spread spectrum communications handbook

Part 1 INTRODUCTION TO SPREAD-SPECTRUM COMMUNICATION Source: SPREAD SPECTRUM COMMUNICATIONS HANDBOOK Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. INTRODUCTION TO SPREAD-SPECTRUM COMMUNICATION Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Chapter 1 A SPREAD-SPECTRUM OVERVIEW Over thirty years have passed since the terms spread-spectrum (SS) and noise modulation and correlation (NOMAC) were first used to describe a class of signaling techniques possessing several desirable attributes for com- munication and navigation applications, especially in an interference envi- ronment. What are these techniques? How are they classified? What are those useful properties? How well do they work? Preliminary answers are forthcoming in this introductory chapter. We will motivate the study of spread-spectrum systems by analyzing a sim- ple game, played on a finite-dimensional signal space by a communications system and a jammer, in which the signal-to-interference energy ratio in the communication receiver’s data detection circuitry serves as a payoff func- tion. The reader is hereby forewarned that signal-to-interference ratio cal- culations alone cannot illustrate many effects which, in subtle ways, degrade more realistic performance ratios, e.g., bit-error-rate in coded digital SS sys- tems. However, the tutorial value of the following simple energy calculations soon will be evident. 1.1 A BASIS FOR A JAMMING GAME The following abstract scenario will be used to illustrate the need for spec- trum spreading in a jamming environment, to determine fundamental design characteristics, and to quantify one measure of SS system perfor- mance. Consider a synchronous digital communication complex in which the communicator has K transmitters available with which to convey infor- mation to a cooperating communicator who possesses K matching receivers (see Figure 1.1).Assume for simplicity that the communication signal space has been “divided equally” among the K transmitters. Hence, with a band- width W ss available for communicating an information symbol in a T s sec- ond interval (0, T s ), the resultant transmitted-signal function space of dimension approximately 2T s W ss is divided so that each transmitter has a 3 Source: SPREAD SPECTRUM COMMUNICATIONS HANDBOOK Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. D-dimensional subspace, D ϭ 2T s W ss /K, in which to synthesize its output signal. Denote an orthonormal basis for the total signal space by c k (t), k ϭ 1,2, ,2T s W ss , i.e., (1.1) where the basis functions may be complex valued, and ( )* denotes conju- gation. Then the signal emitted by the k-th transmitter is of the form (1.2) where (1.3) and {a j } is a data-dependent set of coefficients. We will refer to the above as an orthogonal communication system complex of multiplicity K. Of course, real systems generally radiate real signals.The reader may wish to view m k (t) as the modulation on the radiated signal Re{m k (t) exp (jv c t ϩ u)}. Without loss of generality, we can dispense with the shift to RF during this initial discussion. In a simplified jamming situation, the signal z i (t) observed at the i-th receiver in the receiving complex might be (1.4) where n i (t) represents internally generated noise in the i-th receiver, J(t) is an externally generated jamming signal, and the K-term sum represents the total output signal of the transmitter complex. One signal processing z i 1t2ϭ a K kϭ 1 m k 1t2ϩ J1t2ϩ n i 1t2. N k ϭ 5j: 1k Ϫ 12D 6 j Յ kD6 m k 1t2ϭ a jHN k a j c j 1t2, Ύ T s 0 c j 1t2c * k 1t2dt ϭ e 1, j ϭ k 0, j  k 4 A Spread-Spectrum Overview Figure 1.1. The scenario for a game between a jammer and a communication sys- tem complex. A SPREAD-SPECTRUM OVERVIEW Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. strategy for the i-th receiver is to project the received signal onto the set of basis functions for the i-th transmitter’s signal space, thereby calculating (1.5) In the absence of jamming and receiver noise, the properties of the ortho- normal basis insure that z j ϭ a j , and thus, the i-th receiver correctly discov- ers the data dependent set of coefficients {a j }, used by the i-th transmitter. Both the jamming and receiver noise signals can be expanded in terms of the orthonormal basis as (1.6) (1.7) where J 0 (t) represents that portion of the jamming signal orthogonal to all of the 2T s W ss basis functions used in producing the composite signal. The receiver noise component n 0i (t) likewise is orthogonal to all possible trans- mitted signals.These representations indicate that, in general, the projection (1.5) of z i (t) onto c j (t) in the i-th receiver produces (1.8) The everpresent thermal noise random variable n ij , assumed complex Gaussian, independent, and identically distributed for different values of i and/or j, represents the relatively benign receiver perturbations in the absence of jamming. The jamming signal coefficients J j are less easily clas- sified, and from the jammer’s point of view, hopefully are unpredictable by the receiver. The total energy E J in the jamminig signal J(t) over the time interval (0, T s ) is given by (1.9) Obviously, the energy term involviong J 9 (t) serves no useful jamming pur- pose, and henceforth, will be assumed zero. (In keeping with this conserva- tive aspect of communication system design, we also assume that the jammer has full knowledge of timing and of the set {c j (t)} of basis functions.) The sum in (1.9) can be partitioned into K parts, the i-th part representing the energy E Ji used to jam the i-th receiver. Thus, (1.10) E J ϭ a K iϭ 1 E Ji , E Ji ϭ a jHN i ƒ J j ƒ 2 . E J ϭ Ύ T s 0 ƒ J1t2ƒ 2 dt ϭ a 2T s W ss jϭ 1 ƒ J j ƒ 2 ϩ Ύ T s 0 ƒ J 0 1t2ƒ 2 dt. z j ϭ a j ϩ J j ϩ n ij for all j H N i . n i 1t2ϭ a 2T s W ss jϭ 1 n ij c j 1t2ϩ n 0i 1t2, J1t2ϭ a 2T s W ss jϭ 1 J j c j 1t2ϩ J 0 1t2, j H N i , z j ϭ Ύ T s 0 z i 1t2c * j 1t2dt for all j H N i . A Basis for a Jamming Game 5 A SPREAD-SPECTRUM OVERVIEW Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. A similar partition holds for the total transmitted signal energy E s , namely (1.11) E Si being the energy used by the i-th transmitter. The additive partitions (1.10), (1.11) are a direct result of the orthogonality requirement placed on the signals produced by the transmitter complex. The above signal representations and calculations have been made under the assumption that the channel is ideal, causing no attenuation, delay, or distortion in conveying the composite transmitted signal to the receiver com- plex, and that synchronous clocks are available at the transmitter and receiver for determining the time interval (0, T s ) of operation. Hence, impor- tant considerations have been suppressed in this initial discussion, so that we may focus on one major issue facing both the communication system designer and the jammer designer, namely their allocations of transmitter energy and jammer energy over the K orthogonal communication links. 1.2 ENERGY ALLOCATION STRATEGIES Within the framework of an orthogonal communication system complex of multiplicity K, let’s consider the communicator and jammer to use the fol- lowing strategies for allocating their available energies, E S and E J respec- tively, to the K links. Communicators’ strategy: Randomly select K S links, K S Յ K, for equal energy allocations, each receiving E S /K S units.The remaining links are not utilized. Jammer’s strategy: Randomly select K J receivers for equal doses of jam- ming energy, each receiving E J /K J units. The remaining channels are not jammed. The quantity K S is referred to as the diversity factor of the communication system complex. When K S exceeds unity, the receiver must employ a diver- sity combining algorithm to convert the outputs of the K S chosen links into a single output for the system user. The performance measure to be employed here, in determining the effectiveness of these strategies, will not depend on specifying a particular diversity combining algorithm. The randomness required of these strategies should be interpreted as meaning that the corresponding adversary has no logical method for pre- dicting the choice of strategy, and must consider all strategies equally likely. Furthermore, random selection of communication links by the transmitter should not affect communication quality since all available links are assumed to have equal attributes. (Examples of link collections with non-uniform attributes will be considered in Part 2, Chapter 2.) E S ϭ a K iϭ 1 E Si , E Si ϭ a jHN i ƒ a j ƒ 2 , 6 A Spread-Spectrum Overview A SPREAD-SPECTRUM OVERVIEW Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. The receiving complex, having knowledge of the strategy selected for communication, will collect all E S units of transmitted energy in the K S receivers remaining in operation. However, the amount of jamming energy collected by those same K S receivers is a random variable whose value is determined by which of the jamming strategies is selected ( denotes a binomial coefficient). Under the equally likely strategy assump- tion, the probability that the jammer strategy will include exactly N of the K S receivers in use, is given by (1.12) where (1.13) (1.14) Using (1.12) — (1.14), it is possible to compute the expected total effective jam- ming energy E Jeff sensed by the K S receivers, namely (1.15) E being the expected value operator. Despite the complicated form of Pr(N), it can be verified that (1.16) and hence, that (1.17) More generally, it can be verified that when the communicators use the strat- egy described above, (1.17) is the average total effective jamming energy for any arbitrary distribution of jamming energy. This idealized situation leads one to conclude, based on (1.17), that the receiver can minimize the jammer’s effectiveness energy-wise by not using diversity, i.e., by using K S ϭ 1. Furthermore, the multiplicity K of the orthogonal communication system complex should be made as large as pos- sible to reduce E Jeff , i.e., the complex should be designed to use all of the available bandwidth.The energy-optimal communication strategy (K S ϭ 1) using a single one of the K available communication links, is called a pure spread-spectrum strategy. This strategy, with its accompanying threat to use E Jeff ϭ E J K S K . E5N6ϭ K J K S K , E Jeff ϭ E J K J E5N6, N max ϭ min1K S , K J 2. N min ϭ max10, K J ϩ K S Ϫ K2 Pr1N2ϭ e a K S N ba K Ϫ K S K J Ϫ N b a K K J b , N min Յ N Յ N max a # # ba K K J b Energy Allocation Strategies 7 0, otherwise A SPREAD-SPECTRUM OVERVIEW Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. any of K orthogonal links, increases the total signal-to-jamming ratio from E S /E J at each receiving antenna’s terminals to KE S /E J at the output of the designated receiver, and therefore qualifies as an anti-jam (AJ) modulation technique. The improvement E J /E Jeff in signal-to-jamming ratio will be called the energy gain EG of the signalling strategy played on the orthogonal com- munication system complex. (1.18) Hence, the energy gain for a pure SS strategy is the multiplicity factor of the complex. In this fundamental form (1.18), the energy gain is the ratio of the signal space dimension 2T s W ss perceived by the jammer for potential com- munication use to the total dimension K S D of the K S links’ D-dimensional signal spaces which the receiver must observe. For a fixed T s W ss product, this definition of energy gain makes no distinction between diversity and SS strategies using the same signal space dimension K S D. The reader may rec- ognize the fact that the quantity called the multiplicity factor, or energy gain in this chapter, is sometimes referred to as the processing gain of the SS sys- tem. This nomenclature is by no means universally accepted, and we will instead identify the term processing gain PG with the ratio W ss /R b , where R b is the data rate in bits/second. It is easily verified from (1.18) that process- ing gain and energy gain are identical when R b ϭ K S D/2T s , e.g., for binary orthogonal signalling (D ϭ 2) with no diversity (K S ϭ 1). Two key assumptions were made in showing that the pure SS strategy is best: (1) The channel is ideal and propagates all signals equally well, and (2) the proper performance measure is the total effective jamming energy. If either of the above assumptions is not acceptable, then the jammer’s strat- egy may influence the performance measure, and the optimum diversity fac- tor K S may be greater than one. Indeed, in later chapters it is shown that the use of bit-error rate (BER) as a performance measure implies that the opti- mum diversity factor can exceed unity. Let’s summarize the requirements characteristic of a digital spread-spec- trum communication system in a jamming environment: 1. The bandwidth (or equivalently the link’s signal-space dimension D) required to transmit the data in the absence of jamming is much less than the bandwidth W ss (or equivalently the system’s signal space dimension 2T s W ss ) available for use. 2. The receiver uses inner product operations (or their equivalent) to con- fine its operation to the link’s D-dimensional signal space, to demodu- late the signal, and thereby to reject orthogonal jamming waveform components. 3. The waveforms used for communication are randomly or pseudoran- domly selected, and equally likely to be anywhere in the available band- EG ϭ E J E Jeff ϭ K K S ϭ 2T s W ss K S D . 8 A Spread-Spectrum Overview A SPREAD-SPECTRUM OVERVIEW Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. width (or equivalently, anywhere in the system’s 2T s W ss dimensional sig- nal space). The term pseudorandom is used specifically to mean random in appearance but reproducible by deterministic means. We will now review a sampling of the wide variety of communication sys- tem designs which possess SS characteristics. 1.3 SPREAD-SPECTRUM SYSTEM CONFIGURATIONS AND COMPONENTS 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 K transmitter-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 2T s W ss -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 operandi of 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. Spread-Spectrum System Configurations and Components 9 A SPREAD-SPECTRUM OVERVIEW Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 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).) A SPREAD-SPECTRUM OVERVIEW Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. [...]... given at the website A SPREAD- SPECTRUM OVERVIEW Spread- Spectrum System Configurations and Components 15 Figure 1.3 Continued Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website A SPREAD- SPECTRUM OVERVIEW 16 A Spread- Spectrum Overview the... Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website A SPREAD- SPECTRUM OVERVIEW The Advantages of Spectrum Spreading 33 We will carry out the ensemble-averaging process under the assumption that the spectrum- spreading sequence {cn} is composed of independent, identically distributed random variables, equally likely to be ϩ1 or Ϫ1,... Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website A SPREAD- SPECTRUM OVERVIEW Spread- Spectrum System Configurations and Components 13 nal, or multiple frequency-shift-keyed (MFSK) data on a FH signal.These modulation schemes are the ones of primary interest in this book... Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website A SPREAD- SPECTRUM OVERVIEW 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,...A SPREAD- SPECTRUM OVERVIEW Spread- Spectrum System Configurations and Components 11 2 Stored reference (SR) systems require independent generation at transmitter and receiver of pseudorandom wideband waveforms which are... Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website A SPREAD- SPECTRUM OVERVIEW 18 A Spread- Spectrum Overview magnitude p/2 cause orthogonality, the jammer is forced to view his waveform selection problem as being defined for an orthogonal communication system complex with... Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website A SPREAD- SPECTRUM OVERVIEW 20 A Spread- Spectrum Overview observe the signal in a 2M-dimensional space whose basis over the interval (0, Ts) consists of Re{c(d)(t) exp(j2pfct)} evaluated for each of the M values of d, with... in a closely packed design is TsWss/M 1.5 THE ADVANTAGES OF SPECTRUM SPREADING We have seen the advantages of making a jammer counteract an ensemble of orthogonal communication systems The bandwidth increase which must accompany this SS strategy has further advantages which we will outline here 1.51 Low Probability of Intercept (LPI) Spectrum spreading complicates the signal detection problem for a surveillance... McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website A SPREAD- SPECTRUM OVERVIEW The Advantages of Spectrum Spreading 21 Here F2T is the time-limited Fourier transform F2T5x1t26 ϭ ^ Ύ T x1t2e Ϫj2pftdt, (1.43) ϪT and hence, E{0F 2 T {x(t)}0 2 } is the average energy spectral density... Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright © 2004 The McGraw-Hill Companies All rights reserved Any use is subject to the Terms of Use as given at the website A SPREAD- SPECTRUM OVERVIEW 22 A Spread- Spectrum Overview We consider two possible assumptions regarding the nature of the direct sequence {cn} a Random DS Modulation: If {cn} is a sequence of independent, identically distributed . Part 1 INTRODUCTION TO SPREAD- SPECTRUM COMMUNICATION Source: SPREAD SPECTRUM COMMUNICATIONS HANDBOOK Downloaded from Digital Engineering Library @ McGraw-Hill. to the Terms of Use as given at the website. Chapter 1 A SPREAD- SPECTRUM OVERVIEW Over thirty years have passed since the terms spread- spectrum (SS) and noise modulation and correlation (NOMAC). of dimension approximately 2T s W ss is divided so that each transmitter has a 3 Source: SPREAD SPECTRUM COMMUNICATIONS HANDBOOK Downloaded from Digital Engineering Library @ McGraw-Hill (www.digitalengineeringlibrary.com) Copyright