  Spread spectrum protocols change all of this.  And these limitations are lifting.  The future of cellular telephony lies with advanced forms of spread spectrum.  And to think it all began with Miss Hedy Lamarr!


[1] A dot-product of two vectors is a scalar.  It is the summation of position by position multiplications.  For example, to multiply these two four-dimensional vectors, (1,-1,-1,1) times (1,1,-1,1), do the following:  (1×1) + (-1×1) + (-1x-1) + (1×1) = 2.  So, the scalar ‘2’ equals the dot-product of these two vectors.

 

Charles K. Davis, Ph.D.
Professor; Cameron Endowed Chair of Management & Marketing

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© Copyright by Charles K. Davis, 2014

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