CELLULAR COMMUNICATIONSMIDTERM 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)

0( ) sin( )x t a wt

2 12 22wwT T f w f

w T

0( ) sin(2 ) sin( )tx t a ft a

0 0

2 2

( ) ( ( ), ( )) cos( ), sin( )

, arctan 2

x y

yx y t

x

r t r t r t a wt a wt

ra r r

r

Wavelength and propagation velocity

vvTf

Constructive and Destructive Interference

Doppler Effect

vT

vT Tu u

uf fv

When no relative motion

When moving @U

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

[ : ] [ : ]a b c h c hf f f f f f

a s b s b af f f f f f

2s hf f

2s

hff

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

Power Spectral Density(PSD)

2( ) ( )PSD f X f

Example:1Hz+3Hz

Nonlinear Example: 1Hz+3Hz

f(x1+x2)!=f(x1)+f(x2)

SUI are a basis

Finite Impulse Response Filter

Impulse response

( ) ( 2) ( 1) ( )y n x n x n x n

( 1) 0(0) 1(1) 1(2) 1(3) 0

hhhhh

Convolution 0

( ) ( ) ( )m

c n x n m h m x h

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

c x y

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 Tractdemo

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