Table Of ContentMIMO
Processing for
4G and Beyond
Fundamentals
and Evolution
Edited by
Mário Marques da Silva
Francisco A. Monteiro
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Contents
Foreword .........................................................................................................v
Preface ............................................................................................................xi
Editors ...........................................................................................................xv
Contributors ................................................................................................xvii
1 MIMO Techniques and Applications .....................................................1
MárIO MArquEs dA sIlvA And AMérICO COrrEIA
2 MIMO detection Methods ..................................................................47
FrAnCIsCO A. MOnTEIrO, IAn J. WAssEll, And nunO sOuTO
3 Precoding for MIMO .........................................................................119
dzEvdAn KAPETAnOvIć And FrEdrIK rusEK
4 MIMO Optimized for OFdM ............................................................159
nunO sOuTO And FrAnCIsCO A. MOnTEIrO
5 MIMO Optimized for single-Carrier Frequency-domain
Equalization .......................................................................................211
ruI dInIs, JOãO CArlOs sIlvA, And nunO sOuTO
6 MIMO Optimized for W-CdMA .......................................................249
JOãO CArlOs sIlvA, nunO sOuTO, And ruI dInIs
7 ultrawideband systems and MIMO ...................................................341
vIT sIPAl, BEn AllEn, dAvId J. EdWArds, And WAsIM q. MAlIK
8 Frequency-domain Packet Combining Techniques for uWB ...........377
PAulO MOnTEzuMA, MárIO MArquEs dA sIlvA, And ruI dInIs
9 link and system level simulation for MIMO ...................................405
AMérICO COrrEIA And MárIO MArquEs dA sIlvA
iii
iv ◾ Contents
10 Massive MIMO and Its detection ......................................................449
XIAOlI MA And qI zhOu
11 MIMO Two-Way relay Channel with superposition Coding ...........473
IOAnnIs KrIKIdIs And JOhn s. ThOMPsOn
12 Physical-layer network Coding with Multiple-Antenna relays .......491
dIrK WüBBEn, MEng Wu, And ArMIn dEKOrsy
Index ...........................................................................................................515
Foreword
In the transmission of information over a wireless channel, the channel is modeled
classically as a linear system black box with an input and output, that is, a single
input and a single output (SISO). The input is the connection point from the power
amplifier of the transmitter to the transmitting antenna terminal and the output is
the connection point from the receiving antenna terminal to the radio frequency
(RF) front-end filter of the receiver. The antennas are modeled as a structure that
radiates EM waves that propagate through space. The simplest such antenna struc-
ture is a radiating electric dipole element. With the presence of multipath propaga-
tion in the channel, it becomes evident that the electric field at the receiver location
undergoes variations in amplitude over distances in space of the order of a wave-
length. As a result, variations of the classical wireless channel were employed, where
multiple receiving antenna elements were introduced, or in other words, antenna
structures with multiple interconnection points to the receiver. These antennas were
designed to achieve so-called receiver diversity. The channel could then be modeled
as having a single input and multiple outputs, or in the current terminology SIMO
(single input multiple output). Classical receiver techniques to process the multiple
outputs were referred to as combining techniques. The three classical combining
techniques are selection, equal gain, and maximal ratio combining.
Alternative processing approaches of the signals at the multiple outputs taking
the phase of the received signal into account (or taking the timing of the received
signal into account) result in the receiver antenna structure behaving as a direc-
tional antenna, where the antenna gain is dependent on the direction of arrival—
the technique is referred to as beamforming, or antenna array, or phased array, and
works well when the timing of the received signals at the antenna elements is on the
order of a carrier period; that is, elements are spaced on the order of a wavelength.
Such a technique can also be employed with multiple antenna elements at the trans-
mitter and a single element at the receiver. This results in the system being modeled
as a SISO system with directivity. In either the case of transmitter or receiver beam-
forming, the system may be modeled as a SISO system with directivity.
Over the past 30 years of wireless research, another variation was introduced,
where multiple transmitting antenna elements are introduced, and where an
v
vi ◾ Foreword
information signal is fed into the different elements with various delays. The rela-
tive delays between the signals are much larger than the carrier period and on the
order of the transmission symbol period. This technique became known as delay
transmission diversity and in effect simulated a channel with multipath propa-
gation. Such a channel exhibits what is referred to as frequency diversity in that
the frequency response has a variation over the frequency band of the transmit-
ted signal. The variation with frequency is measured by the coherence bandwidth
parameter and is inversely related to the relative delay of the signals being fed into
the transmitting antenna elements. A SISO channel with the channel multipath
having a small delay spread exhibits what we call frequency flat fading, with its
effect being uncorrectable with any signal processing techniques at the receiver.
The introduction of relative delays at the different transmitting antenna elements
basically transforms the channel into a frequency-selective fading channel, where
appropriate signal processing techniques can then be introduced at the receiver to
correct the effect of fading. Such a receiver utilizes an equalizer and the resulting
signal is insensitive to the precise location of the receiving antenna over several
wavelengths. One form of this scheme, for wideband signals, is a spread spectrum
system (e.g., CDMA*) with a Rake receiver.
The next development in antenna schemes came with the introduction of a
multiplicity of antenna elements at the transmitter but with different information
signals being fed into the different antenna elements. This work was first reported
by DaSilva and Sousa in the mid-1980s as a way to solve the flat fading problem
with narrowband systems, such as those with 30 kHz RF channels (1G in North
America). The flat fading problem of narrowband cellular systems is a result of
narrow RF bandwidth together with a small portable receiver terminal which is not
conducive to receiver antenna diversity. The idea was to find a transmitter diversity
technique that requires a relatively simple receiver. To motivate the idea we imag-
ine such a SISO system with a multipath where, at the receiver, there are a series
of nulls and peaks in the signal strength over distances of the order of half of a
wavelength. If the single antenna at the receiver is located at a null, then we have a
very weak signal. To attempt to mitigate the flat fading, conceptually we imagine
the transmitting antenna being placed in a motor and move it so that the nulls at
the receiver also move and we get diversity. However, we wish to implement such
a system without moving parts, hence we can propose what is called switching
diversity, where the signal at the transmitter is periodically switched between two
antenna elements. Such switching may have undesirable effects in broadening the
spectrum. We therefore considered that switching between two antennas is a form
of transmitting two orthogonal signals in the two antenna elements and, in this
way, we were led to a scheme where a signaling constellation of two dimensions is
created where each dimension is associated with a transmitting antenna element.
In the basic scheme we have the constellation points: (−1, −1), (−1, 1), (1, −1), and
* Code division multiple access.
Foreword ◾ vii
(1,1). We then realized that if we introduce a rotation of this constellation in the
plane we obtain in effect a modulation scheme that, in a sense, has fading resistant
properties.
A variation of the above technique of transmitter diversity was introduced after-
ward by Alamouti where, instead of associating the signals transmitted on the dif-
ferent antennas with a 4-point constellation, a scheme is devised where two symbols
s and s are transmitted over two successive time slots as follows: At time slot 1
1 2
we send s on antenna 1 and s on antenna 2, and in time slot 2 we send −s* on
1 2 2
antenna 1 and s* on antenna 2. This scheme was later coined as space–time coding,
1
although some coding theorists would argue that this is a misnomer as there is no
coding theory involved in the classical sense of coding theory.
The next major development, by Foschini and others, occurred with consider-
ation of enhanced receiver antenna structures where it is possible to install a mul-
tiplicity of antenna elements and achieve some degree of decorrelation between the
signals in the different receiver antenna elements. We consider a system with m
receiving antenna elements and n transmitting antenna elements; that is, a system
with multiple inputs and multiple outputs (MIMO). The channel can then be mod-
eled by a channel gain matrix h = (h ), where h is the path gain between the ith
i,j i,j
transmitting antenna element and the jth receiving antenna element. We model
the inputs to the different antenna elements by the vector x, where the component
x is fed into the ith antenna element and where the vector y models the outputs
i
at the receiver antenna. Thus, we have y = hx. We observe that if the channel has
no multipath components, then we have h = 1 for all i,j, and use of the multiple
i,j
antennas has no benefit in the sense that we cannot separate the signals from the
different transmitter elements to, in effect, recover all the data. In fact, the signals at
each receiver antenna element are all equal to the sum of the inputs to the different
transmitter elements. However, in the case that m = n, and if the matrix h is invert-
ible, we can easily compute x = h−1y. Hence, we can recover x from y; that is, we
can decouple the channel and make it behave as if there are n parallel noninteract-
ing paths. The next observation is that the behavior of this scheme is very much
dependent on the eigenvalues of the matrix h, because in a sense they determine
the signal strength in each of the decoupled paths and eventually the performance
in the presence of noise in each path. The scheme works well if the environment
contains many multipath components.
The analysis of this scheme is usually presented by diagonalizing the matrix h
as follows: h = MΛM*, where Λ is the diagonal matrix of eigenvalues of h and M
is the matrix whose column vectors are the associated eigenvectors. In this form we
can view the effect of h on the channel input signal as three transformations. First,
the multiplication by M* is a form of pre-coding of the channel input vector x, or
changing of coordinate system to make it simple to apply the channel transforma-
tion. Then, the multiplication by Λ, in effect, models the different independent
paths of the channel and, finally, the effect of multiplication by M converts back
into a coordinate system that corresponds to the system under which the real signal
viii ◾ Foreword
observations are made. In the case that the matrix h is not a square, then a similar
decomposition can be achieved using the well-known singular-value decomposi-
tion (SVD): h = uΛv*, where u is an m × m real or complex unitary matrix; Λ is
an m × n rectangular diagonal matrix; and v* is the conjugate transpose of v,
which is an n × n real or complex unitary matrix. We may view the matrix h as
providing the transformation between the input signal x and the output signal y,
hence we have y = hx = uΛv*x.
Considering the input to the channel as a vector of information symbols, the
“signals” in this linear system are finite dimensional vectors. These transformations
become very familiar if we draw a comparison with the area of linear time invariant
(LTI) systems with which we are familiar in an introduction to linear systems. In
those systems, the familiar concepts are time domain, frequency domain, convo-
lution, and transfer function. The direct method of computation of the output is
based on a convolution and is done in one step. The indirect method based on the
frequency domain uses three steps. In a sense performing the multiplication y = hx
is analogous to convolution. Now, using the SVD decomposition of h, we first
compute v*x (analogous to converting the input into the “frequency domain”).
Then, multiplication by the diagonal matrix Λ (simple) is like multiplying by the
transfer function. Finally, multiplication by the matrix u corresponds to convert-
ing back into the analogue of the time domain. In the design of linear systems, we
prefer the frequency domain because it simplifies our understanding of the system
and, in a sense, the above SVD form is preferable to understanding the behavior of
the multipath channel.
Now, MIMO is a technology that has been widely adopted in state-of-the-art
cellular systems such as LTE and systems such as WiFi and WiMax, where con-
figurations up to 4 × 4 (4 transmitting elements and 4 receiving elements) have
been adopted. For instance, bit-rate capacities per link are often quoted in bps/
Hz where the ITU* specifies the target of 15 bps/Hz in the downlink for the LTE†
advanced system. Nevertheless, to achieve these targets, a radio environment with
rich multipath propagation is required. However, when a network assessment is
made, the benefits of MIMO are reduced. To achieve a high degree of multipath,
we need to consider multipath over a wide range of angles of arrival, but in a net-
working context we also have the option of beamforming at the transmitter in order
to reduce interference. Using a narrow beam at the transmitter greatly reduces the
interference on neighboring terminals. However, this beamforming then reduces
the multipath that is required by a MIMO link and the effectiveness of MIMO
then decreases. Ultimately, a MIMO system utilizes propagation modes (or paths),
which have a wide range of angles of departure from the transmitter and angles
of arrival at the receiver. However, these propagation modes, in a sense, cause the
* International telecommunications union.
† Long-term evolution.
Foreword ◾ ix
occupation of more space by extra signal components, which degrade the network
where a number of links are designed to operate simultaneously.
The standard MIMO technique assumes a number of antenna elements that are
relatively close together. The goal is to achieve uncorrelated signals at the different
antenna elements, where the correlation decreases with increased distance between
elements, but at the same time have all the elements as close to one another so that
the overall antenna occupies less space. This is an important issue, especially for
portable terminals and the result is that the form factor of the terminal puts a limit
on the number of elements that we may have at the terminal. Nevertheless, there is
another approach where we may place the antenna elements at significant distances
from each other, especially on the infrastructure side of the link where each element
is connected to a controller using various approaches such as optical links—often
referred to as front-haul. This approach is referred to as virtual MIMO and it is one
of the approaches currently being considered in cellular systems employing the so-
called remote RF in highly dense cell environments. In other words, a base station
feeds a number of remote RF units where the signals from/to these units are jointly
processed at the base station.
As we look into the future, there are a number of possibilities to generalize
MIMO techniques. Currently, most of the systems consider that each input and
output corresponds to an antenna radiating element as in an antenna array. The set
of elements may be replaced by a generalized radiating antenna structure that has a
number of ports to input and output signals. Such a structure may be quite differ-
ent from a set of discrete elements as in the current configurations. One could also
imagine applications and scenarios where the wireless channels and the propaga-
tion modes or paths are under the control of the system designer.
We have discussed MIMO from the standpoint of the transfer of signals from
a transmitter to a receiver, where the essence of the scheme has been the increase
in the dimensionality of the signal space available for the transmission of informa-
tion signals. There is also the important aspect of mapping or coding of general-
ized information signals to the input ports of a MIMO link, and the associated
processing of the signals at the output ports in order to extract the information at
the receiver. A vast amount of research has been performed in the areas of chan-
nel modeling, channel sounding, detection, modulation, coded modulation, and
adaptation to the three major wireless standards of today. A great deal of this work
is documented in the following chapters of this book. Looking into the future, we
can expect this research to continue, especially targeting new antenna structures
where the system permits a larger form factor (more antenna elements), and also the
targeting of various cooperative approaches including hybrids of standard MIMO
and cooperative MIMO. A key issue will be the design of schemes with improved
channel sounding techniques over the current standards, where the overhead for
channel sounding quickly grows with the rank of the MIMO scheme (number of
antennas). The network of the future may very well be a two-tier network, where
each transmission from network infrastructure to mobile hand-held terminal
