In this work, a developed mobile channel model has been designed, which can be used to generate SISO, SIMO, MISO, and MIMO Rayleigh fading channels. Then, Selection Combining (SC), Equal Gain Combining (EGC), and Maximal Ratio Combining (MRC) techniques have been studied and analyzed for receiving diversity (SIMO system). Furthermore, maximal ratio has been studied for transmitting diversity (MISO system), which is known as Maximal Ratio Transmission (MRT). On the other hand, the performance of diversity based on MIMO system by using, Zero Forcing (ZF), and Minimum Mean Square Error (MMSE) techniques have been studied and
tested. In addition to that, Space-Time Block Codes (STBC) have been studied and analyzed for both MISO and MIMO systems. Finally, comparisons between SISO, SIMO, MISO and MIMO systems, in terms of channel capacity, have been studied and analyzed under different cases and channel conditions.
Mobile Application Development-Components and Layouts
Â
Enhancement of Mobile Radio Channel Using Diversity Techniques
1. Enhancement of Mobile Radio
Channel Using Diversity Techniques
A Thesis
Submitted to the Department of Electrical &
Electronic Engineering
University of Technology
In Partial Fulfillment of the Requirements for the
Degree of Master of Science in
Communication Engineering
By
Mohannad Mohammed Abdul-Hussien
Supervised By
Dr. Waâil A.H. Hadi
January 2010
Republic of Iraq
Ministry of Higher Education and Scientific Research
University of Technology
Electrical and Electronic Engineering Department
3. Dedication
To Whom Had Made Me
of What I am... To My
Family, the Cause of My
Success.
Mohannad
4. Thanks to Allah for providing me the great willingness
and strength to finish this work.
I would like to express my deepest thanks and sincere
gratitude to my supervisor Dr. Waâil A.H. Hadi for his
continuing guidance, encouragement, and supports during this
study.
My thanks are expressed to the Department of Electrical
and Electronic Engineering for providing facilities to do this
work.
I wish to express my deepest thanks to my loving family,
thanks to my mother, my father, my brothers and Sister whom
without their unlimited patience this work might never see the
light.
Finally, special words of thanks with gratitude are
devoted to all my friends who provided me any kind of help
during the period of the study, and I couldnât mention them all
in these few lines.
Mohannad Mohammed Abdul-Hussien
December 2009
8. I
Abstract
Diversity is considered one of most effective ways to improve the
performance of transmission in the fading and interference channels. It can be
exploited under, time, frequency or space (spatial) domain. Due to its efficiency
in terms of system resource usage, the diversity type, utilized in the whole of
this thesis is spatial diversity which is applied to a multiple spatially separated
antennas at the transmitter and/or the receiver known as multiple antennas
systems such as Single-Input Multiple-Output (SIMO) system, Multiple-Input
Single-Output (MISO) system, and Multiple-Input Multiple-Output (MIMO)
system. The use of multiple transmit and receive antennas (MIMO system) is
widely accepted in recent years, as a promising technology for future wireless
communication, due to its ability to achieve higher data rates without
increasing the transmission power and bandwidth, in addition to its ability to
improve system reliability through increasing diversity. This work introduces a
comparative studies that determines the diversity and channel capacity
enhancements, resulting from using multiple antennas systems over single
antenna system, which is known as Single-Input Single-Output (SISO) system.
These enhancements were done in term of Bit Error Rate (BER) and bit rate of
data transmission for the diversity and capacity enhancements, respectively.
In this work, a developed mobile channel model has been designed,
which can be used to generate SISO, SIMO, MISO, and MIMO Rayleigh
fading channels. Then, Selection Combining (SC), Equal Gain Combining
(EGC), and Maximal Ratio Combining (MRC) techniques have been studied
and analyzed for receiving diversity (SIMO system). Furthermore, maximal
ratio has been studied for transmitting diversity (MISO system), which is
known as Maximal Ratio Transmission (MRT). On the other hand, the
performance of diversity based on MIMO system by using, Zero Forcing (ZF),
and Minimum Mean Square Error (MMSE) techniques have been studied and
tested. In addition to that, Space-Time Block Codes (STBC) have been studied
and analyzed for both MISO and MIMO systems. Finally, comparisons
9. II
between SISO, SIMO, MISO and MIMO systems, in terms of channel capacity,
have been studied and analyzed under different cases and channel conditions.
All the simulations and measurements were carried out by using
MATLAB R2007a. The main results showed that the (MRC) diversity
technique provides the best BER performance between all other diversity
techniques in SIMO system, where an SNR improvement, by about 34.023 dB,
is achieved over SISO system, at BER=10-5
, when the number of receive
antennas is four (1Ã4 transmission). The same result is obtained for MRT in
MISO system (4Ã1 transmission), in case of full Channel State Information
(CSI) is available at the transmitter. On the other hand, STBC provides the best
BER performance in MIMO system, where an SNR improvement by about
37.198 dB is achieved over SISO system, at BER = 10-5
, when the number of
transmit and receive antennas is two and four, respectively (2Ã4 transmission).
For channel capacity measurements, a maximum capacity of about 19.95
bit/s/Hz at SNR=18 dB was achieved with MIMO system for 4Ã4 transmission
by using Water-Filling (WF) method when CSI is available at the transmitter.
10. III
Abbreviation Definition
2G Second Generation
3G Third Generation
4G Fourth Generation
AMPS Advanced Mobile Phone Service
AWGN Additive White Gaussian Noise
BEP Bit Error Probability
BER Bit Error Rate
BLAST Bell Labs Layered Space -Time
BPSK Binary Phase Shift Keying
CDMA Code Division Multiple Access
CSI Channel State Information
D-AMPS Digital AMPS
dB Decibels
D-BLAST Diagonal-Bell Labs Layered Space-Time
DOA Direction-of-Arrival
DSL Digital Subscriber Line
EGC Equal Gain Combining
EVD Eigen Value Decomposition
FDMA Frequency Division Multiple Access
GSM Global System for Mobile Communication
I.I.D. Independent and Identically Distributed
IEEE Institute of Electrical and Electronic Engineers
IMT-2000 International Mobile Communications-2000
IP Internet Protocol
ISI Inter Symbol Interference
ITU International Telecommunication Union
LOS Line of Sight
MIMO Multiple-Input Multiple-Output
11. IV
MISO Multiple-Input Single-Output
MMSE Minimum Mean Square Error
MRC Maximal Ratio Combining
MRT Maximal Ratio Transmission
MS Mobile Station
OFDM Orthogonal Frequency Division Multiplexing
PDF Probability Density Function
QoS Quality of Service
SC Selection Combining
SIMO Single-Input Multiple-Output
SISO Single-Input Single -Output
SM Spatial Multiplexing
SMS Short Message Service
SNR Signal to Noise Ratio
SOS Sum of Sinusoidal
STBC Space -Time Block Code
STC Space -Time Coding
SVD Singular Value Decomposition
TDMA Time Division Multiple Access
UMTS Universal Mobile Telecommunication System
V-BLAST Vertical Bell Labs layered Space -Time
WCDMA Wideband Code Division Multiple Access
WF Water-Filling
WLAN Wireless Local Area Networks
WMAN Wireless Metropolitan Area Networks
ZF Zero Forcing
12. V
Symbol Definition
B Channel coherence bandwidthC
B BandwidthW
T Symbol durations
T Coherence time of the channelC
v Speed of mobile
c Speed of light
C Channel capacity
f Sampling frequencys
f Carrier frequencyc
f Doppler frequencyd
N Noise power spectral densityo
Eb/N Bit energy to noise ratioo
ðŸðŸðð Effective bit energy to noise ratio
K
Ricean K-factor : power ratio between line-
of-sight and scattered components
I0
Zero order modified Bessel function of the
first kind(.)
M Number of paths for fading channel
M The number of receive antennasR
M The number of transmit antennasT
erfc(.) Complementary error function
P Bit error probabilityb
h Vector of Channel Coefficients
H A MIMO flat-fading channel
I m à m Identity matrixm
ðð ðððððð Maximum Delay Spread of Channel
λ Wavelength
(.) Conjugate of a matrix*
(.) Transpose of a matrixT
13. VI
(.) Conjugate transpose (Hermitian) of a matrixH
(.) Pseudo-inverse of a matrixP
λ(.) Eigen values of matrix
|a| Absolute value of scalar a
||.|| Norm of a vector or a matrix
||.||
Norm of matrix (sum of squared
magnitudes of elements)
2
diag(.)
Elements placed along the diagonal of a
matrix
log2 Base 2 logarithm(.)
ð¥ð¥ï¿œ Estimate of signal x
17. Chapter One: Introduction 1
1.1 Overview of Cellular Communication Systems
Wireless communications is, by any criterion, the fastest growing
part of the communications industry. As it has captured the attention of
the media and the imagination of the public [1]. In recent years,
communications researches have seen an unprecedented growth,
especially related with cellular phones, due to the increasing demand for
the wide variety of end user applications. In addition to accommodating
standard voice, personal mobile communication services must now be
able to satisfy the consumer demand for text, audio, video, multimedia
and Internet services [2]. To meet these demands, there have been many
different generations of mobile communication networks that have
evolved from analog to digital [3].
The first generations (1G) systems were introduced in the mid
1980s, and can be characterized by the use of analog transmission
techniques, and the use of simple multiple access techniques such as
Frequency Division Multiple Access (FDMA) to divide the bandwidth
into specific frequencies that are assigned to individual calls. First
generation telecommunications systems such as Advanced Mobile Phone
Service (AMPS), only provided voice communications and they are not
sufficient for high user densities in cities. They also suffered from a low
user capacity at a rate of 2.4 kbps, and security problems due to the
simple radio interface used [4,5].
18. Chapter One: Introduction 2
In the early 1990s, second generation (2G) systems based on
digital transmission techniques were introduced to provide more robust
communications. The major improvements offered by the digital
transmission of the 2G systems over 1G systems were better speech
quality, increased capacity, global roaming, and data services like the
Short Message Service (SMS). The second generation (2G) systems
provided low-rate circuit and packet data at a rate of 9.6 and 14.4 kbps,
and medium-rate packet data up to 76.8 kbps [6]. The second generation
consists of the first digital mobile communication systems such as the
Time Division Multiple Access (TDMA) based on GSM system, D-
AMPS (Digital AMPS), and Code Division Multiple Access (CDMA)
based on systems such as IS-95 [5].
The third generation (3G) started in October 2001 when Wideband
CDMA or WCDMA network was launched in Japan [3]. The 3G has
become an umbrella term to describe cellular data communications with
a target data rate of 2 Mbps (actually 64⌠384 Kbps) [4]. which enables
many new services, including streaming video, web browsing and file
transfer to be of interest to the customers, the new services should be
cheap and of high quality. An important step for achieving these goals is
the selection of the multiple access method. WCDMA has been selected
as the air interface for these networks. The 3G system in Europe is called
the Universal Mobile Telecommunication System (UMTS) [7].
The fourth generation (4G) systems may become available even
before 3G is fully developed because 3G is a confusing mix of standards.
In 4G systems, it is expected that the target data rate will be up to 1 Gbps
for indoor and 100 Mbps for outdoor environments. The 4G will requires
a channel capacity above 10 times that of 3G systems and must also fully
support Internet Protocol (IP). High data rates are a result of advances in
19. Chapter One: Introduction 3
signal processors, new modulation techniques, such as Orthogonal
Frequency Division Multiplexing (OFDM), and it will have Multiple-
Input-Multiple Output (MIMO) technology at its foundation. The
combination of the above is the promising scheme that can provide
extremely high wireless data rates [8,4].
1.2 General Concept of Spatial Diversity
Due to the inhospitable nature of the radio propagation
environment, i.e. multipath propagation, time variation, and so on, the
wireless channel is unfriendly to reliable communication [9]. However,
transmission over wireless channel using single transmitter and single
receiver, which is known as, Single-Input Single-Output (SISO) system
is not reliable due to its high sensitivity to multipath fading [10]. In fact,
multipath fading, which is typically caused by a reflection from any
physical structure, is an unavoidable phenomenon in wireless
communication environments, because the signals are usually propagated
through a multipath. When passing through a multipath, the signals are
delayed and a phase difference are expected to occur with the signals
passing through a direct path, this causes random fluctuations in received
signal level known as fading which causes severely degradation in the
receiving quality of the wireless link [4,11].
To combat the impact of fading on the error rate, multiple
antennas have been employed at the receiver end only. This technique is
known as spatial diversity or Single-Input Multiple-Output (SIMO)
system, and it refers to the basic principle of picking up multiple copies
of the same signal at different locations in space. The separation between
the multiple antennas is chosen so that the diversity branches experience
independent fading. [12,1,13].
20. Chapter One: Introduction 4
The exploitation of the spatial dimension may take place at the
transmitter as well, known as transmit diversity or Multiple-Input Single-
Output (MISO) system [8]. Spatial diversity provides a diversity gain or
a significantly reduction in the signal-to-noise ratio (SNR) variations
owing to fading, leading to much smaller error probabilities [14]
1.3 Multiple-Input Multiple-Output (MIMO) System
The great potential of using multiple antennas for wireless
communications has only become apparent during the last decade, which
is witnessed new proposals for using multiple antennas systems to
increase the capacity of wireless links, creating enormous opportunities
beyond just diversity [15,16]. In recent years, and due to the increasing
demand for higher data transmission rate, a lot of research based on an
exploitation of the multiple antennas at both transmitter and receiver
which is known as Multiple-Input Multiple-Output (MIMO) systems
were established. They were shown that MIMO systems can provide a
novel means to achieve both higher bit rates and smaller error rates
without requiring extra bandwidth or extra transmission power [17,18].
Whilst spatial diversity protects the communication system from the
effects of multipath propagation when multiple antennas are used at
either the transmitter or receiver, significant capacity increases can be
achieved by using multiple antennas at both ends of the link. In fact, by
using multiple transmit and receive antennas, the multipath propagation
can be effectively converted into a benefit for the communication system
by creating a multiplicity of parallel links within the same frequency
band, and thereby to either increase the rate of data transmission through
Spatial Multiplexing (SM) gain or to improve system reliability through
the increased diversity gain [19,16].
21. Chapter One: Introduction 5
1.4 Literature Survey
In 1993, A. Wittneben [20] proposed one of the earliest form of
spatial transmit diversity, called delay diversity scheme, where a signal is
transmitted from one antenna, then delayed one time slot, and
transmitted from the other antenna. Signal processing is used at the
receiver to decode the superposition of the original and time-delayed
signals.
In 1996, Q. H. Spencer [21] presented a statistical model for the
indoor multipath channel, that includes the angle of arrival and its
correlation with time of arrival, in order to be used, in simulating and
analyzing the performance of array processing or diversity combining.
He also presented his results with two different buildings depending on
simultaneous collecting for time and angle of arrival at 7 GHz.
In 1998, S. M. Alamouti [22] presented a simple two-branch
transmit diversity scheme. Using two transmit antennas and one receive
antenna, the scheme provides the same diversity order as maximal-ratio
combining (MRC) at the receiver, with one transmit antenna, and two
receive antennas. The new scheme does not require any bandwidth
expansion, any feedback from the receiver to the transmitter, and its
computation complexity is similar to MRC.
In 2002, K. Kalliola [23] developed a new systems for radio
channel measurements including space and polarization dimensions for
studying the radio propagation in wideband mobile communication
systems. He demonstrated the usefulness of the developed measurement
systems by performing channel measurements at 2 GHz and analyzing
the experimental data. He also analyzed the spatial channels of both the
22. Chapter One: Introduction 6
mobile and base stations, as well as the double-directional channel that
fully characterizes the propagation between two antennas.
In 2004, A. H. Al-Hassan [24] studied the data transmission over
mobile radio channel. He introduced a software radio receiver design and
simulation, then he attempted to develop this software over mobile radio
channel. He also used many techniques to improve the performance of
the data transmission like equalization and diversity. Selection Switching
Combining (SSC) diversity technique was used in his simulation test.
In 2005, S. H. Krishnamurthy [25] studied the dependence of
capacity on the electromagnetic (EM) waves properties of antennas and
the scattering environment, the limits on performance of parameter
estimation algorithms at the receiver and finally, the fundamental limits
on the capacity that volume-limited multiple-antenna systems can
achieve. He used the theory methods to derive a channel propagation
model for multiple antennas in a discrete-multipath channel environment.
In 2006, M. R. Mckay [26] considers the analysis of current and
future wireless communication systems. The main focus is on Multiple-
Input Multiple-Output (MIMO) antenna technologies. The goal of his
work is to characterize the fundamental MIMO capacity limits, as well as
to analyze the performance of practical MIMO transmission strategies, in
realistic propagation environments.
In 2007 P. Zhan [9] studied the performance of a Maximum SNR
(Max-SNR) scheduler, which schedules the strongest user for service,
with the effects of channel estimation error, the Modulation and Coding
Scheme (MCS), channel feedback delay, and Doppler shift, all taken into
account.
23. Chapter One: Introduction 7
In 2008, D. Q. Trung, N. Prayongpun, and K. Raoof [17]
considered two schemes of antenna selection in correlated Rayleigh
channels, i.e. the Maximal Ratio Transmission (MRT) and Orthogonal
Space-Time Block Code technique (OSTBC). The simulation results
illustrate that, the new antenna selection scheme can obtain performance
close to the optimum selection with low computational complexity.
In 2009, A. Lozano, and N. Jindal [27] provided a contemporary
perspective on the tradeoff between transmit antenna diversity and
spatial multiplexing. They showed the difference between the
transmission techniques that utilizing all available spatial degrees of
freedom for multiplexing and the techniques that explicitly sacrifice
spatial multiplexing of MIMO communication for diversity.
1.5 Aim of the Work
The aim of this thesis can be summarized by the following:
1. Enhancement the performance of mobile radio channel by
exploiting spatial diversity, through the use of multiple antennas in
the transmission and/or reception.
2. Design a developed mobile channel model, which can be used to
generate SISO, SIMO, MISO, and MIMO channels, and to be the
dependent channel model in all the simulations of this thesis.
3. Study and analyze the improvement of capacity gained from using
SIMO, MISO, and especially from MIMO systems.
24. Chapter One: Introduction 8
1.6 Thesis Outline
This thesis is arranged in six chapters as follows:
Chapter one presents an introduction with literature survey and aim of
this thesis.
Chapter two gives a description of wireless fading channel character-
istics including, multipath propagation mechanisms, large scale fading
and small scale fading, then, channel simulator models which are
frequently used in mobile communication system such as, Jakes and
improved Sum-of-Sinusoids (SOS) models are studied.
Chapter three gives an overview of time, frequency, spatial diversity,
channel modeling of SISO system, and diversity combining techniques
in receiver (SIMO system) are introduced using, Selection Combining
(SC), Equal Gain Combining (EGC), and Maximal Ratio Combining
(MRC) techniques. Finally, Transmit diversity techniques (MISO
system), using Maximal Ratio Transmission (MRT), and Space-Time
Block Code (STBC) are studied and analyzed.
Chapter four begins with a brief description of MIMO communication
system. Then, methods of transmission from multiple antennas are
introduced. Later, STBC diversity technique is introduced for MIMO
system. Finally, capacity enhancements from using multiple antennas are
studied and analyzed.
Chapter five presents the simulation results and discussions using the
developed design that proposed for mobile channel modeling, which is
used in all the simulations and measurements.
Chapter six includes the conclusions and suggestions for future work.
25. Chapter Two: Mobile Channel Characteristics 9
2.1 Introduction
Radio channel is the link between the transmitter and the receiver
that carries information bearing signal in the form of electromagnetic
waves. In an ideal radio channel, the received signal would consist of
only a single direct path signal, which would be a perfect reconstruction
of the transmitted signal [5]. However, a real mobile radio channel
experiences a lot of limitations on the performance of wireless systems.
The transmission path can vary from Line-of-Sight (LOS) to complex
environments with obstruction from mountains, foliage, and man-made
objects such as buildings. Unlike fixed or wired channels, which are
stationary and predictable, wireless channels exhibit an extremely
random nature and are often difficult to characterize and analyze. The
speed of motion, for example, impacts on how the signal level fades as
the mobile terminal moves in space. Therefore, the detailed knowledge
of radio propagation characteristics is an essential issue to develop a
successful wireless system [28, 29].
This chapter is organized as follows: A brief qualitative
description of the main propagation mechanism characteristics of fading
channels, fading, large-scale fading, small-Scale fading, types of fading
channels. Finally Jakes model and improved Sum-of-Sinusoids (SOS)
models are presented.
26. Chapter Two: Mobile Channel Characteristics 10
2.2 Multipath Propagation Mechanisms
The mechanisms behind electromagnetic wave propagation
through the mobile channel are wide and varied, however, they can be
generally classified as reflection, diffraction and scattering [30]. They
can be described as follows:
1. Reflection: This occurs when electromagnetic waves bounce off
objects whose dimensions are large compared with the wavelength
of the propagating wave. They usually occur from the surface of
the earth and buildings and walls as shown in Fig. (2.1-a). If the
surface of the object is smooth, the angle of reflection is equal to
the angle of incidence [28].
2. Diffraction: Diffraction occurs when the electromagnetic signal
strikes an edge or corner of a structure that is large in terms of
wavelength, such as building corners, causing energy to reach
shadowed regions that have no LOS component from the
transmitter as shown in Fig. (2.1-b). The received power for a
vertically polarized wave diffracted over round hills is stronger
than that diffracted over a knife-edge, but the received power for a
horizontal polarization wave over the round hills is weaker than
that over a knife-edge [31].
3. Scattering: Scattering occurs when the wave travels through or
reflected from an object with dimensions smaller than the
wavelength. If the surface of the scattering object is random, the
signal energy is scattered in many directions as shown in Fig. (2.1-
c). Rough surfaces, small objects, or other irregularities in the
channel cause scattering [31,32].
27. Chapter Two: Mobile Channel Characteristics 11
All of these phenomena occur in a typical wireless channel as
waves propagate and interact with surrounding objects [14,28].
LOS Component
Ground Plane
(a) Reflection
(b) Diffraction
Building
(c) Scattering
Random Surface
Fig. (2.1) Multipath propagation mechanisms
28. Chapter Two: Mobile Channel Characteristics 12
2.3 Fading
Cellular systems usually operate in urban areas, where there is no
direct line-of-sight (LOS) path between the transmitter and receiver [28].
In such locations and due to multiple reflections from various objects,
the electromagnetic waves propagate along various paths of differing
lengths. The presence of several paths by which a signal can travel
between transmitter and receiver is known as multipath propagation. At
the receiver, the incoming waves arrive from many different directions
with different propagation delays. The signal received at any point in
space may consist of a large number of plane waves with random
distributed amplitudes, phases, and angles of arrival. The received signal
will typically be a superposition of these many multipath components
thereby creating a rapid fluctuation in signal strength at the receiver,
known as multipath fading [30]. Fig. (2.2) shows a scenario with
multipath fading [33].
LOS Component
TX
RX
Diffraction
Fig. (2.2) Multipath propagation Environment
Reflection
Reflection
Scattering
29. Chapter Two: Mobile Channel Characteristics 13
Two different scales of fading have been defined, large scale
fading and small scale fading. Large-scale fading characterizes average
signal strength over large transmitter-receiver (TX-RX) separation
distances (several hundred or thousands of wavelengths), and small-scale
fading characterizes the rapid fluctuations of the received signal over a
short distance (a few wavelengths) or a short time duration [34].
2.3.1 Large-Scale Fading
This phenomenon is affected by prominent terrain contours (hills,
forests, billboards, buildings, etc.) over large transmitter-receiver (TX-
RX
Small-scale fading or simply fading is used to describe the rapid
fluctuations of the amplitude, phases, or multipath delays of a radio
signal over a short period of time or travel distance (a few wavelengths),
so that large-scale path loss effects may be ignored. Small-scale fading
is caused by a number of signals (two or more) arriving at the reception
point through different paths, giving rise to constructive (strengthening)
or destructive (weakening) of the received signal, depending on their
) separation distances (several hundred or thousands of wavelengths)
[34,35]. The receiver is often represented as being shadowed by such
obstacles and the mobile station should move over a large distance to
overcome the effects of shadowing [36].
The large-scale effects are described by their probability density
functions (pdf), whose parameters differ for the different radio
environments [19].
More details of this phenomenon is available in [34, 36, 28, 37]
and will not be described in this work.
2.3.2 Small-Scale Fading
30. Chapter Two: Mobile Channel Characteristics 14
phase and amplitude values. These different signals other than the main
signal are called multipath waves. Multipath in a radio channel is the
cause of the small scale fading, and the three most important effects are
[36, 28, 9]:-
a. Rapid fluctuation in the signal strength over a short distance or time
interval.
b. Random frequency modulation due to different Doppler shifts on
various propagation paths, if there is a relative motion between the
transmitter and receiver.
c. Time dispersion (echoes) caused by multipath propagation delays.
Many physical factors can affect the small-scale fading. The most
important factors include multiple propagation paths, relative motion
between the transmitter and receiver, motion of the scatterers in the
environment, transmitted signal bandwidth, etc. In the typical mobile
communication setup, due to the relatively lower height of the mobile
receiver, there is usually no Line of-Sight (LOS) path. In this scenario,
when the number of independent electromagnetic waves is assumed to be
large, the distribution of the received signal can be considered as a
complex Gaussian process in both its in-phase and quadrature
components [9]. The envelope of the received signal is consequently
Rayleigh distributed. On the other hand, if there is a Line of-Sight (LOS)
path between the transmitter and receiver, the signal envelope is no
longer Rayleigh and the distribution of the signal is Ricean [28]. In this
work, only small-scale fading with Rayleigh distribution is considered.
Small-scale fading is categorized by its spectral properties (flat or
frequency-selective) and its rate of variation (fast or slow). The spectral
properties of the channel are determined by the amount of delay on the
31. Chapter Two: Mobile Channel Characteristics 15
various reflected signals that arrive at the receiver. This effect is called
delay spread and causes spreading and smearing of the signal in time.
The temporal properties of the channel (i.e., the speed of variation) are
caused by relative motion in the channel and the concomitant Doppler
shift. This is called Doppler spread and causes spreading or smearing of
the signal spectrum [32]. This will classified in the following sections.
2.3.2.1 Delay Spread and Coherence Bandwidth
Delay spread causes frequency selective fading as the channel acts
like a tapped delay line filter [28]. It is resulting from the difference in
propagation delays among the multiple paths, and it is the amount of
time that elapses between the first arriving path and the last arriving path
[34]. The reciprocal of delay spread is a measure of channelâs coherence
bandwidth. The coherence bandwidth BC, is the maximum frequency
difference for which the signals are still strongly correlated, and it is
inversely proportional to the delay spread (i.e., the smaller the delay
spread the larger the coherence bandwidth). In general, the coherence
bandwidth BC
On the other hand, if the spectral components of the transmitted
signal are affected by different amplitude gains and phase shifts, the
fading is said to be frequency selective. This applies to wideband systems
, is related to the maximum delay spread ðð ðððððð by [28, 29].
ðµðµð¶ð¶ â
1
ðð ðððððð
(2.1)
If all the spectral components of the transmitted signal are affected
in a similar manner, the fading is said to be frequency nonselective or,
equivalently, frequency flat. This is the case for narrowband systems in
which the transmitted signal bandwidth is much smaller than the
channelâs coherence bandwidth ðµðµð¶ð¶ [38].
32. Chapter Two: Mobile Channel Characteristics 16
in which the transmitted bandwidth is bigger than the channelâs
coherence bandwidth ðµðµð¶ð¶ [38].
2.3.2.2 Doppler Spread and Coherence Time
Relative motion between the transmitter and receiver imparts a
Doppler shift on the signal, where the entire signal spectrum is shifted in
frequency. When multipath is combined with relative motion, the
electromagnetic wave may experience both positive and negative
Doppler shift, smearing or spreading the signal in frequency. This effect
is called Doppler spread. Fig. (2.3) shows how this spreading could
occur in an urban mobile telecommunications environment [32]. In this
figure, as the car moves to the right, the reflections toward the vehicleâs
front end will have a positive Doppler shift and the signal from the tower
will have negative Doppler shift. The magnitude of the Doppler shifts
depends upon the transmitted frequency and the relative velocity of the
mobile station [32].
Fig. (2.3) Illustration of how Doppler spreading can occur.
33. Chapter Two: Mobile Channel Characteristics 17
In general the Doppler shift of the received signal denoted by fd, is
given by [39]:
ðððð =
ð£ð£ððð¶ð¶
ðð
cos ðð (2.2)
where ð£ð£ is the vehicle speed, ððð¶ð¶ is the carrier frequency, Ξ is the
incidence angle with respect to the direction of the vehicle motion, and c
is the speed of light.
The Doppler shift in a multipath propagation environment spreads
the bandwidth of the multipath waves within the range of ððð¶ð¶ ± ðððð ðððððð
,
where ðððð ðððððð
is the maximum Doppler shift when ðð = 0 which is given
by[39,40]:
ðððð ðððððð
=
ð£ð£ððð¶ð¶
ðð
(2.3)
A related parameter to ðððð ðððððð
, called coherence time, ððð¶ð¶, is defined
as the time over which the channel is assumed to be constant [29,32].
ððð¶ð¶ â
1
ðððð ðððððð
(2.4)
Comparing the coherence time TC with the symbol time Ts
provides two general concepts, that is the fading is said to be slow if the
symbol time duration TS is smaller than the channelâs coherence time ððð¶ð¶,
otherwise, it is considered to be fast [32,38]. Fig. (2.4) shows a tree of
the four different types of fading [41].
34. Chapter Two: Mobile Channel Characteristics 18
2.4 Types of Fading Channel
As discussed earlier, multipath fading is due to the constructive
and destructive combination of randomly delayed, reflected, scattered,
and signal components. This type of fading is relatively fast and is
therefore responsible for the small-scale fading. Depending on the nature
of the radio propagation environment, there are different models
describing the statistical behavior of the multipath fading envelope.
Some of these methods are summarized below [38,42].
Small-Scale Fading
(Based on multipath time delay spread)
Flat Fading
1- BW of signal < BW of channel.
2- Delay spread < symbol period.
Frequency Selective Fading
1- BW of signal < BW of channel.
2- Delay spread < symbol period.
Small-Scale Fading
(Based on Doppler spread)
Fast Fading
1- High Doppler spread.
2- Coherence time < Symbol period.
3- Channel variation faster than base
band signal variation.
Slow Fading
1- Low Doppler spread.
2- Coherence time >Symbol period.
3- Channel variation slower than base
band signal variation.
Fig. (2.4) Types of small-scale fading
35. Chapter Two: Mobile Channel Characteristics 19
2.4.1 Rayleigh Fading Distribution
The Rayleigh distribution is frequently used to model the
multipath fading channels with no direct line-of-sight (LOS) path
between the transmitter and receiver. In this case, the channel samples
amplitudes has a Probability Density Functions (PDF) given by
[43,38,44]
ðð(ðð) =
ðð
ðð2
ðððððð ï¿œâ
ðð
2ðð2
ï¿œ , ðð ⥠0 (2.5)
where r is the fading magnitude, ðð = ï¿œð¥ð¥2 + ðŠðŠ2, x and y are
random variables representing the real and imaginary parts of channel
samples. The parameter Ï is the standard deviation of the real and
imaginary parts of the channel samples, and ðð2
denotes the average
power of the channel samples [44,43]
2.4.2 Ricean Fading Distribution
In the LOS situation, the received signal is composed of a random
multipath components whose amplitudes are described by the Rayleigh
distribution, plus a direct LOS component that has essentially constant
power. The theoretical PDF distribution, which applies in this case, was
derived and proved by Ricean and it is called Ricean distribution. It is
given by [45,40].
ðð(ðð) =
ðð
ðð2 ðððððð
â(ðð2+ðŽðŽ2)
2ðð2
ðŒðŒðð ï¿œ
ðŽðŽðŽðŽ
ðð2ï¿œ, ðð ⥠0 (2.6)
where A2
is the LOS signal power and ðŒðŒðð(. ) is the modified Bessel
function of the first kind and zero-order. The Ricean channel is
sometimes described using the K-factor, which is the ratio between the
36. Chapter Two: Mobile Channel Characteristics 20
power of the LOS component and the multipath power components, or
Rayleigh components. The Rician factor is given by [46,40]
ðŸðŸ =
ðŽðŽ2
2ðð2
(2.7)
Observe that when K = 0, the Ricean distribution becomes the
Rayleigh distribution [46].
2.5 Jakes Model
Signal fading due to multipath propagation in wireless channels is
widely modeled using mobile channel simulators. Many approaches have
been proposed for the modeling and simulation of these channels.
Among them, the Jakes model, which has been widely used to simulate
Rayleigh fading channels [47]. Jakes has introduced a realization for the
simulation of fading channel model, which generates real and imaginary
parts of the channel taps coefficients as a superposition of a finite
number of sinusoids, usually known as a Sum-of-Sinusoids (SOS)
model. [20,40]
Jakes starts with an expression representing the received signal as
a superposition of waves which is given by[48]
ð ð ð·ð·(ð¡ð¡) = ðžðžðð ï¿œ ð¶ð¶ðð ðððððð(ðððð ð¡ð¡ + ðððð ð¡ð¡
ðð
ðð=1
ðððððð ðŒðŒðð + ðððð) (2.8)
where ðžðžðð is the amplitude of the transmitted cosine wave, ð¶ð¶ðð is the
random path gain, N is the number of arriving waves, ðŒðŒðð and ðððð are
random variables representing the angle of incoming ray and the initial
phase associated with the ððð¡ð¡â propagation path, respectively, ðððð is the
transmitted cosineâs radian frequency, ðððð is the maximum Doppler
radian frequency shift, i.e., ðððð = 2ðððð/ðððð where v is the relative speed
37. Chapter Two: Mobile Channel Characteristics 21
of the receiver and ðððð is the wavelength of the transmitted cosine wave
[48].
The signal ð ð ð·ð·(ð¡ð¡) can be normalized such that it has unit power
and thus Eq. (2.8) becomes [48]:
ð ð (ð¡ð¡) = â2 ï¿œ ð¶ð¶ðð ðððððð(ðððð ð¡ð¡ + ðððð ð¡ð¡
ðð
ðð=1
ðððððð ðŒðŒðð + ðððð) (2.9)
where ð ð (ð¡ð¡) is the normalized received signal which can be taken
as a reference model.
In the development of this simulator, Jakes makes some
assumptions which have the goal of reducing the number of low
frequency oscillators needed to generate the flat fading signal of Eq.
(2.9). Thus, he selects [48]
ð¶ð¶ðð =
1
â ðð
, ðð = 1, ⊠, ðð (2.10)
and
ðŒðŒðð =
2ðððð
ðð
, ðð = 1, âŠ, ðð (2.11)
ðððð = 0, ðð = 1, ⊠, ðð (2.12)
Furthermore, Jakes chooses N of the form N=4M+2 so that the
number of distinct Doppler frequency shifts is reduced from N to M+1.
Thus, the fading signal may be generated through the use of only M+1
low-frequency oscillators. The block diagram of the simulator is given in
Fig. (2.5) [48]. From the block diagram of the simulator, the simulator
38. Chapter Two: Mobile Channel Characteristics 22
output signal can be written in terms of quadrature components as
follows [48]:
ð ð ï¿œ(ð¡ð¡) = ððï¿œðð(ð¡ð¡) cos ðððð ð¡ð¡ + ððððï¿œð ð (ð¡ð¡)sin ðððð ð¡ð¡, (2.13)
where
ððï¿œðð(ð¡ð¡) =
2
â ðð
ï¿œâ2 cos ðœðœðð+1 cos ðððð ð¡ð¡ + 2 ï¿œ ðððððð ðœðœðð ðððððð ðððð ð¡ð¡
ðð
ðð=1
ᅵ, (2.14)
and
ððï¿œð ð (ð¡ð¡) =
2
â ðð
ï¿œâ2 ð ð ð ð ð ð ðœðœðð+1 cos ðððð ð¡ð¡ + 2 ï¿œ ð ð ð ð ð ð ðœðœðð ðððððð ðððð ð¡ð¡
ðð
ðð=1
ᅵ, (2.15)
ðœðœðð =
ðððð
ðð
ðð = 1,2, ⊠, ðð, (2.16)
ðððð = ðððð ðððððð
2ðððð
ðð
ðð = 1,2, âŠ, ðð (2.17)
39. Chapter Two: Mobile Channel Characteristics 23
ððï¿œðð(ð¡ð¡)
ð ð ï¿œ(ð¡ð¡)
ððï¿œð ð (ð¡ð¡)
cos ðð1 ð¡ð¡
cos ðððð ð¡ð¡
1
â2
cos ðððð ð¡ð¡ âŠ.âŠâŠ.âŠ
â¢
â¢
â¢
â¢
â¢
â¢
ââ
â
â90°
Fig. (2.5) Jakes Rayleigh fading channel simulator
2 ð ð ð ð ð ð ðœðœðð+1 2 cos ðœðœðð+1
2 ð ð ð ð ð ð ðœðœðð 2 cos ðœðœðð
cos ðððð ð¡ð¡
2ð ð ð ð ð ð ðœðœ1 2 cos ðœðœ1
40. Chapter Two: Mobile Channel Characteristics 24
2.6 Improved Sum-of-Sinusoids (SOS) Model
Despite its widespread acceptance, the Jakes model has some
important limitations. As a deterministic model, Zheng and Xiao
proposed an improved sum-of-sinusoids model in [49]. By introducing
randomness to path gain ð¶ð¶ðð, Doppler frequency ðŒðŒðð and initial phase ðððð,
it was proved that this new model matches the desired statistical
properties of Rayleigh channel.
The normalized low-pass fading process of a new statistical Sum-
of-Sinusoids (SOS) simulation model is defined by [49]:
ð ð ï¿œ(ð¡ð¡) = ððï¿œðð(ð¡ð¡) ðððððð ðððð ð¡ð¡ + ððððï¿œð ð (ð¡ð¡) ð ð ð ð ð ð ðððð ð¡ð¡, (2.18)
ððï¿œðð(ð¡ð¡) =
2
â ðð
ï¿œ cos(ðððð ). cos(ðððð ð¡ð¡ ðððððð ðŒðŒðð + ðð)
ðð
ðð=1
(2.19)
ððï¿œð ð (ð¡ð¡) =
2
â ðð
ï¿œ sin(ðððð ). cos(ðððð ð¡ð¡ ðððððð ðŒðŒðð + ðð)
ðð
ðð=1
(2.20)
with
ðŒðŒðð =
2ðððð â ðð + ðð
4ðð
, ðð = 1,2,⊠, ðð (2.21)
where ðð = ðð/4, ðððð = ðððð ððððð ð ðŒðŒðð , ðð, ðð and ðððð are statistically
independent and uniformly distributed over[âðð, ðð] for all ðð. In this work
an improved Sum-of-Sinusoids (SOS) model is considered.
41. Chapter Three: Diversity Techniques 25
3.1 Introduction
Chapter two described how the multipath channel causes
significant impairments to the signal quality in mobile radio
communication systems. As signals travel between the transmitter and
receiver, they get reflected, scattered, and diffracted. In addition, userâs
mobility gives rise to Doppler shift in the carrier frequency. As a result,
those signals experience fading (i.e., they fluctuate in their strength).
When the signal power drops significantly, the channel is said to be in
fade. This gives rise to high Bit Error Rates (BER) [29,28].
To combat the impact of fading on the error rate, diversity
techniques are usually employed which is applied to multi-antenna
systems (the use of multiple antennas at the transmitter and/or the
receiver) [19,42]. The principle of diversity is to provide the receiver
with multiple versions of the same transmitted signal. Each of these
versions is defined as a diversity branch. If these versions are affected by
independent fading conditions, the probability that all branches are in
fade at the same time is reduced dramatically [19].
In a wireless communications system, this results in an
improvement in the required SNR or Es/No
In this chapter, types of diversity techniques will be introduced,
then, receive diversity combining techniques which are, Selection
Combining (SC), Maximal Ratio Combining (MRC) and Equal Gain
is necessary to achieve a
given quality of service in terms Bit Error Rate (BER).[29]
42. Chapter Three: Diversity Techniques 26
Combining (EGC) will be studied and analyzed. Finally, transmit
diversity combining techniques such as, Maximal Ratio Transmission
(MRT) and Space -Time Block Codes (STBC) will be presented.
3.2 Types of Diversity Techniques
Diversity involves providing replicas of the transmitted signal over
time, frequency, or space. Therefore, three types of diversity schemes
can be found in wireless communications [28].
a. Time diversity: In this case, replicas of the transmitted signal are
provided across time by a combination of channel coding and time
interleaving strategies. The key requirement here for this form of
diversity to be effective is that the channel must provide sufficient
variations in time. It is applicable in cases where the coherence
time of the channel is small compared with the desired interleaving
symbol duration. In such an event, it is assured that the interleaved
symbol is independent of the previous symbol. This makes it a
completely new replica of the original symbol [28].
b. Frequency diversity: This type of diversity provides replicas of
the original signal in the frequency domain. This is applicable in
cases where the coherence bandwidth of the channel is small
compared with the bandwidth of the signal [28]. This will assure
that different parts of the relevant spectrum will suffer independent
fades. Frequency diversity can be utilized through spread spectrum
techniques or through interleaving techniques in combination with
multicarrier modulation. For example, Code-Division Multiple-
Access (CDMA) systems such as the Direct-Sequence CDMA and
Frequency-Hopping CDMA as well as the Orthogonal Frequency-
Division Multiplexing (OFDM) systems are based on frequency
diversity, however frequency diversity techniques use much more
43. Chapter Three: Diversity Techniques 27
expensive frequency spectrum and require a separate transmitter for
each carrier [30,25].
c. Space diversity: Recently, systems using multiple antennas at
transmitter and/or receiver gained much interest [50]. The spatial
separation between the multiple antennas is chosen so that the
diversity branches experience uncorrelated fading [12]. Unlike time
and frequency diversity, space diversity does not induce any loss in
bandwidth efficiency. This property is very attractive for high data
rate wireless communications [39]. In space, various combining
techniques, i.e., Maximum-Ratio Combining (MRC), Equal Gain
Combining (EGC) and Selection Combining (SC), may be used at
the receiver. Space-time codes which exploit diversity across space
and time can also be used at the transmitter side [28].
The diversity type which utilized in this thesis is the spatial
diversity and all the combining techniques mentioned above will be
examined in this chapter.
In the category of spatial diversity, there are two more types of
diversity that must be considered:
i. Polarization diversity: In this type of diversity, horizontal and
vertical polarization signals are transmitted by two different
polarized antennas and received correspondingly by two different
polarized antennas at the receiver. The benefit of different
polarizations is to ensure that there is no correlation between the
data streams [39]. In addition to that, the two polarization antennas
can be installed at the same place and no worry has to be taken
about the antenna separation. However, polarization diversity can
achieve only two branches of diversity. The drawback of this
scheme is that a 3 dB extra power has to be transmitted because
44. Chapter Three: Diversity Techniques 28
the transmitted signal must be fed to both polarized antennas at the
transmitter [45].
ii. Angle diversity: This applies at carrier frequencies in excess of 10
GHz. In this case, as the transmitted signals are highly scattered in
space, the received signals from different directions are
independent to each other. Thus, two or more directional antennas
can be pointed in different directions at the receiver site to provide
uncorrelated replicas of the transmitted signals [39].
3.3 Multiple Antennas in Wireless System
A wireless system may be classified in terms of the number of
antennas used for transmission and reception. The most traditional
configuration uses a single transmit antenna and a single receive antenna,
in which case the system is defined as a Single-Input Single-Output
(SISO) system. With multiple antennas at the receiver, the system is
classified as a Single-Input Multiple-Output (SIMO) system. Similarly,
with multiple transmit antennas and a single receive antenna, the system
is a Multiple-Input Single-Output (MISO) system. Finally, if multiple
antennas are employed at both sides of the link, the system is classified
as a Multiple-Input Multiple-Output (MIMO) system [13]. The full study
of MIMO communication will be the subject of chapter four.
3.4 Modeling of Single-Input Single-Output (SISO) Fading Channel
The principle objective of a channel model in communications is
to relate the received signal to the transmitted signal. Let x(t) represent
the baseband signal to be transmitted at time t, then the received signal
y(t) at a stationary receiver is given by the convolution of the channel
impulse response, â(ðð, ð¡ð¡) and x(t) as [30].
45. Chapter Three: Diversity Techniques 29
ðŠðŠ(ð¡ð¡) = ï¿œ â(ðð, ð¡ð¡)
â
ââ
ð¥ð¥(ð¡ð¡ â ðð)ðððð + ðð(ð¡ð¡) (3.1)
Where n(t) is the Additive White Gaussian Noise (AWGN) at the
receiver. Here, it is assumed that the channel impulse response â(ðð, ð¡ð¡) is
a function of both time t, and delay ðð of the channel.
Although the continuous channel representation given by Eq.
(3.1) is natural from an electromagnetic wave propagation point of view,
it is often conceptually convenient to work with an equivalent discrete-
time baseband model, As shown in Fig. (3.1) [51]. Consider the sampling
of the received signal at t = nT with period T, then, at y(n) = y(nT), the
signal at the receiver can be represented as [30,51]
ðŠðŠ(ðð) = ï¿œ ðð(ðð, ðð)ðð(ðð â ðð) + ðð(ðð)
â
ðð=ââ
(3.2)
where â(ðð, ðð) is the channel response at time n to an impulse
applied at time ðð â ðð, n(n) is usually modeled as Additive White
Gaussian Noise (AWGN) with variance ðððð
2
. When ðð(ðð, ðð) does not vary
with n, i.e. h(n,k) = h(0,k), the channel is called time-nonselective/time-
invariant. The input-output relation then becomes [51]:
ðŠðŠ(ðð) = ï¿œ ðð(ðð)ðð(ðð â ðð) + ðð(ðð)
â
ðð=ââ
(3.3)
ðð(ðð)
ðŠðŠ(ðð)ðð(ðð, ðð)ðð(ðð)
Fig. (3.1) Discrete-time baseband equivalent channel model
46. Chapter Three: Diversity Techniques 30
In this thesis, only narrowband frequency-flat systems will be
studied. In narrowband systems, where there is negligible delay, the
channel model can be simplified to [30,51].
ðŠðŠ = âð¥ð¥ + ðð (3.4)
The phase of this type channels is uniformly distributed in [0, 2ðð)
and the amplitude is Rayleigh distributed [51].
3.4.1 Bit Error Probability (BEP) Expression of SISO
System
Consider the simple case of Binary Phase Shift Keying (BPSK)
transmission through a SISO Rayleigh fading channel. In the absence of
fading, the Bit Error Probability (BEP) in an Additive White Gaussian
Noise (AWGN) channel is given by [3,19,50]
ðððð =
1
2
. ðððððððð ᅵᅵ
ðžðžðð
ðððð
ᅵ (3.5)
Where
ðžðžðð
ðððð
is the bit energy to noise ratio, and erfc(x), is the
complementary error function defined as [52,19,18]
ðððððððð(ð¥ð¥) =
1
â2ðð
ï¿œ ððð¡ð¡2
ðððð
â
ð¥ð¥
(3.6)
When fading is considered, the average BEP of SISO system can
be determined by simulation or analytically by integrating over the
Rayleigh Probability Density Function (PDF) of the channel coefficients,
the BEP is therefore given by [46,19].
ðððð,ðððððððððð ðð = ï¿œ
1
2
. ððððððððᅵᅵðŸðŸððï¿œððᅵᅵðŸðŸððï¿œ
â
0
ðððŸðŸðð (3.7)
47. Chapter Three: Diversity Techniques 31
Where ðŸðŸðð is the effective bit energy to noise ratio of Rayleigh
fading channel h, and ððᅵᅵðŸðŸððï¿œ is the Rayleigh fading distribution. For
BPSK, the integration in Eq. (3.7) reduces to the well-known form
[52,50,6]
ðððð,ðððððððððð ðð =
1
2
ï¿œ1 â ï¿œ
ðŸðŸðð
1 + ðŸðŸðð
ᅵ (3.8)
For SISO system, the diversity gain (the number of copies is often
referred to as the diversity gain or diversity order) is equal to one [46].
3.5 Diversity Combining Methods
In section (3.2), diversity techniques were classified according to
the domain where the diversity is introduced. The key feature of all
diversity techniques is a low probability of simultaneous deep fades in
various diversity subchannels. In general, the performance of
communication systems with diversity techniques depends on how
multiple signal replicas are combined at the receiver to increase the
overall received SNR. Therefore, diversity schemes can also be classified
according to the type of combining methods employed [39].
3.5.1 Receive Diversity Techniques
Receive diversity or SIMO system techniques are applied in
systems with a single transmit antenna and multiple receive antennas
(i.e., MR ⥠2). They perform a (linear) combining of the individual
received signals, in order to provide a diversity gain [15,19]. For a SIMO
system, the general input-output relation may be treated similar to that of
SISO system with, appropriately modified Signal to Noise Ratio (SNR),
and it is given by [53,19]
48. Chapter Three: Diversity Techniques 32
ðŠðŠ = ï¿œðžðžð ð âð¥ð¥ + ðð (3.9)
Where ðžðžð ð is the average signal energy per receive antenna and per
channel use, â = [â1, â2 .. . , â ððð ð
]ðð, is the MRÃ1 channel vector for
SIMO system, x and n is the MRÃ1 vectors representing, the transmitted
signal and the Additive White Gaussian Noise (AWGN), respectively, at
the MR
In this section, three receive diversity combining techniques will
be studied and analyzed, which are, Selection Combining (SC), Equal
Gain Combining (EGC), and Maximal Ratio Combining (MRC).
receivers [53,19].
3.5.1.1 Selection Combining (SC)
Selection combining is the simplest combining method, in which
the combiner selects the diversity branch with the highest instantaneous
SNR at every symbol interval, whereas all other diversity branches are
discarded. This is shown in Fig. (3.2) [28,19,15]. With this criterion of
selection, the effective bit energy-to-noise ratio at the output of the
combiner ðŸðŸðð is given by [12,28].
ðŸðŸðð = max{ðŸðŸ1, ðŸðŸ2,⊠, ðŸðŸððð ð
} (3.10)
ðð ððð ð
ðð2
ðð1
ðŠðŠï¿œ
ðŠðŠ2
ðŠðŠ1
ð¥ð¥
âððð ð
â2
â1
â¢
â¢
â¢
Select
Best
Antenna
Fig. (3.2) Block diagram of SC technique
ðŠðŠððð ð
49. Chapter Three: Diversity Techniques 33
For BPSK and a two-branch diversity, the Bit Error Probability
(BEP) in a Rayleigh channel, is given by [19]
ðððð =
1
2
â ï¿œ
ðŸðŸðð
1 + ðŸðŸðð
+
1
2
ᅵ
ðŸðŸðð
2 + ðŸðŸðð
(3.11)
At high SNR,
ðððð â
3
8ðŸðŸðð
2
(3.12)
In general, the diversity gain of MR-branch selection diversity
scheme is equal to MR , indicating that selection diversity extracts all the
possible diversity out of the channel [19].
3.5.1.2 Maximal Ratio Combining (MRC)
Maximal or maximum ratio combining method relies on the
knowledge of the complex channel gains (i.e., it requires the knowledge
of amplitudes and phases of all involved channels), so that the signals
from all of the MR
Then, the received signal is [28,50,19]
branches are weighted according to their individual
SNRs and then summed, to achieve the maximum signal to noise ratio at
the receiver output. Fig. (3.3) shows a block diagram of a maximal ratio
combining technique [50]. If the signals are ðŠðŠðð from each branch, and
each branch has a combiner weight ðððð
ðððððð
given by [28,19]
ðððð
ðððððð
= âðð
â
, ðð = 1, 2, ⊠, ððð ð (3.13)
50. Chapter Three: Diversity Techniques 34
ðŠðŠï¿œ = ï¿œ ðððð
ðððððð
. ðŠðŠðð
ððð ð
ðð=1
= ï¿œ âðð
â
ððð ð
ðð=1
ᅵᅵ ðžðžð ð âðð ð¥ð¥ + ððððï¿œ
= ï¿œ ï¿œ ðžðžð ð |âðð|2
ð¥ð¥ + âðð
â
ðððð
ððð ð
ðð=1
(3.14)
Where âðð
â
is the complex channel gains, representing the weighting
factor of MRC at ððð¡ð¡â receive antenna, ð¥ð¥ is the transmitted signal, ðŠðŠððand
ðððð are the received signal and the AWGN at ððð¡ð¡â receive antenna,
respectively.
This method is called optimum combining since it can maximize
the output SNR, where the maximum output SNR is equal to the sum of
the instantaneous SNRs of all the diversity branches [11]. Exact
expression for the Bit Error Probability (BEP) using MRC with MR
Analogous to the SC case, the diversity gain is equal to the
number of receive branches M
= 2
is given by [46]
ðððð =
1
2
â ï¿œ
ðŸðŸðð
1 + ðŸðŸðð
â
1
4
ᅵ
ðŸðŸðð
(2 + ðŸðŸðð)3
(3.15)
R in Rayleigh fading channels [19].
âððð ð
â
â1
â
â2
â
ðð ððð ð
ðð2
ðð1
ðŠðŠï¿œ
ðŠðŠððð ð
ðŠðŠ2
ðŠðŠ1
ð¥ð¥
âððð ð
â2
â1
â¢
â¢
â¢
Fig. (3.3) Block diagram of MRC technique
â
51. Chapter Three: Diversity Techniques 35
3.5.1.3 Equal Gain Combining (EGC)
Equal gain combining is a suboptimal but simple linear combining
method. It does not require estimation of the complex channel gains for
each individual branch. Instead, the receiver sets the amplitudes of the
weighting factors to be unity(|âðð| = 1) [39].
In general, the EGC combiner weight ðððð
ðžðžðžðžðžðž
for ððð¡ð¡â receive
antenna is given by [39,19]
ðððð
ðžðžðžðžðžðž
= |âðð|ððââ âðð = ððââ âðð , ðð = 1, 2, âŠ, ððð ð (3.16)
Then the received vector is written as [39,19]:
ðŠðŠï¿œ = ï¿œ ðððð
ðžðžðžðžðžðž
. ðŠðŠðð =
ððð ð
ðð=1
ï¿œ ððââ âðð ᅵᅵ ðžðžð ð âðð ð¥ð¥ + ððððï¿œ
ððð ð
ðð=1
= ï¿œ ððââ âðð ᅵᅵ ðžðžð ð |âðð|ððâ âðð ð¥ð¥ + ððððï¿œ
ððð ð
ðð=1
= ï¿œ ï¿œ ðžðžð ð |âðð|ð¥ð¥ + ððââ âðð ðððð (3.17)
ððð ð
ðð=1
In this way all the received signals are co-phased and then added
together with equal gain as shown in Fig. (3.4). The implementation
complexity for equal-gain combining is significantly less than the
maximal ratio combining [39].
52. Chapter Three: Diversity Techniques 36
The Bit Error Probability (BEP) with 2-branch EGC diversity
combining BPSK modulation is given by [12].
ðððð =
1
2
ï¿œ1 â ï¿œ1 â ðððð
2
ᅵ (3.18)
Where
ðððð =
1
1 + ðŸðŸðð
(3.19)
For EGC and MRC, the array gain grows linearly with MR , and is
therefore larger than the array gain of selection combining. However, the
diversity gain of EGC is equal to MR
3.6 Transmit Diversity (MISO) Systems
analogous to SC and MRC [19].
Multiple-Input Single-Output (MISO) systems exploit diversity at
the transmitter through the use of MT transmit antennas in combination
with pre-processing or precoding. A significant difference with receive
diversity is that the transmitter might not have the knowledge of the
MISO channel. Indeed, at the receiver, the channel is easily estimated.
ððâððâ â1
ððâððâ â ðð ð ð
ððâððâ â2
ðð ððð ð
ðð2
ðð1
ðŠðŠï¿œ
ðŠðŠððð ð
ðŠðŠ2
ðŠðŠ1
ð¥ð¥
âððð ð
â2
â1
â¢
â¢
â¢
Fig. (3.4) Block diagram of EGC technique
â
53. Chapter Three: Diversity Techniques 37
This is not the case at the transmit side, where feedback from the
receiver is required to inform the transmitter. However, there are
basically two different ways of achieving direct transmit diversity [19]:
1. when the transmitter has a perfect channel knowledge,
beamforming can be performed using various optimization metrics
to achieve both diversity and array gains
2. when the transmitter has no channel knowledge, pre-processing
known as spaceâtime coding is used to achieve a diversity gain,
but no array gain.
In this section, beamforming technique known as Maximal Ratio
Transmission (MRT) is evaluated and studied, then, Space-Time Block
Codes (STBC) technique known as, the Alamouti scheme is introduced
and analyzed.
3.6.1 Maximal Ratio Transmission (MRT)
This technique, also known as transmit beamforming or Maximal
Ratio Transmission (MRT), assumes that the transmitter has perfect
knowledge of the channel. To exploit diversity, the signal x is weighted
adequately before being transmitted on each antenna [19]. At the
receiver, the signal reads as [37,19]:
ðŠðŠ = ï¿œðžðžð ð âð€ð€ð€ð€ + ðð (3.20)
where â = [â1, . . . , â ðððð
], is the MT Ã 1 MISO channel vector,
ð€ð€ = [ð€ð€1, . . . , ð€ð€ðððð
] is the beamforming weight vector, and ð¥ð¥ is the
transmitted symbol over all transmitted antennas. The choice that
maximizes the receive SNR is given by [19,37,54]
ðððð
ðððððð
=
âðð
â
âââ
, ðð = 1, 2, ⊠, ðððð (3.21)
54. Chapter Three: Diversity Techniques 38
where âðð
â
is the complex conjugate channel of ððð¡ð¡â transmit
antenna, âââ2 = |â1|2 + |â2|2 + â¯+ ï¿œâ ðððð
ᅵ
2
is the beamforming gain
which guarantees the average total transmit energy remains equal to
ðžðžð ð [37,54].
This choice comes to transmit along the direction of the matched
channel, hence it is also known as matched beamforming. Matched
beamforming presents the same performance as receive MRC, but
requires perfect transmit channel knowledge, which implies feedback
from the receiver as shown in Fig. (3.5) [19].
3.6.2 Alamouti Space-Time Block Code Transmit Diversity
Space-time block coding is a simple yet ingenious transmit
diversity which is proposed by Alamouti. It can be applied to both MISO
and MIMO systems with MT =2 and any number of receive antennas (in
this chapter only MISO system is considered) [16,55]. It is usually
Fig. (3.5) Block diagram of MRT technique
âðððð
â2
â1
ð¥ð¥
ð¥ð¥
ð¥ð¥
ðŠðŠ
ð€ð€2
ð€ð€1
â¢
â¢
â¢
Estimate CSI parameters
and feedback
ð€ð€ðððð
55. Chapter Three: Diversity Techniques 39
designed to capture the diversity in the spatial channel without requiring
Channel State Information (CSI) at the transmitter. A full-diversity code
achieves the maximum diversity order of MRÃMT
This scheme can be described by considering the simple case, M
available in the
channel. However, Not all STBCs offer full-diversity order. In addition
to the diversity gain, STBC can also be characterized by its spatial rate,
which is usually known as Spatial Multiplexing (SM) gain, and it is the
average number of distinct symbols sent per symbol time-period [28,16].
T
= 2, MR = 1, which yields the scheme illustrated in Fig. (3.6) [56].
Assume that the flat fading channel remains constant over the two
successive symbol periods, thus the code matrix X has the form [19,56]:
ðð = ï¿œ
ð¥ð¥1 âð¥ð¥2
â
ð¥ð¥2 ð¥ð¥1
â ï¿œ (3.22)
This means that during the first symbol interval, the signal ð¥ð¥1 is
transmitted from antenna 1, while signal ð¥ð¥2 is transmitted from antenna
2. During the next symbol period, antenna 1 transmits signal âð¥ð¥2
â
, and
antenna 2 transmits signal ð¥ð¥1
â
Thus, the signals received in two adjacent
time slots are [56]
Fig. (3.6) Alamouti transmit-diversity scheme with MT = 2 and MR = 1
ð¥ð¥1 âð¥ð¥2
â
ð¥ð¥2 ð¥ð¥1
â
â2
â1
ð¥ð¥ï¿œ1
ð¥ð¥ï¿œ2
TX RX
ð¥ð¥1 , ð¥ð¥2
56. Chapter Three: Diversity Techniques 40
ðŠðŠ1 = ï¿œ
ðžðžð ð
2
(â1 ð¥ð¥1 + â2 ð¥ð¥2)+ðð1 (3.23)
and
ðŠðŠ2 = ï¿œ
ðžðžð ð
2
(ââ1 ð¥ð¥2
â
+ â2 ð¥ð¥1
â)+ðð2 (3.24)
where the factor ᅵ
ðžðžð ð
2
ensures that the total transmitted energy is ðžðžð ð ,
â1 and â2 denote the channel gains from the two transmit antennas to the
receive antenna. The combiner of Fig. (3.6), which has perfect CSI and
hence knows the values of the channel gains, generates the signals
ð¥ð¥ï¿œ1 = â1
â
ðŠðŠ1 + â2 ðŠðŠ2
â
(3.25)
and
ð¥ð¥ï¿œ2 = â2
â
ðŠðŠ1 â â1 ðŠðŠ2
â
(3.26)
So that
ð¥ð¥ï¿œ1 = â1
â
ᅵᅵ
ðžðžð ð
2
( â1 ð¥ð¥1 + â2 ð¥ð¥2)+ðð1ï¿œ + â2 ᅵᅵ
ðžðžð ð
2
(ââ1 ð¥ð¥2
â
+ â2 ð¥ð¥1
â) + ðð2
â
ᅵ
= ᅵ
ðžðžð ð
2
ï¿œ|â1|2 + |â2|2ï¿œ ð¥ð¥1 + â1
â
ðð1 + â2 ðð2
â
(3.27)
and similarly
ð¥ð¥ï¿œ2 = ï¿œ
ðžðžð ð
2
(|â1|2 + |â2|2)ð¥ð¥2 + â2
â
ðð1 â â1 ðð2
â
(3.28)
Thus, ð¥ð¥1 is separated from ð¥ð¥2 [56].
57. Chapter Three: Diversity Techniques 41
3.6.2.1 Summary of Alamoutiâs Scheme
The characteristics of this scheme is given by [28,19]:
1) No feedback from receiver to transmitter is required for CSI to
obtain full transmit diversity.
2) No bandwidth expansion (as redundancy is applied in space across
multiple antennas, not in time or frequency).
3) Low complexity decoders.
4) Identical performance as MRC if the total radiated power is
doubled from that used in MRC. This is because, if the transmit
power is kept constant, this scheme suffers a 3-dB penalty in
performance, since the transmit power is divided in half across
two transmit antennas.
5) No need for complete redesign of existing systems to incorporate
this diversity scheme. Hence, it is very popular as a candidate for
improving link quality based on dual transmit antenna techniques,
without any drastic system modifications.
58. Chapter Four: MIMO Wireless Communication 42
4.1 Introduction
The use of multiple antennas at the transmitter and receiver in
wireless systems, popularly known as MIMO (Multiple-Input Multiple-
Output) technology, has rapidly gained in popularity over the past decade
due to its powerful performance-enhancing capabilities. It has been
widely accepted as a promising technology to increase the transmission
rate and the strength of the received signal, with no additional increase in
bandwidth or transmission power, as compared with traditional Single-
Input Single-Output (SISO) systems, [16,53,14].
MIMO technology constitutes a breakthrough in wireless
communication system design and now itâs considered the core of many
existing and emerging wireless standards such as IEEE 802.11 (for
Wireless Local Area Networks or WLAN), IEEE 802.16 (for Wireless
Metropolitan Area Networks or WMAN) and IEEE 802.20 (for Mobile
Broadband Wireless Access or MBWA) [16].
In this chapter, Spatial Multiplexing (SM) techniques such as,
Zero Forcing (ZF) and Minimum Mean Squared Error (MMSE) will be
studied and analyzed. Then, STBC diversity technique will be introduced
for MIMO system. Finally, the capacities of SISO, SIMO, MISO, and
MIMO systems will be introduced and studied over flat fading Rayleigh
channels with different situations (i.e., the case of channel knowledge or
not).
59. Chapter Four: MIMO Wireless Communication 43
4.2 Benefits of MIMO Technology
The benefits of MIMO technology that help achieve such
significant performance gains are array gain, spatial diversity gain,
spatial multiplexing gain and interference suppression. Some of these
gains are described in brief below [16].
1) Array gain: Array gain indicates the improvement of SNR at the
receiver compared to traditional systems with one transmit and
one receive antenna (SISO system). Array gain improves
resistance to noise, thereby improving the coverage and the range
of a wireless network. The improvement can be achieved with
correct processing of the signals at the transmit or at the receive
side, so the transmitted signals are coherently combined at the
receiver. [55,57].
2) Spatial diversity gain: As mentioned earlier, Multiple antennas
can also be used to combat the channel fading due to multipath
propagation. Sufficiently spaced multiple antennas at the receiver
providing the receiver with multiple (ideally independent) copies
of the transmitted signal in space that has propagated through
channels with different fading. The probability that all signal
copies are in a deep fade simultaneously is small, thereby
improving the quality and reliability of reception [55]
3) Spatial multiplexing gain: MIMO systems offer a linear increase
in data rate through spatial multiplexing, i.e., transmitting
multiple, independent data streams within the bandwidth of
operation. Under suitable channel conditions, such as rich
scattering environment, the receiver can separate the data streams.
Furthermore, each data stream experiences at least the same
channel quality that would be experienced by a SISO system,
60. Chapter Four: MIMO Wireless Communication 44
effectively, enhancing the capacity by a multiplicative factor equal
to the number of streams. In general, the number of data streams
that can be reliably supported by a MIMO channel equals the
minimum of the number of transmit antennas and the number of
receive antennas, i.e., min{MT,MR}. The Spatial Multiplexing
(SM) gain increases the capacity of a wireless network [16].
4) Interference suppression : By using the spatial dimension
provided by multiple antenna elements, it is possible to suppress
interfering signals in a way that is not possible with a single
antenna. Hence, the system can be tuned to be less susceptible to
interference and the distance between base stations using the same
time/frequency channel can be reduced, which is beneficial in
densely populated areas. This leads to a system capacity
improvement [55].
4.3 MIMO Fading Channel Model
For a Multiple-Input Multiple-Output (MIMO) communication
system, shown in Fig. (4.1), with MT transmit and MR receive antennas,
each of the receive antennas detects all of the transmitted signals. This
allows the SISO channel, given in Eq. (3.4), to be represented as a
MTÃMR matrix [30]. For frequency-flat fading over the bandwidth of
interest, the MTÃMR
where âðððð is the Single-Input Single-Output (SISO) channel gain
between the i
MIMO channel matrix at a given time instant may
be represented as [30,16]
ð»ð» =
â£
â¢
â¢
â¡
â1,1 â1,2
â2,1 â2,2
⊠â1,ðððð
⊠â2,ðððð
â® â®
â ððð ð ,1 â ððð ð ,2
â± â®
⊠â ððð ð ,ðððð âŠ
â¥
â¥
â€
(4.1)
th
receive and jth
transmit antenna pair. The jth
column of H
61. Chapter Four: MIMO Wireless Communication 45
is often referred to as the spatial signature of the jth
As for the case of SISO channels, the individual channel gains
comprising the MIMO channel are commonly modeled as zero-mean
Additive White Gaussian Noise (AWGN). Consequently, the amplitudes
of âðððð are Rayleigh distributed random variables [16]. Hence, the
received signal can be represented as in the following equation [47,58].
ðŠðŠ = ï¿œ
ðžðžð ð
ðððð
ð»ð»ð»ð» + ðð (4.2)
transmit antenna
across the receive antenna array.
where y is the MRÃ1 received signal vector, x is the MTÃ1
transmitted signal vector, ðð is the AWGN, and the factor ï¿œ
ðžðžð ð
ðððð
ensures
that the total transmitted energy is Es. The MIMO channel in Fig. (4.1) is
presumed to be a rich scattering environment. Each transmit receive
antenna pair can be treated as parallel sub channels (i.e., SISO channel).
Since the data is being transmitted over parallel channels, one channel
for each antenna pair, the channel capacity increases in proportion to the
number of transmit-receive pairs [44]. This will become clearer when the
analysis of the MIMO channel is discussed.
RXTX
ð¥ð¥1
ð¥ð¥2
ð¥ð¥ ðððð
â¢
â¢
â¢
â¢
â¢
â¢
ðŠðŠ2
ðŠðŠððð ð
ðŠðŠ1
Fig. (4.1) Block diagram of a MIMO system with MT
transmit antennas and MR receive antennas
MIMO
Channel
62. Chapter Four: MIMO Wireless Communication 46
4.4 MIMO Transceiver Design
Transceiver algorithms for MIMO systems may be broadly
classified into two categories: rate maximization schemes and diversity
maximization schemes. MIMO systems within the two categories are
known as Spatial Multiplexing (SM) techniques and spatial diversity
techniques, respectively. A spatial multiplexing techniques such as Bell
Labs layered Space-Time (BLAST) predominantly aim at a multiplexing
gain, (i.e., an increasing in bit rates as compared to a SISO system). In
spatial diversity techniques a maximum diversity gain are provided, for
fixed transmission rate, (i.e., decreasing error rates) such as, space-time
coding techniques [16,15]. which are based on the principle of
appropriately sending redundant symbols over the channel, from
different antennas to increase reliability of transmission [59].
4.5 Spatial Multiplexing (SM)
Spatial Multiplexing (SM) techniques simultaneously transmit
independent data streams, often called layers, over MT transmit antennas.
The overall bit rate compared to a single-antenna system is thus
enhanced by a factor of MT
The earliest known spatial-multiplexing receiver was invented and
prototyped in Bell Labs and is called Bell Labs layered Space-Time
(BLAST) [60,43]. There are two different BLAST architectures, the
Diagonal BLAST (D-BLAST) and its subsequent version, Vertical
BLAST (V-BLAST). The encoder of the D-BLAST is very similar to that
of V-BLAST. However, the main difference is in the way the signals are
without requiring extra bandwidth or extra
transmission power. The achieved gain in terms of bit rate (in
comparison to a single antenna system) is called multiplexing gain
[15,16].
63. Chapter Four: MIMO Wireless Communication 47
transmitted from different antennas. In V-BLAST, all signals from each
layer are transmitted from the same antenna, whereas in D-BLAST, they
are shifted in time before transmission. This shifting increases the
decoding complexity. V-BLAST was subsequently addressed in order to
reduce the inefficiency and complexity of D-BLAST [59]. In this work
only V-BLAST is considered. More details about D-BLAST are
available in [60,43,59], and it is not considered in this work.
4.6 Transmitter and Receiver Structure
The basic principle of all Spatial Multiplexing (SM) schemes is as
follows. At the transmitter, the information bit sequence is split into MT
The signals transmitted from various antennas propagate over
independently scattered paths and interfere with each other upon
reception at the receiver [39]. There are several options for the detection
algorithm at the receiver, which are characterized by different trade-offs
between performance and complexity.
sub-sequences (demultiplexing), that are modulated and transmitted
simultaneously over the transmit antennas using the same frequency
band. At the receiver, the transmitted sequences are separated by
employing an interference-cancellation type of algorithm [15]. The basic
structure of a Spatial Multiplexing (SM) scheme is illustrated in Fig.
(4.2).
A low-complexity choice is to use a linear receiver, e.g., based on
the Zero Forcing (ZF) or the Minimum-Mean-Squared-Error (MMSE)
criterion. However, the error performance is typically poor, especially
when the ZF approach is used (unless a favorable channel is given or the
number of receive antennas significantly exceeds the number of transmit
antennas). In general, it is required that MR ⥠MT in order to reliably
64. Chapter Four: MIMO Wireless Communication 48
separate the received data streams. However, if the number of receive
antennas exceeds the number of transmit antennas (MR >MT) case, is
satisfied, a spatial diversity gain is accomplished [16,57].
4.7 Zero-Forcing (ZF) Method
The most simple, but also the least efficient decoding method is
matrix inversion. As matrix inversion exists only for square matrices,
there is a more general expression known as, pseudo-inverse matrix,
which can be used for a square and non square matrices. The interference
is removed by multiplying the received signal y given in Eq. (4.2) with
the pseudo inverse of the channel matrix. This is also called Zero Forcing
(ZF) method. Hence, the ZF combiner weight GZF
Where H
is given by [57,60,19].
ðºðºðððð = ï¿œ
ðððð
ðžðžð ð
ð»ð»ðð = ï¿œ
ðððð
ðžðžð ð
(ð»ð» ð»ð» ð»ð»)â1 ð»ð» ð»ð» (4.3)
P
=(HH
H)-1
HH
, is a pseudo inverse of the channel matrix,
H is the channel matrix, and HH
is the complex conjugate transpose of
the channel H. For 2 Ã 2 channel, the HH
Information
H term is given by [50]
bit sequence
Demultiplexing
TX RX
â¢
â¢
â¢
MT MR
â¢
â¢
â¢
Detection
Algorithm
Estimated
bit sequenceMIMO
Channel
Fig. (4.2) Basic principle of Spatial Multiplexing (SM)
MT Sub-sequences
65. Chapter Four: MIMO Wireless Communication 49
ð»ð» ð»ð» ð»ð» = ï¿œ
â11
â
â21
â
â12
â
â22
â ï¿œ ï¿œ
â11 â12
â21 â22
ᅵ
= ᅵ
|â11|2 + |â21|2 â11
â
â12 + â21
â
â22
â12
â
â11 + â22
â
â21 |â12|2
+ |â22|2 ï¿œ (4.4)
As stated above, the interfering signals is totally suppressed by
multiplying the received signal y given in Eq. (4.2) with the ZF weight
GZF
The main drawback of the zero-forcing solution is the
amplification of the noise. If the matrix H
, giving an estimated received vector ð¥ð¥ï¿œ [14,43].
ð¥ð¥ï¿œ = ðºðºðððð ðŠðŠ = ðºðºðððð ᅵᅵ
ðžðžð ð
ðððð
ð»ð»ð»ð» + ððï¿œ
= ð¥ð¥ + ðºðºðððð ðð (4.5)
H
H has very small eigenvalues,
its inverse may contain very large values that enhance the noise samples
[14]. The diversity gain (diversity order) achieved using this detection
method is just MR - MT
4.8 Minimum Mean-Square Error (MMSE) Method
+1 [57,43]. A bit better performance is achieved
using similar method called Minimum Mean-Square Error (MMSE),
where the SNR is taken into account when calculating the matrix
inversion to achieve MMSE [57].
A logical alternative to the zero forcing receiver is the MMSE
receiver, which attempts to strike a balance between spatial interference
suppression and noise enhancement by minimizing the expected value of
the mean square error between the transmitted vector x and a linear
combination of the received vector GMMSE y [60,39,14]
min ðžðž{(ð¥ð¥ â ðºðºðððððððð ðŠðŠ)2} (4.6)
66. Chapter Four: MIMO Wireless Communication 50
where ðºðºðððððððð is an MR à MT
Where E
matrix representing the MMSE
combiner weight and it is given by [19,39]
ðºðºðððððððð = ï¿œ
ðððð
ðžðžð ð
ï¿œð»ð»ð»ð» ð»ð» +
ðððð
ðžðžð ð
ðŒðŒðððð ï¿œ
â1
ð»ð»ð»ð» (4.7)
s is the transmitted energy, No is the noise energy and IMT
is an MT Ã MT
As the SNR grows large, the MMSE detector converges to the ZF
detector, but at low SNR, it prevents the worst eigenvalues from being
inverted [60].
identity matrix. An estimated received vector ð¥ð¥ï¿œ is
therefore given by [19].
ð¥ð¥ï¿œ = ðºðºðððððððð ðŠðŠ = ð¥ð¥ + ðºðºðððððððð ðð (4.8)
4.9 Space-Time Block Coding (STBC) Method
In this section the example of Alamouti scheme of 2Ã1 MISO
transmission (given in chapter three) is extended to 2 Ã 2 MIMO
transmission. Analogous to the MISO case, consider that two symbols ð¥ð¥1
and ð¥ð¥2 are transmitted simultaneously from transmit antennas 1 and 2
during the first symbol period, while symbols âð¥ð¥2
â
and ð¥ð¥1
â
are transmitted
from antennas 1 and 2 during the next symbol period, see Fig. (4.3) [19].
â22
â21
â11
â12
ð¥ð¥1 , ð¥ð¥2
ð¥ð¥2 ð¥ð¥1
â
ð¥ð¥ï¿œ1
ð¥ð¥ï¿œ2
ð¥ð¥1 âð¥ð¥2
â
TX RX
Fig. (4.3) Alamouti scheme with MT = 2 and MR = 2