A pure spread-spectrum strategy, employing only a single link at any time, can be mechanized more efficiently than the system with potential diversity factor K, shown in Figure 1.1. In an SS system, the Ktransmitter-receiver pairs of Figure 1.1 are replaced by a single wideband communication link having the capability to synthetize and detect all of the waveforms poten- tially generated by the orthogonal communication system complex.The pure SS strategy of randomly selecting a link for communication is replaced with an equivalent approach, namely, selecting a D-dimensional subspace for waveform synthesis out of the system’s 2TsWss-dimensional signal space. This random selection process must be independently repeated each time a sym- bol is transmitted. Independent selections are necessary to avoid exposing the communication link to the threat that the jammer will predict the sig- nal set to be used, will confine his jamming energy to that set, and hence, will reduce the apparent multiplicity and energy gain to unity.
Three system configurations are shown in Figure 1.2, which illustrate basic techniques that the designer may use to insure that transmitter and receiver operate synchronously with the same apparently random set of signals. The portions of the SS system which are charged with the respon- sibility of maintaining the unpredictable nature of the transmission are double-boxed in Figure 1.2. The modus operandiof these systems is as follows:
1. Transmitted reference(TR) systems accomplish SS operation by trans- mitting two versions of a wideband, unpredictable carrier, one (x(t)) modulated by data and the other (r(t)) unmodulated (Figure 1.2(a)).
These signals, being separately recovered by the receiver (e.g., one may be displaced in frequency from the other), are the inputs to a correla- tion detector which recovers the data modulation. The wideband carrier in a TR-SS system may be a truly random, wideband noise source, unknown by transmitter and receiver until the instant it is generated for use in communication.
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10 A Spread-Spectrum Overview
Figure 1.2.Simple SS system configurations.(The notation ˆz(t) is used to denote an estimate of z(t).)
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2. Stored reference(SR) systems require independent generation at trans- mitter and receiver of pseudorandom wideband waveforms which are identical in their essential characteristics (Figure 1.2(b)). The receiver’s SS waveform generator is adjusted automatically to keep its output in close synchronism with the arriving SS waveform. Data detection, then, is accomplished by cross-correlation. The waveform generators are ini- tialized prior to use by setting certain parameters in the generating algo- rithm, thereby denying the jammer knowledge of the waveform set being used (even if the jammer has succeeded in determining the generator’s structure).
3. Matched filter(MF) systems generate a wideband transmitted signal by pulsing a filter having a long, wideband, pseudorandomly controlled impulse response (Figure 1.2(c)). Signal detection at the receiver employs an identically pseudorandom, synchronously controlled, matched filter which performs the correlation computation. Matched fil- ter systems differ from SR systems primarily in the manner in which the inner-product detection process is mechanized, and hence, have exter- nally observed properties similar to those of SR systems.
Certainly, a pure TR system has several fundamental weaknesses including:
(1) The system is easily spoofed since a jammer can in principle transmit a pair of waveforms which are accepted by the receiver, (2) relatively poor per- formance occurs at low signal levels because noise and interference are pre- sent on both signals which are cross-correlated in the receiver, (3) the data is easily determined by any listener who has access to both transmitted sig- nals, and (4) the TR system’s two channels may require extra bandwidth and may be difficult to match. Some of the problems associated with TR systems may be mitigated by randomly changing parameters of one of the commu- nication links (e.g., by protecting one of the TR wideband links with an SR- like technique). Historical examples of SR-protected TR systems will be given in the next chapter.
Spread-spectrum waveform generators for SR systems employing the fol- lowing general modulation formats have been built. The output of an SS waveform generator is given the generic name c(t) and is a (possibly com- plex-valued) baseband representation of the SS waveform.
1. Recorded modulation:The waveform w(t) of duration Tpis recorded, and if necessary, extended periodically to give
(1.19) The utility of this type of signal is limited by the problem of distribut- ing recordings to transmitter and receiver so that reuse of a waveform is not necessary.
2. Frequency hopping (FH): Assuming that p(t) is a basic pulse shape of duration Th(usually called the hop time), frequency-hopping modulation
c1t2 a
n
w1tnTp2.
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has the form
(1.20) In all likelihood, the complex baseband signal c(t) never physically appears in the transmitter or receiver. Instead, the pseudorandomly gen- erated sequence {fn} of frequency shifts will drive a frequency synthe- sizer to produce a real-valued IF or RF carrier-modulated version of c(t).
The sequence {fn} of random phases is a by-product of the modulation process.
3. Time hopping(TH): Assuming that the pulse waveform p(t) has dura- tion at most Ts/MT, a typical time hopping waveform might be
(1.21) In this example, time has been segmented into Tssecond intervals, with each interval containing a single pulse pseudorandomly located at one of MTlocations within the interval.
4. Direct sequence(DS) modulation:Spread-spectrum designers call the waveform
(1.22) direct sequence modulation. Here, the output sequence {cn} of a pseudo- random number generator is linearly modulated onto a sequence of pulses, each pulse having a duration Tccalled the chip time.
5. Hybrid modulations: Each of the above techniques possesses certain advantages and disadvantages, depending on the system design objec- tives (AJ protection is just one facet of the design problem). Potentially, a blend of modulation techniques may provide better performance at the cost of some complexity. For example, the choice
(1.23) may capture the advantages of the individual wideband waveforms c(i)(t) and mitigate their individual disadvantages.
Three schemes seem to be prevalent for combining the data signal d(t) with the SS modulation waveform c(t) to produce the transmitted SS signal x(t).
1. Multiplicative modulation:Used in many modern systems, the transmit- ted signal for multiplicative modulation is of the form
(1.24) Mechanization simplicity usually suggests certain combinations of data and SS formats, e.g., binary phase-shift-keyed (BPSK) data on a DS sig-
x1t2Re5d1t2c1t2ej1vctfT26. c1t2∏
i c1i21t2 c1t2 a
n
cnp1tnTc2 c1t2 a
n
pat an an MTbTsb. c1t2 a
n
exp3j12πfntfn2 4p1tnTh2.
12 A Spread-Spectrum Overview
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nal, or multiple frequency-shift-keyed (MFSK) data on a FH signal.These modulation schemes are the ones of primary interest in this book.
2. Delay modulation:Suggested for use in several early systems, and a nat- ural for mechanization with TH-SS modulation, this technique transmits the signal
(1.25) 3. Independent (switching) modulation:Techniques (1) and (2) are sus- ceptible to a jamming strategy in which the jammer forwards the trans- mitted signal to the receiver with no significant additional delay (a severe geometric constraint on the location of the jammer with respect to the transmitter and receiver), but with modified modulation. This repeater strategy, which if implementable, clearly reduces the multiplicity factor Kof the SS system to unity, can be nullified by using a transmitted sig- nal of the form
(1.26) Here the data signal, quantized to M levels, determines which of M distinct SS modulations c(d)(t),d1, . . . , 2, . . . ,M, is transmitted. The key assumption here is that even though the jammer can observe the above waveform, it cannot reliably produce an alternate waveform c(j(t))(t),j(t) d(t), acceptable to the receiver as alternate data modu- lation. The cost of independent data modulation is a clearly increased hardware complexity.
The data demodulation process in a digital SS system must compute inner products in the process of demodulation. That is, the receiver must mecha- nize calculations of the form
(1.27) where in general mT(t) and mR(t) represent complex baseband signals and (mT,mR) is their inner product. However, one or both of these complex base- band signals usually appears in modulated form as a real IF or RF signal
(1.28) The inner product (1.27) can be recovered from the modulated signal(s) in several ways, as illustrated in Figure 1.3. For example, the receiver can first demodulate the signal xT(t) to recover the real and imaginary parts of mT(t) and then proceed with straightforward correlation or matched filtering operations using baseband signals. On the other hand, as indicated in Figures 1.3(c) and 1.3(d), there are alternative ways to compute the inner product, which do not require that both signals be shifted to baseband first.
In all cases, the heart of the SS receiver is its synchronization circuitry, and the heartbeats are the clock pulses which control almost all steps in forming
xi1t2Re5mi1t2ej1vitfi26, iT, R.
1mT, mR2 0TSmT1t2m*R1t2dt
x1t2Re5c1d1t221t2ej1vctfT26. x1t2Re5c1td1t22ej1vctfT26.
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14 A Spread-Spectrum Overview
Figure 1.3. Examples of correlation-computing block diagrams.The dashed portions of the diagrams can be eliminated when the modulations mT(t) and mR(t) are real and, in addition, the local oscillator is phase-coherent, i.e.,fe0. Solid line processing is often called the “in-phase” channel, while the dashed line processing is called the
“quadrature” channel.
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Figure 1.3. Continued.
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the desired inner product. Recovery of Re{(mT, mR)} and Im{(mT, mR)}
requires three levels of synchronization.
1. Correlation interval synchronization:Correlators require pulses to indi- cate when the interval of integration is to begin and when it is to end.
In the bandpass correlator of Figure 1.3(d), interval sync not only pro- vides the timing for the sampling operation, but also initializes the nar- rowband filter’s state to zero at the beginning of each correlation interval. Typically, in DS systems these signals correspond to the data symbol clock pulses. In FH systems in which the data symbol time exceeds the hop time, the interval sync pulses must indicate the dura- tion of a single frequency, since correlation operations spanning random phase transitions are not generally useful.
2. SS generator synchronization:Timing signals are required to control the epoch of the system’s SS waveform generator’s output and the rate at which that output is produced. Direct sequence systems employ a clock ticking at the chip rate 1/Tcfor this purpose, while FH systems have a similar clock operating at the hopping rate 1/Th.
3. Carrier synchronization:Ideal reduction of the SS signal to baseband in the receiver is possible if a local oscillator (or oscillator network) is avail- able whose output is in frequency and phase synchronism with the received signal’s carrier (i.e.,fe 0 in Figure 1.3). The above level of carrier sync is often available in DS systems, but usually only frequency synchronism is attained in FH systems.
In some SS systems, the above synchronization signals are derived from a single clock; in others, the carrier local oscillator is independent of the clock signals which control its modulation. Automatic control circuitry generally is included to align the receiver’s clocks for proper demodulation of the incoming signal, although some systems have been built in which ultrastable clocks are initially aligned and then are allowed to drift in a free-running mode until communication is concluded. Proper operation of the correlation computing circuits generally requires control of the symbol clock epoch to within a small fraction of the correlation interval’s duration T. Similarly, it is necessary to adjust the SS generator clock’s ticks to within a small frac- tion of the reciprocal of the SS modulation’s short-term bandwidth, i.e., the bandwidth of the energy spectrum of the SS reference waveform within a correlation interval. Section 1.5.3 will indicate that the SS generator clock error for DS and FH systems must be a small fraction of Tcand Th, respec- tively, to maintain correlator operation at nearly maximum output signal lev- els, as required.
Frequency synchronous operation of correlation detectors requires that the phase drift between the incoming carrier (excluding SS modulation) and the receiver’s local oscillator, over a correlation interval, be a fraction of radian, i.e., the quantity fein Figure 1.3 may be assumed nearly constant dur- ing the correlation computation. (Phase synchronism of the local oscillator requires, in addition, that febe near zero.) The bandpass correlator is a fre-
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quency synchronous device requiring that the input to its narrowband filter be centered in its passband to an error tolerance of a fraction of the recip- rocal of the correlation time.
Output threshold crossing techniques, similar to those used in radar detec- tion, are an alternative to MF output sampling in Figure 1.3(b), and may have higher tolerance to synchronization errors than SR/DS systems. However, any realized tolerance to synchronization errors implies a potential weak- ness to repeater jamming.