ECE 4710: Lecture #30 1

MSK PSD

Quadrature MSK baseband waveforms are

Bandpass MSK signal (IQ representation)

IQ waveforms are orthogonal (independent) PSD of complex envelope g(t) isand since x(t) & y(t) have same basicshape

t 0 , )5.0cos()( bc TtRAtx t 0 , )5.0sin()( bc TtRAty

)2sin()5.0sin()2cos()5.0cos(

)2sin()()2cos((t) )(

tftRAtftRA

tftytfxts

cccc

cc

)()()( fff yxg PPP )()( ff yx PP

)(2)( ff xg PP

m(t) = ±1

ECE 4710: Lecture #30 2

MSK PSD

MSK PSD is

Pulse shape is truncated cosine (or sine) over 2Tb

FT of truncated cosine is

)( shape pulse baseband of FT is )( where

)(1

)(2)(2

tffF

fFT

ffb

xg PP

elsewhere ,0

2 , )5.0cos()()(

t

TttRAtxtf bc

])4(1[)2cos(4

)( 2fTfTTA

fFb

bbc

bT2t

ECE 4710: Lecture #30 3

MSK

Two types of MSK Type I

» Pulse shape on x(t) and y(t) alternates between positive and negative half cosinusoid

» Differential encoding Fast Frequency Shift Keying (FFSK)

Yields one to one relationship between ±1 m(t) data and fH / fL

Type II» Pulse shape on x(t) and y(t) is always a positive half cosinusoid

» No one to one relationship between m(t) data (±1) and fH / fL

» fH / fL determined by m(t) data and encoding

PSDs for both MSK types (I & II) are the same

ECE 4710: Lecture #30 4

MSK PSD

Complex envelope PSD

Observations FNBW

» MSK 0.75 R» QPSK 0.5 R

50% smaller!!

1st sidelobe» QPSK 13.4 dB» MSK 23 dB!!

22

2

2

2

])4(1[

)2(cos16)(

fT

fTTAf

b

bbcg

PMSK

QPSK or OQPSK

Note that MSK is

Binary M = 2

ECE 4710: Lecture #30 5

MSK vs. QPSK BW

MSK signal has 50% larger FNBW relative to QPSK Need wider channel BW for RF signal Spectral efficiency is not as good

MSK sidelobes are much smaller than unfiltered QPSK Truncated cosine pulse shape for MSK Rectangular pulse shape for unfiltered QPSK Adjacent Channel Interference (ACI) from MSK is very

good compared to unfiltered QPSK

ECE 4710: Lecture #30 6

GMSK

MSK baseband waveforms can be filtered to further reduce sidelobe levels

Raised cosine (RC) filter for QPSK Eliminate all sidelobes Satisfies Nyquist criterion No ISI @ proper sampling

point within symbol period RC filter cannot be used for filtering MSK envelope

MSK is constant envelope enables non-linear Class C PA

RC filtered MSK would have sidelobes regenerated by non-linear Class C PAs

ECE 4710: Lecture #30 7

GMSK

Gaussian MSK = GMSK use Gaussian shaped filter to further improve spectral efficiency of MSK

Filter rectangular m(t) waveforms prior to generating IQ baseband waveforms x(t) & y(t) Before data are frequency modulated on carrier Cannot filter x(t) & y(t) as that would make MSK not have a

constant envelope Gaussian filter transfer function

)2/2(ln)/( 2GBf

G eH bandwidthfilter dB 3GB

ECE 4710: Lecture #30 8

GMSK

Gaussian Filter Significantly reduces spectral sidelobes Affect on FNBW is very minor for reasonable filter BW Does NOT satisfy Nyquist criterion

» Will cause unwanted ISI if BG is too narrow

How do we quantify reasonableness or narrowness?» Bandwidth-Bit Duration Product BG Tb

» MSK FNBW is 0.75 R = 0.75 / Tb

» BG Tb provides normalized measure of filter BW wrt signal BW

» Tradeoff narrow filter BW vs. increasing ISI

ECE 4710: Lecture #30 9

GMSK

Gaussian Filter Reasonable BG Tb

» 0.3 to 0.5

» Greater than 0.5? sidelobe levels not

reduced enough

» Less than 0.3? ISI becomes too large

GMSK normally specified by

amount of filtering» Example: 0.3 GMSK is

GMSK with BG Tb = 0.3

MSK

QPSK or OQPSK

0.3 GMSK

ECE 4710: Lecture #30 10

GMSK

Even though m(t) data is shaped by Gaussian filter response GMSK is still a constant envelope modulation method just like MSK Gaussian filtered data used to frequency modulate carrier Carrier envelope remains constant Non-linear Class C amps used

» Excellent DC to RF efficiencies (80-90%)» Enables long operation of mobile devices relying upon battery

power supply

Constant envelope also means GMSK is less susceptible to signal fading and interference which occurs during transmission thru channel

ECE 4710: Lecture #30 11

GSM

Global System for Mobile (GSM) First digital standard developed for cellular telephone Developed in Europe in late 1980’s and widely deployed in

early 1990’s» Long before digital PCS cell phones in U.S. in late 1990’s

Significant use in non-European markets (Asia, South America, etc.)

Most widely used 2G cell phone standard in the world» Leads market share of all other technologies by factor of 3-4

T-Mobile and AT&T Mobile in U.S. used GSM after 2002 Modulation method for GSM is 0.3 GMSK

ECE 4710: Lecture #30 12

Type 1 MSK with differential encoding Very simple use of FM Tx with differentially encoded m(t)

Doesn’t require separate IQ waveforms, x(t) & y(t), generated from m(t)» No need for two IQ oscillators

Simple = Fast Fast Frequency Shift Keying (FFSK)

MSK Generation

CriterionMSK 42

1 RhRF

ECE 4710: Lecture #30 13

MSK Generation

Type I MSK with no differential encoding IQ waveforms must be generated !! Parallel method of generation

ECE 4710: Lecture #30 14

MSK Generation

Type II MSK MSK is specific case of BPSK Serial generation filters BPSK RF (bandpass) signal with

off-center BPF

ECE 4710: Lecture #30 15

MSK Spectral Efficiency

MSK is special case of BFSK with minimum F NNBW spectral efficiency is better than BPSK but worse than QPSK 30-dB BW spectral efficiency is 4 better than QPSK

» Low sidelobe levels low ACI

» Also better than 64 QAM!

Note that BPSK with

RCF & r = 0.5 has = 0.667 same as

MSK

ECE 4710: Lecture #30 16

MSK & GMSK

MSK & GMSK for mobile radio applications Low sidelobe level and low ACI

» Large number users spaced very close together in frequency domain with minimal interference between channels

» Support large number of users

Non-coherent Rx for demodulation» No carrier synchronization» Simple & inexpensive Rx

Constant envelope» Non-linear Class C PA with high DC to RF efficiency» Long battery life for mobile units