Wireless digital communications

1Wireless Communication & Mobile Networks – Spring 2010 Dr Daniel So

Lecture 2 Basics on Wireless Communications


Lecture Aims

• Revision of digital modulation schemes– Goldsmith Ch 5– Haykin Ch 3.1 – 3.7– Rappaport Ch 6.8 – 6.10

• Learn how to estimate noise in a system– Rappaport Appendix B– Haykin Ch 2.8

• Introducing radio waves and propagation– Rappaport Ch 4.1 – 4.4


Modulation Basics

• Digital data contains 0s and 1s– Difficult to transmit over wireless channels

• Transmitting zero is identical to no transmission• Infinite spectrum due to frequency spectrum of square pulse

• Needs to convert binary data to analogue signal for RF transmission– Transmit in the licensed or allowed frequency band

• Revision of basic digital modulation schemes, and some modulation schemes for wireless communications


Basic Modulation Schemes (I)

• Typical carrier signal

– 3 possible modulation method• Phase φ, Amplitude A & Frequency fc

• Quadrature carrier signal

– AI=In phase amplitude; AQ=quadrature phase amplitude– I & Q are orthogonal

– Occupy the same bandwidth as the one with only I or Q component (Why waste?)

( ) [ ]φπ += tfAts c2cos

( ) [ ] [ ]tfAtfAts cQcI ππ 2sin2cos +=

[ ] [ ] 02sin2cos0

=∫T

cc dttftf ππ


Basic Modulation Schemes (II)

• Phase Shift Keying (PSK)– Use different phases of the quadrature carrier signal for different

binary data (d)• E.g. BPSK: φ=0° for d=0; φ=180° for d=1

• Quadrature Amplitude Modulation (QAM)– Use the amplitude of the quadrature carrier signal to carry the

data• E.g. 4-QAM: For d={00, 01, 10, 11}• {AI,AQ}={(1,1), (-1,1), (1,-1), (-1,-1)}/√2• Same as QPSK

• Frequency Shift Keying (FSK)– Use different frequencies of the carrier signal to represent

different binary data• E.g. BFSK: fc=f1 for d=0; fc=f2 for d=1

0001

11 10


Basic Modulation Schemes (III)

• Factors affecting the choice of modulation in wireless communications– Bandwidth efficiency

• Throughput data rate per Hertz: η = R/B bps/Hz– Power efficiency

• Required SNR at a certain BER/FER– Other factors

• Implementation complexity• Non-linearity of power amplifier • Adjacent channel interference• Robustness


Modulation Types (I)

• Linear modulation (e.g. PSK, QAM)– Signal amplitude varies with the modulating signal m(t)

• A: amplitude• fc: carrier frequency• PSK = linear modulation?

– Spectral efficient– Non-constant envelope

• Requires power inefficient linear amplifiers– Class A or AB amplifiers: 30-40% DC power converted to RF power– Use more battery power

• Introduces distortion with power efficient non-linear amplifiers– Occupies more bandwidth and becomes spectral inefficient again!

( ) ( ) ( )[ ]tfjtAmts cπ2expRe= ( ) ( ) ( ) ( )[ ]tftmtftmA cQcI ππ 2sin2cos −=

( ) ( ) ( ) ( ) ( )ncncnc tftftf θπθπθπ sin2sincos2cos2cos −=+


Modulation Types (II)

• Non-linear modulation (e.g. FSK, MSK)– Usually the signal frequency (or phase) varies with the modulating

signal– Constant envelope

• Can use power efficient non-linear amplifiers– Class C amplifiers: 70% efficiency

– Spectral inefficient

Power efficient application⇒ Non-linear Modulation

Bandwidth efficient application⇒ Linear modulation


Pulse Shaping

• Modify the spectral shape of the signal to fit the spectral mask– Multiply the filter response to the signal frequency response

• Filter the baseband signal before modulator (avoid ISI)– Convolve the filter impulse response to the time domain signal


Linear Modulation (M-PSK)

• M-PSK

– θn is the M uniformly spaced phase values

– Constant envelope if square pulse is used

– Becomes non-constant when pulse shaping is applied

• Require linear power amplifier

( ) nnI atm θcos== ( ) nnQ btm θsin==

0 0.5 1 1.5 2 2.5 3 3.5 4-500

-400

-300

-200

-100

0

100

200

300

400

500

Symbol Period (T)

Am

plitu

de

8PSK Signal with Gaussian pulse shaping filter at 0.5 roll off


Linear Modulation (M-QAM)

• M-QAM (k = log2M bits)

– Non-constant envelope• Require linear power amplifier

– Use the same bandwidth as M-PSK• Both using quadrature carrier

– Better power efficiency in higher order modulation

• M=16, BER=10-6, SNR=15 (M-QAM) & 18.5 (M-PSK)

• M=64, BER=10-6, SNR=18.5 (M-QAM) & 28.5 (M-PSK)

( ) ( )1,,3,1 −±±±== Matm nI K

( ) ( )1,,3,1 −±±±== Mbtm nQ K

0 0.5 1 1.5 2 2.5 3 3.5 4-5

-4

-3

-2

-1

0

1

2

3

4

5

Symbol Period (T)

Am

plitu

de


Offset QPSK (I)

• 180° phase transition causes a rapid change in signal– Generates high frequency components– Even worse with non-linear power amplifier

• High spectral re-generation with rapid zero-crossing

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Symbol Period (T)

Am

plitu

de

QPSK signal with Gaussian pulse shaping filter at 0.5 roll-off

Rapid zero-crossing


Offset QPSK (II)

• Offset QPSK– Aims to avoid this rapid 180° phase transition – mI(t) and mQ(t) are offset in time by half a symbol period 0.5Ts

• i.e. 1 bit period Tb


Offset QPSK (III)

0 0.5 1 1.5 2 2.5 3 3.5 4-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Symbol Period (T)

Am

plitu

de

OQPSK signal with Gaussian pulse shaping filter at 0.5 roll-off

– Phase transitions occur at every half of a symbol period, but islimited to ±90 °

– Same spectral occupancy as QPSK• Delay in time = phase change in frequency domain

– Less spectral regeneration with non-linear power amplifier


Tutorial Question

• Determine the phase when the sequence 010011011000 is modulated with Offset QPSK – Initialise phase π/4, mapping: 00→π/4, 01 →3π/4, 11→-3π/4, 10

→-π/4

Odd 0 0 1 0 1 0 0

Even 0 1 0 1-3π/4 3π/4

0013π/4 -3π/4 -π/4 π/4 π/4Phase π/4 3π/4 3π/4 π/4 -π/4 π/4


π/4-QPSK

• Compromise between OQPSK and QPSK

• Shift ± π/4 in signal constellation for consecutive symbols– E.g. transmit even symbols with

π/4 phase shift• Maximum phase transition

limited to 135°


π/4-QPSK

• Less spectral re-growth than QPSK, but higher than OQPSK• Less transition than OQPSK• Simpler receiver design with non-coherent detection• Usually work with differential encoding

– Differential encoding• The difference between the past and current symbols contain the current data

– π/4-DQPSK– E.g. current phase

θk = θk-1 + φk• Input bits = 11, φk = π/4• Input bits = 01, φk = 3π/4• Input bits = 00, φk = -3π/4• Input bits = 10, φk = -π/4


Tutorial Question

• Determine the phase when the sequence 010011011000 is modulated with– π/4-QPSK (mapping 1: 00→π/4, 01 →3π/4, 11→-3π/4, 10 →-π/4,

mapping 2: 00→0, 01 →π/2, 11→π, 10 →-π/2)– π/4-DQPSK (Initial phase: 0, Phase shift mapping 00→π/4, 01

→3π/4, 11→-3π/4, 10 →-π/4)• Ans:

– π/4-QPSK

– π/4-DQPSK

Symbols 01 00 11 01 10 00Phase 3π/4 0 -3π/4 π/2 -π/4 0

Symbols 01 00 11 01 10 00Phase 3π/4 π π/4 π 3π/4 π


Non-linear Modulation

• Modulate the baseband signal into the phase of the carrier

• Constant envelope– Can use power efficient non-linear amplifiers– E.g. Frequency Shift Keying FSK

• Have abrupt phase transition

• If φ(d; t) is continuous in amplitude – Modulated signal is continuous in phase– Instead of using the data bit (discontinuous) directly to modulate

the carrier, the integral of the data bit (continuous) is used.• Continuous Phase Frequency Shift Keying (CPFSK)

( ) ( )[ ]tffAts c Δ+= π2cos1 ( ) ( )[ ]tffAts c Δ−= π2cos2

( ) ( )[ ]tdtfAts c ;2cos φπ +=


CPFSK (I)

• Signal representation

– where• d = input data bit {+1,-1}• fd = peak frequency deviation• h = 2fdT = modulation index

– Phase is continuous• +/- 1 are the input binary bits• Line represents the phase of carrier

signal

( ) ( )[ ] ( ) ( )TntnTdT

dTftfAtdtfAtst

dcc 1,22cos;2cos +≤≤⎥⎦⎤

⎢⎣⎡ +=+= ∫ ∞−

ττππφπ

( )[ ]nnndcnnc hdntdffATnTthdtfA πθππθπ −++=⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

++= 2cos2cos

∑−

−∞=

=1n

kkn dhπθ


CPFSK (II)

• Data = [1 0 1 1 0]– f1=1.3Hz for d=1, f2=0.7Hz for d=0

FSK CPFSK

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1FSK - f1=1.3Hz, f2=0.7Hz

time0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1CPFSK - f1=1.3Hz, f2=0.7Hz

time


Minimum Shift Keying (MSK)

• Orthogonal FSK signals

– Minimum frequency separation must be 1/2T– FSK signals must be orthogonal to have minimum detection error

• CPFSK – The 2 modulated signals (when d=+1 & –1) are separated by h/T– Hence, when h = 0.5, CPFSK yields best performance

• MSK is a special case of CPFSK, where h = 0.5– Minimum frequency separation for CPFSK– Constant envelope with continuous phase

• Good for wireless communications

( ) ( ) 00 21 =∫T

dttsts


MSK


Gaussian-filtered MSK (GMSK)

• A Gaussian filter is applied to the data (rectangular pulse) before the MSK modulator

– The filter has a Gaussian-shaped frequency response– Reduce the sidelobe of the signal spectrum

• Bandwidth efficient– Power efficient amplifier can be used

• Power efficient– Disadvantage

• Create Inter-Symbol Interference (ISI)– Used in current GSM systems


GMSK


Decibel (I)

• Decibel (dB) for power ratio– A logarithmic ratio

– Very useful and commonly used in communications • Can represent very small values in reasonable numbers (e.g. 10-10 = -100dB)• Many multiplicative terms become additions

– If X=a*b*c

– Useful numbers• Factor of 2 = addition of 3dB• Factor of 1/2 = subtraction of 3dB• Factor of 10 = addition of 10dB

( ) XdBX 10log10=

( ) )()()(log10log10log10 101010 dBcdBbdBacbadBX ++=++=


Decibel (II)

• dBW & dBm– dBW is the signal power in Watts in dB

• 0dBW=1W– dBm is the signal power in milli-watts in dB

• 1mW=0dBm=-30dBW

• Rules– dB+dB=dB– dBm+dB=dBm– dBm-dBm=dB– dBm+dBm = ?

( ) )(log10 10 WPdBWP =

( ) ( ) dBdBWPWPmWPdBmP 30)(1000*)(log10)(log10 1010 +===


Introduction to Radio Waves (I)

• Why antenna radiates?– Radiation occurs whenever a current flows through a wire with a

certain frequency• Electric and magnetic field

– Transmission line theories


Introduction to Radio Waves (II)

• Antennas– Many different types– Passive device

• i.e. no gain– Isotropic antenna

• Hypothetical lossless antenna having equal radiation in all direction• The reference of 0dBi

– Realistic antennas• Has a maximum gain larger than 0dBi

– Doesn’t mean it is active, but is directional such that in some direction, the power is larger than in other directions

• Gain at a particular direction

( ) ( )antenna isotropican ofdensity flux Power

,direction in density flux Power , φθφθ =TG


Introduction to Radio Waves (III)

• When a signal is injected into the antenna– Radio wave is generated and propagates through the wireless

channel– The received signal can be severely distorted


Introduction to Radio Waves (IV)

• Three level model– Path loss

• Models the signal attenuation in large transmitter-receiver (T-R) separation• Generally, attenuation increases when T-R increases• Caused by the wave propagation through space

– Shadowing• Models the signal power at same T-R separation but different locations• The signal variation in a circular loci• Caused by change of environment in different locations

– Multipath fading• Models the rapid variation within a distance of few wavelengths• Caused by constructive or destructive interference resulted from multiple

arrival paths


Free Space Propagation Model (I)

• Consider a radio wave with power Pt from an isotropic antenna– At a distance d, the power flux density (power per unit area) is

– The power Pr captured by an antenna with effective area Ae is

– For isotropic receive antenna

– Hence, the received power for isotropic antenna is

• Power attenuates in a squared rate on distance and frequency

24Area Surface dPP tt

d π==Φ

et

edr Ad

PAP 24π=Φ=

πλ4

2

=isoA

( ) ( )22

2

22

444 dfcP

dPP tt

disor ππλ

πλ

==Φ=−


Free Space Propagation Model (II)

• Now consider realistic antennas– Transmit antenna with gain Gt

• When no direction is specified for the gain, the maximum is used– Receive antenna with gain Gr

– Maximum antenna gain

– Hence, the received power for realistic antennas is

• Also known as the Friis equation– The path loss is defined as

eiso

e AAAG 2

4λπ

==

( ) p

rttrttr L

GGPdGGPP == 2

2

4πλ

( ) ( )( )2

2

4log10

ddBLdBPL p π

λ−==


Free Space Propagation Model (III)

• Assumptions– Receiver at far-field d>>λ

• Plain wave model can be used (E, H & propagation direction are orthogonal)– The max beam of the Tx antenna points to the max beam of the

Rx antenna• Both Gt and Gr are at max

– Free space propagation• No obstacles or reflectors, not even the ground!

• Reference distance d0– A known received power reference point

• Could be measured or predicted value – Received power can be written as

( ) ( )2

00 ⎟

⎠⎞

⎜⎝⎛=

dddPdP rr


Tutorial Question

• The ground transmitter for a low earth orbit (LEO) satellite is 1000km away from the satellite. The carrier frequency is 1.5GHz, and the transmission power is 10dBW. The antenna gain of the transmitter is 15dBi and the receiver is 2dBi. Calculate the received power in free space propagation model in dBm. – Ans: λ = 0.2m, d = 1000km, Gt = 15dBi, Gr = 2dBi, Pt = 30dBW

( )dB

dPL 96.155

100000042.0log10

4log10

2

2

2

=⎟⎠⎞

⎜⎝⎛

×−=−=

ππλ

dBmdBWPLGGPP rttr 96.9896.12896.15521510 −=−=−++=−++=


Noise (I)

• System performance is controlled by signal-to-noise ratio (SNR)– Received signal power can be estimated from the models– Noise must be separately calculated

• Thermal noise

– k = 1.38x10-23 J/K (Boltzmann’s constant)– T0 = 290K (room temperature)– B = bandwidth– N0 = Noise power spectral density

BNBkTPn 00 ==


Noise (II)

• Noise figure– The ratio increase on noise power at the output of the device

• Noise figure measures the additional noise generated by the device• If device is noiseless (F=1), the input noise is only amplified

– Noise figure is usually expressed in dB• The smaller the noise figure (close to 0dB), the lower the noise

– Equivalent noise temperature Te• Noise generated by the device can be considered as additional thermal noise

Te K• At room temperature, input noise = kT0B:

power noiseInput Gain Devicepower noiseoutput Actual

noiseless is device ifpower noiseOutput power noiseoutput Actual

×==F

( )0

0

0

0

TTT

BGkTBkTkTGF ee +=

+= ( ) 01 TFTe −=


Noise (III)

• Output noise power

• Two cascaded devices– At input of device 2, the noise power density = G1F1N0

– Output of device 2 = Gain x (input noise + additional noise)( ){ }

1

21

021

020112 11G

FFNGG

NFNFGGF −+=

−+=

BFGNBFGkTPn 00 Power NoiseInput Gain Device Figure Noise ==××=


Noise (IV)

• Cascaded system– Overall noise figure

– System equivalent temperature

– Antenna is always considered to have unity gain• Remember that antenna gain is the ratio of max strength/isotropic?

– Hence, a system with antenna is

• Noise is significantly reduced if the first device has high gain but low noise– Importance of low noise amplifier (LNA)!

L+−

+−

+=21

3

1

21

11GG

FG

FFFsys

L+++=21

3

1

21 GG

TGTTT

syse

L++++=21

3

1

21 GG

TGTTTT Aesys


Signal to Noise Ratio

• The received wireless signal might be very small – Could be in the order of 10-11W– How could we detect such signal?

• Performance of communication system is governed by the signal to noise ratio (SNR)– If the noise is even smaller, the received signal can be detected

• That’s why LNA is very important in wireless communication systems!

• SNR calculation– SNR after the RF devices (e.g., antenna, amplifiers, mixer etc)

• Output received power is also amplified!

FkTBP

PGPSNR r

n

r ===Power NoiseOutput

Power ReceivedOutput


Tutorial Question• For the previously considered LEO satellite, the antenna of the

receiver has a noise figure of 3dB. The low noise amplifier (LNA) has a noise figure of 0.5dB and a gain of 10dB. The overall system noise figure is 10dB and an overall system gain of 20dB. The system has a bandwidth of 1MHz Calculate the noise figure of the satellite, and the received SNR (assume shadow facing space temperature = 120K).– Ans: Fant=3dB=2, FLNA=0.5dB=1.122, GLNA=10dB=10,

Fsys=10dB=10, Gsys=20dB=100

– Pn = FtotGLNAGsyskTB = 3.022 *10*100*1.38e-23*120*1e6 = 5e-12= -113.0dBm

– SNR = GLNAGsysPr/Pn = 10+20-98.96+113 = 44dB

022.310

1101122.121

1 =−

+−+=−

+−+=LNA

sysLNAanttot G

FFFF


Summary

• Modulation Techniques– Linear modulation– Non-linear modulation

• Introduction to Radio Waves• Free Space Propagation Model• Noise figure and SNR calculation

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Wireless digital communications

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