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AN INTRODUCTION TO SPREAD SPECTRUM CHARLES E. COOK AND HOWARD S. MARSH

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Reliable detection at the communications receiver when interference is present.

M ODERN military communications systems are , increasingly adopting the digital method of transmitting information. In a digital communica- -

tions (or data) link, the information to be sent is represented by a sequence of electronic pulses. In the simplest form of digital signal transmission, these pulses are referred to as binary digits, or “bits.” Each pulse, or bit, is the smallest amount of data that can be communicated, and the messages to be sent ‘are composed of larger sets of these bits. The manner in which message information is imparted to the data bits is the subject of information modulation, a topic well covered in most basic texts on communications.” The subject addressed here is the reliable detection, at the communica- tions receiver, of the individual bits when interference is present, so that the information carried by the sequence of data bits can be recovered. The time duration of a data bit implies a minimum bandwidth capability for the communica- tions link. Thus, it is important to understand the basic concept of bandwidth involved in any criteria for reliable reception.

Basic Concepts of Bandwidth The notion of bandwidth is fundamental to any discussion

of communications, particularly spread spectrum communi- cations. Bandwidth is simply the range of frequencies contained in the signal. When a signal is modulated onto a radio frequency carrier wave, the radio frequency bandwidth is often referred to as the radio channel width.

Spread Bandwidth Spread spectrum systems make use of radio frequency

signal bandwidths which far exceed the minimum bandwidth required to transmit their digital data. That is, 1 kb/s data may be modulated into a bandwidth of 1 MHz rather than 2 kHz. The signal’s spectrum is therefore “spread” over a radio frequency channel greater than that necessary to

*See, for example, M. Schwartz, W. R. Bennett, and S. Stein, Communications Systems and Techniques, McCraw-Hill, 1966.

transmit the information. This can provide significant protection against interference such as jamming, as discussed later [ 1-31.

Information Bandwidth

Since data rate and minimum bandwidth are related, it is possible to define the information bandwidth of any digital bit stream. Digital communications systems generally require radio frequency bandwidths somewhat greater than the digital data rates. In many cases, a factor of 2: 1 t a n be used to express bandwidth in terms of bit rate. If the bit stream contains 1 kb/s of data, the information bandwidth is 2 kHz, using the 2:l relationship just cited. In general, the information bandwidth is equal to the minimum signal bandwidth necessary to support the given data rate.

Channel Bandwidth

The channel bandwidth is the radio frequency spread which contains the radio signal. Channel bandwidth must always be equal to or greater than information bandwidth. Otherwise, the channel could not support the required information transmission, and at least some of the data would be lost. On the other hand, channel bandwidth may be arbitrarily larger than the information bandwidth, without compromising the signal’s information rate.

Two common techniques for spreading the signal spectrum are discussed in this paper. One is known as pseudorandom noise modulation (or direct sequence modulation) and the other i s known as frequency hop. Each of these techniques will spread the radio signal’s power over a broad channel, far in excess of the minimum bandwidth necessary to transmit the data in the signal. Used either individually or in conjunction with one another, pseudorandom modulation and frequency hop can provide very powerful defenses against interfering signals.

A Criterion for Information Reception The effectiveness of a digital communications system in the

presence of interference is often measured by the rate at which

0163-6804/83/0300-0008 $01.00 @ 1983 IEEE

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MARCH 1983 .

errors in the reception of the information bits are made. This is referred to as the bit error rate (BER). If the interference is assumed to be gaussian noise, the BER is a minimum in any system in which the signal-to-noise ratio of the individual bits is a maximum. Theoretical analysis has shown that the signal-to-noise ratio is optimized for white gaussian noise interference when the receiver is implemented as a “matched filter” [4,5].

The characteristics of matched filters can be designated by either a frequency response function or a time response function, each related to the other by a Fourier transform operation. In the frequency domain, the matched-filter transfer function H(f) is the complex conjugate function of the spectrum of the signal tdbe processed in an optimum fashion. Thus, in general terms

H(f) = kS”(f)exp (-j27rTd) (1)

where S(f) is the spectrum of the input signal s(t), and Td is a delay constant required to make the filter physically realizable. The normalizing factor, k, and’the delay constant are generally ignored in formulating the underlying significant relationship, usually expressed as

H(f) = S”(f). (2)

The corresponding time domain relationship between the signal to be operated upon and the matched filter is obtained from the inverse Fourier transform of H(f). This leads to the result that the impulse response of the matched filter is a replica of the time inverse of the known signal function. Thus, if h(t) represents the matched-filter impulse response, the general relationship equivalent to (1 ) is

h(t) 7 ks(T, - t). (3)

As above, the arbitrary delay term Td can be ignored to point out the basic important relationship

h(t) = ks(-t). (4)

Figure 1 illustrates the conjugate relationship of the signal spectrum and its matched filter frequency and phase response. When the receiver is implemented in this manner, the signal-to-noise ratio can be expressed as

( s / N ) = &/No) (5) where

Eb = the energy in joules (watt-seconds) contained in each

N o = the density (watts/hertz) of the noise interference

and the ratio (watt-seconds)/(watts/hertz) is dimensionless, as a signal-to-noise ratio should be.

The type of noise referred to so far in the discussion is that which is randomly generated within the communications receiver, analogous to “snow” on a TV picture or background hiss in a weakly received radio station. When a communica- tions receiver is employed in a military application, noise and other types of interference can be deliberately introduced into the receiver by an external jamming source. When this is done, spread spectrum signals can be used in the communi-

bit

cations system to offset the effect of the external jammer. Following is a description of spread spectrum techniques useful in combating various types of interference; the example of a pseudonoise spread spectrum signal illustrates the operation of a matched filter receiver.

Reducing the Effect of Noise Jamming The utility of spread spectrum techniques can be illustrated

easily in the case of noise jamming, since this is most directly related- to the problem of signal-to-noise ratio optimization mentioned in the previous section.

The total power generated by a jamming system is constrained by the size of the jamming equipment which can be mounted on the jamming vehicle. This is generally independent of the finer details of the jamming format, and thus jammers are considered to be power limited systems. In the case of a noise jammer, the total power output under continuous noise jamming conditions is given by

P , = B W Nj watts (6)

where

BW = effective bandwidth of the noise jamming, and Nj = spectrum density (watts/hertz) of the noise jamming

If the bandwidth of the jamming signal is equal to or greater than that of the signal bit being received, the signal-to-noise ratio at the receiver output can be expressed as

( S / N ) = Eb/(No f Nj) . (7),

If the jamming noise is much larger than the receiver noise, this is approximated by

( S / N ) = Eb/Nj (8)

and there is a subsequent large increase in the BER of the system, often to such an extent that the system becomes useless.

How can the effect of this type of jamming on the system BER be minimized? It will be noted from (6) that if the jammer were forced to have a wider bandwidth, it would have to reduce its noise power density, N j , under the power limited condition. This would increase the effective signal-to-inter- ference ratio at the receiver given by (8). The use of spread spectrum signal techniques ‘is intended to accomplish precisely this result.

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Spreading the Bandwidth of the Information Bit In order to force the jammer to lower its noise power density

by increasing its bandwidth, it seems logical that the signal bandwidth must also be widened by some spectrum spreading method. Figure 2 illustrates one method of doing this by chopping up an information bit into smaller increments of time which are designated as “chips.” In order that these chips do not blend into each other and thus wipe out.the spectrum widening inherent in an individual chip they are given discrete identities by imposing a phase code sequence upon them, as shown in Fig. 1 , where<‘+><dicates a Oo phase reference and ‘-’ indicates a lJOo phase reference. These phase code sequences are designated as pseudonoise (PN) codes because of certain mathematical properties they possess[6,7]f These make them appear somewhat noiselike if intercepted by a receiver which does not know the exact code sequence. It is sufficient to note that the fact that this PN sequence is known at a particular receiver permits the use of a matched filter so that the desired information bit is enhanced in the receiver relative to the interfering noise.

The way the individual chips in the “chip-coded” bit are identified is critical to the operation of the matched filter receiver (also known as an optimum receiver since it yields the optimum signal-to-noise ratio if properly “matched” to the signal). In the example shown in Fig. 2, the chips within the bit are coded in accord with the short PN sequence, +++-+--. The optimum matched filter that processes this sequence is shown in Fig. 3 , and is comprised of an electrical delay line tapped at delay intervals which correspond to the chip time duration. In a purely digital receiver, this delay line may take the form of a shift register similar to those used in computers. Each tap of this delay line feeds into an arithmetic operator matched in sign to a specific coded chip in the sequence. In this figure, these are shown as an array of phase shifters (it has been noted that the + and - values of the coded chips can be realized electronically as two signal phase shifts which differ by 180O). It can be seen that the signs of the phase shifters in the array, viewed from right to left, yield the same PN sequence as that of the chip code on the information bit. The outputs of the array of phase shifters are fed to a common

f \

* Pickholtz, et al. [8 ] provide an excellent summary of the properties of PN codes (or sequences) and their generation by feedback shift registers. These sequences are relatively long (Zk - 1 elements for a k-stage shift register) before repeating and the number of ones and zeroes, indicated as ‘+’ and ‘-’ in the above discussion, differ by one element.

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addition device to produce the matched filter output. Figure 4 presents a simplified block diagram of a communications system to illustrate the conceptual relationship of spread spectrum waveform generation and matched filter processing in the receiver to the overall system.

How the Matched Filter Functions

When the signal bit is received at the matched filter input, it progresses down the tapped delay line shown in Fig. 3. The chip designated “1” enters the delay line first, followed by chip “2,” and so on. When the entire bit has entered the delay line, chip 1 appears at tap output l’, chip 2 at tap output 2‘, and so on to chip 7 at tap output 7’. As shown’ in Fig. 3, the arithmetic operation produced by the phase shifters on each bit results in phase shifter outputs all having the same sign. Thus, when they appear at the input of the adder under this condition, the output of the adder is seven times the value of a single chip. In terms of electrical signals, the peak voltage level at the matched filter output for this example is seven times the peak voltage level of the chip-coded bit which was. fed into the matched filter. This condition occurs only at the instant in which all the chips and phase shifter signs are perfectly matched. At other times, when the bit is only partially in the delay line, either before or after the instant when all the chips are added “in-phase,’’ the signs of the chips and those of the phase shifters do not match up and the filter output is a smaller value. The result of this process is the waveform, shown in Fig. 5, which has a compressed (compared to the original sequence duration) central triangular spike seven units high and one chip wide at its half-amplitude point. The large central signal is flanked by much lower level responses over an interval twice.that of the coded input signal. It is this narrowing down, or time compression, of the PN coded bit that makes this form of spread spectrum processing effective against other forms of jamming and interference. Although the PN sequences used in practice are generally longer and more complex than the seven-chip example used here, PN sequences -have found widespread application because they are fairly easy to realize with modern digital technology.

Although processing of spread spectrum signals is discussed here in terms of matched filter receivers, equivalent

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MARCH 1983

results can be obtained with a correlation receiver. The correlation receiver provides an undistorted delayed replica of the transmitted signal s(t) for each signal path delay time fd of interest. When the received signal u(f) contains s(f - fd) the correlator output is

= l Y 2 : - td)df + ltd+T (noise)s(t - td)dt. (9)

This 'expression represents the energy in the data bit of duration Tplus the contribution from the correlation between noise and the chip-coded bit. Using (4), the output of the matched filter for the same received signal ~ ( t ) is assuming Td is equal to T,

y(i) = u(r) s(T - t + r ) dr 6' (10)

for fd < t < t d + T. At the sampling time t = fd + T, we have

t d + T

y(td i- T ) =Js(T - td) U ( T ) dr. ( 104 td

Thus, the correlated received signal equals the output of the matched filter at the appropriate sampling instant.

It is at this instant that the matched filter output has reached a maximum. Since the path delay fd is often not known, the correlation receiver must, in principle, have available replica signals for a large range of path delays. Pickholtz, et al. discuss a variety of correlator implementations for PN spread spectrum signals [8].

Figure 6 shows that the correlation process wipes out the coded chip structure of the received signal, thereby collapsing its spectrum to that of the original unspread data bit. Interference spectra, having minimal or no correlation with

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the replica signal, are not collapsed. Thus, a narrow band filter can eliminate most of the interference. If the interference happens to be narrow band to begin with, then the correlation process spreads the interference spectrum in much the same way as the desired signals at the transmitter were spread; this also lets a narrow band filter following the correlator get rid of most of the interference energy. Equations (9) and (10) indicate that either correlation or matched filtering achieve an equivalent advantage, or processing gain, against similar types of interference.

Spread Spectrum Processing Gain I t can be seen that the increase in the voltage level of the

desired information bit at the output of the matched filter provides the physical insight as to why the use of the spread spectrum signal and the associated matched filter results in improved performance against the interfering jammer.

This improvement in performance can be quantified in terms of a processing gain provided by the matched filter. In the PN sequence used for illustration, the peak signal at the matched filter output was increased by a factor precisely equal to the number of chips in the bit. The noise input to the filter, not being modulated by the PN sequence, would not be coherently built up in the same manner, but would increase

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somewhat through the noncoherent summation of the noise passed through the phase shifters to the adder. This results in a processing gain at the matched filter output for this simple case that is given by

Processing gain in dB = 10 log [number of chips per bit]. (1 1)

This describes a peak power gain over the external interference noise (not the receiver thermal noise) experi- enced by the desired information bit. A more general definition that can be applied is

Processing gain = 10 log [chip rate/data rate] dB. ( 1 l a )

If the correlator implementation is used, the improvement in signal-to-noise ratio is given by the ratio of the spread spectrum bandwidth B, to the bandwidth Bn of the narrowband filter following the correlator. Ideally, B , would be matched to the collapsed spectrum width so that

B , - chip rate B, data rate - -

and the optimum processing gain for the correlator is identical to (1 la).”

A spread spectrum figure of merit that is derived from the

+Data or information rate may be expressed in terms of bits or symbols. The value of B, should be appropriate to the unit of information used.

1 processing gain is the jamming-to-signal margin J / S defined by -

( J / S ) d B = [Processing Gain - ( S / N ) & ] d B . (1 3)

where (S/Njmin is the required signal-to-noise ratio (including processor losses relative to the interference) at the processor output to realize the desired BER. Equation (13) indicates the excess of received interference over received signal which can be tolerated at the receiver input.

Assume, for example, that processing gain equals 1000 (30 dB) and that the output signal-to-noise power ratio must be 10: 1 for adequate reception. Thus, signals at the processor output can be detected reliably even when the noise or interference at the input is up to 100 times the input signal power. This is obviously a powerful advantage against interference.

Does the Jammer Really Have to Spread its Spectrum, Too?

The argument for using a spread spectrum signal ,was based on (6). This expression indicated that the jamming power density, and hence jamming effectiveness, would decrease if the jammer could be forced to radiate its available power over a broader bandwidth of frequencies than that occupied by the uncoded information bit alone. The discussion presented in the section titled “A Criterion for Information Reception” indicated how the bandwidth of this bit of information could be spread over a wider band of

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MARCH 1983

frequencies, and the resulting signal processed through a matched filter in the communications receiver.

The question can naturally be asked, What if the jammer does not choose to spread its spectrum, but continues to concentrate its energy in the original bandwidth associated with the uncoded (or unspread) bit? This situation is shown in Fig. 7, where the jammer occupies only a relatively small portion of the total signal spectrum. Narrowband (or tone) interference and wideband noise have, in general, equivalent jamming effectiveness against PN-type signals. However, it would be very straightforward for.the receiver to employ a narrow-band interference elimination filter to get rid of the jamming signal almost completely without seriously de- grading the receiver response to the desired signals. This would be analogous to inserting an Amateur Band frequency trap in a TV set. Thus, if the jammer decides not to spread its spectrum in response to the spread spectrum strategy of the communication system, it could be in a much worse position.

For example, if a narrowband filter ,provided 20 dB of rejection, the effectiveness of the narrowband interference would be approximately 20 dB less than that of the spectrum- matched wideband noise interference. If the interference is more sophisticated than continuous noise transmissions (such as burst-noise or burst-CW) then interleaving and forward error correction may be combined with the use of spread spectrum to minimize the interference effectiveness.

Using Spread Spectrum to Combat Other Types of Jamming or Interference

It was mentioned in the section titled “Spreading the Bandwidth of the Information Bit” that the spread spectrum matched-filter characteristic of narrowing or time-com- pressing the output signal could be effective in combating other forms of jamming or interference. These can be categorized as:

0 impulsive interference 0 multipath 0 repeater jamming 0 mutual interference with other PN codes The effect of the spread spectrum matched filter against

these types of interference is sketched in Figs. 8 and 9. Impulsive noise (such as narrow pulses and lightning strokes) can have the same spectrum bandwidth as the c,hip-coded information bit, but will lack the correct PN code sequence. In this case, as shown in Fig. 8(a), the effect of the matched filter

in the receiver is to smear out and reduce in amplitude (conservation of energy) the interfering uncoded impulses while at the same time building up the peak amplitude of the correctly coded information bit.

Signals that come into the receiver from a multiple bounce propagation path or from a repeater jammer always have some amount of time delay relative to the direct path signal. Thus, as shown in Fig. 8(b), if the time compression produced by the matched filter yields a narrow enough signal at its output, the direct path signal can be separated from any other signal that comes in at a somewhat later time. ’ The effectiveness of this is a function of the bandwidth of the spread spectrum signal, since any multipath or repeater delay less than the chip width will interfere with the direct path signal.

Figure 9 shows how the matched filter for the PN sequence illustrated in Fig. 2 reacts to another (different) PN code of the same length. Since the second PN code is not matched to the receiver filter, it does not build up to the same peak value as the correct signal and thus cannot interfere to the same degree as another signal having the same PN sequence. This makes it possible for several “friendly” spread spectrum communi- cators to operate simultaneously in the same frequency band. Of course, there is.a limit to how many can be on the air at once, since some additive interference results as more users are present. As might be. expected, the number of simul- taneous users is governed by the spread spectrum processing gain.

Where Does Frequency Hopping Fit?

The kind of spread spectrum technique illustrated by the use of a PN sequence produces an instantaneous spreading of the transmitted bandwidth. It may be that the ‘resulting processing gain is still not enough to overcome the effects of some kinds of jammers. It would be possible to use even narrower chip widths (and thus wider bandwidth and more chips per bit), but there is a practical limit to this imposed by the capabilities of the physical devices used to generate spread spectrum signals. .

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An alternative method of forcing the jammer signal to cover a wider spectrum is to randomly hop the transmitted frequency of the information symbol on a symbol-by-symbol basis. This spreads the spectrum sequentially rather than instantaneously. Assuming that the jammer will decide to spread its energy over the entire frequency-hopped spectrum, the potentially available processing gain is then given by

Processing gain = 10 log [hopped bandwidth/information bandwidth]( 14)

However, the jammer may decide to concentrate on just a few of the hopped frequencies, assuming that it is more effective to attempt to cause errors in only some of the information bits. In this case, the effective processing gain realized by the receiver would be less than that given by (14). If the information bit or symbol is also spread by means of PN coding discussed earlier, then the use of both frequency hopping and PN codes provides a processing gain given by

Processing Gain = 10 log [chip rate/date rate] + 1 0 log [hopped bandwidth/chip bandwidth] (14(a))

A system that uses both techniques is referred to as a hybrid. Hybrid spread spectrum systems are useful when a single technique such as PN coding does not provide an adequate J / S margin.

Figure 10 indicates a sequence of 5-bit data words which are frequency hopped on a bit-by-bit basis. The frequencies used to construct a random (or pseudorandom) sequence of hops range from f l to fN, where N is relatively large. In this example, the hopping sequence is not commensurate with the word size. This illustrates the fact that the receiver, perhaps a long distance from the transmitter, must be able not only to synchronize with and track the hopping sequence, but also to demodulate the data in synchronism with the word size. Methods of acquiring and tracking frequency-hopped signals are also discussed by Pickholtz, et al. [8].

The fact that frequency hopping does not provide instantaneous coverage of the broad signal band leads to consideration of the rate at which the hops occur. Clearly, the

faster the hopping, the more nearly the frequency hop approximates true spectrum spreading. Two basic character- izations of frequency hopping are fast frequency hop and slow frequency hop. These are distinguished from one another by the amount of time spent at each discrete frequency before hopping to the next.'

The time scale that normally separates fast'frequency hop from slow frequency hop is the length of time necessary for propagation of the radio signal from the transmitter to the receiver or jammer. Since the speed of propagation is roughly 1,000 feet per microsecond (ft/ps), the time scale is on the order o f 1 0 ps for ranges on the order of several miles.

The two types of frequency hopping are discussed below.

Slow Frequency Hop When slow frequency 'hop is employed, the carrier

frequency remains constant for time periods far in excess of the propagation time. Several milliseconds is a reasonable '

dwell time in this case. This usually allows many data bits to be transmitted at each frequency, and the resulting trans- mitter and receiver equipment is simpler and less expensive than that for a faster frequency hop.

The disadvantage of slow frequency hop is that an enemy can implement smart jammers that could defeat the antijam protection in many instances. This can be accomplished by providing the jammer with a search receiver that scans the signal frequency band and locates the transmission; then the jammer's power can be concentrated at the frequency where the signal is being transmitted. If the jammer can adapt quickly enough, it may be able to follow the slow frequency hop.

On the other hand, slow frequency hop can be used to interleave many frequency multiplexed channels within the same frequency hop band. In this application, each channel could be assigned a unique carrier frequency within the

+Sometimes the number of bits per hop is used to distinguish slow frequency hop from fast frequency hop.

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MARCH 1983

overall band. The frequency assignments would be changed from time to time so that each channel would hop among the frequencies in the band in coordination with the other channels, but in a manner that would appear random to the jammer.

This would make it difficult for the jammer to “zero in” on a specific target signal. That signal would be lost among all the others in the band. The jammer would either have to implement alternate techniques (such as direction finding) to separate the signals or resort to broad-band interference. This latter option would dilute jammer power over the entire frequency hop band and provide antijam protection equivalent to spread spectrum modulation over that bandwidth.

As a consequence, slow frequency hop can be useful either against simple jammers or in conjunction with frequency division multiplexing of many signals in the wide bandwidth range of the hop. In many cases, these features, along with the lower relative cost compared with fast frequency hop, may make this technique attractive.

Fast Frequency Hop

As the name implies, fast frequency hopping involves very rapid retuning of the signal and very short dwell times at each frequency. Generally, a fast hop is applied to defeat the smart jammer’s attempt to measure signal frequency and tune the interference to that portion of the band. To defeat this tactic, the signal must be hopped to a new frequency before the jammer can complete its measurement, retuning, and interference functions.

The required hopping rate is determined by considering time delays introduced by signal propagation to the receiver and jammer, and time delays involved in processing and tuning at the jammer. These delays provide some time “window” during which the signal is virtually immune to smart jamming. The fast frequency hop should dwell for a time short enough to fit within this “window.”

The “safe window” during which’the receiver is free from smart jammer interference is given by the time difference between the arrival of the direct signal and the arrival of the interference. This time difference ( TD) is

where ~

Ti = time for jammer to process intercepted signal, tune’ to correct frequency and commence transmission

Dtj = distance from transmitter to jammer Djl = distance from jammer to receiver Dtl = distance from transmitter to receiver

c = velocity of light

If the dwell time at each signal frequency is less than TD, the interference will arrive after the receiver has hopped to a new frequency and the jammer will be defeated. The correspond- ing fast frequency hopping rate is ~ / T D hops per second.

As an example, to obtain a worst case estimate for To,

assume that the jammer adapts infinitely fast to each frequency change. That is, the quantity Ti becomes zero. Then the value of TD equals the difference in the propagation time along the indirect path from transmitter to jammer and then to receiver and the propagation time along the direct path from transmitter to receiver.

As noted, signal propagation speed is approximately 1,000 ft/ps. This means that a path difference of one nautical mile would correspond to a To of roughly 6 ps. If the frequency hop dwell time is less than 6 ps, the receiver would be defended against all jammers for which the indirect path (through the jammer location) is one nautical mile or more greater than the direct path to the receiver. The frequency hop rate corresponding to 6 ps dwell time is equal to .1.7 X 105 hops per second.

As suggested earlier, the jammer can choose to jam only a fraction of the total hopped band, since it only needs to interfere with a sufficient number of the hops to exceed the desired BER. To deal with this problem, a frequency hopped system will rely on powerful error correcting codes [9] that allow information from the unjammed frequencies to be used in aiding the jammed frequencies. Consequently, error detecting and correcting codes are usually integral parts of any pseudorandom frequency hopped system. When error correction codes, pseudorandom chipping, and pseudo- random frequency hop are combined in a communications system, the result can be very significant protection. against external noise, unintentional interference, and intentional jamming.

Other forms of coherent spread spectrum signals are based on frequency modulation, multilevel phase modulation (as compared to the simple binary +/- coding illustrated here), and intra-bit (coherent) frequency hopping. In practice these may also be combined with noncoherent frequency hopping. Although the formats of spread spectrum signals can be markedly different, a common definition of the resulting processing gain can be stated as

Processing gain = 10 log [spread bandwidth/unspread bandwidth]. (16)

Conclusion The initial discussion presented here on generating and

processing spread spectrum signal waveforms has been framed in terms of filters that collapse the spread spectrum coded bit in time and increase its peak amplitude as the means of discriminating against different types of interfering signals, ranging from broadband noise to the mutual interference resulting from “friendly” PN coded signals in the same band of frequencies having different PN code sequences.

In practice, the spread spectrum processor may just as well take the form of a correlator, rather than a matched filter, that collapses the wideband spectrum of the chip-coded information bit back into its original narrow spectrum width. In this case, interfering signals not being matched to the correlator function remain as wideband signals that are effectively reduced by the narrow passband o f the correlator.

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IEEE COMMUNICATIONS MAGAZINE 1 Whether the implementation is a matched filter or a

correlator, the theoretically available processing gains are the same. The equivalence of matched filter and correlator processing was discussed. These were shown to yield identical results provided that the output signals of each are detected at the correct time instants; this serves to point out that the receiver must be time synchronized to the incoming signal if the benefits of spread spectrum coding are to be realized. If the spread spectrum system is a hybrid one that combines both PN coding and frequency hopping, the synchronization must also include that of the hopping sequence itself. The topic of synchronization is not within the purview of this discussion. Suffice it to say that communica- tion design engineers have developed fairly elegant methods of bringing a receiver into synchronization with an incident signal, thus making the application of spread spectrum waveform techniques entirely practical.

As we have noted, the basic concepts of spread spectrum communications have been presented here in terms of overcoming the effects of unwanted external interference. Spread spectrum has much broader.application than just that of interference rejection. Two Special Issues of the IEEE Transactions on Communications on spread spectrum communications contain papers that cover many of the other uses of spread spectrum and provide extensive literature references for those who wish to pursue further study of this topic [ 1,2]. A bibliography of selected publications follows the list of references for this article.

References [ 11 IEEE Transactions on Communications-Special Issues on Spread

Spectrum Communications, COM-25, August 1977. [2] IEEE Transactions on Communications-Special Issue on Spread

Spectrum Communications, COM-30, part I , May 1982. [3] Conference Record, 1982 IEEE Military Communications Conference,

IEEE Service Center, Piscataway, NJ, October 1982. [4] P.M. Woodward, Probability and Information Theory, with Applica-

tions to Radar, Oxford: Pergamon Press, 1953. [5] C.E. Cook and M. Bernfeld; Radar Signals: An Introduction to Theory

and Application. New York: Academic Press, 1967. [6] S.W. Golomb, Shift Register Sequences, San Francisco: Holden Day,

1967. [7] R. Gold, “Optimal binary sequences for spread spectrum multiplexing,”

IEEE Trans. Inform. Theory, IT-13, pp. 619-621, 1967. [8] R.L. Pickholtz, D.L. Schilling, and L.B. Milstein, “Theory of spread-

spectrum communications.” IEEE Trans. Commun., COM-30, pp. 855-884, May 1982.

Cambridge, MA: M.I.T. Press, 1972.

..

[9] W.W. Petersonand E.J. Weldon, Jr., Error Correcting Codes, 2nd ed.,

Bibliography [ 11 R.A. Scholtz, “The origins of spread-spectrum communications,” IEEE

Trans. Commun., COM-30, pp. 822-854, May 1982. [2] M.P. Ristenbatt and J.L. Daws, Jr., “Performance criteria for spread-

spectrum communications,” IEEE Trans. Commun., COM-25, pp. 756-763, August 1977.

[3] R.C. Dixon, Spread Spectrum Systems, New York: John Wiley &Sons, 1976.

[4] J.K. Holmes, Coherent Spread Spectrum Systems, New York: John Wiley & Sons, 1982.

[5] A.J. Viterbi, “Spread-spectrum communications-myths and realities,” IEEE Communications Magazine, pp. 11-18, May 1979.

[6] D.J. Torrieri, Principles of Military Communication Systems, Dedham, MA: Artech House, 1981.

[7] R.A. Dillard, “Detectability of spread-spectrum signals,” IEEE Trans. Aerosp. Electron. Syst., AES-16, pp. 526-537, July 1979.

[8] L.B. Milstein, R.L. Pickholtz, and D.L. Schilling, “Optimization of the processing gain of an FSK-FH system,” IEEE Trans. Commun., COM-28, pp. 1062-1079, July 1980.

[9] R.W. Nettleton and G.R. Cooper, “Performance of a frequency-hopped differentially modulated spread-spectrum receiver in a Rayleigh fading channel,” IEEE Trans. Veh. Technol., VT-30, pp. 14-29, Feb. 1981.

Charles E. Cook received the B.S. degree from Harvard College, Cambridge, MA, in 1949 and the M.E.E. degree from the Polytechnic Institute of Brooklyn, Brooklyn, NY, in 1954.

After two years with Melpar, Inc., he joined the Sperry Corporation in 195 1, where he was responsible for original research on the development and application of large time-bandwidth signal processing to high power radar systems. Since 1971 he has been with the MITRE Corporation, Bedford, MA, where he currently holds a senior staff position in the Communications Division and is a principal investigator on programs concerning the vulnerability and survivability of command, control, and ,communications systems. He holds several basic patents on pulse compression and spread spectrum radar and communications signal processing techniques, and is coauthor (with M. Bernfeld) of Radar Signals-An Introduction to Theory and Application (New York: Academic Press).

He has been a guest lecturer at the University of Pennsylvania, the Polytechnic Institute of Brooklyn, and for the IEEE Boston Section Radar Series. He has authored or coauthored a number of journal papers on the design and application of large time-bandwidth and spread spectrum signals, air traffic control beacon interference, and the antijam effectiveness of netted communications links. He was elected a Fellow of the IEEE in 1972 for contributions to signal processing theory and radar design. He is editor for Communications Systems Discipline of the IEEE Transactions on Com- munications and was a co-guest editor for the May 1982 Special Issue of the Transactions on Spread Spectrum Communications.

Mr. Cook is a member of Sigma Xi.

Howard S. Marsh received the B.S. degree in physics from the Rensselaer Polytechnic Institute in 1963 and. the Ph.D. degree in physics from Cornell University in 1969. He joined The MITRE Corporation in 1969 as a member of the technical staff. His early assignments were in the areas of sensor technology, air traffic control systems, navigation systems, and aircraft landing systems. He participated in the joint FAA/DoD Microwave Landing System Phase I , and evaluated and has served on the Radio Technical Commission for Aeronautics (RTCA) special committee on MLS implementation. He was responsible for positioning, navigation, and guidance analyses in the context of military command, control, and communications (C3) systems. Dr. Marsh transferred to the MITRE C3 Division site in McLean, VA, where he has served as a group leader of the Tactical Communications Group in the Navy C3 Systems Engineering Department, providing technical management for communications tasks in support of the Naval Air Systems Command and the Office of the Chief of Naval Operations. He was promoted to associate department head in 1981. In 1982 he joined the MITRE site in Brussels, Belgium, where he is special assistant in the office of the Scientific Advisor, Supreme Headquarters, Allied Powers in Europe (SHAPE).

Dr. Marsh is a member of the Navy League and the New York Academy of Sciences.

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