DEPARTMENT OF INFORMATICS
31 October/ 7 November 2002
D. Gesbert: IN256 Signal Processing 4 Communications1 of 50
David Gesbert
Signal and Image Processing Group (DSB)
http://www.ifi.uio.no/~gesbert
Course book: Chap. 6 & 7 Wireless Communications: Principles and
Practice. Sec. Ed. Th. Rappaport
IN256: SP4COM Signal Processing in Wireless
Communications
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Comparing to this intro course, the supporting book is far more detailed.
For the sake of clarity, not all book notations are used or followed here.
This set of slides contains an introduction to the theory and practice of
digital transmission over wireless systems. The substance of the course
is adjusted to fit into 4x45min.
Important disclaimer
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• Diversity
• Equalization
• Demodulation
• Wireless propagation modeling
7 November (2hrs):
D. Gesbert: IN256 Signal Processing 4 Communications3 of 50
• Pulse shaping and Nyquist criterion
• Digital linear modulations
• Generic communication chain
• Introduction: Motivations and definitions
31 October (2hrs):
Outline
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FDD: Frequency division duplex
MOS: Mean opnion score (voice quality)
ML: Maximum likelihood estimation
i.i.d.: identically independent distribution
ISI: Intersymbol interference
EIRP: Equivalent Isotropic Radiated Power
GSM: Global System for Mobile
3G: Third Generation Wireless
GPRS: General Packet RadioServices
extension of GSM to data
MIMO: Multiple input multiple output
BER; Bit Error Rate
CCI: Co−channel interference
D. Gesbert: IN256 Signal Processing 4 Communications4 of 50
TDD: Time division duplex
BWA: Broadband wireless access
ZF: Zero Forcing inversion
TX: Transmit
SU: subscriber unit (Mobile)
SNR: Signal to noise ratio
SINR: Signal to noise+interference ratio
SIMO: Single input multiple output
RX: Receive
MISO: Multiple input Single output
MMSE: Minimum mean square error
BTS: Base Station Transceiver
Definitions and acronyms
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optimized
constraint
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Broadband MIMO Channel Models
Physical Layer
Link Layer
Transport/Network (TCP/IP)
SYSTEM LAYER
Using signal processing to optimize performance...
Example: Wireless Internet System
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Examples of applications: Signal processing is a key component in a
wide range of communications systems: GSM (SMS, voice), DECT
(cordless phones), WCDMA, WiFi, ...and wired systems: DSL, ISDN, and
many more....
Goal: “To use signal processing techniques in order to maximize data
rates (Bits/Sec), spectrum efficiency (Bits/Sec/Hz), and quality
(minimize Bit Error Rate) for transmission over digital communications
mediums” (for example: wireless medium)
Motivations
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• Forward Error Coding (or ”channel coding”): Redundancy is added to
the source in order to protect from random bit errors occurring
during transmission (due to noise).
• Source coding and compression: the analog (e.g. speech) or digital
source (e.g. internet data) is digitized and/or compressed to occupy
the least amount of resource for transmission
(time/frequency/power). Redundancy is minimized/eliminated.
Signal processing’s main functions at the physical (PHY) layer:
Functional Blocks and Definitions
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• Carrier modulation: The pulse-shaped symbol signal is up converted
to the desired carrier frequency. The signal is fed to the antenna.
• Pulse shaping: Each symbol is transmitted successively using an
analog pulse.
• Bit-to-symbols digital modulation: The encoded binary source bi is
mapped to voltage-level (possibly complex) symbols sk . Each symbol
corresponds to a group of bits is drawn from a modulation
constellation. The constellation has only a finite number M of
possible symbols (or ’states’) to use (e.g. 2, 4, 8 states etc.).
Functional Blocks and Definitions (II)
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• Low pass filtering: All elements of noise outside the baseband are
filtered out.
• Matched-filtering: The signal is convolved with the time-reversed
version of the pulse signal.
• Carrier demodulation (down-conversion): The pass-band signal is
captured by the antenna(s) and converted from carrier frequency (e.g.
2GHz) down to baseband (low frequency).
Upon reception, the dual operations are performed:
Functional Blocks and Definitions (III)
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• Channel decoding: The error protection code (FEC) is decoded to
remove some bit errors.
• symbol demodulation: The estimated symbols are converted back to
bits.
• Equalization: A digital filter is applied to compensate for distorsions
brought by the propagation channel. In doing so, the frequency
response of the channel is equalized.
• Sampling and quantization: the time continuous signal is converted
into a discrete time digital signal.
Functional Blocks and Definitions (IV)
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Example: The GSM functional blocks
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2πjfct
= Amr (t) cos(2πjfct) − Ami(t) sin(2πjfct)
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m(t) remains at low frequencies, while s(t) is centered around a high
carrier frequency fc. Example: fc = 900MHz or 1800MHz for GSM.
m(t) contains the digital information while A determines the transmit
power.
A is the amplitude, m(t) = mr (t) + jmi(t) is the so-called (normalized)
complex envelope of the transmitted signal s(t).
s(t) = < Am(t)e
The transmitted signal is real valued:
The RF signal model
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symbol
modulation
1/Ts
sk
antenna
pulse shaping
m(t)
p(t)
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1/Tb
bi
binary source
Transmitter
z(t)
Diversity
equalization
slicer
symbol
demodulation
^
sk
estimated source
^
bi
D. Gesbert: IN256 Signal Processing 4 Communications13 of 50
p(−t)
kTs
Receiver
y(t) match−filter
noise n(t)
channel
h(t)
antenna
The transmission/reception block diagram can be simplified by
ignoring up and down conversions to carrier frequency (we also ignore
here the coding modules):
The Baseband model
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k=−∞
sk p(t − kTs)
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Where p(t) is said to be the pulse shaping filter.
m(t) =
∞
X
m(t) carries the digital information by convolving the complex symbols
sk with an analog pulse p(t):
• We assume a digital linear modulation, with complex alphabet A.
Cardinal(A) = M. sk ∈ A, for all k..
• The baseband model is the signal model that uses the complex
envelope m(t) to represent the transmitted signal (a simplification to
get rid of the carrier terms):
Baseband signal model
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• Other modulations exist that are not digital (like FM) or not linear
(like FSK or GMSK used in GSM).
• Popular digital linear modulation include M-PSK and M-QAM
• The spectral efficiency (SE) of an M-ary modulation is defined by the
number of transmitted bits per symbol sk . SE = log2(M ).
• A M-ary modulation is a modulation in which each symbol sk takes
on one of M possible complex values.
Typical digital linear modulation
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101
110
8−PSK
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111
011
010
100
000
001
4−PSK (QPSK)
01
00
D. Gesbert: IN256 Signal Processing 4 Communications16 of 50
11
10
• 4-PSK is a particular example (also called QPSK -quadrature phase
shift keying) very popular in mobile wireless systems.
• PSK= “Phase Shift Keying”. The information is encoded in the phase
of the complex modulation symbol sk .
M-PSK modulation
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−3
−3
−1
1
16−QAM
−1
1
3
3
4−QAM (QPSK, or 4−PSK)
01
00
D. Gesbert: IN256 Signal Processing 4 Communications17 of 50
11
10
• 16-QAM and 256-QAM are popular “high speed” modulations for
internet access (wireless or DSL).
• 4-QAM is identical to 4-PSK (also called QPSK).
• QAM= “Quandrature and amplitude modulation”. The information is
encoded separately in the in-phase part of the complex symbol (its
real part) and the quadrature part (its imaginary part).
M-QAM modulation
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Example: The NRZ (non return to zero) waveform:
Once mapped into complex symbols, the data is converted into an
analog voltage-level signal waveform.
The digital waveform
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A typical example of pulse shaping filter:
The pulse shaping filter
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A typical “Nyquist pulse” for p(t) is the ”raised cosine”: see p. 286-287.
The roll-off factor α determines the bandwidth expansion.
p(0) = K, p(kTs) = 0 ∀k 6= 0
In order to avoid Intersymbol interference (ISI), one uses pulse shaping
filters that realize the so-called Nyquist criterion (see page 284).
The Nyquist criterion
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Problem: Upon transmission, the signal is convolved with a propagation
channel which can close the eye as seen by the receiver.
By superposing all possible values taken by mr (t) or mi(t), we can
visualize the probability of detection errors. When the pulse shaping
filter satisfies the Nyquist criterion, the eye is said to be “open”.
The eye diagram
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• Co-channel interference: interference caused by other cells reusing
the same frequency carrier.
• Multipath delay spread: When the paths arrive with significantly
different delays, it causes intersymbol interference.
• Multipath fading: The signal is received as superposition of many
different paths with different propagation distances (hence different
phases). The fading coefficient is modeled as complex Gaussian (also
called ’Rayleigh fading’).
• Additive noise n(t). The noise is usually modeled as additive white
Gaussian.
Wireless communications is a challenging task because of:
Limitations of wireless communications
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Scatterers local to mobile
Scatterers local to base
D. Gesbert: IN256 Signal Processing 4 Communications23 of 50
Remote scatterers
Wireless propagation diagram
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xxxx
xxxx
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co-channel Tx user
Tx
ISI
Rx
co-channel Rx user
noise
fading
D. Gesbert: IN256 Signal Processing 4 Communications24 of 50
Tx CCI
Rx CCI
Diagram of limitations
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h(t) = α0(t)δ(t − τ0) + α1(t)δ(t − τ1) + .. + αK (t)δ(t − τK )
y(t) = Am(t) ∗ h(t) + n(t)
where the channel h(t) is composed of K paths, each with a attenuation
coefficient:
The complex envelope of the received signal is y(t):
Assumptions: We place ourselves after frequency down-conversion so
we can use the complex envelope for representation of the received
signal.
The received signal model (baseband)
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z(t) = y(t)∗p(−t) = Am(t)∗h(t)∗p(−t)+n(t)∗p(−t) = Am(t)∗h(t)∗p(−t)+n0(t)
The received signal is filtered using a time-reversed pulse shaping filter
to maximize energy at sampling time kTs and reduce noise:
Receiver matched-filtering
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With hef f (t) given by:
k=−∞
sk hef f (t − kTs) + n0(t)
D. Gesbert: IN256 Signal Processing 4 Communications27 of 50
hef f = A ∗ p(t) ∗ h(t) ∗ p(−t)
z(t) =
∞
X
The effective channel hef f (t) takes into account all filtering effects
(transmit and receive filters and propagation) between the data symbols
and z(t):
The effective channel
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1
τ1
α
τ2
α2
τ3
α3
multipath channel h(t)
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energy
time delay t
τ4
α4
energy
effective channel h eff
(t)
time delay t
D. Gesbert: IN256 Signal Processing 4 Communications28 of 50
Effective channel
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or equivalently
k=−∞
D. Gesbert: IN256 Signal Processing 4 Communications29 of 50
sk hef f (n − k) + n0(n)
sk hef f ((n − k)Ts) + n0(nTs)
∞
X
k=−∞
z(n) =
z(nTs) =
∞
X
After sampling (at the symbol rate Ts), the filtered received signal is:
Discrete time signal model
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• Diversity techniques: For example using multiple receive antennas to
reduce fading probability.
• An equalizer: to eliminate the intersymbol interference (ISI).
In addition to filtering with time-reversed pulse shaped, the receiver
compensates for the channel imperfection using:
Advanced Signal processing at the receiver
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ŝn = z(n) ∗ heq (n) = sn + n0(n) ∗ heq (n) = sn + n00(n)
At the output of heq , we have symbol estimates ŝn:
Hef f (f )Heq (f ) = 1
hef f (n) ∗ heq (n) = δ(n)
or equivalently, in the frequency domain:
The equalizer is a digital filter heq (n) implemented at the receiver which
tries to suppress ISI. In the frequency domain, the filter “equalizes” the
response of the effective channel hef f (n).
Channel Equalization
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E|sn − z(n) ∗ heq (n)|2is minimum
We look for heq , filter of chosen size P , such that:
Example: minumum square error equalizer:
As a compromise, we can use “optimal filters”.
In practice, we use a finite length filter for heq , so it is impossible to
completely invert the effective channel.
MMSE Equalization
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where Rz = E(zzH ) and rzs = E(zs∗n), and with
z = [z(n), z(n − 1), .., z(n − P + 1)]T .
Rz h∗eq = rzs
We can show that heq is found from:
To find the coefficients of the MMSE filter, we stack all the coefficients of
heq in a vector heq = [heq (0), heq (1), ..., heq(P − 1)]T .
The MMSE Solution
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• Time: by retransmitting the data at multiple time instants, or by
spreading the message over time using FEC coding.
• Frequency: using frequency hopping over multiple frequency carriers
• Space: using multiple antennas
Various diversity domains:
⇒ this improves the Bit Error Rate (BER)!
The idea of diversity is that if one observes the same signal/information
through several independent channels, the probability that at least one
channel is of acceptable quality is increased.
Diversity Techniques
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50
100
150
350
400
450
500
D. Gesbert: IN256 Signal Processing 4 Communications35 of 50
200
250
300
Time in Milliseconds
The Power of Diversity
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−125
0
−120
−115
−110
−105
−100
−95
−90
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Signal Level in dB
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The Power of Diversity (BER vs. SNR))
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Diversity using multiple antennas
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s
Phases
estimation
2
1
h
h
(1)
Antenna
selection
(2)
y
D. Gesbert: IN256 Signal Processing 4 Communications38 of 50
2 2
w =h*
1
w =h*1
Weights
phases
estimation
Receive Diversity
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Receive Diversity Algorithms
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• Sub-optimum techniques: Equal gain combining, switching.
— Non Linear: max likelihood detection
— Linear: MMSE combining
• Optimum techniques
• The signal is received over p antennas, i.e.
Z(n) = [z1(n), z2(n), .., zp(n)]T
• The channel on the i-th antenna (i = 1, .., p) has no ISI
(i)
(hef f (n) = hef f δ(n)). The channel is said to be “flat fading”.
Assumptions:
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Z(n) = Hsn + N (n)
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E|WoT Z(n) − sn|2 minimum
Problem: Find Wo such that
where Z(N ) collects the signals received on p antennas. sn is the
(1)
(p)
transmitted symbol sequence. H = [hef f , .., hef f ]T is the channel vector
of size p. N (n) is the white noise vector over p antennas.
Received signal model:
MMSE Antenna diversity combining (I)
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(1)
(2)
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Notice how this equation is similar toD.the
previous MMSE equalizer!
Gesbert: IN256 Signal Processing 4 Communications41 of 50
Rz = E(Z(n)Z(n)H )
rzs = E(s∗nZ(n))
where σv2 is the variance of noise samples.
Wo = [(HH H + σv2I)−1H]∗
Rz Wo∗ = rzs
(HH H + σv2I)Wo = H
Wiener-Hopf equation:
MMSE diversity combining (II)
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— Joint space-time coding
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— Space to Time Diversity algorithms
— Space to Frequency Diversity algorithms
• Without Channel Feedback: Easier in FDD systems or TDD with high
mobility
• With Channel Feedback
Smart antennas Exist at BTS for RX side. How do we reuse them in TX
side?
Transmit Diversity Algorithms
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1
2 2
w =h*
w =h*1
1
h
h
2
y
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• In case of broadband channels, MRC can be applied at each
subcarrier. Otherwise, space-time filter must be used for w.
• Same formulation for MRC than in receive processing.
s
Weights
phases
estimation
TX diversity with feedback
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• Idea is to create random fast fading in a domain where
interleaved-coded information can recover from it.
• The particularity of all these techniques is to rely on coding to work!
• Space-Time Coding techniques
• Transformed Domain Techniques
TX Diversity without Feedback
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source
source
source
..
..
..
..
..
..
..
..
space-time
encoder
Z
decoder
t
DeInt/FEC
f
D. Gesbert: IN256 Signal Processing 4 Communications45 of 50
power
power
equalizer
Transformed Domain Techniques
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• The idea is to send multiple signals at the same time into the channel
matrix, then estimate and invert the matrix to separate the signals at
the receiver.
• The goal is to ’open spatial parallel channels’ by using the fact that
the channel becomes a matrix.
• A MIMO channel is obtained by using multiple antennas at
transmitter AND receiver.
MIMO=Multiple input , Muliptle output
Spatial Multiplexing using MIMO
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b3 b6 ...
b2 b5 ...
DEPARTMENT OF INFORMATICS
b1 b2 b3 b4 b5 b6 ...
b1 b4 ...
A3
A2
A1
Modulation and mapping
*
*
*
*
*
*
*
*
*
*
*
*
A3
A2
A1
*
** * * *
* * * * **
* * * * ** **
** ** ** **
* * * **** * *
* * **
C3
C2
C1
***
*****
*
*
* **
****
**
***
***
******
***
***
***
***
*
***
***
**
**
**
*
****
****
**
C3
C2
C1
b3 b6 ...
b2 b5 ...
b1 b4 ...
b1 b2 b3 b4 b5 b6 ...
D. Gesbert: IN256 Signal Processing 4 Communications47 of 50
*
* * * * **
* ** * ***
* * ** * * ***
* * * *** **
* *** ** * *
* * **
B3
B2
B1
* *
* * **
* * * ****
* * * * * **
* * *** **
* * * ** * *
* * ** *
B3
B2
B1
Spatial Multiplexing Example
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SIGNAL PROCESSING
Zero Forcing Solution:
DEPARTMENT OF INFORMATICS
MMSE Solution:




D. Gesbert: IN256 Signal Processing 4 Communications48 of 50
ŝ = HH (HHH + Rn)−1z
ŝ = H−1x
z1
h11 h12 ..
s1
  
 
=
z
h
..
h
 2   21 22   s2  + n
:
:
:
: :

MIMO Spatial Multiplexing
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modulation
modulation
coding
*
*
*
*
*
*
*
modulation
weighting/mapping
*
*
*
*
*
*
*
*
*
modulation
weighting/mapping
MIMO
coding
MISO
coding
SIMO
coding
DEPARTMENT OF INFORMATICS
0010110
0010110
0010110
0010110
SISO
demodulation
*
*
demodulation
*
*
weighting/demapping
*
*
*
*
*
*
decoding
decoding
decoding
decoding
0010110
TX−RX Diversity
TX−RX Space Time Coding
MIMO Spatial Multiplexing
TX Diversity Space Time Coding
TX Diversity MRC
0010110
RX Diversity
RX Beamforming
Conventional System
(time only processing)
0010110
0010110
D. Gesbert: IN256 Signal Processing 4 Communications49 of 50
weighting/demapping
** * * *
***
* *
* **
** * * *
***
* *
* **
*
*
*
*
demodulation
*
*
demodulation
** * * *
***
* *
* **
** * * *
***
* *
* **
Space time Processing Algorithms
General Smart Antenna Algorithms
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An early MIMO laptop prototype (1999), Iospan Wireless Inc. Ca.
MIMO-in-a-Laptop
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