1. ©1999 BG Mobasseri111/20/2015 SPREAD SPECTRUM Hiding Information in noise

2. ©1999 BG Mobasseri211/20/2015 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. ©1999 BG Mobasseri311/20/2015 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. ©1999 BG Mobasseri411/20/2015 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. ©1999 BG Mobasseri511/20/2015 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) TbTb TcTc b(t) c(t)

6. ©1999 BG Mobasseri611/20/2015 Notations There are a number of important parameters in SS –b(t): data sequence –c(t): spreading sequence –T b : bit length –T c : chip length –N=T b /T c : number of chips per bit –N=3 in this figure TbTb TcTc b(t) c(t)

7. ©1999 BG Mobasseri711/20/2015 Communications model: Jamming The classic jamming model is shown below. we will demonstrate that an SS signal provides superior protection against intentional jamming b(t) c(t) m(t) X i(t) r(t) interference

8. ©1999 BG Mobasseri811/20/2015 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. ©1999 BG Mobasseri911/20/2015 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. ©1999 BG Mobasseri1011/20/2015 Where is the “spread”? It is said that spread spectrum signal looks like random noise to all others but why? Consider this

11. ©1999 BG Mobasseri1111/20/2015 PN sequence Generation PN sequences can be generated by a set of flip-flops with appropriate taps 100 + outputSoSo S1S1 S2S2 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. ©1999 BG Mobasseri1211/20/2015 m-sequences The preceding sequence repeats itself with a period of 2 3 -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 length or m-sequences

13. ©1999 BG Mobasseri1311/20/2015 Properties # of 1’s are always one more than the number of 0’s Period: 2 m -1 Very desirable (tight) correlation More on this next

14. ©1999 BG Mobasseri1411/20/2015 Autocorrelation of m- sequences Let c(t) be an m-sequence. Its autocorrelation function is given by TbTb Shifted by  <T c

15. ©1999 BG Mobasseri1511/20/2015 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()Rc() 1 -1/N 

16. ©1999 BG Mobasseri1611/20/2015 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) 12345 +++ N=2 5 -1=31, taps at [5,4,2,1]

17. ©1999 BG Mobasseri1711/20/2015 Example A PN sequence is generated using a feedback shift register of length 4. The chip rate is 10 7 pulses per second. Find –a):PN sequence length –b): Chip duration –c):PN sequence period Answers –a): if an m-sequence, period is 2 4 -1=15. Less if not –b): 1/10 7 =10 -7 sec –c):T=NT c =15x10 -7 sec

18. ©1999 BG Mobasseri1811/20/2015 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=T b /T c In other words PGis given by the number of chips within a bit

19. ©1999 BG Mobasseri1911/20/2015 General Rule Bandwidth spreads by a factor equal to the processing gain spread bandwidth W ss =(T b /T c )W=PGxW

20. ©1999 BG Mobasseri2011/20/2015 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=2 19 -1~2 19 –There are 2 19 chips inside a bit, i.e. T b =NT c –Therefore, R c =1/T c =N/T b =2 19 x 28.8 Kb/sec Since bandwidth is proportional to bitrate, the new bandwidth is now 2 19 or 57 dB higher than the unspread signal

21. ©1999 BG Mobasseri2111/20/2015 Communications model: Jamming The classic jamming model is shown below. we will demonstrate that an SS signal provides superior protection against intentional jamming b(t) c(t) m(t) X i(t) r(t) interference

22. ©1999 BG Mobasseri2211/20/2015 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) c(t) z(t) Data pn seq.

23. ©1999 BG Mobasseri2311/20/2015 Signal+Jammer at the Output Let’s walk the spread spectrum signal through the receiver desired data interference

24. ©1999 BG Mobasseri2411/20/2015 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. ©1999 BG Mobasseri2511/20/2015 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. ©1999 BG Mobasseri2611/20/2015 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. ©1999 BG Mobasseri2711/20/2015 Processing Gain The improvement in SNR is caused by the processing gain, T b /T c. This ratio can be several hundreds or thousands SNR gain can be as high as 1000(30dB)

28. ©1999 BG Mobasseri2811/20/2015 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. ©1999 BG Mobasseri2911/20/2015 Jammer acts as white noise Comparison of the two BER expressions Equivalently, E b =PT b where P is the average signal power. Then

30. ©1999 BG Mobasseri3011/20/2015 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/(E b /N o ) In dB jm=PG-E b /No

31. ©1999 BG Mobasseri3111/20/2015 Example Digital data is running with bit-lengthT b =4.095 ms.This data is spread using a chip length of T c =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 E b /No=10 to achieve BER= 10 -5.

32. ©1999 BG Mobasseri3211/20/2015 Interpretation The processing gain is T b /T c =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. ©1999 BG Mobasseri3311/20/2015 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. ©1999 BG Mobasseri3411/20/2015 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. ©1999 BG Mobasseri3511/20/2015 CDMA Signal Model In CDMA, kth user’s signal is spread by a PN code a k unique to the subscriber M users can be on at the same time

36. ©1999 BG Mobasseri3611/20/2015 How are users separated? The familiar correlation receiver will do the job a1 a2 a3 b1 b3 b2 X X X

37. ©1999 BG Mobasseri3711/20/2015 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. ©1999 BG Mobasseri3811/20/2015 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. ©1999 BG Mobasseri3911/20/2015 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. ©1999 BG Mobasseri4011/20/2015 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. ©1999 BG Mobasseri4111/20/2015 Generating an FH/MFSK Signal k-bit segments of the PN code drive the synthesizer-->2^k frequencies M-ary FSK Freq synthesizer PN code generator BPF FH/MFSK X

42. ©1999 BG Mobasseri4211/20/2015 Parameters of the Slow FH Chip: an individual FH/MFSK tone of shortest duration In general, R c =max(R h,R s ) For slow FH R c =1 per sec R s =1 per sec R h =1/3 per sec 1 FH chip

43. ©1999 BG Mobasseri4311/20/2015 Illustrating Slow FH frequency Rs 1/Rh time 1/Rs 001110011001PN 4 FSK tones, 8 hops, PN period 16,

44. ©1999 BG Mobasseri4411/20/2015 Fast FH Carrier frequency hops several times within one symbol one symbol

45. ©1999 BG Mobasseri4511/20/2015 Time-Frequency Plane of Fast FH time frequency symbol 4 MFSK tones, 2 hops per symbol(hop rate=bitrate), 8 possible hops