Development of Complex Curricula for Molecular Bionics and Infobionics Programs within a consortial* framework**
Consortium leader
PETER PAZMANY CATHOLIC UNIVERSITY
Consortium members
SEMMELWEIS UNIVERSITY, DIALOG CAMPUS PUBLISHER
The Project has been realised with the support of the European Union and has been co-financed by the European Social Fund ***
**Molekuláris bionika és Infobionika Szakok tananyagának komplex fejlesztése konzorciumi keretben
***A projekt az Európai Unió támogatásával, az Európai Szociális Alap társfinanszírozásával valósul meg.
Ad hoc Sensor Networks
Digital modulation
Érzékelő mobilhálózatok
Digitális moduláció
Dr. Oláh András
Lecture 3 review
• Signal propagation overview
• Path loss models
• Log Normal Shadowing
• Narrowband Fading Model
• Wideband Multipath Channels
Outline
• Advantage of digital modulation
• Bandwidth of signals
• ISI-free system requirements
• IQ modulator
• Constellation and “eye” diagrams
• Tradeoff between spectral efficiency and power efficiency
• Linear and constant envelope modulation scheme
• Spread Spectrum Modulation
Structure of a wireless communications link
Modulation
• It is defined as a technique of mapping the information signal to a transmission signal (modulated signal) which is better suited for the operating medium (i.e. the wireless channel).
• The transmitted radio signal can be described as
• By letting the transmitted information change the amplitude, the frequency, or the phase to carry the information we get the three basic types of digital modulation techniques:
– ASK (Amplitude Shift Keying) – FSK (Frequency Shift Keying) – PSK (Phase Shift Keying)
( ) ( ) cos 2 ( ( ) )
s t = A t π ft + Θ t
Amplitude Frequency Phase
Constant amplitude
Modulation (cont’)
( ) ( ) cos 2 ( ( ) )
s t = A t π ft + Θ t
Advantage of digital communications
• It allows information to be “packetized”
– It can compress information in time and efficiently send as packets through network.
– In contrast, analog modulation requires “circuit-switched” connections that are continuously available.
• Inefficient use of radio channel if there is “dead time” in information flow.
• It allows error correction to be achieved
– Less sensitivity to radio channel imperfections.
• It enables compression of information.
– More efficient use of channel.
• It supports a wide variety of information content.
– Voice, text and email messages, video can all be represented as digital bit streams.
Digital modulation
• Better performance and more cost effective than analog modulation methods (AM, FM, etc.)
• Performance advantages:
– the digital transceivers are much cheaper, faster and more power-efficient than analog transceivers;
– higher data rates are achieved compared to analog with the same signal bandwidth;
– powerful error correction techniques make the signal much less susceptible to noise and fading, and equalization can be used to mitigate ISI [→see later];
– more efficient multiple acces strategies (spread spectrum techniques applied to digital modulation can remove or combine multipath, resist interference, and detect multiple users simultaneously);
– better security and privacy for digital systems;
– combination of multiple information types (voice, data, & video) in a single transmission channel;
– implementation of modulation/demodulation functions using DSP software (instead of hardware circuits).
Digital modulation (cont’)
• Choice of digital modulation scheme
• Many types of digital modulation methods → small differences
• Performance factors to consider (corresponding metrics)
– low Bit Error Rate (BER) at low S/N (BER performance) – resistance to interference and multipath fading
– high data rate
– high spectral efficiency (SE [bps/Hz])
– easy and cheap implementation of mobile units (Receiver complexity) – transmission power amplifier linearity requirements (linearity)
– efficient use of battery power in mobile unit (Power efficiency, PE)
• No existing modulation scheme can simultaneously satisfy all of these requirements.
• Each one is better in some areas with trade-offs of being worse in others.
Bandwidth of a signal: the concept
Many definitions depending on application. Recall from DSP course
FCC definition (99%)
Frequency ranges of a some natural signals
Biological Signals
Type of Signal Frequency Range [Hz]
Electroretinogram 0 - 20
Pneumogram 0 - 40
Electrocardiogram (ECG) 0 -100
Electroenchephalogram (EEG) 0 - 100
Electromyogram 10 - 200
Sphygmomanogram 0 - 200
Speech 100 - 4000
Seicmic signals Seismic exploration signals 10 - 100 Eartquake and nuclear explosion signals 0.01-10
Electromagnetic signals
Radio bradcast 3x104 - 3x106
Common-carrier comm. 3x108 - 3x1010
Infrared 3x1011 - 3x1014
Visible light 3.7x1014 - 7.7x1014
A simplified communication modell
Recall from ICT course
PROBLEM:
Bandlimited channel !
Digital signal transmission over analog channel
Recall from ICT course
PROBLEM:
1. Nyquist pulse are noncausal and of infinite duration.
2. We cannot implement the ideal lowpass filter in practice.
3. It decays very slowly (~1/t).
ISI-free system requirements
Recall from ICT course
0
1 0
0 otherwise
l l
g =δ = l =
( )
FT( )
g t →G f
( )
FT S( )
1 1
n
g nT G f G f n
T T
→ = + =
∑
1f 2
≤ T
Nyquist criterion for ISI-free communication: (Not to mention the ISI caused by the coherence
bandwidth of the wireless channel.)
ISI-free system requirements (cont’)
• Nyquist criterion:
• Observations:
– To satisfy the Nyquist criterion, the channel bandwidth B must be at least 1/(2T)
– For the minimum bandwidth the impulse response is Nyquist pulse.
– The pulse shape g(t) fulfills the Nyquist criterion if it is center- symmetric for 1/2T: (basis pulse shapping)
Recall from ICT course
( )
FT S( )
1 1
n
g nT G f G f n
T T
→ = + =
∑
ISI-free system requirements (cont’)
Nyquist Pulse
( ) ( )
N
sin f T g t
f T π
= π
B=1/T
B ~ 1/T
Raised-Cosine Pulse
( ) ( ) ( )
( )
RC 2
sin cos
1 2
t T t T
g t
t T t T
π απ
π α
= −
α=0
B=(1+α)1/T
Recall from ICT course
Nyquist criterion with matched filtering
Recall from ICT course
T R
1 1
n
n n
G f G f
T T T
+ + =
∑
( )
( )
R
2
min R B
G f B
G f df
−
∫
GR(f) = GT(f)* matched filter
( ) ( ) ( )2
T R
G f G f = G f
Uncorrelated ηk :
( ) { } 0
k l k 0
N k l R k E
k l η η− =
= =
≠
( ) 0 R( )2 0 ( )
Sη f = N G f = N G f
Error probability
Recall from ICT course
( )
BERBPSK = Φ − SNR
{ } { } ( ) { } ( )
( )
{ } ( ) { ( ) } ( )
{ } { }
0 0 0
ˆ ˆ ˆ
Pr Pr 1 1 1 Pr 1 1 1
Pr sgn 1 1 1 Pr sgn 1 1 1
1 1 1 1
Pr 1 0.5 Pr 1 0.5 1
2
BER y y y y p y y y p y
y y p y y y p y
N N N
η η
η η
= ≠ = = = − = − + = − = = =
= + = = − = − + + = − = = =
= ≥ + < − = − Φ + Φ − = Φ −
• It describes the ability of a modulation technique to preserve the quality of digital messages at low power levels (low SNR):
required PE = Eb / N0 for a certain BER (e.g. 10-3)
where Eb : energy/bit and N0 : noise power/bit
• Tradeoff between signal power and fidelity:
– as Eb / N0 ↓, than BER ↑
• It depends on the particular type of modulation employed.
Receiver sensitivity or power efficiency (PE)
Bandwidth efficiency or spectral efficiency (SE)
• Ability of a modulation technique to accommodate data in a limited BW
SE = R / B,
where R is the data rate, B is the system bandwidth.
• Trade of between R data rate and B bandwidth:
– as R ↑, than B ↑
• For a digital signal
s s
1 so as , and
R B R T B
∝ ∝ T → ↑ ↑
M-ary Keying
• each pulse or “symbol” having m finite states represents n = log
2M bits/symbol
– e.g. M = 0 or 1 (2 states) → n = 1 bit/symbol (binary) – e.g. M = 0, 1, 2, 3, or 4 (4 states) → n = 2 bits/symbol
• E.g.: when a system is changed from binary to 4-ary:
– In the case of binary: "0" = - 1V and "1" = 1 V
– In the case of 4-ary: "0" = - 1V, "1" = - 0.33V, "2" = 0.33 V, "3" = 1 V
• What would be the new data rate compared to the old data rate if
the symbol periods were kept constant?
• Most famous result in communication theory.
– B : bandwidth
– C : channel capacity (bps) of real data (not retransmissions or errors)
– To produce error-free transmission, some of the bit rate will be taken up using retransmissions or extra bits for error control purposes.
– Lower bit error rates from higher power results more real data
– As noise power PN increases, the bit rate would still be the same, but SEmax decreases.
• SEmax is fundamental limit that cannot be achieved in practice.
Maximum SE: Shannon’s theorem (1948)
Recall from ICT course
Claude Elwood Shannon (1916-2001)
S b
max 2 2
N 0
log 1 P log 1 E
C R
SE B P N B
= = + = +
Fundamental trade-off between SE and PE
• If SE improves then PE deteriorates (or vice versa)
– One may need to waste more power to get a better data rate.
– One may need to use less power (to save on battery life) at the expense of a lower data rate.
• SE vs. PE is not the only consideration, we use other factors to evaluate, e.g.:
– resistance to interference and multipath fading;
– easy and cheap implementation in mobile unit;
– etc.
• The canonical form of a band pass transmitted radio signal is
where ej2πft is the carrier factor.
• The signal s(t) can be written as
• We will define the following quantities
• The complex envelope of s(t) is now written as
and
( ) ( )
cos( ( ) )
Re{ ( )
ej2πftej ( )t}
s t = A t ωt + Θ t = A t Θ
( ) ( )
cos( ( ) )
cos( ) ( )
sin( ( ) )
sin( )
s t = A t Θ t ωt − A t Θ t ωt
( )
I j Qs tɶ = +s s
( )
Re{ ( )
ej2πft}
s t = s tɶ
Recall from Chapter 3
( ) ( ) ( ( ) )
( ) ( ) ( ( ) )
I
Q
cos sin
s t A t t
s t A t t
= Θ
= Θ
Constellation diagrams
• Plot I/Q samples on x-y axis
• The constellation diagram provides a sense of how easy it is to distinguish between different symbols
• Assign each I/Q symbol to a set of digital bits (eg. Gray code)
Constellation diagrams
• Noise corrupts sampled I/Q values
• The points in the constellation diagram no longer consist of single dots for each symbol
• What is the best way to match received I/Q samples with their corresponding symbols?
(Detection)
Constellation diagrams properties
• Distance between signals is related to differences in modulation waveforms
– Large distance → easy to discriminate → good BER at low SNR – Power Efficient related to density
• Occupied BW ↓ as number of signal states ↑
– If we can represent more bits per symbol, then we need less BW for a given data rate.
– Small separation → “dense” → more signal states/symbol → more information/Hz !!
– Bandwidth Efficient
• Key idea: wrap signal back onto itself in periodic time intervals and retain all traces
– Similar to the action of an oscilloscope
• Increasing the number of symbols eventually reveals all possible symbol transition trajectories
– It shows the ISI present as well as timig jitter present.
• Eye diagram allows visual inspection of the impact of sample time and decision boundary choices
– Large eye opening implies less vulnerability to symbol errors
Eye diagrams
Binary Phase Shift Keying (BPSK)
• Phase transitions force carrier amplitude to change from “+” to “−”.
–Amplitude varies in time.
Quaternary Phase Shift Keying (QPSK)
• Four different phase states in one symbol period
• Two bits of information in each symbol
• double the SE of BPSK → or twice the data rate in same signal BW
• same PE (same BER at specified Eb/N0)
Transmit power amplifier
When a modulation signal encounters a nonlinearity the signal becomes distorted and its occupied frequency bandwidth increases (spectrum re-growth). The most significant source of nonlinearity comes from the transmission PA.
Offset QPSK
QPSK OQPSK
Quaternary Phase Shift Keying (QPSK)
• OQPSK ensures there are fewer baseband signal transitions applied to the RF amplifier, helps eliminate spectrum regrowth after amplification.
Frequency Shift Keying (FSK)
• Constant Envelope as compared to AM
–Linear: Amplitude of the signal varies according to the message signal.
–Constant Envelope: The amplitude of the carrier is constant, regardless of the variation in the message signal. It is the phase that changes.
M-ary Phase Shift Keying (MPSK)
• The SE ↑ with M↑
• The PE ↓ with M↑
M-ary QAM
• Basic trade-off: Better bandwidth efficiency at the expense of power efficiency
–More bits per symbol time → better use of constrained bandwidth
–Need much more power to keep constellation points far enough apart for acceptable bit error rates.
M-ary FSK
• Frequencies are chosen in a special way so that they are easily separated at the demodulator (orthogonality principle).
• M-ary FSK transmitted signals:
–fc = nc / 2T for some integer nc
–The M transmitted signals are of equal energy and equal duration
• The SE of an M-ary FSK signal ↓ with M↑
• The PE ↑ with M↑
–Since M signals are orthogonal, there is no crowding in the signal space
2 s
( ) cos ( )
0 0,1,...,
i c
s t E n i t
T T
t T i M
π
= +
≤ ≤ =
Given a modulation scheme and a targeted BER then the communication system designer can determine the SE (spectral efficiency) and the PE (Eb/N0 required to maintain the average BER target).
• The transmitter expands (spreads) signal Bs bandwidth many times with a p(t)
spreading code and the signal is then collapsed (despread) in receiver side with the same code.
• Other signals created with other codes just appear at the receiver as random noise.
• Processing Gain (PG)= Bs /BT
Spread Spectrum Modulation (SSM)
Spread Spectrum Modulation (SSM) advantage
• Resistant to narrowband interference.
• It allows multiple users with different codes to share same the wireless channel
– no frequency reuse needed
– rejects interference from other users
• It combats multipath fading → if a multipath signal is received with enough delay (more than one chip duration), it also appears like noise.
• As number of simultaneous users ↑ the SE↑
Spreading codes
• Signal spreading is done by multiplying the data signal by a pseudo-noise (PN) code or sequence
– the pseudo-noise signal looks like noise to all observers except those who know how to recreate the sequence.
Spreading codes: PN codes
• Binary sequence with random properties → noise-like (called
"pseudo-noise" because they are not noise technically)
• ≈ equal #’s of 1’s and 0’s
• Very low correlation between time-shifted versions of same sequence
• Very low cross-correlation between different codes
– each user assigned unique code that is approximately orthogonal to all other codes
– the other users’ signals appear like random noise!
• Direct Sequence (DS)
– Multiply baseband data by PN code (same as above) – Spread the baseband spectrum over a wide range.
– The Rx spread spectrum signal
– where m(t) : the data sequence and p(t) the PN sequence
• Frequency Hopping (FH)
– Randomly change fc with time
– In effect, this signal stays narrowband but moves around a lot to use a wide band of frequencies over time.
– Hopset: the set of possible carrier frequencies – Hop duration: the time during between hops – Classified as fast FH or slow FH
• fast FH: more than one frequency hop during each Tx symbol
• slow FH : one or more symbol are Tx in the time interval between frequency hops.
( )
( ) 2 s ( ) ( ) cos 2
i c
s
s t E m t p t f t
T π θ
= +
Spread spectrum modulation and the multiple access
• With Spread Spectrum Modulation, users are able to share a common band of frequencies yielding a multiple access technique
– TDMA: Users share a band of frequencies, but use a different time slot – FDMA: Users share a band of frequencies, but use a different slice of
frequency
– SSM enables CDMA (Code Division Multiple Access): Users share a band of frequencies and a number of time-slots, but each use a different spreading code.
