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CHAPTER 1INTRODUCTION
1.1Introduction
In communication systems, aduplex communication system is a point-to-point
system composed of two connected parties or devices that can communicate
with one another in both directions, simultaneously. An example of a duplex
device is a telephone. The people at both ends of a telephone call can speak at
the same time; the earphone can reproduce the speech of the other person as
the microphone transmits the speech of the local person, because there is a
two-way communication channel between them.
Duplex systems are employed in many communications networks, either to
allow for a communication "two-way street" between two connected parties or
to provide a "reverse path" for the monitoring and remote adjustment of
equipment in the field.
Systems that do not need the duplex capability use instead simplex
communication in which one device transmits and the others just "listen."
Examples are broadcast radio and television, garage door openers, baby
monitors, wireless microphones, radio controlled models, surveillance cameras,
and missile telemetry. There are two types of duplex communications. They
are:
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1. Half Duplex
2. Full Duplex
A half-duplex (HDX) system provides communication in both directions, but
only one direction at a time (not simultaneously). Typically, once a party begins
receiving a signal, it must wait for the transmitter to stop transmitting, before
replying (antennas are of trans-receiver type in these devices, so as to transmit
and receive the signal as well).
An example of a half-duplex system is a two-party system such as a walkie-
talkie, wherein one must use "Over" or another previously designated command
to indicate the end of transmission, and ensure that only one party transmits
at a time, because both parties transmit and receive on the same frequency.
A full-duplex (FDX), or sometimes double-duplex system, allows
communication in both directions, and, unlike half-duplex, allows this to
happen simultaneously. Land-line telephone networks are full-duplex, since
they allow both callers to speak and be heard at the same time, the transition
from four to two wires being achieved by a Hybrid coil. A good analogy for a
full-duplex system would be a two-lane road with one lane for each direction.
Two-way radios can be designed as full-duplex systems, transmitting on one
frequency and receiving on another. This is also called frequency-division
duplex. Frequency-division duplex systems can be extended to farther
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duplex mode. The latter operation requires a spatial separation between
transmit and receive antennas to reduce loop-back interference from the
transmit antennas to the receive antennas.
From signal processing point of view AF relays offer interesting challenges,
especially when the AF relay operates infull-duplex mode: Adaptive algorithms
are required for loop-back interference cancellation. Furthermore, the effect of
interference must be incorporated into analytical performance studies. Spectral
shaping of the transmitted signal requires advanced techniques for digital filter
design. The research benchmarks AF relays with DF relays taking into account
the aforementioned issues. We cooperate with High-frequency and microwave
engineering group to gain understanding of the actual propagation
environment and loop-back interference with full-duplex relays
Full-duplex infrastructure relays
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resources into orthogonalresources and results in an orthogonalization of the
transmissions and receptionsperformed by a wireless device. Consequently, all
currently deployed wireless devicesoperate in half-duplex fashion, where same
frequency simultaneous transmission andreception of signals is not possible.
The key challenge in achieving full-duplex wireless communications, where a
devicecan transmit and receive signals over-the-air at the same time and in the
samefrequency band, is the large power differential between the self-
interference createdby a devices own wireless transmissions and the received
signal of interest comingfrom a distant transmitting antenna. This large power
differential is due to the factthat the self-interference signal has to travel much
shorter distances than the signalof interest. The large self-interference spans
most of the dynamic range of the Analogto Digital Converter (ADC) in the
received signal processing path, which in turn dramaticallyincreases the
quantization noise for the signal-of-interest. Thus to achievefull-duplex it is
essential to mitigate the self-interference of thereceivedsignal is the same
channel. Hence,spectrum resources are utilized efficiently but as a downside
therelay is subject to loop interference(LI) due to signal leakagefrom the relays
transmission to its own reception. The earlierliterature often pessimistically
sees this self-interference as aninsurmountable problem, and resorts to the
half-duplex modeby allocating separate time slots or frequency bands for
relayreception and transmission. This is a simple way to avoid interferenceby
splurging spectrum.
1.3 Problem Outline
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There are so many methods proposed to mitigate the loopback self interference
of Relays in full duplex communication. The previous approach used the
concept of time domain cancellation to mitigate the self interference; the main
drawback of this Time domain Cancellation is its blindness to the spatial
domain, e.g., low rank of channel matrix is not expected to result in better
isolation. Additionally, the scheme is sensitive to both channel estimation noise
and transmit signal noise. In fact, TDC adds a new signal in the relay input
whichmay actually lead to degraded isolation compared to pure
naturalisolation with high channel estimation noise. The one and only
advantageof time-domain cancellation is that it does not distort thedesired
signal or reduce the input and output dimensions of therelay.
1.4 Objective:
This work focuses on technical problemin full-duplex relaying: How to mitigate
the loop interferenceefficiently?For investigating and comparing several
solutions, our main motivation is to improve the spectral efficiency ofrelay
systems by avoiding the need of two channel uses for one end-to-end
transmission that is inherent for half-duplex relays. Throughout the work, the
mitigation schemes are categorized into three subtypes: A) natural isolation, B)
time-domain cancellation, and C) spatial suppression. Consequently, we aim at
showing that the loop interference can be mitigated sufficiently and, thus, the
full-duplex mode becomes a feasible and viable alternative for the half-duplex
mode.
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1.5 Methodology:
In this work we set up a generic system model that explicitlyaccounts for the
loop interference, the relay processingdelay, and the imperfections of the side
informationexploited in the mitigation of loop interference. Thesespecifics are
important we summarize Natural isolation that is needed in order toavoid relay
receiver saturation, and digital MIMO time-domaincancellation, which
generalizes theschemes used in SISO repeaters. We propose and analyze
novelspatialsuppression schemes based on antenna selection, beam
selection,null-space projection, and minimummean square error (MMSE)
filters. For every scheme, we explicitly the minimize the self-interference as the
optimization target and providegeneral solutions for the optimal filters.
Examples 14show why [25][28] present only simplified or suboptimalspecial
cases for some of our general schemes and we introduce the combination of
timedomaincancellation and spatial suppression for reducingthe effect of
imperfect side information in mitigation. The mitigation schemes are compared
extensivelywith simulations on bit-error rate and isolationimprovement. The
results verify that the loop interferencecan be mitigated significantly or even
eliminatedcompletely in the ideal case, but, in practice, there willbe some weak
residual interference due to imperfect sideinformation used for mitigation.
Cellular, Wi-Fi and Bluetooth networks are arguably the four mostcommonly
used wireless networks. Out of these four networks, the first one to be
deployedwas the cellular network, which operates at distances in the order of
kilometersand uses mobile devices which transmit at powers close to 30 dBm.
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For these values oftransmit powers and distances between communicating
devices, it seemed unfeasibleto cancel the self-interference enough to enable
full-duplex wireless communications.
1.6 Thesis outline
The complete thesis of the above work is outlined in six chapters:
Chapter1 gives the basic introduction about the communication system and
the uses of relays in Duplex communication. It also gives the basic problem in
the last approach and as solution for that problem.
Chapter2 gives the complete literature survey of the project
Chapter3 gives the basic system model used in full Duplex communications
using relays; it also gives the mathematical representation of the signals
(original and interference).
Chapter4 provides the information about the previously used design
methodologies for the mitigation of self interference and also gives the Newly
proposed mitigation algorithms.
Chapter5 gives the performance evaluation of the proposed approach and also
gives the comparison results between the proposed approach and previously
proposed approaches.
Finally chapter6 gives the conclusions of the work
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CHAPTER 2
LITERATURE OUTLINE
The literature on MIMO relaying can be classified as follows based on how the
self-interference problem is treated: 1) earlier papers, e.g., [1][11], consider
half-duplex relaying in which the loop interference is inherently avoided. Some
papers, e.g., [1][6], develop half-duplex protocols for the case in which the
direct source-destination link is blocked. Our results are directly applicable for
the full-duplex counterparts of these systems and enable more spectrally-
efficient implementation once the loop interference is appropriately mitigated.
The other papers, e.g., [7][11], exploit the direct link as an extra diversity
branch. The direct link is orthogonal by design in the half-duplex mode
whereas the destination receives superposition of the direct and relayed
transmissions in the full-duplex mode. Also for these systems, the full-duplex
counterparts are feasible with proper signal separation in the destination.
2) Some information theory-oriented papers, e.g., [10][19], study various full-
duplex relaying schemes without considering the deleterious effect of the loop
interference albeit otherwise presenting many seminal contributions. In
particular, these papers tend to provide minimal (if any at all) explanations and
references for the mitigation of the loop interference. Our results will support
this body of literature by providing validation and a retroactive reference for
a central baseline assumption not verified in detail before. 3) The smallest
group of earlier papers accounts explicitly for the effect of the loop interference
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in full-duplex relaying. The early results consider exclusively single-
inputsingle-output (SISO) repeaters, see, e.g., [20][23]. For full-duplex MIMO
relays with loop interference, our literature search elicited preliminary ideas
[24], [25] and recent studies [26][31] conducted in parallel with our work
reported first in [32]. These papers tackle the problem of loop interference
mitigation in a limited scope, e.g.,restricting the system to support only one
spatial streamor providing suboptimal solutions. Moreover, the relay
processing delay is neglected in [28][30], which, asdiscussed in [32], renders
the relay practically impossibleto implement or makes the loop interference not
harmful.Reference [31] studies loop channel estimation in full-duplexMIMO
relays and, thus, supports our analysis whichstarts presuming that such side
information is alreadymade available.
Analog SISO repeaters have been employed for a long time incellular networks.
Instead, we consider modern, sophisticated,digital relays that are capable of
baseband signal processing,and, in particular, employ multiantenna
techniques. Some prototypesof full-duplex MIMO relays have already been
developed,see, e.g., [33] and [34]. After mitigating the loop interference
asshown herein, they become a viable solution to transparentlyboost the
coverage of future cellular systems.
2.2 Relay Communication
Relay communication refers to the technology that the communication
between the source and the destination is established or enhanced by one or
more than one relays. The relays can be dedicated relay stations that are built
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to support the wireless link, or other mobile users that are selected to facilitate
the data transmission from the source to the destination. Relay communication
is also termed cooperative communication, which we use in this dissertation
without distinction.
From the network aspects, traditional wireless communication systems,
e.g., cellular mobile communication networks, are centralized. There, the
transmission scenarios are point-to-point (single user), one-to-many
(broadcast) or many-to-one (multi-access), which can all be categorized as
single-hop transmission. However, in relay communication, the transmission of
information from the source to the destination consists of at least two-hops.
Thismulti-hop transmissionmodel makes the relay communication scenarios
more versatile and the research on it more difficult. Although relay
communication is still a young research topic, many important results have
been achieved, which makes it a fertile field of research. We summarize the
important relaying strategies and the state-of-the-art research results in this
section
2.2.2 Advantages and Challenges of Relay Communication
Relay communication can provide the benefits that traditional single-hop
communication cannot achieve in many practical scenarios. Relay
communication has drawn wide interests from both academia and industry
[35]. For practical systems, we summarize the advantages of relay
communication over single-hop communication as follows.
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Combating signal attenuation The adverse effects of wireless channels
include pathloss, shadowing and fading effects. The signal strength decays
exponentially with the distance between the source and the destination. When
the distance between the source and destination is too large, the signal
attenuation becomes too high due to pathloss, which makes it impossible for
the source and destination to communicate. By placing relays between the
source and the destination, the distance between the source and the relay and
the distance between the relay and destination is shortened. As a result, the
signal strength can be boosted a lot. Moreover, due to the signal strength
improvement, the source can use higher modulation symbol alphabets to
transmit more data in each channel use. In this way, relaying technology not
only increases the coverage of the system, but also improves the data rate
transmitted to the users.
Combating shadowing effects In large cities and hilly areas, tall buildings and
mountains typically block signals transmitted from the source to the
destination. Such effect is called shadowing. Relays provide another path to
circumvent the obstruction. In those scenarios, relaying is maybe the only way
to provide services in shadowing environments.
Combating fading effects The fading effects arise due to the multipath
propagations that lead to the fluctuations in received signals. Diversity is an
effective way to combat the signal fluctuation due to the fading effects. The
cooperative diversity introduced by the cooperative communication brings
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higher link reliability to the users [36,37], where multiple independently faded
signals from the source and the relay are combined at the destination.
Low costFuture cellular communication systems will move to higher frequency.
As a result, the coverage of each cell will shrink a lot compared to present
cellular communication systems. Building more base stations can be the
solution, but the cost of building those base stations will be very high. A low-
cost alternative will be building relays to extend the coverage of each cell. Thus
relay communication provides low-cost solutions for future generation wireless
communication systems.
Infrastructure-less network: In traditional cellular networks, the whole
system operation depends on the centralized control, e.g., from the base
station. However, in military services or due to the disasters like earthquakes,
infrastructure-less networks such as ad hoc networks are preferable. Such
networks do not rely on a preexisting infrastructure such as dedicated routers
or base stations. Instead, each node participates in the routing by forwarding
data for other nodes. That is each node can act as a relay, and the choice of
relay nodes are determined dynamically based on the network connectivity.
Despite all those benefits that may be available by incorporating cooperative
communication into future wireless communication systems, there are also
challenges for implementing cooperative communications. Those challenges
include:
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interference to other users. Furthermore, sending data to the destination via
relays leads to increased traffic for the whole system.
Spectral efficiency loss The major problem of current relays is that they
cannot transmit and receive data using the same time-frequency channel. This
half-duplex constraint leads to the spectral efficiency loss compare to direct
transmissions.
2.3 Relaying Strategies
There are three relaying strategies discussed by Peters et. al [38] which are
one-way relaying, two-way relaying and shared relaying as illustrated in the
following 2 [6]. As shown in the figure, the eNodeB is equipped with one
antenna per sector and one RN serving a single UE in its vicinity. On the other
hand, the relay station nodes are shared between eNodeBs of three adjacent
cells which use the same frequency.
The concept of one-way relaying is illustrated in the following Fig.2.3. The
datatransmission is divided into four frames as denoted by the number: In the
downlink, 1) the eNodeB transmits to RN, followed by 2) RN forwards the signal
to UE. Then, during uplink, 3) UE transmits to RN and finally 4) RN forwards
UEs signal to eNodeB.
As an enhancement to one-way relaying, two-way relaying is more efficient
where the data transmission is done in two phases as shown in Fig.2.4. During
the first phase, both eNodeB and UE transmit their signals to the RN and then
in second phase, after proper signal processing, the RN forwards the signals to
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both eNodeB and UE. Therefore, the transmission duration would be half of the
time taken for one-way relaying.
Shared relaying is cost-saving as number of RNs to be deployed is reduced by
allowing the RN to be shared by three cells. Also, as mentioned in [38], shared
relay has advantage over one-way relaying compared to two-way relaying. This
is due to the interference that might occur during the simultaneous
transmissions of two-way relay, combining with the fact that the shared relay
itself has to handle the multiple signals from eNodeBs of the three adjacent
cells.
a) One-way and two-way relaying
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b) Shared relaying
Fig.2.2. Relaying strategies with frequency reuse of factor 6 where each cell is
divided into 6sectors. a) Frequency reuse pattern for one-way and two-
wayrelays deployed in one cell. b)Frequency reuse pattern for shared relay
deployed in 3 adjacent cells.
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Fig.2.3. One-way relaying
Fig.2.4. Two-way relaying
2.4 Relay Transmission Schemes
Over the past decade, numerous relay transmission schemes have been
developed tobe implemented in our cellular network technology. In [38], the
transmissiontechniques include:
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real signalswith noise and interference. Thus, those undesired signals are also
amplified andretransmitted along with the original signals.
Another relaying strategy is decode-and-forward where the signals are decoded
bythe relay node, re-encoded and lastly forwarded to desired destination. In
this relayingstrategy, noise and interference are discarded from being
transmitted together with thereal signals but with the price of longer delay due
to decoding and re-encodingprocess. The relay structures can be categorized
into Layer 2 (L2) relay and Layer 3(L3) relay, depending on its function. The
transmissions involved can be both inbandand outband as well, as in L1 relay.
In the later chapters we will see the in brief about the relaying strategies.
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CHAPTER 3SYSTEM MODEL
Relaying, i.e., multihop communication, is a promisingtechnique to provide
lower transmit powers, higherthroughput and more extensive coverage in
future wirelesssystems. Likewise, single-hop multiple-input multiple-output
(MIMO) transmission has attracted wide research interest, andemerging
wireless systems utilize extensively MIMO techniquessuch as spatial division
multiplexing. Hence, if relaysare used, they need to be equipped with antenna
arrays aswell to avoid a key-hole effect, i.e., squashing multiple spatialstreams
through a rank-one device. This paper focuses on thecombination of MIMO and
relaying techniques and developsnew baseband signal processing techniques to
improve spectralefficiency.
An essential classification of relaying techniques is betweenfull-duplex and
half-duplex operation modes. In fact, the choiceof the operation mode is a
fundamental tradeoff between spectralefficiency and self-interference. A full-
duplex relay receivesand transmits at the same time on the same channel.
Hence,spectrum resources are utilized efficiently but as a downside therelay is
subject to loop interference (LI) due to signal leakagefrom the relays
transmission to its own reception. The earlierliterature often pessimistically
sees this self-interference as aninsurmountable problem, and resorts to the
half-duplex modeby allocating separate time slots or frequency bands for
relayreception and transmission. This is a simple way to avoid interferenceby
splurging spectrum.
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3.1 System model:
Let us consider the generic wireless multihop network illustratedin the upper
left corner of Fig. 1. The network comprisesnodes operating in both half-duplex
and full-duplex modes andit is not restricted to any specific multihop routing
protocol ormultiple access strategy for the simultaneous transmissions.Wethen
focus on two-hop communication through any full-duplexrelay (R) node from a
set of source (S) nodes to a set of destination(D) nodes as illustrated in the
lower right corner of Fig. 1.The full-duplex relay receives and transmits
simultaneously onthe same frequency which necessitates to model explicitly
theresulting loop interference (LI) signal.The sources and the destinations have
in total transmitand receive antennas, respectively, and the relay is
equippedwith receive and transmit antennas. Before applyingmitigation
techniques the relay is likely implemented with spatiallyseparated receive and
transmit antenna arrays which constitutes natural isolation. However, the
followingresults are also applicable in full-duplex relaying with asingle antenna
array which is optimistically considered in [26].We set in this special
case.
3.1.1. Signal Model
The signal model is built upon frequency-flat block-fadingchannels as in the
majority of related papers, see, e.g., [1][19],[25], [26], [28][30]. This implies
that the system exploits
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Fig.3.1. A wireless multihop network containing a full-duplex relay subject to
loop interference.
orthogonal frequency division multiplexing (OFDM) for broadbandtransmission
over multipath channels, and the signalmodel represents a single narrowband
subcarrier.
For time instant , let matrices , , and
represent the respectiveMIMO channels from all sources to
the relay, from the relayoutput to the relay input, and from the relay to all
destinations.
The sources transmit the combined signal vector ,and the relay
transmits signal vector while it simultaneouslyreceives signal
vector . This createsa feedback loop from the relay output to the
relay input throughchannel .
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The relaying protocol is denoted by the generic function
which generates an output sample based on the sequence ofinput samples and
causes integer processing delay . Wefocus on the mitigation of the loop
interference and, thereby,keep the proposed schemes transparent and
applicable with most of the readily available relaying protocols. Remark 1: The
processing delay is strictly positive because we consider wideband
transmission over multipath channels in contrast to [28][30]. In particular,
omitting the delay causes severe causality problems in the practical
implementation of relaying protocols: It is impossible to process a subcarrier
and retransmit the OFDM symbol before the respective OFDM symbol is first
completely received and demodulated. Furthermore, the loop signal may not be
harmful at all with zero processing delay because the relay transmission only
amplifies the same input signal. See [32] for more discussion on the
consequences of neglecting the processing delay. Finally, the respective
received signals in the relay and in thedestinations can be expressed as
where and are additive noisevectors in the relay
and in the destinations, respectively. Allsignal and noise vectors have zero
mean. Signal and noise covariancematrices are denoted by ,
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, and . For clarity, we willomit the time
indices in the rest of the work.
3.1.2. Side Information for Mitigation Techniques
We consider mitigation techniques that can be implementedtransparently, i.e.,
using only information that the relay is expectedto know by design or is able to
measure by itself. In otherwords, mitigation may exploit knowledge of only
, and . However, we assume that the available side informationis
degraded due to the following non-idealities which manifestthemselves in the
form of noise. In this paper, the noise is assumedto be completely unknown for
the mitigation schemeswhile some additional information such as the
covariance ornorm bounds of the errors could facilitate a robust approach.
1) Channel Estimation Noise:The relay may exploit anyoff-the-shelf technique
or one of the schemes developed specificallyfor full-duplex relays [23], [31] to
obtain the respectiveestimates and of and .We model the
practicallynon-ideal estimation process by defining estimation noises and
such that the estimates differ from the truechannel values:
All elements of and are assumed to be independent(both mutually
and from the corresponding channels)circularly symmetric complex Gaussian
random variables. Thevariance of the estimation noise is defined by relative
estimation error such that
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for all i,j. Analogous relation holds between and .
2) Transmit Signal Noise:The relay knows perfectly the digitalbaseband signal
it generates, but the actual transmittedsignal cannot be exactly known. This
is because any practicalimplementation of conversion between baseband and
radiofrequency is prone to various distortion effects such as carrierfrequency
offset, oscillator phase noise, AD/DA conversion imperfections,I/Q imbalance,
and power amplifier nonlinearityamong others.We model the joint effect of all
imperfections byintroducing additive transmit distortion noise such that
Furthermore, we model all elements of with independentzero-mean random
variables, and define their variance with relativedistortion . The covariance
matrix of the transmit noisebecomes
We assume that and are uncorrelated which implies that
in which
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CHAPTER 4
MITIGATION OF LOOP INTERFERENCE
In migitation of loop interference in full duplex MIMO relays we first decouple
the mitigation of loop interferencefrom the design of the relaying protocol and
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develop solutionsthat transform the relay to an
equivalentinterference-free relay. Here and
represent the input and output dimensions (or the number of spatialstreams)
reserved for the relaying protocol.
The target is to make residual loop interference so infinitesimalthat it can be
regarded simply as additional relay inputnoise. Thus, we transform the signal
model from (2) to
where and are the respective receiveand transmit signal
vectors of the equivalent interference-freerelay , and
represent therespective equivalent MIMO channels from all
sources to theinterference-free relay and from the interference-free relay to
alldestinations, and is the equivalent receiver noisevector including
all residual loop interference after mitigation.
The covariance matrix of is .
Remark 2:The equivalent interference-free relay appliesrelaying protocol
to obtain from according to (1). By decouplingthe mitigation from the
protocol, the relay may adopt,directly or after minor modifications, any of the
protocols designedfor cases without loop interference in [1][19]. However,the
system setup or the relaying protocol may still affect thechoice of and .
4.1 Reference Mitigation Schemes
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4.1.1) Natural Isolation:The relay installation should guaranteesome natural
isolation (represented by ) to facilitate theusage of signal processing
techniques which provide additionalman-made isolation. This is because, in
practice, the dynamicrange of the relay receiver circuitry is limited, and, thus,
largedifference in power levels may saturate the receiver renderingany attempt
to recover the desired signal futile.With separated receive and transmit antenna
arrays, naturalisolation arises from the sheer physical distance between the
arrays,and rational installation guarantees obstacles in betweenthe arrays to
block the line-of-sight. For this purpose, the installationmay exploit
surrounding buildings or add a shieldingplate [22]. Furthermore, antenna
elements can be directionaland pointed at opposite directions [20], [22], and
their polarizationsmay be orthogonal. If the same antenna array is used forboth
receiving and transmitting as in [26], all natural isolationcomes solely from the
duplexer connecting the input and outputfeeds to the same physical antenna
element. However, isolationoffered even by the most high-end duplexers may
not be sufficientfor communication.
Exploiting the signal model from (2), the mean square error(MSE) matrix of the
relay input signal is given by
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Fig.4.1. Time-domain loop interference cancellation in a full-duplex MIMO
relay by subtracting an estimate of the loop signal.
which yields the loop interference power as
In the following, we presume that all means of improving naturalisolation have
been first exploited and then concentrate onsignal processing techniques to
mitigate the residual interference,i.e., the effect of . Measurements
show that naturalisolation is not often sufficient alone [20], [22], [34].
Hence,our study excludes the exceptional setups in which natural isolationis
large without any additional mitigation, e.g., a relaywith the receive array
placed outdoors and the transmit arrayproviding underground coverage in a
tunnel.
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4.1.2) Time-Domain Cancellation (TDC): Cancellation is basedon the
reasonable presumption that the relay always knows itsown transmitted signal
at least approximately. If the relay canalso determine the loop channel, the
interference signal maybe replicated and removed from the received signal. In
practice,the relay may apply conventional analog precancellationto improve the
feasibility of the digital mitigation techniques forlower dynamic range. However,
the implementation of the electronicsbecomes expensive and difficult if the
respective circuitis more sophisticated than a phase shifter that removes one
(ideallythe strongest) multipath component.
The considered TDC scheme is a straightforward MIMO extensionfor earlier
SISO schemes [21][23], implemented as illustratedin Fig. 2 (similar structures
are used in [28][32]):
The relay contains a feedback loop with MIMO cancellationfilter .
Thus, (2), (5), and (7) can be related as
and
The equivalent receiver noise vector of the interference-free relay becomes
in which the residual loop interference channel is
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Fig.4.2. Spatial loop interference suppression in a full-duplex MIMO relay by
using linear receive and transmit filters.
The MSE matrix of the relay input signal becomes
The first term includes the channel estimation error and thesecond term arises
due to the transmit signal noise. Cancellationcan only minimize the known
part of the first term by choosing which results in .
Thereby, (12) yieldsthe residual interference power as
If cancellation is not used, i.e., , (12) reduces to (8).
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The main drawback of TDC is its blindness to the spatial domain,e.g., low rank
of is not expected to result in betterisolation. Additionally, the scheme is
sensitive to both channelestimation noise and transmit signal noise
as shownby (13). In fact, TDC adds a new signal in the relay input whichmay
actually lead to degraded isolation compared to pure naturalisolation with high
channel estimation noise. The advantageof time-domain cancellation is that it
does not distort thedesired signal or reduce the input and output dimensions of
therelay, i.e., and .
4.2. Novel Spatial Suppression Schemes
To exploit the extra degrees of freedom offered by the spatialdomain, we
propose that the relay applies MIMO receive filter and MIMO
transmit filter as illustrated in Fig. 3. Now (2), (5), and (7) can be
relatedas
and .
Throughout the work, we normalizefilter gains to and
with allschemes.
The equivalent receiver noise vector of the interference-free relay becomes
in which the residual loop interference channel is
Based on (14), the residual interference power is given by
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Interference can be suppressed by designing and tominimize the first
term and/or by designing only to minimizethe second term that is due to
transmit signal noise. Since(15) is a matrix equation, it needs to be first
translated into ascalar value before formulating an optimization problem: In
thispaper, the Frobenius norm is adopted for this purpose whileother metrics,
rendering different optimization targets, are alsoavailable. On the other hand,
(16) for spatial suppression is reducedto mere natural isolation given in (9)
when and .
Spatial suppression comes at the cost of a reduction in theinput or output
dimensions comparing to TDC. However, (14)reveals readily one significant
advantage over cancellation: thereceive filter can be designed to suppress
the potential loopinterference that is due to the transmit signal noise .
The implementation differs depending on the procedure:
Independent design: One filter is designed without knowledgeof the other
filter which can be replaced byI.
Separate design: One filter is designed given the other.
Joint design: The filters are designed together.
Next we consider these procedures with antenna selection, beamselection, null-
space projection, and MMSE filtering.
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4.2.1) Antenna Selection (AS):The simplified receive antennaselection scheme
studied in [25] inspires us to formulate loopinterference suppression based on
generalized antenna subsetselection. To that end, the respective receive and
transmit filtersare implemented with row and column selection matrices
(seeSection I-C) that are scaled to normalize the gains:
To reduce the gain of the residual loop interference channelgiven in (15), we
define the objective for suppression as
decreasing the known part of . By substituting (17)
The optimal joint filter design is found by calculating theFrobenius norm for all
combinations and choosingthe lowest. Although one may easily
devise suboptimal methodsof lower complexity, only global search gives the
exact optimumin the general case. However, it is feasible because the numberof
antennas is in practice reasonably small.
Let us then consider the design of to illustrate the separatefilter design (the
procedure is symmetric for designing ).Now needs to be first fixed
based on any spatial suppressionscheme and the unique solution for
issimply one of the combinations. If the transmit filter is
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not known (as in independent filter design) or not yet selected,one can
substitute , which reduces the objective to .
Example 1: The scheme of [25] is limited to the special caseof and
, i.e. , :When , is
minimized by selecting
Table 1
Algorithm for optimal joint beam selection
---------------------------------------------------------------------------------------------
Design and to select rows and columns of as follows
Step1: Select in total min { + }, max { }} rows and columns such that
all combinations pick only off-diagonal elements of. For this sub solution
=0.
Step2: To satisfy objective. Select the rest of the rows and columns such that
the final selection matrices pick only the + -max{ smallest singular
values.
-------------------------------------------------------------------------------------------------
if and otherwise. In thegeneral MIMO case of any , and
, such singlecomparison is not sufficient for the optimal filter design that
issolved in the above paragraphs for different variations.
4.2.2) Beam Selection (BS):General (eigen)beam selection isbased on the
singular value decomposition (SVD) of
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in which submatrices and contain the basis vectorsassociated with
zero singular values. The diagonal matrix comprises the singular
values, , sorted in descending order.
By choosing beam selection matrices as
the objective is transformed from (18) to
as , by definition. Filter design becomesconceptually similar
to AS, but row and column selection isbased on the effective diagonal channel
instead of .
Remark 3: Objective readily indicates that BS is superiorto AS. In (22) most row
and column combinations pickoff-diagonal elements of that are zero by
definition leadingto for many subsolutions whereas in (19) all
elementsof are practically nonzero, i.e. , for all subsolutions.In
other words, AS is optimal only when limiting thesearch space to binary
selection matrices while BS solves theoptimization target with general complex
matrices.Intuitively, the optimal joint BS could be solved by testingall
combinations as with AS. However, the diagonalizedstructure of the effective
loop channel facilitates directoffline selection based on
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and such thatonly the SVD is calculated for each channel representation:
Theoptimal joint selection is obtained with the algorithm given inTable I.
If , Step 2 is omitted andBS reduces to null-space
projection discussed in the next section.On the other hand, separate and
independent filter designsapply only Step 2 for all rows and columns.
Let us assume that in thefollowing. One
straightforward illustrative solution can be obtainedwith the optimal joint BS
algorithm as
in which , and are identity matrices of ,
and dimensions, respectively. In fact,the optimal joint BS algorithm
translates (22) to
For the general case, this shows that BS may cause residual loopinterference
even if the side information is perfect. In the nextsection, this motivates to
consider the special cases of beam selectionthat ideally eliminate all
interference.
Example 2: Compared to our general BS solution, the schemeof [28] is not only
suboptimal but also limited to the specialsymmetric case of and
: The beams areselected by in which is anzero
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matrix andI is an identity matrix. Thispicks the smallest
singular values transforming (22) to
This is larger than (24) obtained with (23) because the schemedoes not exploit
the possibility to suppress interference by kicking the off-diagonal elements of
in Step 1. The suboptimalitycan be also interpreted to be the consequence
ofindependent filter design instead of joint design.
4.2.3) Null-Space Projection (NSP): Next we develop spatialsuppression
schemes that can eliminate all loop interference inthe ideal case with perfect
side information similarly to TDC.This is desirable when the loop interference is
dominating butAS or general BS does not offer sufficient attenuation.
In null-space projection, and are selected suchthat the relay receives
and transmits in different subspaces,i.e., transmit beams are projected to the
null-space of the loopchannel combined with the receive filter and vice versa.
Thecondition can be stated for joint or separate filter design as
to eliminate the known part of the first term in (16). Similarly,for suppressing
the transmit signal noise, the condition becomes , partly eliminating
the second term in (16).
One solution for joint NSP can be obtained with the optimaljoint BS algorithm
given in Table I, if , and are low enough w.r.t. and .
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Firstly, atotal of beams are selected in Step 1 correspondingto
different singular values. Secondly, the lastterms in (24) are zero if
. Thus, input and output
beams maycorrespond to the same singular values after Step 2 and still, i.e.
, satisfying also the condition in(26). This proves that
the BS algorithm results in null-spaceprojection whenever
This condition defines also the general existence of joint NSP,if and
are additionally constrained to be of full rank.Even if is rank deficient,
is of full rank in practicedue to the estimation noise which also causes residual
loop interference.Thereby, the condition in (27) can be alternatively
evaluatedusing the anticipated value of based on prior informationor
by defining with a threshold below whichthe singular values are
rounded to zero.
Remark 4:
For the case , the total number for antennas is minimized
with NSP selecting
orwhen (full rank), or by selectingor
when
(minimum rank).
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Choosing may be preferable due to transmit noise.For separate filter
design, let us recall that the Moore-Penrosepseudo inverse is unique,
always exists, and satisfies by definition. For designing
separately given , we can, thereby, apply projection matrix
If . Separate design for is given bya similar projection
matrix which is obtained by replacing and above with and
, respectively.
Example 3:The scheme of [27] is limited to the simple specialcase of
and : When , is
guaranteed directly by . In the general MIMO case of any
and , the optimal filter design, solved in the above
paragraphs,becomes more involved.For designing one filter independently, the
above schemesmay be exploited by setting the other filter to identity.
However, simpler design is obtained by choosing
because the row space of should be in the left null space of or by
choosing because the column space of should be in
the null space of .
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Joint design solutions satisfying the NSP condition in (26)are not unique in
most cases. For example, Step 1 in the optimaljoint BS algorithm allows to
choose rows and columns in differentways. Furthermore, general BS inherits
the same propertyexcept that the subsolution picking the nonzero diagonal
valuesof is unique in Step 2. Selection between the solutions withthe same
cost can be done based on any other performance criterionas illustrated by the
next example.
Example 4: The scheme of [26] is limited to the case of
and : When the SVD of theloop channel is
,is guaranteed either by
, or by , . Although not
recognized in [26],also , can be used if .
Compared to Example 3, the extra receive antenna facilitatesadditionalselection
diversity available for reducing the effectof transmit signal noise. In our general
MIMO case of any , and , the optimal filter design becomes more
involvedand the applicability of NSP is governed by (27).
4.2.4) Minimum Mean Square Error (MMSE) Filtering:The previousspatial
suppression schemes aim at minimizing the effectof loop interference at the
cost of spatially shaping the usefulsignal which does not happen with TDC. In
order to reducethe effect of this drawback with spatial suppression, a
minimumMSE scheme is developed next to both minimize the distortionand
attenuate the loop interference.
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Now and as with TDC. Thus, the
MSE matrix of the relay input signal is given by
(29)
Inwhich For separate filter design
given , the minimum MSE receivefilter is derived from the condition
yielding
Which needs to be scaled to satisfy . Note thatMMSE filtering
requires knowledge of and signal covariancematrices as opposed to the other
mitigation schemes.
Condition to minimize MSE at the transmitside reduces to the
condition for null-space projection givenin (26). Therefore, the evident order for
joint filter design isto firstly minimize interference at the transmit side using
anyscheme, and then secondly design the receive filter using (30).
4.2.5) Combining Cancellation and Spatial Suppression:
Time-domain cancellation suffers from residual interferencethat is due to the
transmit signal noise, while spatial suppressionmay need many extra antennas
for efficient mitigation. Hence,the combination could offer high isolation with
conservativenumber of antennas in the presence of transmit signal noise.
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Combining yields the residual interference channel given by
, cf. (11) with mere cancellation and(15) with mere
suppression. Thus, filter design can be performedfor one scheme first if the
other scheme is consequently designedgiven the residual channel. The
implementation admitsfour variations for independent and separate filter
design [32],but we will now focus on joint filter design, which is possible inmost
scenarios.
The performance evaluation of the above presented work is illustrated in next
chapter
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Chapter5Results
In this chapter, the performance evaluation of the proposed method is going to
be discussed. There is also discussion about the comparison results of the
proposed approach with the previously proposed approaches.. In the
simulations, all channels aremodeled with Rayleigh fading and the transmitted
signals areassumed to be spatially white with unit power per stream. The relay
receiver noise is white andGaussian with, and imperfect side information
usedin mitigation is generated as explained in above chapter.
0 5 10 15 20 25 300
5
10
15
20
25
30
1
2
3
4
5
6
7
8
9
10
11
12
13
1415
selected path for Communication
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0 2 4 6 8 10 12 14 16 18 200
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
P?natural[db]
BER
natural isolation
TDC(.02,.02)
NSP(.02,.02)
TDC(0,.02)
NSP(0,0.02)
TDC(.02,0)
NSP(.02,0)
half duplex
0 2 4 6 8 10 12 14 160
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
antenna selection AS
F1?P(x)
3x4:0.94
2x4:1.88
3x3:2.20
1x4:3.25
2x3:3.63
2x2:5.75
1x3:6.18
1x2:10.05
1x1:22.63
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0 2 4 6 8 10 12 14 160
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x[db]
F1?P(x)
3x4:3.06
2x4:7.37
3x3:7.86
1x4:21.81
2x3:23.57
1 2 3 4 5 6 7 8 9
0
5
10
15
20
25
30
35
40
45
?H
??P1[db]
NSP,2x4
NSP,3x4
NSP,3x3
NSP,2x4
NSP,3x3
TDC,4x4
BS,3x3
BS,2x4
BS,3x3
BS,2x4
BS,3x4
BS,3x4
BS,3x4
1 2 3 4 5 6 7 8 90
5
10
15
20
25
30
35
40
45
et
??P1[db]
NSP,4x3
NSP,4x4
NSP,3x4
TDC,3x3
BS,4x4
BS,4x3
BS,4x4
BS,3x4
BS,4x3
BS,3x4
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0 2 4 6 8 10 12 14 16 18 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x[db]
F1?P(x)
BS(3):5.04
BS(2):8.15
MMSE(3):8.77
MMSE(2):14.76
TDC(1):25.20
TDC(2):25.30
TDC(3):25.34
MMSE(1):40.20
NSP(1):40.52
0 2 4 6 8 10 12 14 16 18 200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x[db]
F1?P(x)
BS(4):7.80
BS(3):11.56
TDC(1):25.25
TDC(2):25.32
TDC(3):25.35
TDC(4):25.36
NSP(2):29.67
both(4):34.49
both(3):34.49
both(2):34.49
both(1):36.81
NSP(1):40.51
0 2 4 6 8 10 12 14 16 180
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x[db]
F1?P(x)
AS,3x4(3):1.29
AS,3x4(2):1.62
AS,4x4(4):2.20
AS,4x4(3):2.57
BS,3x4(3):5.04
BS,3x4(2):8.12
BS,4x4(4):7.86
BS,4x4(3):11.87
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Chapter6CONCLUSION
Full-duplex MIMO relaying has large potential for spectrallyefficient wireless
transmission. In this work, we concentratedon solving the main associated
technical problem, i.e., the mitigationof relay self-interference. We extended the
earlier SISOcancellation schemes for the MIMO relay case and proposednew
solutions that suppress the interference in the spatial domain:antenna and
beam selection, null-space projection, andMMSE filtering. We also discussed
the issues that need to beconsidered when combining cancellation and spatial
suppression.Errors in the side information used for mitigation wereidentified as
the practical limitation to prevent complete interferenceelimination obtainable
in the ideal case. However, oursimulations illustrated that the proposed
schemes offer significantmitigation such that the residual interference may be
regardedas mere additional noise.
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