Signals and Systems - Electrical Engineering

736 CHAPTER 12: Applications of Discrete-Time Signals and Systems

spectrum using a code to differentiate the different users. The objective of these three techniques is

to maximize the radio spectrum utilization.

Spread Spectrum—A Famous Actress Idea

Not surprisingly, the first mention of the use of frequency hopping, a form of spread spectrum, for secure communications

came from a patent by Nikolas Tesla in 1903. As you recall, Tesla is the world-renowned Serbian-American inventor, and

physicist, and mechanical and electrical engineer who pioneered amplitude modulation.

The most celebrated invention of frequency-hopping was, however, that of Hedy Lamarr and George Antheil, who in 1942

received a U.S. patent for their “secret communications system,” in which they used a piano-roll for frequency-hopping.

This was during World War II, and their idea was to stop the enemy from detecting or jamming radio-guided torpedoes.

To avoid the jammer, in frequency-hopping spread spectrum the transmitter changes in a quasi-random way the center

frequency of the transmitted signal. Hedy Lamarr (1913–2000) was an Austrian-American actress and communications

technology innovator, while George Antheil (1900–1959) was an American composer and pianist. Their patent was never

applied, and it would be many years before the technology was actually deployed. Ms. Lamarr conceived the idea of hopping

from frequency to frequency just as a piano player plays the same notes, but in different octaves. Their concept eventually

provided the basis for the CDMA airlink, which Qualcomm commercialized in 1995. Today, CDMA and its core principles

provide the backbone for wireless communications, thanks to the creative vision of an extraordinary woman [70, 74, 62].

Spread Spectrum

A spread-spectrum system is one in which the transmitted signal is spread over a wide frequency

band, much wider than the bandwidth required to transmit the message. Such a system would take a

baseband voice signal with a bandwidth of a few kilohertz and spread it to a band of many megahertz.

Two types of spread-spectrum systems are:

n Direct-sequence system:A digital code sequence with a bit rate higher than the message is used to

obtain the modulated signal.

n Frequency-hopping system:The carrier frequency is shifted in discrete increments in a pattern

dictated by a code sequence. We will not consider this here.

Direct-Sequence Spread-Spectrum

Suppose the messagem(t)we wish to transmit is a polar binary signal, and that a spreading codec(t),

also in polar binary form, is modulated by the message to obtain the modulated baseband signal

x(t)=m(t)c(t) (12.21)

The sequencec(t)is pseudo-random, unpredictable to an outsider, but that can be generated deter-

ministically. Each user is assigned uniquely one of these sequences—that is, the spreading codes

assigned to two users are not related at all. Moreover, the bit rate ofc(t)is much higher than that of

the message. As in many other modulation systems, the modulated baseband signalx(t)has a much

higher rate than the message, and as such its spectrum is much wider than that of the message that is

already wide given that it is a sequence of pulses. This can also be seen by considering thatx(t)as the

product ofm(t), andc(t), its spectrum is the convolution of the spectrum ofm(t)with the spectrum

ofc(t)with a bandwidth equal to the sum of the bandwidths of these spectra.