Theory of Spread-Spectrum Communications-A Tutorial

IEEE TRANSACTIONS ON COMMUNICATIONS, VOL.NO. COM-30, 5, MAY 1982 855 Theory of Spread-Spectrum Communications-A Tutorial RAYMOND L. PICKHOLTZ, FELLOW, I ~EE,DONALD L. SCHILLING, FELLOW,IEEE, AND LAURENCE B. MILSTEIN, SENIOR MEMBER, IEEE AbstracrSpread-spectrum communications, with its inherent ill- Themeans by which thespectnim is spread is crucial. terferenceattenuation capability, has over the years become an Several of the techniques are “direct-sequence” .moduldtion increasinglypopular technique for use inmany different systeml:. in which a fast pseudorandomly generated sequence causes Applications range from antijam systems, to code division multiple access systems, to systems designed to combat multipath. It is the phase transitions in the carrier containipg data, “frequency intention of this paper to provide a tutorial treatmentof the theory c% hopping,” in which the carrier iscaused to shift frequency spread-spectrumcommunications, including adiscussion on the in a pseudorandom way, arid “time hopping,” wherein bursts applicationsreferred to above, on theproperties of commom of signalare initiated at pseudorandom times. Hybrid com- spreadingsequences, and on techniquesthat can he used for a(- binations of these techniques are frequently used. quisition and tracking. Although the current applications for spread spectrum continue to be primarily for military communications, there I. INTRODUCTION is a growing interest in the use of this technique for mobile PREAD-spectrum systems have been developedsince radio networks (radio telephony, packet radio, and amateur Sabout the mid-1950’s. The initial applications have bee1 radio), tiining and positioning systems, somespecialized to military antijamming tactical communications, to guidance applications in satellites, etc. While the use of spread spectrum systems, to experimental ahtimultipath systems, and t3 naturally means that each transmission utilizes a large amount other applications [l]. A definition of spread spectrurl of spectrum, this may be compensated for by the interference that adequately reflects the characteristics of this techniqu: reduction capability inherent in the useof spread-spectrum is as follows: techniques, so thata considerable number of users might share the same spectral band. There are no easyanswers to “Spread spectrum is a means of transmission in which the question of whether spread spectrum is better or worse the signal occupies a bandwidth in excess of the mini- than conventional methods for such multiuser channels. mum necessary to send the information; the band spread However, the one issue that is clear is that spread spectrum is accomplished by means of a code which is independent affords an opportunity to give a desiredsignal a power ad- of the data, and a synchronized reception with the code vantageover many types of interference, including most at the receiver is used for despreading and subsequent data recovery.” intentional interference (i.e., jamniing). In this paper, we confine ourselves to principles related to the design and Under this definition, standard modulation schemes such as analysis of various important aspects of a spread-spectrum FM and PCM which also spread the spectrum of an informa- communications system. The emphasis will be on direct- tion signal do not qualify as spread spectrum. sequence techniques aild frequency-hopping techniques. There are many reasons for spreading the spectrum, and if The major systems questions associated with the design of done properly, a multiplicity of benefits can accrue simulta- a spread-spectrum system are: How is performance measured? neously: Some of these are What kind of coded sequences are used and what are their properties? How much jamming/interference protection is 0 Antijamming achievable? What is the performance of any user pair in an 0 Antiinterference environment where there are many spread spectrum users 0 Low probability of intercept (code division Multiple accessj? To what extent does spread 0 Multiple user random access communications with selec- spectrum reduce the effects of multipath? How is the relative tive addressing capability timing of the transmitter-receiver codes established (acquisi- i High resolution ranging tion) and retained (tracking)? 0 Accurate universal timing. It is the aim of this tutorial paper to answer some of these questions succinctly, and in the process, offer some insights Manuscript received December 22, 1981; revised February 16, 1982 into this important communications technique. A gldssafy of R. L. Pickholtz is with the Department of Electrical Engineering anc the symbols used is provided at the end of the paper. Computer Science, George Washington University, Washington, DC’ 20052. 11. SPREADING AND DiMENSIONALITY- D. L. Schilling is with the Department of ,Electricai Engineering City College of New York, New York, NY 10031. PROCESSING GAIN L. B. Milstein is with the Department of Electrical Engineering ant A fundamental issue in spread spectrum is how this Computer Science, University of California at San Diego, La Jolla CA 92093. technique affords protection against interfering signals with 0090-6778/82/0500-0~355$00.750 1982 IEEE 856 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. COM-30, NO. 5, MAY 1!282 finite power. The underlying principle is that of distributing uses random (rather than pseuodrandom) sequences, is as a relatively low dimensional (defined below) data signal in a follows. Suppose we consider transmission by meansof D high dimensional environment so that a jammer with a fixed equiprobable and equienergy orthogonal signalsimbedlded amount of total power (intent on maximum disruption of in an n-dimensional space so that communications) is obliged to either spread that fixed power over,all the coordinates, thereby inducing just a little iriter- ference in each coordinate, or else place all of the power into a small subspace, leaving the remainder of the space interference free. where A brief discussion of a classical problem of signal detection in noise should clarify the emphasis on finite interference power. The “standard” problem of digital transmission,in the presence of thermal noise is one where both transmitter and receiver know the set of M signaling waveforms{Si(t), 0 Q t < T; 1 < i bM}. The transmitter selects one of the waveforms and where {&(t); 1 f k G n} is an orthonormal basis spanning every T seconds to provide a data rate of log2M/T bitsis. If, the space, i.e., for example, S,(t) is sent, the receiver observes r(t) = S,(t) + n,(t) over [0, TI where n,(t) is additive, white Gaussian noise (AWGN) with (two-sided) power spectral density q0/2 W/Hz. It is well known [3] that the signal set can be completely specified by a linear combination of no more than D < M The average energy of each signal is orthonormal basis functions (seebelow), and that although the white noise, similarly expanded, requires an infinite number of terms, only those within the signalspace are “relevant” [3]: We say thatthe signal set defined aboveis D-dimensional if the minimum number of orthonormal basis (the overbar is the expected value over the ensemble). functions required to define all the signalsis D.D can be In order to hide this D-dimensional signal set in the larger shown to be [3] approximately 2BDT where BD is the total n-dimensional space, choose the sequence of coefficients (approximate) baildwidth occupancy of the signal set. The Sik independently (say, by flipping a fair coin if a binary optimum (minimum probability of error) detector in AWGN alphabet is used) such that they have zero mean and corre- consists of a bank of correlators or filters matched to each lation signal, and the decision as to which was thetransmitted signal corresponds to the largest output of the correlators. Given a specific signal design, the performance of such a l<iGD. system is well known to be a function only of the ratio of the energy per bit to the noise spectral density. Hence, against Thus, the signals, which are also assumed to be known to the white noise (which has infinite power and constant energy receiver (i.e., we assume the receiver had been supplied the in every direction), the use of spreading (large 2BDT) offers sequences Sik before transmission) but denied to the jammer, no help. The situation is quite different, however, when the have their respective energies uniformly distributed over the “noise” is a jammer with a fixed finite power. In this case, n basis directions as far as the jammer is concerned. theeffect of spreading the signal bandwidth so that the Consider next ajammer jammer is tmcertain as to where in the large space the components are is often to force the jammer to distribute its finite n power over many different coordiqates of the signal space. J(t) = x Jk@k(t); 0 < t b T (3) Since the desired signal can be “collapsed” by correlating k= 1 the signal at the receiver with the known code, the desired signal is protected against a jammer in the sense that it has with total energy an effective power advantage relative to the jammer. This rT n power advantage is oftenproportional to the ratio of the J2(t)dt = k= 1 Jk2 4 EJ dimensionality of the space of code sequences to that of the I, 2 data signal. It is necessary, of course, to “hide” the pattern by which thedata are spread. This is usually done ‘hth a which is added to the signal with the intent to disrupt c.om- pseudonoise (PN) sequence which has desired randomness munications. Assume that the jammer’s signal is independent properties and which isavailable to the cooperating trans- of the desired signal.One of the jammer’s objectives is to mitter and receiver, but denied to other undesirable users devise a strategy for selecting the components Jk2 of his of the common spectrum. f=ed total energy EJ so as to minimize the postprocessing A general model which conveys these ideas, but which signal-to-noiseratio (SNR) at the receiver.

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