[34]

756 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-25, NO. 8, AUGUST 1977

Performance Criteria for Spread Spectrum Communications MARLIN P. RISTENBATT, SENIOR MEMBER, IEEE, AND JAMES L. DAWS, JR., MEMBER, IEEE

Abstrucr-The criteria for antijam (AJ) and anti-intercept (AI) sys- = tems are described, in terms of the appropriate action taken by the jam- ’ mer or interceptor. Avoiding pseudonoise (PN) sequences which can be partially or totally predicted is a foremost criteria, especially for AJ, and use of nonlinear feedforward logic (NFFL) with long-period linear maximal sequences appears attractive.

A frequency-hopping (FH) system must anticipate a multitone jamming signal, and an error-control code is necessary. A novel method for generating a multitone signal using repeating maximal sequences is described. PN systems must anticipate a tone jammer, and now an error- control code may be needed to assure that sporadic PN sequence correlation with the tone does not reduce the processing gain.

Any AI system must anticipate that the interceptor may, if advan- tageous, integrate his decision energy over many communicator symbols (up to the message length). Now spreading both in frequency and in time may be valuable.

Finally, the use of an automatic adaptive data rate is suggested to realize flexibly either AJ or AI objectives.

I I. INTRODUCTION

N spread spectrum systems either the RF bandwidth (W) and/or the total time epoch of the signal is “spread” beyond

that required for basic signaling to provide special functions or to cope withunintended parties. Special functions, which may be of interest to civilian as well as military users, are ranging, multiple-access, selective addressing, antimultipath, and minimum power-density signa1ing.l

Military communicators, who are the chief developer of spread spectrum techniques, build antijam (AJ) systems if the unintended par ty is a jammer and an t i - in te rcept2 (AI) systems if avoidance of signal intercept is important. There is also interest in antispoof (IFF)3 signaling, but this will not be treated here.

This paper describes quantitatively the system performance criteria for AJ and AI systems in terms of the appropriate action taken by the unintended party. The potential availability of new spectrum regions, made accessible by device develop- ments, now makes impressive processing gains achievable by spread spectrum system designers. The same new technology is, of course, available to the unintended party.

The major purpose of this paper is to note the quantitative relation between the AJ and/or AI system goal and the goal of the corresponding unintended party. A secondary purpose is

Manuscript received January 19, 1976; revised April 6 , 1977. The authors are with the Cooley Electronics Laboratory, Depart-

ment of Electrical and Computer Engineering, University of Michigan, Ann Arbor, MI 48104.

’ This refers to (a) the use of data rate reduction to aliow communication with devices having very limited power capability, or (b) frequency spreading to afford negligible interference to nearby (relatively) narrowband receivers.

’AI systems are frequently called “low probability of intercept (LPI)” systems or “covert communications.”

31dentify Friend or Foe (IFF) refers to the process of using a pri- vate “password” signal to identify oneself as being a member of the de- fined group.

to relate the pseudonoise (PN) sequence properties, which are used to achieve the spreading, to the AJ system goals. A final purpose is to advance certain new concepts and ideas for consideration.

Section I1 describes the common spread spectrum approaches in general terms. Section I11 describes the PN code ‘sequence properties that are influential in practical systems. Sections IV and V treat AJ and AI systems, respectively. The final section proposes a concept for flexible AJ and AI operation.

11. GENERAL SPREAD SPECTRUM ASPECTS

We will assume that the information to be communicated is digital, stemming either from a data terminal or digitized voice or video. Figure 1 shows a general block diagram of a digital spread spectrum system. A digital source of rate R b/s is first encoded via a block or convolutional code; a block error-detecting code will be used if the link is involved in retransmission (ARQ), and a convolutional code will be used if forward-only transmission is involved (see Ref. 1). Specific reasons for coding with spread spectrum are treated later. The rate entering the spread spectrum modem is the product of bit stream R and the code-rate. The modem output is spread over a total RF bandwidth W, and the time epoch may be expanded if the message is finite-length. The common spread spectrum systems are: frequency hopping (FH), direct-sequence pseudonoise (PN), time-hopping (TH), and chirp, plus combinations of these. Specific block diagrams of these systems are available elsewhere (Refs. 2 , 3, and this issue) and will not be repeated here.

In FH systems, a single hop of bandwidth wh and length th(whth = 1) is pseudorandomly hopped over the total bandwidth W, under the control of k-tuples from a PN-sequence used as a random-number generator, as suggested in Fig. 2. Usually frequency-shift-keying (FSK), either binary or M-ary, is used to frequency-offset the hop-stream produced by the random-number generator.

In direct-sequence PN systems, the PN sequence forms a series of “chips” that phase-shift-key (PSK) a carrier; this code modulation can be either binary or quaternary. Then binary data sequentially phasershifts successive k-tuples of such sequence chips (Fig. 3). The resulting PN signal covers the total bandwidth W, at all times, as indicated in Fig. 3(d).

In a TH system, the RF signal is dispersed in time, with PN code-determined time gaps between signal elements. This forms a type of intermittent signal which is useful for AI signaling, and may be useful for fall-back AJ signaling. In a chirp system, one possibility is t o use an up-chirp for a (data) binary “one” and a down-chirp for a binary “zero” forming a series of up- or down-sweeps in FT space (Ref. 4). For AJ, one adds FH to the chirp start-frequency, to afford protection against a chirp jammer.

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RISTENBATT AND DAWS: PERFORMANCE CRITERIA FOR SPREAD SPECTRUM 757

R(;) or

R R(code-rate) w Dota

Recelver Decoder

lnterceqtzr- - - - -

L _ - - _ _ - - - _ _ _ _I

Fig. 1. Spread spectrum system and unintended parties.

0 0 0 c t-’”.$ t

Symbol

Fig. 2. Frequency versus time sketch for FH.

Transmttted,r-d/‘ / \ -. Frequency ,/ “ Spectrum k w = + 4 f

Id )

Fig. 3. PN Signal formation. (a) PN sequence. (b) Binary data. (c) Chip and data modulated time waveform, (d) Corresponding (filtered) spectrum.

Each type of spread spectrum system requires PN code sync; hence one must acquire sync either from a “cold start” or within an u priori uncertainty interval if continuous-clocking is used. The u priori uncertainty interval is determined by the maximum possible path-delay.

Spread spectrum applications are sensibly divided into the cases where (a) the links are relatively “isolated”; or (b) the links are relatively “dense” and interacting. The isolation may stem either from physical separation of platforms (remote ship or airplane) or from antenna-beaming (satellite uplinks).

Traditional dense applications occur in omnidirectional communication links among tactical mobile vehicles or aircraft. In dense applications, where many radios are within range of each other, frequency-management and self-interference (near-far) must be handled, as well as unintended parties. In isolated applications, usually a single radio link must cope only with the unfriendly jamming or with the possible signal exploitation after interception.

When adopting spread spectrum techniques in isolated cases, the major contest is between platforms, and the ‘‘processing gain” of the system versus that of the unintended party. In dense cases, however, spread spectrum techniques offer yet .another dimension-the denial of obvious frequency channelization to the unintended party. Traditionally this channelization provides the underlying basis for intercept- then-jam strategies. Potential jammers are able to monitor the spectrum activity in dense environments and relate specific spectrum activity to particular types of vehicles or organiza- tions, for selective jamming. Adoption of spread spectrum in a frequency region should significantly alter the ability of unintended parties to make sense out of the spectrum activity.

Finally, we note that spread spectrum system design is heavily influenced by the particular frequency region, both because the physical channel has characteristic propagation and noise properties, and because electronic transceivers vary somewhat for the different frequency regions. It is sensible to divide the major candidate channels into the categories of: (1) extremely low frequency (ELF)/very low frequency (VLF); ( 2 ) high-frequency (HF); (3) line-of-sight (L0S)-VHF/UHF/ SHF; and (4) satellite-relay. ELF/VLF appears useful for long- distance, very low data-rate systems; HF features long distance, variable propagation, and moderate data rates. The VHF/UHF frequencies are typical for military LOS applications, and these channels would form a dense application if spread spectrum is adopted. SHF is not yet crowded with many radios, and may be the spectrum region where spread spectrum is adopted for dense and isolated environments. The satellite link has a unique, long distance capability, either broadcast or point-to-point, and can support a high processing gain. Optical links (not listed above) achieve substantial gain against an unintended party by virtue of the extreme radiation directivity, and may not need spread spectrum except in rare cases.

111. PN SEQUENCE ASPECTS

The PN sequences that are used for the spreading in any system must meet the two critical criteria of: (1) denying any information about future sequence k-tuples to the unintended party, and ( 2 ) permitting practical implementation, including convenient code changes. Sometimes it is desirable for the sequence autocorrelation behavior to have a high peak-to-side- lobe ratio, for acquisition sync purpose^.^ Finally, proper k-tuple statistics are desirable, depending on the type of system (see below).

Denying future information is probably the foremost

4 A sequence specially suited to acquisition sync may be used first, followed by a long code.


758 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-25, NO. 8 , AUGUST 1977

EJ F Nonlinear

L Sequence

(C)

Fig. 4. Sequence generators. (a) LFSR. (b) NFFL using single LFSR. (c) NFFL with multiple LFSR’s.

criteria; if future sequence values are not totally uncertain, the unintended party should be able to reduce the intended system processing gain, at least in AJ systems. This means that the PN code period must exceed the time between code changes, and the code must not be “crackable” in the encryption sense.

Practical and efficient implementation techniques for PN sequences center around use of shift-registers (Refs. 5,6). Since crackability is such an important issue, it appears sensible to categorize PN code generators, according to increasing complexity, into the classes of: (a) linear feedback shift- registers (LFSR); (b) one or more LFSRs with nonlinear feedforward logic (NFFL); and (c) general nonlinear feedback shift-registers (NLFSR). Other ad hoc cases are possible, but are ignored here.

Linear sequences are the least complex and limit the logic used in the generator to modulo-two addition. LFSR’s can generate linear maximal sequences, m-sequences, using selected stages of an r-stage shift register as shown in Fig. 4(a). The correct selection of the feedback stages will result in a maximal sequence of lengthL = 2‘ - 1. Although rn-sequences have been thoroughly studied (Ref. 5 through Ref. 12), they are practically useless when unintended parties are involved (at least for AJ). The classical properties of m-sequences are: (1) maximal length for an r-stage generator; (2) maximum possible peak/side-lobe autocorrelation over the period L; (3) large number of possible maximal connections (codes) per r-register; and (4) balanced k-tuple statistics. The major problem is that an unintended party need only 2r successive sequence bits to crack .the sequence : determine the feedback connections and the initial state of the r-register.

In 1973 we found (Ref. 10) that the relatively simple procedure of adding nonlinear logic (AND, OR, INVERT,

. etc.) to an LFSR in a feedforward fashion, as in Fig. 4(b), significantly increases the complexity of cracking. Our measure of complexity here is the number of consecutive sequence bits that must be known for ~ r a c k i n g . ~ This was found by evaluating the register length of the equivalent linear generator. This length, in turn, was found using Massey’s algorithm (Ref. 1 l), which is a general solution to synthesize the shortest linear generator capable of generating a prescribed finite sequence of bits. We found that the number of stages

’Another measure of complexity has recently been proposed, based on the number of independent k-tuples-see Ref. 1 3 .

(JVm) in the linear equivalent generator of an r-stage maximal generator to which an m-order nonlinearlity is added, is practically always given by:

f l m =2 i=O (;) where

m = maximum number of inputs to any single nonlinear

r = number of stages in the LSRG (3 = binomial coefficient.

gate

Since 2(JVm) consecutive error-free bits are required to crack the sequence, the cracking complexity increases very rapidly with r and m. For example, a 17-long LFSR has an , N m of 3,214 for m = 4 and 13 1,072 for m = 17. In certain rare cases Eq. (1) is violated (see Refs. 10, 12).

Another type of NFFL uses multiple LFSRs with a nonlinear feedforward logic, such as in Fig. 4(c). A generator proposed by Geffe (Ref. 14) uses three LFSRs with two 2nd order AND gates. Groth (Ref. 15) has proposed a yet-more- complex NFFL arrangement.

The basic properties of the general NLFSR, which also have an equivalent linear generator, are treated in Ref. 6 ; crackability studies of such generators are presumably done only by official encryption parties.

Special sequence generators aimed at improved code acquisition sync properties have been (Refs. 16, 17) and continue to be pursued (Refs. 18,19). Any special techniques must withstand exploitation by an unintended party.

The possible use of code division multiple-access (CDMA, Ref. 1) motivated examination of cross-correlation behavior between different sequences. The so-called Gold sequences (Ref. 8) which are generated by modulo-:! addition of selected m-sequences, provide a set of sequences (one for each value of relative phase shift between the m-sequences) that have a stated bound on the pair-wise cross-correlation, taken over the full period. Since actual systems are integrating over a k-tuple which is small compared with full-period (k < L ) , it is the partial-period cross-correlation results that are of interest. Both Gold (Ref. 20) and Daws (Ref. 7) have shown that the average partial period cross-correlation between two maximal sequences of the same length for a fixed value of relative offset is equal to the full period cross-correlation for that value of offset. The Gold codes, with bounded full-period cross- correlation will, for the partial-period case, have a bounded mean value of cross-correlation and the same spread (variance) as any other sequences of the same length. Thus the Gold codes result in a partial-period correlation that is statistically as low as possible for codes of a given length. The practical utility of these results are currently uncertain, both because they apply to linear sequences and because the comparative value of CDMA is not yet assured.

A remaining sequence issue is the k-tuple behavior. This is best postponed to the next AJ section.


IV. ANTIJAM PERFORMANCE CRITERIA

FH

If FH with FSK modulation is the AJ technique, then the first system concern is to assure sufficiently rapid hopping so as to deny any possibility of follower-jamming for the geometry-determined path delays. We may note that surface- acoustic-wave (SAW) devices form the basis of compressive receivers capable of very rapid frequency-determination (Ref. 21). We recently designed and built (Ref. 22) a breadboard frequency-follower, capable of locating a lone frequency- hopping signal within 5100 Hz over a 100 MHz band (650 to 750 MHz) in a period of 1.5 ms. The follower design centered around a recent’ SAW dispersive delay line6 having a com- pression ratio of lo4 (250 MHz bandwidth, 40 ps differential delay).

Assuming sufficiently rapid hopping, the system design should then anticipate a multitone jamming signal. To justify this we need to distinguish the hop-decision error-rate (PE’) from the final error-rate (PE) after the error-control encoding/ decoding is included. The minimum jammer power is that power required to cause an error-rate higher than the specified

The jammer’s best strategy is to space a series of tones across the bandwidth (W), where the (received) power per jammer tone slightly exceeds the system’s received power per hop. Whenever a hopping receiver’s instantaneous band.width (Mwh) lands on a jamming tone, the conditional error- probability is:

PE.

M - 1 P’(E1hit) =--

M

where

P’(E 1 hit) = error-probability conditional on a jammer tone being in a receiver bandwidth

binary. M = the level of FSK modulation; M = 2 for

The jammer must use as many such tones as required to exceed the system PE requirement. Further, the tones will be spaced no closer than Mwh so that no more than one tone can appear in the modulation bandwidth. Assume that both the FH and the FSK positions are spaced at the orthogonal ( l / t h ) nonoverlap positions. Then:

w = NfWh

where

W = total RF bandwidth N f = number of orthogonal bins in total W wh = bandwidth of single hop

‘A 10,000: 1 Linear FM Reflective Array Dispersive Filter devel-

Then the hop-decision PE’ would be:

pEI = - - - - (M-1) M - 1 Nj N .

NflM N f

where

Nj = number of jamming tones N f = number of orthogonal frequencies.

RISTENBATT AND DAWS: PERFORMANCE CRITERIA FOR SPREAD SPECTRUM

oped and built by Hughes Aucraft Company. minus sign corresponding to an rn-sequence is a series of equal-

759

(2)

Equation (2) allows us to observe that, if no error-control coding were used, the minimum required jammer power is heavily dependent on the specified error-rate. A typical error-rate of or less would permit a jammer to use a power much smaller than predicted by the processing gain (w/wh). Error-control coding (see Fig. 1) serves to make the symbol decision span a series of hops. PE now depends on the code and on the PE’. In general, a good code causes the required jammer power to rise close to that value predicted by the white-Gaussian noise (WGN) model:

J = j o W

where

J = total jammer power io = effective “noise power density”

= J/W.

For example, if a binary FSK with a given error-control code can be approximated as constitutingincoherent orthogonal signals, with symbol energy E,, then the PE is approximated by (Ref. 24)

where

E, = ST S = received signal power T = symbol length

In FH systems the PN sequence is used as a random number generator. In this case the possible frequencies, and hence the k-tuples, should be approximately equally likely. The k will be less than r, since the required large L = 2‘ - 1 exceeds the 2k hop possibilities even for impressive processing gains. This k < r factor contributes to the difficulty of cracking the PN sequence. Since all linear rn-sequences will have equally likely k-tuples ( k < r) over a period, addition of an NFFL can be arranged to exhibit a similar property in the nonlinear output sequence.

Since multitone signals are the optimum nonadaptive jammer against FH, it is interesting to note a particularly simple way to generate flexible, multitone signals. A readily available, near-optimum digital technique consists of using periodic repetitions of a linear rn-sequence. The amplitude spectrum of a periodic series of impulses having a plus or



height lines, extending indefinitely in frequency, with spacing between the lines given by:

1 f c Awj = - =- period L

where

Awj = tone spacing f, = clock frequency of shift-register L = sequence length in bits. Since a jammer prefers a near-constant envelope signal, one

starts with the rectangular-wave form of an m-sequence (the usual form). The equally-spaced spectrum lines now have a sin x/x amplitude behavior, with the first zero occurring at f,. One can obtain a near-constant tone amplitude by using a digital filter which both: (1) passes only the portion out to about f,/2, and (2) compensates in amplitude, so that the output has essentially flat tones.

We constructed a breadboard of a multitone jammer which has a total bandwidth of 100 MHz, with tones spacings as low as 1 kHz. The m-se,quences were clocked at 150 MHz, and used to PSK an R F carrier. The digital filter has a passband of 50 MHz. When the result was balanced-modulated up to a higher frequency, the bandwidth was automatically doubled.

PN If a system uses direct-sequence PN for AJ, then it should

anticipate a (single) tone jammer, placed near or at the PN carrier frequency. A tone jamming signal is the best practical nonadaptive interference because: (a) it stresses the carrier suppression issue of balanced-modulators (if used)-see Ref. 3 ; and (b) it benefits from any unbalance in the k-tuples.

For PN systems the number of sequence bits per information symbol ( k ) is determined by the desired bandspreading factor and is typically much larger than the length of the shift-register generating the sequence. It is interesting to note that one would like every sequence k-tuple to have an equal number of ones and zeros (be balanced) since serious unbalance increases the correlation with the jamming tone. Serious and frequent unbalance would cause significant correlation with the jamming tone, and reduced processing gain.

If the PN code were a linear m-sequence, we know (Ref. 9) that the k-tuple balance when k > r (but k < L ) does not differ significantly from that of truly random sequences. Although slightly nonoptimum against a tone, they would be optimum against a broadband jammer.

Nonlinear sequences using NFFL are potentially very unbalanced since the individual nonlinear AND or OR circuits have an unbalanced output for balanced inputs. Therefore some care must be taken in the design of the NFFL to get reasonable balance properties. One common technique for achieving the desired balance is to add (modulo-2) the original maximal sequence to the output of the nonlinear elements. In this case it may be noted that if the output of the nonlinearity is very unbalanced (for example, very .few ones) the resulting

sequence is the original maximal sequence with errors. Although the linear equivalent generator would be quite long (as noted above), the original linear maximal may be a good approxima- tion for the output sequence.

We note, however, that as the processing gain increases, k becomes increasingly greater than r, and the k-tuples from the LFSR approach better balance. If reasonable care is taken in designing the NFFL, the same tendency should hold. Further, the error-control code (Fig. 1) will smooth over occasional tone correlations produced by unbalanced k-tuples.

V. ANTI-INTERCEPT PERFORMANCE CRITERIA

Spread spectrum techniques can implement an AI (or covert) communication systkm, where ’ the. requirement is to minimize the exploitation of the communication signal for purposes of detecting and position-fixing the signal emitting platform. Keeping any required ,communication covert ’is especially important for those platforms that are difficult t o detect and position-fix by other means. Since minimum transmitted energy contributes to AI, covert signals are usually minimum data rate (R) continuous signals, or relatively short, finite digital messages. It is desirable for the communicator to estimate the propagation loss via feedback techniques and use only the correct power.

AI seems to make sense for isolated (as opposed t o dense) cases, dealing with a single or group of remote platforms. The interceptor usually has two goals: (1) detect presence of signal of interest in midst of natural noise and RFI; and (2) locate position of the’ emitter (see Fig. 1). The detection portion is evaluated in terms of.detection probability (Po) and false- alarm probability (PF,A , ) In general, the detection step involves integration of received power over either the entire message (if finite), or over the maximum practical value for continuous signals. Often detection includes a recognition step’, using some recognizable feature, to confirm that the signal is of interest. The position-fixing is evaluated in terms of the “rms-error- distance” (Drms).

In LOS and satellite channels, the detector background should be natural noise, with little propagation from distant RFI sources. Then a successful detection may amount also to recognition. In the HF case, however, the interceptor receives propagation from quite distant sources, and may have a “needle in a haystack” problem. In such a case, the interceptor will usually divide the detection step into two phases: (1) initial sort; and (2) recognition. The initial sort or editing processing attempts to sieve, both in frequency and in time, so as to pass that part of the T-W space that appears most likely to contain a signal. A following recognition step continuously examines the initial sort output and makes any “alarm” decisions.

It appears desirable for the communicator to choose a signal as close in appearance to the background (noise or RFI) as possible since this maximizes the difficulty of recognizing the signal. Thus, in satellite and LOS-links, where the background is white Gaussian noise, the covert signals might use filtered direct-sequence PN signals, which have time and


RISTENBATT AND DAWS: PERFORMANCE CRITERIA FOR SPREAD SPECTRUM 76 1

frequency properties approximating those of white Gaussian noise.

It is instructive to compare the communicator and intercept performance equations for a finite message. Two important communicator requirements are the total information bits (N) in the message, and the error-probability (PE). The total number of transmitted symbols (Nt) in the message is determined by the level of M chosen for the signaling:

The symbol error-probability is determined by the received energy-to-noise-density (E,/no = ST/no), and is a function of the M-level and the coding method used.

While the communicator must make Nt (M-ary) decisions during the message epoch, the interceptor can base his detection and position-fix accuracy on the entire message (a single decision per message). In principle, the detection capability is limited by the total energy (to noise density) received by the interceptor. For weak (Sl/no Wl 1) unknown signals in white Gaussian noise the energy detector, usually called a radiometer at microwave frequencies and above, is the optimum.

If the signal energy is spread or dispersed evenly over a total time (TI) and a total bandwidth W, then the interceptor can integrate only up to TI , and use an intercept bandwidth Wl < W. Then the “detectability index (d)” (Ref. 23,24), which determines the detection-probability (Po) and accompanying false-alarm probability (PF.a,), is given by

where

T = length of M-ary symbol or signal S I = average signal power received by interceptor Nt = number of transmitted symbols in message no = noise power density.

It is seen that detectability (d) is minimized if Nt is minimized and TI and Wl are maximized. The SI will be controlled by the communicator’s E, = ST requirement, and by the interceptor distance from the emitter, relative to that of the communication receiver.

Hence, we see that spectrum spreading, including time- hopping, using pseudorandomized gaps, if the message is finite, is desirable since the gap pattern is known to the communicator but unknown to the interceptor. Although Eq. (3) specifies the theoretical detection constraint, in practice one is often limite~d by both: (1) ability to find a relevant noise-alone T- W space to measure background noise for setting the decision threshold, and (2) the (message-long) signal processing limita- tion of a given complexity level.

While the interceptor detection objective is to maximize the Po for a fixed (small) P F . A , , the position-fix objective is to minimize the D,,,. Position-fixing requires finding at least

two “directions” or line-of-bearings. If the Sl/no is adequate and one has a carrier component available, direction-finding (DF) can be measured in terms of the period of the carrier-cycle, assuming the cycle ambiguity can be resolved in some fashion. Another DF approach, also requiring moderate SNR, is to combine antenna elements so as to form multiple-lobes. For weak, wide-band signals the optimum approach is to estimate the relative time delay of the signal as received at two or more positions. This time delay is estimated by correlating the two receptions.

The accuracy of position-fixing is discussed in Ref. 23. Although the position-fixing accuracy theoretically goes up as TIWl increases, it is important to recognize that this theoretical accuracy can only be achieved if the Sl/no is above a certain minimum threshold.

VI. AUTOMATIC DATA RATE FOR AJ/AI

Finally, we propose consideration of the concept of automatic data rate variation. One increases both AJ and AI as data rate decreases. AI increases both because intercepted SI/n0 decreases and time hopping can be used. For’AJ, a decreasing rate permits a larger receiver integration, T, and hence a higher symbol energy E,.

Since either AJ or AI objectives may be as important as data rate, at various times, it appears desirable to provide for automatic data rate variation so that the communicator can cope with what he perceives to be the greatest current threat (data rate, AJ, or AI). We visualize a link where two terminals are operating either half-duplex or full-duplex. The forward- link data rate is t o be automatically changed as necessary with no visible signal change, to operate, normally without repeats (or retransmission) as jamming or intercept conditions change. Provision of automatic rate changes means that the communicator need only set in the criteria to either: (1) meet whatever jamming threat he encounters so long as he is able to tolerate data rate reduction, or (2) minimize his exposure to an envisaged detection threat by approprjately restraining power output. . . s .

Such a flexible mode of operation is attractive from a number of different viewpoints. First of all it tends to change the basic “game” between the communicator and the unintended party. An unintended party considering construction of a jammer will face the proposition that: (1) he may not be able to deny communication, but only minimize the rate, and (2) he will not know how well he is doing. An equivalent position occurs for the potential interceptor. He may face an intercepted Sl/no below his threshold.

A flexible data rate is sensible from another point of view. Field-dispersed equipment constitutes an investment to accomplish certain communication goals. Automatic variable data rate implements a more flexible utilization of that investment than any other method.

A final, significant advantage of this automatic approach should be an increased reliability since any unexpected system losses will result in a reduced rate rather than in total disabling:



ACKNOWLEDGMENT

The authors would like to acknowledge the many helpful discussions with Ervin Holland-Moritz. [61

GLOSSARY OF SYMBOLS

detectability index energy integrated by interceptor energy per communicator information symbol clock frequency of a shift-register generator single-sided jammer power density total jammer poGer .

number of PN code bits in a symbol (either direct- sequency or frequency hop), or number of information bits in a block codeword length of PN code’or sequence in bits linear feedback shift register order of nonlinear logic number of alternative information modulation symbols number of information bits in finite message number of orthogonal frequencies in total W number of jamming tones’in’total W nonlinear feed’ forward logic nonlinear feedback,shift register number of transmitted symbols in finite message number of stages in the equivalent linear generator of an NFFL generator total number of bits, information plus check, in a block codeword final error rate, including .error-control coding/ decoding hop-decision error rate number of shift-register stages source data rate in b/s received power from system transmitter power received by interceptor, from system transmitter symbol time for system time per hop in FH largest intercept integration time bandwidth per hop in FH total bandspread bandwidth intercept bandwidth (W, < W) tone spacing of multitone jammer

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A. Lempel and J. Ziv, “On the Complexity of Finite Sequences,” Trans. Information Theory, Vol. IT-22,’No. 1, January 19’76,

P. ‘R. Geffe, “How to Protect Data with Ciphers That Are Really Hard to Break,” Electronics, January 4, 1973. E. J. Groth, “Generation of Binary Sequences with Controll- able’ Complexity,” IEEE Trans. on Information Theory, Vol. IT-17; No. 3, May 1971. ’ “Communication Techniques-Deep Space Range Measure- ment,”’Jet Propulsion’Laboratory Research Summary No. 36-1, Vol. 1 , California Institute of Technology, Pasadena, California, February 15; 1960, pp. 3946. M. P. Ristenbatt; “Pseudo-Random Binary Coded Waveforms,” Chapter 4, Modern Radar Analysis, Valuation a.nd System De- sign, R. s. Berkowitz, Ed., Wiley & Sons, 1965. N. B. Chakrabarti and M. Tomlinson, “Design of Sequences with Specified Autocorrelation and %ross Correlation,” IEEE Trans. Communications, Vol., COM-24, No. 11, November 1976, pp. 1246-1251. W. P. Baier, “On Parasitic Correlation Peaks in Cross-Correla- tion Circuits for Binary Pseudorandom Sequences,” IEEE Trans. Communications, Vol. COM-24, No. 10, October 1976,

R’. Gold, Code Synthesis Study, Final Report, Vol. I1 Robert Gold A’ssoc., Los Angeles, California, 15 June 1973. J. B. Harrington and R. B. Nelson; “Compressive Intercept Re- ceiver Uses SAW Devices for Signal Sorting with Stability and Flexibility,” SAW Series No. 5, Microwave J., September 1974,

E. K. Holland-Moritz, J. L. Daws, .Jr., G. W. McClure, andM. P. Ristenbatt, “A Transponder Against FH Signals Using a SAW Device,” Abstract, paper presented Adhoc Symposium on Spread Spectrum Communications, 7-9 September 1976, Monte- rey, California, p. 10. M. P. Ristenbatt, “Estimating Effectiveness of Covert Communi- cations,” Proc. I9 73 Symposium on Spread Spectrum Communi- cations, Vol. 1, TD 271, 13-16 ‘March 1973, Naval Electronics Laboratory Center, San’Diego,’California, pp. 113-1 18. A. D. Whalen, Detection o f Signals in Noise, Academic Press Electrical Science Series, New York, 1971.

pp. 75-81.

pp. 1143-1147.

pp. 57-62.

Equipments, ,Magnavox Communications and Navigation, Tor- rance, California, January 1973.

[3] R. C. Dixon; Spread Spectrum Systems, Wiley & Sons, New Marlin P. Ristenbatt (S’51-M’60-SM’70) was born in Lebanon, Pa., on York, 1976. October 12, 1928. He received the B.S.E.E. and M.S.E.E. degrees from

[4] J. Otto, “Cheping RPV Data Links for ECM Protection,”Micro- Pennsylvania State University, University Park, in 1952 and 1954, re- ’ waves, December 1974, pp. 54-60. spectively, and the Ph.D. degree in electrical engineering from the Uni-

[5] T.’ G. Birdsall and M. P. Ristenbatt, Introduction to Linear versity of Michigan, Ann Arbor, in 1961.

” ~~~


IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-25, NO. 8, AUGUST 1977 763

He joined Cooley Electronics Laboratory of the University of Michigan’s Electrical and Computer Engineering Department in 1956 and worked on digital communication systems and countermeasures using spread spectrum techniques. In 1965 he became group Leader of Communications, and has pursued various aspects of special digital communications, including lowdetectability and antijam communications. He is a Lecturer in the ECE Depart- ment and chairs an annual continuing education

course on Digital Communications. He is the author of a basic circuits text (3rd edition): Semiconductor Circuits: Linear and Digital (Engle- wood Cliffs, N.J.: Prentice-Hall, 1975).

James L. Daws, Jr. (”65) was born in Sioux City, Iowa, on June 11, 1931. He received the BSE(EE), MSE, and Ph.D. degrees from the

, ’ University of Michigan, Ann Arbor, in 1959, 1961, and 1969, respectively.

He joined the Cooley Electronics Laboratory of the University of Michigan’s Electrical and Computer Engineering Department in 1957 and worked on the generation of sequences using shift register generators. He has continued to pursue the properties and applications of se-

quences along with various other aspects of spread spectrum communication systems. In addition to the research he is currently a Lecturer in the ECE Department at the University of Michigan.

Optimization of Coded Spread Spectrum System Performance GAYLORD K. HUTH, MEMBER, IEEE

Abstract-Error correction coding techniques significantly improve performance of spread spectrum communication systems in environments containing jamming, multipath, and unregulated multiple access. This paper investigates the optimization of spread spectrum system performance for time-varying unknown interference. Noncoherent frequency hopping (FH) spread spectrum modulation, and hybrid FH-PN incorporating a direct sequence PN modulation on each hopped frequency are studied. For FH or FH-PN, the data modulations considered are differential phase-shift-keying (DPSK), differential quadriphase-shift-keying (DQPSK), and multiple-frequency-shift-keying (MFSK). Both block and convolutional error correction coding techniques are studied as a means of improving the spread spectrum performance.

I. INTRODUCTION

0 PTIMIZATION of the performance of a communication system operating over a general channel in the presence

of unknown interference requires determining the worst case interference for each communication system. Thus, to maximize communication system performance in terms of probability of error or average interference power requires that: (1) the performance of each modulation/coding technique available to the communicator be determined for each possible interference; ( 2 ) the worst case interference, which minimizes the communication system performance, be established for each modulation coding technique; and (3) the communicator select the modulation/coding technique which provides the maximum performance against the worst case interference. In this way, the best possible communication system performance is achieved for unknown interference [ 11 .

Manuscript received February 3, 1976; revised April 2, 1977. The author is with the Axiomatix Corporation, Marina del Rey,

CA 90291.

Traditionally, Monte Carlo simulation techniques have been used to evaluate the performance of a modulation/ coding technique for time-varying interference. However, the effort required to optimize a communication system in the presence of unknown interference using Monte Carlo simulations is extremely large. In this paper, the system performance optimization is performed using analytical estimation techniques for probability of error versus signal- to-interference power ratio. These analytical performance estimates are easily evaluated and the necessary evaluation of system parameters and interference types can be quickly performed. Thus, the performance estimate is derived for each modulation/coding technique in the presence of each type of interference.

11. DATA MODULATION FOR FH AND FH/PN SPREAD SPECTRUM MODULATION

The data modulations considered for FH and FH/PN spread spectrum modulation are multiple-frequency-shift-keying MFSK), multiple-code-shift-keying (MCSK), binary differential phase-shift-keying (DPSK), and differential quadriphase-shift- keying (DQPSK). It should be noted that MFSK and MCSK give equivalent performance if FH/PN is used for the spread spectrum modulation.

It is important to note that only noncoherent frequency hopping is being considered since large hopping bandwidths make it impractical to maintain phase coherence across the total bandwidth. Therefore, each hop has an independent phase but the phase is constant over the hop. Constant phase is required for MFSK, MCSK, DPSK, and DQPSK. For DPSK and DQPSK, the hop rate must be slower than the bit rate


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