CELLULAR COMMUNICATIONS MIDTERM REVIEW

Representing Oscillations   w is angular frequency    Need two variables to represent a state  Use a single 2D variable to represent a state as a vector (a phasor)

Wavelength and propagation velocity

Constructive and Destructive Interference

Doppler Effect When no relative motion When

Fast fading: Multipath

ISI

Example

Example: Sawtooth Frequency Domain X(k)=1/k

Ambiguity problem

Ambiguity in frequency domain

Nyquist sampling frequency  Signal band  Avoid aliasing  Nyquist sampling frequency  Maximum frequency without aliasing

Time vs. Frequency  Short pulse in time domain->wide spectrum

Power Spectral Density(PSD)

Example:1Hz+3Hz

Nonlinear Example: 1Hz+3Hz f(x1+x2)!=f(x1)+f(x2)

SUI are a basis

Finite Impulse Response  Filter  Impulse response

Convolution

Convolution in Frequency Domain  x(t), y(t) are signals  X(f), Y(f) are their spectrum  What is the spectrum C(f) of  Convolution theorem C=X*Y (multiplication)  Convolution in the time domain===Multiplication in the frequency domain

Amplitude Modulation(AM)  Change amplitude of the signal according to information  Simplest digital form is “on-off keying”(telegraph Morse code)

Audio AM

Frequency Modulation

Phase Modulation  Another form of FM

Circular 16-QAM

Frequency Hopping

Example :DSSS with PN  Transmitter/Receiver should be able to generate same synchronized Pseudo Random Noise sequences

OFDM  Select orthogonal carriers  Reach maximum at different times  Can pack close without much interference  More carriers within the same bandwidth

Hierarchy of speech coders

 -Law

Vector quantization  Encode a segment of sampled analog signal (e.g. L samples)  Use codebooks of n vectors  Segment all possible samples of dimension L into areas of equal probability  Very efficient at very low rates( R=0.5 bits per sample)

DPCM and prediction

Sub-band coding  Human ear does not detect error at all frequencies equally well

Human Vocal Tract demo

Voice Generation Model

LPC

Mean Opinion Score Quality Rating

Codec MOS rating

Binary Symmetric Channel  Transmission medium introduce errors  Demodulator produces errors  Model as a channel  Memoryless: probability of error is independent from one symbol to the next  Symmetric: any error is equally probable  Binary Symmetric Channel (BSC)

Error Correcting Codes (ECC)  Redundancy added to information  Encode message of k bits with n (n>k) bits  Example: Systematic Encoding  Redundant symbols are appending to information symbols to obtain a coded sequence  Codeword

Error correction vs. Error Detection  Error-detection  Detect that received sequence contains an error  Request retransmission  ARQ: Automatic Repeat Request/Query (HSDPA)  Error-correction  Detect that received sequence contains an error  Correct the error  Forward Error Correction  “A Code allows correction of up to p errors and detection up to q (q>p) errors”

Block Codes vs. Convolution Codes  Block Codes  Encode information block by block  Each block encoded independently  Encoding/Decoding is a memoryless operation  Convolutional Codes  Next symbol depend on a history of inputs/outputs

Linear Codes  Linear combination of valid codewords is also a codeword  Code distance is a minimum among all nonzero codeword weights (number of 1s)  Linear space spanned by basis:

Syndrome  Syndrome depends only on error pattern  Different errors=>different syndromes except for the addition of codeword  Can identify error patterns of weight w<=t by looking at the syndrome  One-to-one between syndromes and errors w<=t

Convolution Codes

Decoding: Viterbi Algorithm  Errors on the channel  Find path with minimal total errors

Trellis Coded Modulation (TCM)  Combined coding and modulation scheme  Make most similar signals (phases) represent most different/distance codewords

Turbo Codes  Use 2 convolutional codes on the same data  Feed data in different order to the encoders