1. Spread Spectrum Techniques

2. Class Contents Spread Spectrum Concept
Key Characteristics
Frequency Hopping Spread Spectrum
Mathematical Treatment using BPSK
Example of FHSS using MFSK
Slow FHSS
Fast FHSS
FHSS bandwidth
Direct Sequence Spread Spectrum
Example using BPSK
DSSS bandwidth
Spreading Sequences
PN Sequences
Properties of the PN sequences

3. Spread Spectrum
Transmission technique invented in 1940 for military type applications.
It can be used to transmit analogue or digital data using an analogue signal.
Immune to frequency jamming
Immune to various kinds of noise and multipath distortion.

4. Spread Spectrum Can be used to hide encrypting signals
Only a receiver with the same spreading code can recover the information
Several users can independently use the same higher bandwidth with very little interference

5. Key Characteristics of SS system.
TRANSMITTER:
Input data is modulated around a carrier frequency. (typically: BFSK,MFSK,BPSK)
Sequence of bits is further modulated using a sequence of bits known as “spreading code”
Signal is transmitted over a broader BW.

6. Key Characteristics of SS system
RECEIVER:
The spreading code is used to demodulate the SS signal
The modulated signal is fed into a demodulator to recover the original data.

7. Spread Spectrum System
Chanel Decoder is Actually an FSM/MFSK Demodulator

8. Frequency Hopping Spread Spectrum.
The signal is broadcast over a seemingly random series of radio frequencies.
The signal is hopping from frequency to frequency at fixed intervals.
To recover the signal, the receiver needs to be switching frequencies in a synchronous manner with the transmitter
Attempts to jam the signal in a frequency band only knock a few bits

9. Frequency Hopping Spread Spectrum.

10. Frequency Hopping Spread Spectrum.
The width of each channel corresponds to the bandwidth of the input signal
The sequence of channels is dictated by the spreading code.
The transmitter uses a frequency channel for a fixed time interval and then changes to another according to the spreading sequence

11. Frequency Hopping Spread Spectrum.

12. Frequency Hopping Spread Spectrum.

13. Frequency Hopping Spread Spectrum
Mathematical Treatment:
Using BFSK, the input signal is:
where:
A: Amplitude of signal
f0: base frequency
bi: value of the ith bit of data (+1 and -1, for binary 1 and 0)
f: frequency separation
T: bit duration; data rate = 1/T

14. Frequency Hopping Spread Spectrum
Mathematical Treatment:

15. Frequency Hopping Spread Spectrum
Mathematical Treatment:
The frequency synthesizer generates a constant frequency tone whose
Frequency hopes between the set of 2k frequencies.
During the ith bit interval and the ith hop:

16. Frequency Hopping Spread Spectrum
Mathematical Treatment:
This signal is multiplied by the spreading sequence:
Using the trigonometric Identity:

17. Frequency Hopping Spread Spectrum
Mathematical Treatment:
In Frequency this product signal is the same signal spread
to a different frequency
On the transmitter a band pass filter centred on the sum frequency is used
To generate the signal to be transmitted (FHSS signal).

18. Frequency Hopping Spread Spectrum
Mathematical Treatment:
FHSS signal out of the transmitter:

19. Frequency Hopping Spread Spectrum
Mathematical Treatment:
At the receiver, the signal is again multiplied by the spreading code:

20. Frequency Hopping Spread Spectrum
Mathematical Treatment:
Using the same trigonometric Identity:
Again a bandpass filter is used, but this time to block the difference frequency
This is an attenuated version of the original signal.

21. Frequency Hopping Spread Spectrum
Mathematical
Treatment:

22. Frequency Hopping Spread Spectrum
Example using MFSK:
The data is encoded using MFSK M=4
For FHSS, the MFSK signal is translated to a new frequency every Tc seconds

23. Frequency Hopping Spread Spectrum
Example using MFSK:
For a data rate of R, the duration of a bit is T = 1/R
The duration of a signal element is Ts = L . T
Comparing Ts and Tc, FHSS can be classified in two:
Slow-frequency-hop spread spectrum
Tc ≥ Ts
Fast-frequency-hop spread spectrum
Tc < Ts

24. Frequency Hopping Spread Spectrum
Example using MFSK – Slow FHSS:
For slow FHSS, we set Tc=2Ts. And we will use k=2 (jump every 2 symbols)

25. Example using MFSK – Slow FHSS:

26. Frequency Hopping Spread Spectrum
Example using MFSK – Fast FHSS:
For fast FHSS, we set Tc=Ts/ 2.
And we will keep k=2

27. Example using MFSK – Fast FHSS:

28. Frequency Hopping Spread Spectrum
Bandwidth :
MFSK bandwidth is Wd = 4.fd.
FHSS scheme has k=2  22 blocks of frequencies with
4 frequencies in each block.
The total FHSS bandwidth is:
Each 2 bits of the PN sequence is used to select one
block of channels.

29. Direct Sequence Spread Spectrum
Each bit of the original sequence is represented by multiple bits in the transmitted signal using a spreading code.
The spreading code “spreads” the signal across a wider frequency band in direct proportion to the number of bits used.

30. Direct Sequence Spread Spectrum
And exclusive or (XOR) is used to combine the signal with the spreading
code
AB 1
XOR truth table

31. Direct Sequence Spread Spectrum
Example:

32. Direct Sequence Spread Spectrum
Example using BPSK:
Binary data is represented using +1 and -1 to represent binary 1 and 0
To generate the DSSS signal, sd(t) is multiplied by the PN sequence c(t),
which takes values of +1 and -1.

33. Direct Sequence Spread Spectrum
Example using BPSK:

34. Direct Sequence Spread Spectrum
Example using BPSK:
incoming signal s(t), is multiplied again by c(t).
for any bit stream c(t).c(t) = 1.That recovers the original signal:

35. Direct Sequence Spread Spectrum
Bandwidth Considerations:
The information signal has a bit width of T. The data rate will be 1/T
The frequency spectrum width of the signal, depending on the encoding
Technique is roughly 2/T:

36. Direct Sequence Spread Spectrum
Bandwidth Considerations:
The spectrum of the PN signal is roughly 2/Tc:

37. Direct Sequence Spread Spectrum
Bandwidth Considerations:
The amount of spreading that
is achieved is a direct result
of the data rate of the
PN sequence:

38. Spreading Sequences
The spreading sequence c(t), is a sequence of binary bits shared by the transmitter and receiver
Spreading consists of multiplying (XOR) the input data by the spreading sequence.
The bit rate of the spreading sequence is higher than that of the data.

39. Spreading Sequences
At the receiver, the spreading is removed by multiplying by an exact copy of the spreading code synchronized with the transmitter.
The spreading codes are chosen so that the resulting signal is noise like:
There should be an approximately equal number of 0s and 1s, and few or no repeated patterns

40. PN sequences Ideal sequence is a random sequence
The transmitter and receiver must have an exact copy of the sequence: a predictable way is needed to generate the same bit stream at transmitter and receiver
A PN generator will produce a periodic sequence that eventually repeats but that appears to be random.

41. PN sequences
PN sequences are generated by an algorithm using some initial value called “SEED”
The algorithm is deterministic and therefore produces sequential numbers that are not statistically random.
If the algorithm is good, the sequence will pass many reasonable tests of randomness.
These numbers are referred to as “Pseudorandom numbers of Pseudonoise sequences”

42. Properties of the PN sequence
The two must important properties of a PN sequence are RANDOMNESS & UNPREDICTABILITY
To validate randomness the following criteria are used:
Uniform Distribution: The frequency of occurrence of each number should be approximately the same. On a binary sequence, this is expanded in:
Balance Property: In a long sequence, the fraction of binary 1s should approach ½

43. Properties of the PN sequence
Run Property: A run is defined as a sequence of all 1s or all 0s. The appearance of alternate digits signal the beginning of a new run. About ½ of the runs of each type should be of length 1, ¼ of length 2, 1/8 of length 3, and so on.
Independence: No one value in the sequence can be inferred from others.
In spread spectrum, the correlation property also applies to a PN sequence:
Correlation Property: If a period of a sequence is compared term by term with a cycle shift of itself, the number of terms that are the same differs from those that are different by at most 1.