SPREAD SPECTRUM

1. SPREAD SPECTRUM Hiding Information in noise

2. Origins of Spread Spectrum • Military communication has always been concerned with the following two issues • Security • Jam resistance • In civilian communications, above issues take on different interpretations • privacy • unintentional interference

3. Spread Spectrum:Data Hiding • Spread spectrum is in effect a way to “hide” information • Useful information is buried in noise. To an eavesdropper, the intercepted message looks juts like noise • The intended receive however is able to recover the information from noise using a special “key”

4. Types of Spread Spectrum • There are two main types of spread spectrum • Direct Sequence(DS) • Frequency Hopping(FH) • in DS/SS, digital data is multiplied by another bitstream running several hundred times faster • In FH/SS, carrier frequency, normally fixed, jumps around in a “random” manner known only to the intended receive

5. Direct Sequence • Take the baseband digital data b(t) and modulate it by a “random” bit pattern c(t). The resulting bitstream is m(t)=c(t)b(t) b(t) Tb Tc c(t)

6. Notations • There are a number of important parameters in SS • b(t): data sequence • c(t): spreading sequence • Tb: bit length • Tc: chip length • N=Tb/Tc: number of chips per bit • N=3 in this figure b(t) Tb c(t) Tc

7. Communications model: Jamming • The classic jamming model is shown below. we will demonstrate that an SS signal provides superior protection against intentional jamming m(t) b(t) r(t) X c(t) i(t) interference

8. Spreading Code: PN Sequences • Clearly, randomness is at the heart of spread spectrum • However, if truly random codes are used to spread the signal, receiver would never be able to recover the information • Therefore, we need a “pseudo” random noise known as PN sequences. Pseudo because if you wait long enough, they will repeat

9. Main Features of PN Sequences • To a casual observer, a PN sequence looks like a random alternations of +/-1. • In truth, however, a PN sequence repeats. Can you spot the period here? • The key to “cracking” the code is to find where the period ends

10. Where is the “spread”? • It is said that spread spectrum signal looks like random noise to all others but why? • Consider this

11. PN sequence Generation • PN sequences can be generated by a set of flip-flops with appropriate taps + 1 0 0 So S1 S2 output Initial state: 100 1 0 0 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 0 output: 0 0 1 1 1 0 1 0

12. m-sequences • The preceding sequence repeats itself with a period of 23-1=7 • In general, for an m-stage shift register, the period is at most • If the period is equal to the above, we have maximal lengthor m-sequences

13. Properties • # of 1’s are always one more than the number of 0’s • Period: 2m-1 • Very desirable (tight) correlation • More on this next

14. Autocorrelation of m-sequences • Let c(t) be an m-sequence. Its autocorrelation function is given by Tb Shifted by  <Tc

15. Behavior of autocorrelation • The significant property of correlation here is that it can discriminate against the slightest shifts. In fact, shift of just a single chip drops the function by a factor of N Rc() 1  -1/N

16. How to pick an m-sequence? • Once you pick a length N, the question is how do we generate an m-sequence? • N, fixes the number of shift register stages but you can connect them in many ways • Only a few connections give you valid m-sequences(see Table 9.1 and Figure 9.4) + + + 1 2 3 4 5 N=25-1=31, taps at [5,4,2,1]

17. Example • A PN sequence is generated using a feedback shift register of length 4. The chip rate is 107 pulses per second. Find • a):PN sequence length • b): Chip duration • c):PN sequence period • Answers • a): if an m-sequence, period is 24-1=15. Less if not • b): 1/107=10-7 sec • c):T=NTc=15x10-7 sec

18. Processing Gain • Probably the single most important component of an SS system is a quantity called processing gain(PG) • PG is defined by PG=N=Tb/Tc • In other words PGis given by the number of chips within a bit

19. General Rule • Bandwidth spreads by a factor equal to the processing gain spread bandwidth Wss=(Tb/Tc)W=PGxW

20. Bandwidth of an SS signal: example • Want to know the bandwidth of a digital signal running at 28.8 Kb/secafter spreading • Consider a m=19 stage shift register • PN sequence period N=219-1~219 • There are 219 chips inside a bit, i.e. Tb=NTc • Therefore, Rc=1/Tc=N/Tb=219x 28.8 Kb/sec • Since bandwidth is proportional to bitrate, the new bandwidth is now 219 or 57 dB higher than the unspread signal

21. Communications model: Jamming • The classic jamming model is shown below. we will demonstrate that an SS signal provides superior protection against intentional jamming m(t) b(t) r(t) X c(t) i(t) interference

22. Jamming Scenario • A jammer or interference i(t) tries to interfere with a spread spectrum signal • The corrupted spread spectrum signal at the receiver is put through a conventional correlation detector r(t) z(t) c(t) Data pn seq.

23. Signal+Jammer at the Output • Let’s walk the spread spectrum signal through the receiver interference desired data

24. Stopping the Jammer • The jammer appears as c(t)*i(t). In other words we have created a spread spectrum signal out of the jammer! • The bandwidth of a SS signal is very large making it look like white noise. Therefore, a lowpass filter integrator) will let the message b(t) through but will stop most of the jammer appearing as c(t)*i(t)

25. DS/BPSK • So far we have looked at DS/SS in baseband. • For the actual transmission we need to modulate the signal • Spreading can be done either before or after carrier modulation. See Fig. 9.7, 9.8 and 9.9 while listening to this slide

26. How does SS provide Protection against Jamming? • It can be shown that the SNR at the input and output of correlation detector is given by

27. Processing Gain • The improvement in SNR is caused by the processing gain, Tb/Tc. This ratio can be several hundreds or thousands • SNR gain can be as high as 1000(30dB)

28. BER in the Presence of Jamming • A DS/BPSK in Gaussian noise had a BER of • In the presence of jammer(but no noise)

29. Jammer acts as white noise • Comparison of the two BER expressions • Equivalently, Eb=PTb where P is the average signal power. Then

30. Jamming Margin • We just saw that processing gain helps counter jamming power • The ratio of jammer power to signal power is called Jamming margin J/P=PG/(Eb/No) • In dB jm=PG-Eb/No

31. Example • Digital data is running with bit-lengthTb=4.095 ms.This data is spread using a chip length of Tc=1 microsecond using DS/BPSK. What is the jamming margin if the required BER= 10-5.? • In the presence of random noise alone we need Eb/No=10 to achieve BER= 10-5.

32. Interpretation • The processing gain is Tb/Tc=4095. Plugging these numbers in the JM expression, we get JM |db=10log4095-10log(10)=26.1 dB • We can maintain BER at the desired level even in the presence of a jammer 26dB(400 times) higher than the desired signal

33. CDMA:spread spectrum at work • Code Division Multiple Access is one of the two competing digital cellular standards (IS-54). The other is TDMA-based IS-136 • In this area, Comcast has adopted IS-136. Bell Atlantic and Sprint PCS have gone the way of CDMA. • These digital services coincide with the AMPS infrastructure

34. Differences among the three • AMPS is an example of FDMA. Users are on all the time but on different frequency bands • TDMA uses the same 30KHz band of AMPS but services 3 users. Users are on only during their time slot. • In CDMA, there is neither frequency nor time sharing. Everyone is on simultaneously thus taking up the whole spectrum

35. CDMA Signal Model • In CDMA, kth user’s signal is spread by a PN code ak unique to the subscriber • M users can be on at the same time

36. How are users separated? • The familiar correlation receiver will do the job X b1 a1 b2 X a2 b3 X a3

37. Frequency Hopping SS • Transmitter and receiver always operate on a known frequency band. Once found, anyone can listen in • Imagine a scenario where carrier frequency “hops” around in a random pattern • This pattern is known only to the intended receiver thus nobody else can follow the hop

38. FH/MFSK • One obvious way to implement FH is to use MFSK. • In the conventional MFSK, carrier frequency jumps are controlled by the message • In FH/MFSK, jumps are controlled by a PN sequence

39. FH Modalities • Slow frequency hopping • Symbol rate Rs of the MFSK signal is an integer multiple of Rh, the hop rate; several symbols are transmitted on each frequency hop three symbols,same carrier freq.

40. FH Modalities • Fast frequency hopping • The hop rate Rh is an integer multiple of the MFSK symbol rate Rs; the carrier frequency will change several times even before the symbol ends. one symbol

41. Generating an FH/MFSK Signal • k-bit segments of the PN code drive the synthesizer-->2^k frequencies FH/MFSK M-ary FSK X BPF Freq synthesizer PN code generator

42. Parameters of the Slow FH • Chip: an individual FH/MFSK tone of shortest duration • In general, Rc=max(Rh,Rs) • For slow FH 1 FH chip Rc=1 per sec Rs=1 per sec Rh=1/3 per sec

43. Illustrating Slow FH frequency 1/Rs Rs time 1/Rh PN 001 110 011 001 4 FSK tones, 8 hops, PN period 16,

44. Fast FH • Carrier frequency hops several times within one symbol one symbol

45. Time-Frequency Plane of Fast FH frequency time symbol 4 MFSK tones, 2 hops per symbol(hop rate=bitrate), 8 possible hops