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

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

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

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

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

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

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

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:

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

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

Error Results for 2-POLSK Error Condition:

2-POLSK Performance Error probability: BER curve:

N-POLSK Performance Freedom in constellation choice