1. 6.441 Final Project: Theory of Polarization Shift Keying (POLSK) Modulation
Matt Willis
5/11/06

2. Motivations POLSK is of professional interest
Multi-level transmission; that is,
Intuitive Error Analysis
Generic Feature of Electromagnetic Waves

3. Overview of Optical Communications System
Channel Performance
Input Alphabet
TransmissionMedium
Transmitter
Modulator
Receiver

4. Light Modulation Schemes
Light propagating along z-axis, 1-D transverse electric field:
Have amplitude, frequency, and phase at our disposal

5. Polarization: Plane Wave Representation
Light propagating along z-axis, 2-D transverse electric field:

6. Polarization: Poincare Sphere Representation
Consider the following coordinate transformation:
This transformation defines a sphere called the Poincare sphere
where

7. Features of the Poincare Sphere Representation
“Linear” polarizations (∆ = 0) located along (x,y,0) equator
“Circular” polarizations are located at North and South poles
If S1 and S2 are orthogonal according to Hermitian product, they map onto antipodal points on the Poincare sphere

8. Encoding Procedure
Partition the surface area of the sphere into n disjoint regions
Assign to each region a representative vector,
Choose an encoding function that maps the input alphabet onto the set of reference vectors:

9. Decoding Procedure
Example: 2-POLSK, where E: {0,1} --> {(0,0,1), (0,0,-1)}

10. Channel/Noise Model
State of Polarization is transmitted noiselessly, that is:
White shot noise is accumulated during photodetection process

11. Error Results for 2-POLSK
Error Condition:

12. 2-POLSK Performance
Error probability:
BER curve:

13. N-POLSK Performance
Freedom in constellation choice