l5

Lecture 5: Spread Spectrum Techniques

What is Spread Spectrum?

Spreading a signal over a bandwidth ( $B_{s s}$ ) much larger than the minimum required bandwidth ( $B$ ).

Key Goals:

Jamming Resistance: Harder for an adversary to disrupt the entire spread signal.
Security/Confidentiality: Difficult to intercept without the correct Spreading Code.
Multiple Access: Several users can share the same channel with minimal interference.
Multiplexing vs. SS: Multiplexing aims for bandwidth efficiency; SS aims for robustness and security.

Frequency Hopping Spread Spectrum (FHSS)

The signal is broadcast over a seemingly random series of radio frequencies, hopping at fixed intervals.

Hopping Sequence: Dictated by a Pseudonoise (PN) sequence.
Synchronization: Receiver must hop in sync with the transmitter to decode.
Advantages:
- Eavesdroppers hear only "blips".
- Jamming only affects a few bits on a specific frequency.

FHSS with MFSK

Commonly used with Multiple Frequency Shift Keying (MFSK).

Transmitted signal: $s_{i} (t) = A \cos (2 π f_{i} t)$ .
Carrier frequency changes every $T_{c}$ seconds.

Example: FHSS Calculation

Given:

PN Sequence: $4 bits$ ( $k = 4$ )
Bit Rate of PN: $64 bps$

a. Total Number of Possible Hops

The number of unique frequency channels is $2^{k}$ :

Hops = 2^{4} = 16

b. Time to Finish a Complete Cycle

The time for one full PN sequence cycle:

Time per PN bit = \frac{1}{Bit Rate} = \frac{1}{64} s

Time for 4 bits = 4 \times (\frac{1}{64}) = \frac{1}{16} = 0.0625 seconds

Summary

Spread spectrum improves reliability and security in wireless channels.
FHSS specifically uses frequency agility to avoid interference and jamming,
as seen in standards like Bluetooth.

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