Spread Spectrum (SS)

Jan De Nayerlaan, 5 B-286 Sint-Katelijne-Waver Belgium www.denayer.be Spread Spectrum (SS) introduction ir. J. Meel jme@denayer.wenk.be Studiedag Spread Spectrum - 6 okt. 99 In the period o nov. 997 - nov. 999 a Spread Spectrum project was worked out at the polytechnic DE NAYER instituut. The goal o this project was the hardware/sotware implementation o a Direct Sequence Spread Spectrum (CDMA) demonstrator in the 2.4 GHz ISM band. A measurement environment (Vector Signal Analyzer, IQ-modulator, Bit Error Rate Tester) was build out, resulting in a set o experiments based on this demonstrator. The project results where communicated with SMO s (Small and Medium Organisations) interested in Spread Spectrum. These notes were used to introduce the SMO s in the subject o Spread Spectrum.This Spread Spectrum project was sponsered by: Vlaams Instituut voor de bevordering van het Wetenschappelijk Technologisch onderzoek in de industrie (Flemisch Gouvernment) Sirius Communications Rotselaar - Belgium V2 dec 99

CONTENTS. DEFINITION OF SPREAD SPECTRUM (SS)...3 2. BASIC PRINCIPLE OF SPREAD SPECTRUM SYSTEMS: DSSS AND FHSS...3 BASIC PRINCIPLE OF DIRECT SEQUENCE SPREAD SPECTRUM (DSSS )...5 3. MODULATION...6 3.2 DEMODULATION...7 3.2. pn r = pn t...7 3.2.2 pn r pn t...8 4. PERFORMANCE IN THE PRESENCE OF INTERFERENCE...9 4. NARROWBAND INTERFERENCE... 4.2 WIDEBAND INTERFERENCE... 5. PSEUDO-NOISE SEQUENCES... 2 RANDOM WHITE GAUSSIAN NOISE... 2 PSEUDO-RANDOM NOISE... 3 5.3 PROPERTIES OF SEQUENCES... 3 TYPES... 5 5.4. m-sequence... 5 5.4.2 Barker Code... 8 5.4.3 Gold Codes... 8 Hadamard-Walsh Codes... 2 6. TRANSMITTER ARCHITECTURE... 22 7. RECEIVER ARCHITECTURE... 22 DECORRELATORS... 23 8. MATCHED FILTER... 23 8.2 ACTIVE CORRELATOR (INTEGRATE AND DUMP)... 24 9. SYNCHRONIZATION... 24 9. ACQUISITION PHASE (COARSE SYNCHRONIZATION)... 25 9.. Serial Synchronization (Sliding Correlator)... 25 9..2 Serial/Parallel Synchronization... 26 9.2 TRACKING PHASE (FINE SYNCHRONIZATION)... 27. MULTIPLE ACCESS... 28. MULTIPATH CHANNELS... 3 2. JAMMING... 3 3. ISM BANDS... 32 EVALUATION OF SS... 33 5. REFERENCES... 33 DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 2

. Deinition o Spread Spectrum (SS) A transmission technique in which a pseudo-noise, independant o the inormation data, is employed as a modulation waveorm to spread the signal energy over a bandwidth much greater than the signal inormation bandwidth. At the receiver the signal is despread using a synchronized replica o the pseudo-noise. 2. Basic principle o Spread Spectrum Systems: DSSS and FHSS DSSS FHSS d t S / P Spreading pn t I Q M-PSK Modulator tx d t M-FSK Modulator od Spreading FH Modulator tx hi pn t RF RF pn t n FW RF baseband bandpass baseband bandpass pseudo shit o thephase random coherentdemodulatio n pseudo shit o therequency random noncoherent demodulation hop channel RF -R c RF +R c RF 2 3 4 5 6 7 ch RF N W SS W SS = N. ch instantaneously: broadband instantaneously: smallband on average: broadband Direct Sequence Spread Spectrum (DSSS) A pseudo-noise sequence pn t generated at the modulator, is used in conjunction with an M-ary PSK modulation to shit the phase o the PSK signal pseudorandomly, at the chipping rate R c (=/ ) a rate that is an integer multiple o the symbol rate R s (=/T s ). The transmitted bandwidth is determined by the chip rate and by the baseband iltering. The implementation limits the maximum chiprate R c (clock rate) and thus the maximum spreading. The PSK modulation scheme requires a coherent demodulation. A short- system uses a length equal to a data symbol. A long- system uses a length that is much longer than a data symbol, so that a dierent chip pattern is associated with each symbol. DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 3

Frequency Hopping Spread Spectrum A pseudo-noise sequence pn t generated at the modulator is used in conjunction with an M-ary FSK modulation to shit the carrier requency o the FSK signal pseudorandomly, at the hopping rate R h. The transmitted signal occupies a number o requencies in time, each or a period o time T h (=/R h ), reerred to as dwell time. FHSS divides the available bandwidth into N channels and hops between these channels according to the sequence. At each requency hop time the generator eeds the requency synthesizer a requency word FW (a sequence o n chips) which dictates one o 2 n requency positions hi. Transmitter and receiver ollow the same requency hop pattern. The transmitted bandwidth is determined by the lowest and highest hop positions and by the bandwidth per hop position ( ch ). For a given hop, the instantaneous occupied bandwidth is identical to bandwidth o the conventional M-FSK, which is typically much smaller than W ss. So the FSSS signal is a narrowband signal, all transmission power is concentrated on one channel. Averaged over many hops, the FH/M-FSK spectrum occupies the entire spread spectrum bandwidth. Because the bandwidth o an FHSS system only depends on the tuning range, it can be hopped over a much wider bandwith than an DSSS system. Since the hops generally result in phasediscontinuity (depending on the particular implementation) a noncoherent demodulation is done at the receiver. With slow hopping there are multiple data symbols per hop and with ast hopping there are multiple hops per data symbol. DSSS FHSS symbol symbol d t d t h4 + o - o pn t h3 h2 pn t.d t h chip short N c T h hop ast hopping chip symbol symbol d t d t h4 - o pn t h3 + o h2 pn t.d t h chip long N c T h hop slow hopping chip DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 4

3. Basic principle o Direct Sequence Spread Spectrum (DSSS ) For BPSK modulation the building blocks o a DSSS system are: Spreading Despreading Input d t tx b Modulator tx channel rx Demodulator rx b d r Output pn t pn r RF RF baseband bandpass baseband Input: Binary data d t with symbol rate R s = /T s (= bitrate R b or BPSK) Pseudo-noise pn t with chip rate R c = / (an integer o R s ) Spreading: In the transmitter, the binary data d t (or BPSK, I and Q or QPSK) is directly multiplied with the sequence pn t, which is independant o the binary data, to produce the transmitted baseband signal tx b : tx b = d t. pn t The eect o multiplication o d t with a sequence is to spread the baseband bandwidth R s o d t to a baseband bandwidth o R c. Despreading: The spread spectrum signal cannot be detected by a conventional narrowband receiver. In the receiver, the received baseband signal rx b is multiplied with the sequence pn r. I pn r = pn t and synchronized to the sequence in the received data, than the recovered binary data is produced on d r. The eect o multiplication o the spread spectrum signal rx b with the sequence pn t used in the transmitter is to despread the bandwidth o rx b to R s. I pn r pn t, than there is no despreading action. The signal d r has a spread spectrum. A receiver not knowing the sequence o the transmitter cannot reproduce the transmitted data. To simpliy the description o modulation and demodulation, the spread spectrum system is considered or baseband BPSK communication (without iltering) over an ideal channel. DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 5

3. Modulation Spreading Despreading Input d t pn t tx b channel rx b pn r d r Output T s (symbol) T s + d t - t -R s R s (chip) + pn t - t -R c R c N c. + tx b - t -R c R c time requency Spread spectrum systems are spreading the inormation signal d t which has a BW ino, over a much larger bandwidth BW SS : BW ino R s << BW SS R c The SS-signal spectrum is white noise-like. The amplitide and thus the power in the SS-signal tx b is the same as in the original inormation signal d t. Due to the increased bandwidth o the SS- DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 6

signal the power spectral density must be lower. The bandwidth expansion actor, being the ratio o the chip rate R c and the data symbol rate R s, is usually selected to be an integer in practical SS systems: BWSS R c Tb SF = Gp = = = = N c BW R T 3.2 Demodulation in o s c Spreading Despreading Input d t pn t tx b channel rx b pn r d r Output 3.2. pn r = pn t + rx t b -R c R c - + pn r - t -R c R c N c. T s + T s d r - t -R s R s time requency DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 7

To demodulate, the received signal is multiplied by pn r, this is the same sequence as pn t (the pseudo-noise used in the transmitter), synchronized to the sequence in the received signal rx b. This operation is called (spectrum) despreading, since the eect is to undo the spreading operation at the transmitter. The multiplier output in the receiver is then (since pn r = synchronized pn t ) : d r = rx b. pn r = (d t. pn t ). pn t The sequence pn t alternates between the levels - and +, in the example: pn t = + + + - + - - The alternation is destroyed when the sequence pn t is multiplied with itsel (perectly synchronized), because: Thus: pn t. pn t = + or all t autocorrelation Ra (τ=) = average (pn t. pn t ) = + The data signal is reproduced at the multiplier output: d r = d t I the sequence at the receiver is not synchronized properly to the received signal, the data cannot be recovered. 3.2.2 pn r pn t I the received signal is multiplied by a sequence pn r, dierent rom the one used in the modulator, the multiplier output becomes: d r = rx b. pn r = (d t. pn t ). pn r In the receiver, detection o the desired signal is achieved by correlation against a local reerence sequence. For secure communications in a multi-user environment, the transmitted data d t may not be recovered by a user that doesn t know the sequence pn t used at the transmitter. Thereore: crosscorrelation Rc (τ) = average (pn t. pn r ) << or all τ is required. This orthogonal property o the allocated spreading s, means that the output o the correlator used in the receiver is approximately zero or all except the desired transmission. DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 8

4. Perormance in the presence o intererence To simpliy the inluence o intererence, the spread spectrum system is considered or baseband BPSK communication (without iltering). intererence Intererence Spreading i.pn t Spreading i Despreading d t Input d t tx b rx b d r Output pn t channel pn r =pn t The received signal rx b consists o the transmitted signal tx b plus an additive intererence i (noise, other users, jammer, ): rx b = tx b + i = d t. pn t + i To recover the original data d t, the received signal rx b is multiplied with a locally generated sequence pn r that is an exact replica o that used in the transmitter (that is pn r = pn t and synchronized). The multiplier output is thereore given by: d r = rx b. pn t = d t. pn t. pn t + i. pn t The data signal d t is multiplied twice by the sequence pn t, whereas the unwanted intererence i is multiplied only once. Due to the property o the sequnence: pn t. pn t = + or all t The multiplier output becomes: d r = d t + i. pn t The data signal d t is reproduced at the multiplier output in the receiver, except or the intererence represented by the additive term i. pn t. Multiplication o the intererence i by the locally generated sequence, means that the spreading will aect the intererence just as it did with the inormation bearing signal at the transmitter. Noise and intererence, being uncorrelated with the sequence, become noise-like, increase in bandwidth and decrease in power density ater the multiplier. Ater despreading, the data component d t is narrow band (R s ) whereas the intererence component is wideband (R c ). By applying the d r signal to a baseband (low-pass) ilter with a bandwidth just large enough to accommodate the recovery o the data signal, most o the intererence component i is iltered out. The eect o the intererence is reduced by the processing gain (G p ). DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 9

4. Narrowband intererence Spreading narrowband intererence Despreading Input d t tx b rx b d r Output pn t channel pn r d t () rx b () d r () data-signal narrowband intererence DS-signal (spread) whitened intererence DS-signal (despread) -R s R s -R c R c -R c -R s R s R c The narrowband noise is spread by the multiplication with the sequence pn r o the receiver. The power density o the noise is reduced with respect to the despread data signal. Only /G p o the original noise power is let in the inormation baseband (R s ). Spreading and despreading enables a bandwith trade or processing gain against narrow band interering signals. Narrowband intererence would disable conventional narrowband receivers. The essence behind the intererence rejection capability o a spread spectrum system: the useull signal (data) gets multiplied twice by the sequence, but the intererence signal gets multiplied only once. 4.2 Wideband intererence Spreading wideband intererence Despreading Input d t tx b rx b d r Output pn t channel pn r d t () data-signal user A wideband intererence user B rx b () DS-signal user A (spread) whitened intererence user B d r () DS-signal user A (despread) -R s R s -R c R c -R c -R s R s R c Multiplication o the received signal with the sequence o the receiver gives a selective despread o the data signal (smaller bandwidth, higher power density). The intererence signal is uncorrelated with the sequence and is spread. Origin o wideband noise: DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum

Multiple Spread Spectrum users: multiple access mechanism. Gaussian Noise: There is no increase in SNR with spread spectrum. The larger channel bandwidth (R c instead o R s ) increases the received noise power with G p : N ino = N.BW ino N SS = N.BW ss = N ino.g p The spread spectrum signal has a lower power density than the directly transmitted signal. Spreading Gaussian noise Despreading Input d t tx b rx b d r Output pn t channel pn r rx b () Gaussian noise DS-signal (spread) data-signal d t () Spread -R c R c Despread whitened Gaussian noise d r () DS-signal (despread) data-signal rx b () -R s R s Gaussian noise data-signal -R c -R s R s R c -R s R s DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum

5. Pseudo-Noise Sequences 5. Random White Gaussian Noise Zero-mean White Gaussian Noise (WGN) has the same power spectral density G WGN () or all requencies. The adjective white is used in the sense that white light contains equal amounts o all requencies within the visible band o electromagnetic radiation. The autocorrelation unction o WGN is given by the inverse Fourier transorm o the noise power spectral density G WGN (): Ra WGN ( τ) = + GWN(t).GWN(t + τ) dt = F N { G ()} = δ ( τ) WGN 2 The autocorrelation unction Ra WGN (τ) is zero or τ. This means that any two dierent samples o WGN, no matter how close together in time they are taken, are uncorrelated. The noise signal WGN(t) is totally decorrelated rom its time-shited version or any τ. The amplitude o integrated (bandlimited) WGN has a Gaussian probability density distribution p(wgni): p(wgni) = e σ 2π 2 n 2 σ WGNi(t) WGNi t p(wgni) Ra WGN (τ) G WGN () N /2 δ(τ).n /2 τ DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 2

5.2 Pseudo-Random Noise A Pseudo-Noise () sequence acts as a noiselike (but deterministic) carrier used or bandwidth spreading o the signal energy. The selection o a good is important, because type and length o the sets bounds on the system capability. The sequence is a Pseudo-Noise or Pseudo-Random sequence o s and s, but not a real random sequence (because periodic). Random signals cannot be predicted. The autocorrelation o a has properties simular to those o white noise. Pseudo-Random: Not random, but it looks randomly or the user who doesn t know the. Deterministic, periodical signal that is known to both the transmitter and the receiver. The longer the period o the spreading, the closer will the transmitted signal be a truly random binary wave, and the harder it is to detect. Statistical properties o sampled white-noise. Length: Short : The same sequence or each data symbol (N c. = T s ). Long : The sequence period is much longer than the data symbol, so that a dierent chip pattern is assosiated with each symbol (N c. >> T s ). 5.3 Properties o Sequences Balance Property In each period o the sequence the number o binary ones diers rom the number o binary zeros by at most one digit (or N c odd). pn = + + + - + - - = + When modulating a carrier with a coding sequence, one-zero balance (DC component) can limit the degree o carrier suppression obtainable, because carrier suppression is dependant on the symmetry o the modulating signal. Run-length Distribution A run is a sequence o a single type o binary digits. Among the runs o ones and zeros in each period it is desirable that about one-hal the runs o each type are o length, about one-ourth are o length 2, one-eigth are o length 3, and so on. Autocorrelation The origin o the name pseudo-noise is that the digital signal has an autocorrelation unction which is very similar to that o a white noise signal: impuls like. The autocorrelation unction or the periodic sequence pn is deined as the number o agreements less the number o disagreements in a term by term comparison o one ull period o the sequence with a cyclic shit (position τ) o the sequence itsel: Ra( τ) = NcTc/2 -NcTc/2 pn(t).pn(t+ τ) dt It is best i Ra(τ) is not larger than one count i not synchronized (τ=). DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 3

pn() = + + + - + - - pn() = + + + - + - - + + + + + + + = Σ = 7 = Ra(τ=) pn() = + + + - + - - pn() = + + - + - - + + + - - - + - = Σ = -= Ra(τ=) Ra(τ) N c =7 - -6 -N c -5-4 -3-2 - 2 3 4 5 6 N c τ/ + pn t t - -R c DC= R c N c. /N c For sequences the autocorrelation has a large peaked maximum (only) or perect synchronization o two identical sequences (like white noise). The synchronization o the receiver is based on this property. Frequency Spectrum Due to the periodic nature o the seqeunce the requency spectrum has spectral lines which become closer to each other with increasing sequence length N c. Each line is urther smeared by data scrambling, which spreads each spectral line and urther ills in between the lines to make the spectrum more nearly continuous. The DC component is determined by the zero-one balance o the sequence. Cross-correlation: Cross-correlation describes the intererence between s pn i and pn j : Rc( τ) = NcTc/2 -NcTc/2 pn (t).pn (t + i j τ) dt Cross-correlation is the measure o agreement between two dierent s pn i and pn j. When the cross-correlation Rc(τ) is zero or all τ, the s are called orthogonal. In CDMA multiple users occupy the same RF bandwidth and transmit simultaneous. When the user s are orthogonal, there is no intererence between the users ater despreading and the privacy o the communication o each user is protected. In practice, the s are not perectly orthogonal; hence the cross-correlation between user s introduces perormance degradation (increased noise power ater despreading), which limits the maximum number o simultaneous users. DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 4

5.4 Types 5.4. m-sequence A Simple Shit Register Generator (SSRG) has all the eedback signals returned to a single input o a shit register (delay line). The SSRG is linear i the eedback unction can be expressed as a modulo-2 sum (xor). (x,x 2,,x n ) = c x + c 2 x 2 + + c n x n 2 3 4 5 6... L out The eedback unction (x,x 2,,x n ) is a modulo-2 sum o the contents x i o the shit register cells with c i being the eedback connection coeicients (c i ==open, c i ==connect). An SSRG with L lip- lops produces sequences that depend upon register length L, eedback tap connections and initial conditions. When the period (length) o the sequence is exactly N c = 2 L -, the sequence is called a maximum-length sequence or simply an m-sequence. An m-sequence generated rom a linear SSRG has an even number o taps. I an L-stage SSRG has eedback taps on stages L, k, m and has sequence, a i, a i+, a i+2, than the reverse SSRG has eedback taps on L, L-k, L-m and sequence, a i+2, a i+, a i,. SSRG [5,3] 2 3 4 5, a i, a i+, a i+2,... image reverse SSRG [5,2] 2 3 4 5, a i+2, a i+, a i,... [5,2] = - - - - - - - - - - - - - - - [5,3] = - - - - - - - - - - - - - - - DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 5

In the ollowing table the eedback connections (even number) are tabulated or m-sequences generated with a linear SSRG (without image set). L N c =2 L - Feedback Taps or m-sequences # m-sequences 2 3 [2,] 2 3 7 [3,] 2 4 5 [4,] 2 5 3 [5,3] [5,4,3,2] [5,4,2,] 6 6 63 [6,] [6,5,2,] [6,5,3,2] 6 7 27 [7,] [7,3] [7,3,2,] [7,4,3,2] 8 [7,6,4,2] [7,6,3,] [7,6,5,2] [7,6,5,4,2,] [7,5,4,3,2,] 8 255 [8,4,3,2] [8,6,5,3] [8,6,5,2] 6 [8,5,3,] [8,6,5,] [8,7,6,] [8,7,6,5,2,] [8,6,4,3,2,] 9 5 [9,4] [9,6,4,3] [9,8,5,4] [9,8,4,] 48 [9,5,3,2] [9,8,6,5] [9,8,7,2] [9,6,5,4,2,] [9,7,6,4,3,] [9,8,7,6,5,3] 23 [,3] [,8,3,2] [,4,3,] [,8,5,] 6 [,8,5,4] [,9,4,] [,8,4,3] [,5,3,2] [,5,2,] [,9,4,2] [,6,5,3,2,] [,9,8,6,3,2] [,9,7,6,4,] [,7,6,4,2,] [,9,8,7,6,5,4,3] [,8,7,6,5,4,3,] 247 [,2] [,8,5,2] [,7,3,2] [,5,3,2] [,,3,2] [,6,5,] [,5,3,] [,9,4,,] [,8,6,2,] [,9,8,3] [,,9,8,3,] 76 For every set [L, k,, p] eedback taps listed in the table, there exists an image set (reverse set) o eedback taps [L, L-k,, L-p] that generates an identical sequence reversed in time. properties balance For an m-sequence there is one more one than zero in a ull period o the sequence. Since all states but the all-zero state are reached in an m-sequence, there must be 2 L- ones and 2 L- - zeros. run-length distribution For every m-sequence period, hal the runs (o all s or all s) have length, one-ourth have length 2, one-eight have length 3, etc. For each o the runs there are equally many runs o s and s. autocorrelation The autocorrelation unction o the m-sequence is or all values o the chip phase shit τ, except or the [-, +] chip phase shit area, in which correlation varies linearly rom the - value to 2 L - = N c (the sequence length). DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 6

The autocorrelation peak increases with increasing length N c o the m-sequence and approximates the autocorrelation unction o white noise. Other s can do no better than equal this perormance o m-sequences! Ra(τ) 3 N c = 3 25 2 SSRG [5,3] 5 5 - -5 - -5 5 5 τ/tc crosscorrelation Cross-correlation is the measure o agreement between two dierent s. Unortunatly, crosscorrelation is not so well behaved as autocorrelation. When large numbers o transmitters, using dierent s, are to share a common requency band (multi-user environment), the sequences must be careully chosen to avoid intererence between users. Rc(τ) [5,3] - [5,2] crosscorrelation Rc(τ) [5,3] - [5,4,3,2] crosscorrelation 2 8 6 4 2-2 -4-6 -8 - + -5-5 5 5-9 τ/tc 8 6 +7 4 2-5 -5 5 5-2 -4-6 -8 - -9 τ/tc security The m-sequence s are linear, and thus not usable to secure a transmission system. The linear s are easily decipherable once a short sequential set o chips (2L+) rom the sequence is known. (The overall system could still be secure i the inormation itsel where end by a cryptographically secure technique). DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 7

5.4.2 Barker Code The number o stages L in the SSRG also determines the length (period) N c =2 L o the m- sequence s. The Barker gives s with dierent lengths and simular autocorrelation properties as the m-sequences. Barker () = - - - - - = + (balanced) Barker (3) = - - - - = + 5 (unbalanced) The autocorrelation unction o the balanced chip Barker is shown in the next igure. Ra(τ) 2 N c = 8 6 4 2 - -5-4 -3-2 - 2 3 4 5 τ/tc 5.4.3 Gold Codes The autocorrelation properties o the m-sequences cannot be bettered. But a multi-user environment (Code Devision Multiple Access) needs a set o s with the same length and with good cross-correlation properties. Gold sequences are useull because a large number o s (with the same length and with controlled crosscorrelation) can be generated, although they require only one pair o eedback tap sets. Gold s are product s achieved by the exclusive or-ing (modulo-2 adding) o two maximum-length sequences with the same length (actor s). The sequences are added chip by chip by synchronous clocking. Because the m-sequences are o the same length, the two generators maintain the same phase relationship, and the s generated are o the same length as the two base s which are added together, but are nonmaximal (so the autocorrelation unction will be worse than that o m-sequences). Every change in phase position between the two generated m-sequences causes a new sequence to be generated. m-sequence (τ = ) clk Gold-sequence (k) m-sequence 2 (τ = k. ) DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 8

Any 2-register Gold generator o length L can generate 2 L - sequences (length 2 L - ) plus the two base m-sequences, giving a total o 2 L + sequences. In addition to their advantage in generating large numbers o s, the Gold s may be chosen so that over a set o s available rom a given generator the autocorrelation and the crosscorrelation between the s is uniorm and bounded. When specially selected m- sequences, called preerred m-sequences, are used the generated Gold s have a three valued crosscorrelation. L N c normalized 3-value crosscorrelation Odd 2 L - -/N c -(2 (L+)/2 + )/N c (2 (L+)/2 - )/N c Even 2 L - -/N c (not k.4) -(2 (L+2)/2 + )/N c (2 (L+2)/2 - )/N c Frequency o occurence ~.5 ~.25 ~.25 ~.75 ~.25 ~.25 This important subset o Gold s are the Preerred Pair Gold s. L N c =2 L - preerred pairs o m-sequences 3-value bound crosscorrelations 5 3 [5,3] [5,4,3,2] 7 - -9-29% 6 63 [6,] [6,5,2,] 5 - -7-27% 7 27 [7,3] [7,3,2,] 5 - -7-3% [7,3,2,] [7,5,4,3,2,] 8* 255 [8,7,6,5,2,] [8,7,6,] 3 - -7 +2% 9 5 [9,4] [9,6,4,3] 3 - -33-6% [9,6,4,3] [9,8,4,] 23 [,9,8,7,6,5,4,3] [,9,7,6,4,] 63 - -65-6% [,8,7,6,5,4,3,] [,9,7,6,4,] [,8,5,] [,7,6,4,2,] 247 [,2] [,8,5,2] [,8,5,2] [,,3,2] 63 - -65-3% Predictable cross-correlation properties are necessary in an environment where one must be picked rom several s which exist in the spectrum. Only part o the generated Gold s are balanced. [5,4,3,2] = - - - - - - - - - - - - - - - [5,3] () = - - - - - - - - - - - - - - - Gold() = - - - - - - - - - - - - - - - - - - - Σ Gold() = -7 = not balanced [5,4,3,2] = - - - - - - - - - - - - - - - [5,3] () = - - - - - - - - - - - - - - - Gold() = - - - - - - - - - - - - - - - Σ Gold() = = balanced DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 9

SSRG [5,3] 2 3 4 5 Gold-sequence SSRG [5,4,3,2] 2 3 4 5 Ra(τ) 3 N c = 3 25 2 5 5 +7-5 -5-5 - τ/tc - -9 Rc(τ) Gold() cross Gold() +7 Rc(τ) +7 Gold() cross Gold(2) 5 5-5 -5 5 5 τ/tc - -5 5 5 - - -5 τ/tc - -9 - -9 Rc(τ) 5 Gold() cross Gold(3) +7 Rc(τ) 5 +7 Gold() cross Gold(4) -5 - -5 5 5 τ/tc - 5 5 - - τ/tc -5-5 -9-9 - - DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 2

DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 2 5.4.4 Hadamard-Walsh Codes The Hadamard-Walsh s are generated in a set o N = 2 n s with length N = 2 n. The generating algorithm is simple: [] H with H H H H H 2 N / 2 N / 2 N / 2 N / N = = The rows (or columns) o the matrix H N are the Hadamard-Walsh s. = = = H H H 8 4 2 In each case the irst row (row ) o the matrix consist entirely o s and each o the other rows contains N/2 s and N/2 s. Row N/2 starts with N/2 s and ends with N/2 s. The distance (number o dierent elements) between any pair o rows is exactly N/2. For H 8 the distance between any two rows is 4, so the Hamming distance o the Hadamard is 4. The Hadamard-Walsh can be used as a block in a channel enr: each sequence o n bits identiies one row o the matrix (there are N =2 n possible rows). All rows are mutually orthogonal:.h h jk N k ik = = or all rows i and j. The cross-correlation between any two Hadamard-Walsh s o the same matrix is zero, when perectly synchronized. In a synchronous CDMA system this ensures that there is no intererence among signals transmitted by the same station. Only when synchronized, these s have good orthogonal properties. The s are periodic, which results in less spreading eiciency and problems with synchronization based on autocorrelation.

6. Transmitter Architecture A typical architecture o a Direct Sequence Spread Spectrum (DS-SS) transmitter: d t mod MAP I Q SPREAD I chip Q chip chip ilter chip ilter IQ-MOD DAC sample tx(if) pn I pn Q cos( IF ) sin( IF ) generator sinewave chip n. IF 7. Receiver Architecture A typical architecture o a Direct Sequence Spread Spectrum (DS-SS) receiver: rx(if) ADC IQ-DEMOD chip ilter chip ilter I chip Q chip DESPREAD N ct c N ct c (.)dt (.)dt I corr Q corr demod MAP d r sample cos( IF ) sin( IF ) pn I pn Q sinewave generator NCO sample NCO ϕ chip ϕ IF n. IF chip SYNCHRONIZATION LOOPS DLL loop ilter PLL loop ilter The basic building blocks o a DS-SS (digital) receiver are: coherent IQ vector-demodulator with waveorm synthesizer (Direct Digital Synthesis) at the IF-carrier requency ( IF ) and chip matched ilters (usually Square Root Raised Cosine) despreading (correlation o the received symbols with the locally generated -sequence(s) pn I and pn Q ) decorrelated IQ to data demodulator mapping synchronization loops or the IF-carrier ( IF, phase error ϕ IF measured ater despreading to reduce the inluence o noise) and chip requency ( chip ) DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 22

8. Decorrelators Two decorrelator architectures can be used or despreading spread spectrum signals: the matched ilter and the active correlator. They are optimum rom a SNR point o view. 8. Matched Filter A typical matched ilter implements convolution using a inite impuls response ilter (FIR) whose coeicients are the time reverse o the expected sequence, to de the transmitted data. DELAY LINE Rc[rx b,h] iq c (t) iq c (t- ) iq c (t-2 ) iq c (t-(n c -) )... h h h Nc-2 h Nc-... + Rc[iq c,h] 2N c N c For the given example: pn t = [pn pn pn 2 pn 3 pn 4 pn 5 pn 6 ] = [+ + + - + - -] h = [h h h 2 h 3 h 4 h 5 h 6 ] = [- - + - + + +] The output o the FIR ilter is the convolution o the received IQ-demodulated and iltered signal iq c (I chip or Q chip on the receiver architecture blockdiagram) with the FIR impulsreponse h=[ h h h Nc- ]. Due to the time reversion, the output o the ilter is the correlation o rx b with the local sequence. Rc( τ) = N c i= iq (t c i.t c ).h i = N c i= iq (t c i.t c ).p Nc i In the shown example, sample o the received signal per chip is taken ( sample = chip ). To increase the accuracy o synchronisation oversampling with a actor s can be used. In this case there are s samples per chip ( sample = s. chip ). The dimensions o the matched ilter are also increased with a actor s (each ilter coeicient h i is used s time). I the receiver is not synchronized, then the received signal will propagate through the matched ilter, which outputs the complete correlation unction. The large peak conirms that the correct is indeed being received and provides accurate timing inormation or the synchronisation o the received signal. The output Rc o the FIR matched ilter is immediately the decorrelated data: the polarity o the large correlation peaks indicates the data value. DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 23

8.2 Active Correlator (Integrate and Dump) When timing inormation is already available, then the simpler active correlator receiver can be used. This receiver only operates correctly when the local sequence pn r is accurately matched and correctly timed, with respect to the spreading within the received signal rx b. Synchronization can be obtained by sliding the reerence signal through the received signal. This can be an extremely slow process, however, or large spreading waveorms (long s). Rc[iq c,pn r (τ)] iq c N c T c (.)dt Rc[iq c,pn r (τ) ] Rc(N c ) τ t N c 2 N c pn r integrate dump Rc(2 N c ) 9. Synchronization For its proper operation, a SS communication system requires that the locally generated sequence (pn r used in the receiver Rx to despread the received signal) is synchronized to the sequence o the transmitter generator (pn t used to spread the transmitted signal in the transmitter Tx) in both its rate and its position. Due to the sharp peak in the autocorrelation unction, a misalignment in the sequence o /2 gives a loss o a actor 2 in processing gain. Sources o Synchronization Uncertainty Time uncertainty: Uncertainty in distance between Tx-Rx (propagation delay) Relative clock shits Dierent phase between Tx-Rx (carrier, sequence) Frequency uncertainty: Relative velocity v r between Tx-Rx (Doppler requency shit) aects the carrier requency carrier (with c the speed o light in the propagation medium): doppler carrier = carrier(± For a carrier requency o 2.4 GHz this gives a requency shit carrier = 2.2Hz/km/hr. For a relative velocity v r = km/hr this gives carrier = 22Hz. The process o synchronizing the locally generated sequence with the received sequence is usually accomplished in two steps. The irst step, called acquisition, consists o bringing the DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 24 v r ) c

two spreading signals into coarse alignment with one another. Once the received sequence has been acquired, the second step, called tracking, takes over and continuously maintains the best possible waveorm ine alignment by means o a eedback loop. This is essential to achieve the highest correlation power and thus highest processing gain (SNR) at the receiver. 9. Acquisition Phase (Coarse Synchronization) The acquisition problem is one o searching throughout a region o time and requency (chip, carrier) in order to synchronize the received spread-spectrum signal with the locally generated sequence. Since the despreading process typically takes place beore carrier synchronization, and thereore the carrier is unknown at this point, most acquisition schemes utilize noncoherent detection. A common eature o all acquisition methods is that the received signal and the locally generated sequence are irst correlated with a coarse time step (mostly /2) to produce a measure o simularity between the two. This measure is then compared to a threshold to decide i the two signals are in synchronism. I they are, a veriication algorithm is started. To prevent alse locking, it is necessary to dwell or some time to test synchronism. Than the tracking loop takes over. For proper synchronization, a peaked autocorrelation is required rom the sequence. Matched Filter (parallel) A matched ilter calculates the correlation unction at each sample timestep T sample. This gives the shortest acquisition time but the ully parallel implementation requires a lot o hardware. The hardware increases with the length and and oversampling actor s. Thereore it is mostly used or short s. Active Correlator (serial) An active correlator needs an integration over a total period N c. o the sequence to calculate one point o the correlation unction. Less hardware is needed, but a larger acquisition time is required. This can be reduced by using parallelism as explained below. 9.. Serial Synchronization (Sliding Correlator) iq c pn r N c T c (.)dt c /N c threshold detector acquisition indication (every N c ) generator c chip clock generator search control: i no signal advance /2 The sliding correlator is based on the correlation result o one active correlator. The correlator cycles through the time uncertainty, usually in discrete time intervals o /2 seconds or less. The correlation is perormed over the period o the sequence T s = N c.. Ater each integration interval the correlator output is compared with a threshold to determine i the known sequence is present. I the threshold is not exceeded, the known sequence o the receiver (pn r ) is advanced by /2 seconds and the correlation process is repeated. These operations are perormed until a signal is detected or until the search has been perormed over the time DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 25

uncertainty interval T u. For a coarse time step o /2 the worst case acquisition time is (T u = N c ): T acq = [T u / /2]. N c = 2 N c T u = 2 N c 2 This becomes unaccepatable long or long s (large N c ). 9..2 Serial/Parallel Synchronization Early pn r (t+ /2) N c T c (.)dt c /N c iq c pn r (t) Precise N T c c (.)dt threshold detector c /N c Late pn r (t- /2) N c T c (.)dt acquisition indication (every N c ) c /N c generator c chip clock generator search control: i no signal advance 3 /2 More active correlators are placed in parallel (3 in this example) with sequences spaced one hal chip ( /2) apart. Ater the integration period N c. the results o the correlator outputs are compared. The correlation unction is thus calculated in 3 successive points (spaced one hal chip apart). When no comparator output exceeds the threshold the sequences are advanced over 3 /2 seconds. When the threshold is exceeded, the correlator output with the largest output is chosen. For a search with 3 parallel correlators over the time uncertainty T u interval in time steps o /2 the worst case acquisition time is(t u = N c ): T acq = [T u / 3 /2]. N c = 2/3 N c T u = 2/3 N c 2 The search time is reduced at the expense o a more complex and costly implementation. DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 26

9.2 Tracking Phase (Fine Synchronization) The tracking maintains the generator at the receiver in synchronism with the received signal. This is needed to achieve maximum processing gain. For a sequence phase error o /2 the processing gain is reduced with a actor 2. N c Late (N c -)/2 Ra(t) Early Delay-Locked Loop (DLL) - -2 - -/2 /2 2 τ/tc The locally generated pn r (t) o the tracking loop is oset in phase rom the incoming pn(t) by a time τ, with τ < /2. In the DLL, two sequences pn r (t + /2 + τ) and pn r (t - /2 + τ) are delayed rom each other by one time chip ( ). The Early and Late outputs are the evaluation o the autocorrelation unction at two timepoints: c e = Ra(τ - /2) c l = Ra(τ + /2). Precise N c T c (.) dt threshold detector d r pn r (t+τ) Early N c T c (.) dt latch pn r (t+ /2+τ) c e iq c generator c c /N c chip clock generator Y - + pn r (t- /2 +τ) Late N c T c c /N c (.) dt latch c l When τ is positive, the eedback signal Y(t) instructs the chip clock generator (NCO = numerical controlled oscillator) to increase its requency, thereby orcing τ to decrease. When τ is negative, the eedback signal Y(t) instructs the numerical controlled oscillator (NCO) to decrease its requency, thereby orcing τ to increase. -c e Y - /2 /2 c l τ DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 27

. Multiple Access Code Division Multiple Access (CDMA) is a method o multiplexing (wireless) users by distinct (orthogonal) s. All users can transmit at the same time, and each is allocated the entire available requency spectrum or transmission. CDMA is also know as spread-spectrum multiple access SSMA. CDMA does not require the bandwidth allocation o FDMA, nor the time synchronization o the indivividual users needed in TDMA. A CDMA user has ull time and ull bandwidth available, but the quality o the communication decreases with an increasing number o users (BER ). In CDMA each user: has it s own uses the same RF bandwidth transmits simultaneously (asynchronous or synchronous) Input user d t Spreading pn d.pn Modulator tx channel rx Demodulator rx b = d.pn + d 2.pn 2 + d 3.pn 3 +... + d N.pn N d r +N u pn Output Input user 2 d 2t pn 2 2 d.pn 2 tx 2 Modulator tx 3... tx N Correlation o the received baseband spread spectrum signal rx b with the sequence o user only despreads the signal o user. The other users produce noise N u or user. rx b d r user 3 user N user user 3 user N user 2 user 2 user -R c R c -R s R s Only that portion o the noise produced by the other users alling in the inormation bandwidth [- R s, R s ] o the receiver, will cause intererence with the desired signal. DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 28

The set o s must have the ollowing properties: autocorrelation or good synchronization low crosscorrelation (orthogonal s) or low MAI Useul s are: Gold s, Kasami s (asynchronous CDMA) Hadamard-Walsh s (synchronous CDMA) Multiple Access Intererence (MAI) The detector receives a signal composed o the sum o all users signals, which overlap in time and requency. Multiple access intererence (MAI) reers to the intererence between directsequence users and is a actor which limits the capacity and perormance o DS-CDMA systems. In a conventional DS-CDMA system, a particular user s signal is detected by correlating the entire received signal with that user s waveorm. The conventional detector does not take into account the existence o MAI. Because o the intererence among users, however, a better detection strategy is one o multi-user detection. Inormation about multiple users is used jointly to better detect each individual user. Near-Far problem Suppose: Wireless channel Multi-users (transmitters) using the same channel One receiver Each user is a source o intererence or the other users, and i one is received with more power, than that user generates more intererence or the other users. It is important that the receiver gets the same power rom each transmitter. The use o power control ensures that all users arrive at about the same power P rx at the receiver, and thereore no user is unairly disadvantaged relative to the others. The signal-to-noise intererence power ratio at the receiver input or N u simultaneous users is: SNR = (N u P rx ).P rx = (N u ) rx b user 6 user 4 user 3 user -R c R c 2 3 4 5 6 7 8 DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 29

. Multipath Channels In wireless channels there exists oten multiple path propagation: there is more than one path rom the transmitter to the receiver. Such multipaths may be due to: Atmospheric relection or reraction Relections rom ground, buildings or other objects rx d - rx r = n. λ/2 rx d + direct path rx r relected path = ading dip N c Rad (t) - -2-2 Ra r (t) τ/tc Multipaths may result in luctuations in the received signal level (ading). Each path has its own attenuation and time delay. It is important to keep the direct path and reject the others. Assume that the receiver is synchronized to the time delay and RF phase o the direct path. The signals at the receiver can be rom: the direct path, other paths, white noise, intererence. Suppose two discrete paths: a direct path and only one non-direct path (delayed by a time τ compared to the direct path). Spreading rx d Despreading Input d t tx b Modulator tx channel rx r rx Demodulator rx b d r Output pn t pn r RF RF τ = dierential time delay between the two paths < τ < T θ = random angle phase between the carrier o the direct and the non-direct path α = attenuation o the secundary path DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 3

The signal at the receiver can be expressed as: rx = rx d + rx r + n =A d t (t) pn(t) cos(ω t) + α A d t (t-τ) pn(t-τ) cos(ω t + θ) + n(t) For the receiver, synchronized to the direct path signal, the output o the correlator, can be written as: d (t = N r c T ) = c NcTc N T c [ c B.pn(t).pn(t) + C.pn(t).pn(t τ) n(t) ] pn(t).rx(t) dt = + o The sequence has an autocorrelation unction with the property: pn(t) pn(t) = pn(t) pn(t-τ) o Multipath signals that are delayed by a chip period or longer relative to the desired signal (outdoor relections) are essentially uncorrelated and do not contribute to multipath ading. The SS System eectively rejects (mitigation) the multipath intererence like in the case o CDMA. dt d (t = N T ) = d + r c c t n with n = noise and multipath intererence The that arrives rom the non-direct channel(s) is not synchronized to the o the direct path and is rejected. 2. Jamming The goal o a jammer is to disturb the communication o his adversary. The goals o the communicator are to develop a jam-resistant communication system under the ollowing assumptions: Complete invulnerability is not possible The jammer has a priori knowledge o most system parameters, requency bands, timing, traic,... The jammer has no a priori knowledge o the spreading Protection against jamming waveorms is provided by purposely making the inormation-beating signal occupy a bandwidth ar in excess o the minimum bandwidth necessary to transmit it. This has the eect o making the transmitted signal assume a noise-like appearance so as to blend into background. The transmitted signal is thus enabled to propagate though the channel undetected by anyone who may be listening. Spread spectrum is a method o camoulaging the inormation-bearing signal. DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 3

3. ISM Bands ISM (Industrial, Scientiic,and Medical) requency bands are reserved or (unlicensed) spread spectrum applications. Poperties or higher requencies: - higher path loss, shorter distance - higher implementation cost + less intererence + more channels, higher throughput Regulations or the 2.4 GHZ ISM band: ISM-Band Bandwith 92-928 MHz 26 MHz 2.4-2.4835 GHz 83.5 MHz 5.725-5.85 GHz 25 MHz Maximum Transmit Power Geographic Location Compliance Document mw [4 W EIRP] USA FCC 5.247 mw EIRP (P t.g t ) Europe ETS 3 328 mw/mhz Japan MPT ordinance 79 USA FCC ( Federal Communications Commission) Europe ETS (European Telecommunication Standard): FHSS DSSS Peak Power Density (ETS 3 328) mw / khz EIRP mw / MHz EIRP FHSS = Frequency Hopping Spread Spectrum 2 non-overlapping channels (hopping posistions) dwell time/channel 4 ms each channel occupied at least once during 4.(#channels).(dwell time/hop) DSSS = Direct Sequence Spread Spectrum Spread spectrum modulation that does not satisy the constraints o the FHSS speciication. DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 32

4. Evaluation o SS Positive. Signal hiding (lower power density, noise-like), non-intererence with conventional systems and other SS systems 2. Secure communication (privacy) 3. Code Division Multiple Access CDMA (multi-user) 4. Mitigation (rejection) o multipath, hold only the direct path 5. Protection to intentional intererence (Jamming) 6. Rejection o unintentional intererence (narrowband) 7. Low probability o detection and interception (LPI) 8. Availability o licence-ree ISM (Industrial, Scientiic and Medical) requency-bands Negative 9. No improve in perormance in the presence o Gaussian noise. Increased bandwidth (requency usage, wideband receiver). Increased complexity and computational load 5. Reerences. Sklar B., A structured Overview o Digital communications - A Tutorial Review - Part I, IEEE Communications Magazine, August 983 2. Sklar B., A structured Overview o Digital communications - A Tutorial Review - Part II, IEEE Communications Magazine, October 983 3. B. Sklar, Digital Communications, Prentice-Hall, 988, chap 4. J.G. Proakis, Communication Systems Engineering, Prentice-Hall, 994, chap 5. Glover and Grant, Digital Communications, Prentice Hall, 997, chap 5 6. Viterbi, CDMA Principles o Spread Spectrum Communication, Addison-Wesley, 995 7. Raymond L. Pickholtz, Donald L. Schilling and Laurence B. Milstein, Theory o spreadspectrum communications- A Tutorial, IEEE Trans. on Communications, vol. com-3, no. 5, May 982, pp. 855-884 8. R.C. Dixon, Spread Spectrum Systems with commercial applications, John Wiley & Sons, Inc., 994 9. J.K. Holmes, Coherent Spread Spectrum Systems, John Wiley & Sons, 982. M.K. Simon, Spread Spectrum Communications Handbook, Mc Graw-Hill, Inc., 994. Shimon Moshavi, Bellcore, Multi-user Detection or DS-CDMA Communications, IEEE communications magazine, October 996, pp. 24-36 2. E. Dinan and B. Jabbari, Spreading Codes or Direct Sequence CDMA and Wideband CDMA cellular Networks, IEEE communications magazine, October 996, pp. 24-36 DE NAYER (ir. J. Meel) IWT HOBU-onds Spread Spectrum 33