Wireless Interference Networks
HAMED FARHADI
Doctoral Thesis in Telecommunications Stockholm, Sweden 2014
TRITA-EE 2014:064 ISSN 1653-5146
ISBN 978-91-7595-391-5
Department of Communication Theory SE-100 44 Stockholm SWEDEN Akademisk avhandling som med tillst˚and av Kungl Tekniska h¨ogskolan framl¨agges till offentlig granskning f¨or avl¨aggande av teknologie doktorsexamen i telekom- munikation fredagen den 19 December 2014 klockan 13.15 i h¨orsal F3, Lindsted- tsv¨agen 26, Stockholm, Sweden.
© 2014 Hamed Farhadi, unless otherwise noted.
Tryck: Universitetsservice US AB
Wireless interference networks refer to communication systems in which multiple source–destination pairs share the same transmission medium, and each source’s transmission interferes with the reception at non-intended destinations. Optimizing the transmission of each source–destination pair is interrelated with that of the other pairs, and characterizing the performance limits of these networks is a challenging task. Solving the problem of managing the interference and data communications for these networks would potentially make it possible to apply solutions to several existing and emerging communication systems.
Wireless devices can carefully coordinate the use of scarce radio resources in order to deal effectively with interference and establish successful communications.
In order to enable coordinated transmission, terminals must usually have a cer- tain level of knowledge about the propagation environment; that is, channel state information (CSI). In practice, however, no CSI is a priori available at terminals (transmitters and receivers), and proper channel training mechanisms (such as pilot- based channel training and channel state feedback) should be employed to acquire CSI. This requires each terminal to share available radio resources between chan- nel training and data transmissions. Allocating more resources for channel train- ing leads to an accurate CSI estimation, and consequently, a precise coordination.
However, it leaves fewer resources for data transmissions. This creates the need to investigate optimum resource allocation. This thesis investigates an information- theoretic approach towards the performance analysis of interference networks, and employs signal processing techniques to design transmission schemes for achieving these limits in the following scenarios.
First, the smallest interference network with two single-input single-output (SISO) source–destination pairs is considered. A fixed-rate transmission is desired between each source–destination pair. Transmission schemes based on point-to- point codes are developed. The transmissions may not always attain successful communication, which means that outage events may be declared. The outage prob- ability is quantified and the ǫ-outage achievable rate region is characterized. Next, a multi-user SISO interference network is studied. A pilot-assisted ergodic interfer- ence alignment (PAEIA) scheme is proposed to conduct channel training, channel state feedback, and data communications. The performance limits are evaluated, and optimum radio resource allocation problems are investigated. The analysis is ex- tended to multi-cell wireless interference networks. A low-complexity pilot-assisted opportunistic user scheduling (PAOUS) scheme is proposed. The proposed scheme includes channel training, one-bit feedback transmission, user scheduling and data transmissions. The achievable rate region is computed, and the optimum number of cells that should be active simultaneously is determined. A multi-user MIMO interference network is also studied. Here, each source sends multiple data streams;
specifically, the same number as the degrees of freedom of the network. Distributed transceiver design and power control algorithms are proposed that only require local CSI at terminals.
Tr ˙adl¨osa interferensn¨atverk ¨ar kommunikationssystem d¨ar flera par av k¨allor och destinationer delar p ˙a samma ¨overf¨oringsmedium och varje k¨allas s¨andning st¨or mottagningen vid icke-avsedda destinationer. Optimering av data¨overf¨oringen f¨or varje par av k¨allor och destinationer samverkar med optimeringen f¨or de andra paren, och att karakterisera prestandagr¨anserna f¨or dessa n¨atverk ¨ar d¨arf¨or en ut- manande uppgift. Om problemet med hantering av st¨orningar och datakommu- nikation f¨or dessa n¨atverk l¨oses, kan dessa l¨osningar potentiellt till¨ampas p ˙a flera befintliga och kommande kommunikationssystem.
Tr ˙adl¨osa apparater kan noggrant samordna anv¨andningen av begr¨ansade ra- dioresurser f¨or att effektivt hantera st¨orningar och skapa tillf¨orlitlig kommunikation.
F¨or att m¨ojligg¨ora samordnad ¨overf¨oring m ˙aste terminalerna oftast ha en viss niv ˙a av kunskap om utbredningsmilj¨on, dvs. kanaltillst ˙andsinformation (CSI). I prak- tiken finns dock a priori ingen CSI p ˙a terminalerna och l¨ampliga kanaltr¨aningsmeka- nismer (t.ex. pilotbaserad kanaltr¨aning och kanaltillst˙ands ˙aterkoppling) b¨or anv¨and- as f¨or att f¨orv¨arva CSI. Detta inneb¨ar att varje terminal m ˙aste dela tillg¨angliga radioresurser mellan kanaltr¨aning och data¨overf¨oring. Ju fler resurser som tillde- lats f¨or kanaltr¨aningen, desto noggrannare blir CSI-uppskattningen och d¨armed blir samordningen b¨attre. Dock ¨ar f¨arre resurser kvar f¨or data¨overf¨oring. Effektiva metoder f¨or att genomf¨ora resursf¨ordelningen m ˙aste d¨arf¨or unders¨okas. En informa- tionsteoretisk strategi f¨or prestandaanalys av interferenssn¨atverk utreds och signal- behandlingstekniker anv¨ands f¨or att utforma ¨overf¨oringssystem som uppn ˙ar dessa gr¨anser. Denna avhandling behandlar samordnad ¨overf¨oring i f¨oljande scenarier.
F¨orst unders¨oks det minsta interferensn¨atverket, best ˙aende av tv ˙a single-input single-output-par (SISO-par) med k¨allor och destinationer. En ¨overf¨oringsmetod med fast datatakt ¨onskas mellan varje par av k¨allor och destinationer, givet ett bivil- lkor p ˙a anv¨and effekt. ¨overf¨oringssystem baserade p ˙a punkt-till-punkt Gaussiska koder utvecklas d¨arf¨or. ¨overf¨oringarna uppn ˙ar inte alltid tillf¨orlitlig kommunika- tion, och avbrott kan d¨arf¨or f¨orekomma. Avbrottssannolikheten kvantifieras och ǫ- avbrottsdatataktsregionen karakt¨ariseras. D¨arefter studeras ett fleranv¨andarinterfe- rensn¨atverk med SISO-noder. Ett pilotassisterat system med ergodisk interferen- suppr¨atning (PAEIA) f¨oresl ˙as f¨or att genomf¨ora kanaltr¨aning, kanaltillst ˙ands ˙aterko- ppling och datakommunikation. Prestandagr¨anser utv¨arderas, och problemet med optimal radioresursallokering studeras. Ett fleranv¨andarinterferensn¨atverk med mul- tiple-input multiple-output-noder (MIMO-noder) studeras ocks ˙a. H¨ar s¨ander varje k¨alla lika m ˙anga datastr¨ommar som till ˙ats av frihetsgraderna av n¨atverket. Dis- tribuerad design av mottagare och s¨andare samt effektstyrningsalgoritmer som en- bart kr¨aver lokal CSI vid terminalerna f¨oresl ˙as. Analysen utvidgas ocks ˙a till ett fler- anv¨andarinterferensn¨atverk med flera celler. Ett pilotassisterat l ˙agkomplexitetssyst- em f¨or opportunistisk anv¨andarschemal¨aggning f¨oresl ˙as. Det f¨oreslagna systemet omfattar kanaltr¨aning, en-bits ˙aterkoppling, anv¨andarschemal¨aggning samt data¨ove- rf¨oring. Den uppn ˙abara datataktsregionen ber¨aknas och det optimala antalet celler som skall vara aktiva samtidigt best¨ams.
It is a pleasant task to express my thanks to all those who contributed in many ways to the success of my PhD study and made it an unforgettable experience for me. Foremost, I owe my deepest gratitude to my advisor Prof. Mikael Skoglund.
I am grateful to Mikael for welcoming me to the Department of Communication Theory, and for giving me the freedom to pursue my research interests. His openness to ideas, insightful suggestions, and supports enriched my PhD research. I also wish to thank my co-advisor Prof. Chao Wang for his valuable helps and supports through different stages of my research and for being a good friend of me all these years. It was a great pleasure for me to work with Mikael and Chao.
I would like to thank Prof. Vahid Tarokh at Harvard University for giving me the opportunity to visit his research group. It has been an honor to work with him.
I really appreciate his kind hospitality during my stay at Cambridge. This research visit has broadened my view on research, tremendously. I wish to thank Dr. Jinfeng Du at MIT for all his valuable helps and cares during the period of my stay at Cambridge. I am also thankful to Dr. Mohsen Farmahini and Alireza Mehrtash for all their kind helps during this visit. I am also grateful to all friends at SEAS who made my time enjoyable and rewarding. Karin Demin and Kathleen Masse helped me a lot in the administrative issues of this visit.
I wish to acknowledge the John and Karin Engblom foundation, Knut and Alice Wallenbergs foundation, Ericsson Research foundation, Qualcomm, and the Euro- pean School of Antennas for the financial support of the trips for the research visit and the conferences that I participated. Swedish Foundation for Strategic Research is acknowledged for the financial support of my PhD study.
I would like to take the opportunity to thank Prof. David Gesbert for acting as the opponent for this thesis. I also thank Prof. Erik Larsson, Prof. Tommy Svensson, and Prof. Jeong Woo Cho for acting on the grading committee, and Prof. Joakim Jaldén for doing the quality review of the thesis.
My sincere thanks also goes to my colleagues whom I had valuable discussions and collaborations. In particular, I am grateful to Prof. Lars Rasmussen for shar- ing his valuable international academic career experiences and being a source of inspiration for good academic practice. I also wish to thank Prof. Carlo Fischione for collaborations on the problems of mutual interest. I would like to thank Dr.
Per Zetterberg for providing a fantastic wireless test-bed network for the real-time evaluation of algorithms proposed in this thesis and for his valuable insights on the practical considerations of wireless system design. Also, I am thankful to Nima Na- jari Moghadam for test-bed implementation and real-time measurements of some algorithms proposed in this thesis. It was a pleasure to work with Nima and Per.
I gratefully acknowledge the discussions with my colleagues from KTH, Link¨oping University, and Ericsson Research within the RAMCOORAN project cooperation.
Prof. Michail Matthaiou and Prof. Mats Bengtsson are acknowledged for valuable comments on my research. I wish to thank Dr. Majid Nasiri Khormuji for being al-
ways available for fruitful discussions and research collaborations; Peter Larsson for sharing his valuable industrial research experiences; Dr. Mohammadreza Gholami for sharing his experiences; and Dr. Themistoklis Charalambous for discussions on the problems of common interest. Dr. Nafiseh Shariati is acknowledged for being always available for great conversations on various topics. I acknowledge the great discussions with Prof. Tobias Oechtering, Frédéric Gilbert Gabry, and Efthymios Stathakis regards our collaborative efforts on the implementation of interactive teaching. I am also very thankful to Dr. Ali Zaidi, Hadi Ghauch, and Dr. Nicolas Schrammar for our scientific collaborations. I wish to thank Nan Li, Hadi Ghauch, Farshad Naghibi, and especially Chao and Mikael for helping me proofread the thesis and for their valuable suggestions and feedbacks. I am thankful to Rasmus Brandt for his kind helps in editing the Swedish parts of this thesis. I also thank the computer support group for providing reliable resources, and Raine Tiivel and Dora S¨oderberg for all their kind helps in administrative issues. I wish to thank all my past and present colleagues at the Department of Communication Theory and the Department of Signal Processing for making a friendly working environment.
Especial thanks go to my officemate Iqbal Hussain. It was so nice to share the office with Iqbal all these years. I enjoyed after work Thai dinner events with Kittipong and Hieu!
I would like to take this opportunity to acknowledge all individuals who have inspired or have encouraged me to do research. In particular, I am thankful to my teachers at KTH, University of Tehran, and Iran University of Science and Technology from whom I’ve learned a lot during years of study.
My friends Maksym Girnyk, Karina, Farshad Naghibi, Serveh Shalmashi, Eu- hana Ghadimi, Somayeh Salimi, Elaheh Jafari, Nafiseh Shariati, Amirpasha Shi- razinia, ¨Alla, Arash Owrang, Ehsan Olfat, Majid Gerami, and Ghazaleh Panahan- deh in various ways made living in the beautiful city of Stockholm an enjoyable and memorable experience for me.
I offer my warmest thanks to my parents for all their endless love and supports.
My father was my most inspiring teacher and his caring relationships with students deeply influenced my view on teaching and education. I wish to thank my brothers for all their encouragements. Last but not least, I would like to thank my beloved wife Maryam for all the happiness she brought to my life and all her patience during my work on this thesis. If it was not her patience, I wouldn’t be able to work on this thesis.
Hamed Farhadi Stockholm, November 2014
Contents ix
List of Figures xiii
List of Notations xv
List of Acronyms xvii
1 Introduction 1
1.1 Wireless Network Operations Overview . . . 5
1.2 Thesis Scope and Contributions . . . 6
2 Background 21 2.1 Wireless Interference Networks . . . 21
2.2 Two-user Interference Networks . . . 22
2.3 K-user (K > 2) Interference Networks . . . . 23
2.3.1 Achievable Degrees of Freedom Region . . . 25
2.3.2 Interference Alignment for MIMO Interference Networks . 26 2.3.3 Interference Alignment for SISO Interference Networks . . 28
2.3.4 Ergodic Interference Alignment . . . 31
2.4 Wireless Interference Networks with Imperfect CSI . . . 32
3 Two-user Interference Networks: Point-to-Point Codes 35 3.1 Two-user SISO Interference Network . . . 36
3.2 Orthogonal Transmission Scheme . . . 38
3.3 Non-Orthogonal Transmission Schemes . . . 40
3.3.1 Direct Decoding at Both Receivers . . . 40
3.3.2 Successive Interference Cancellation at Both Receivers . . 45
3.3.3 Successive Interference Cancellation at One Receiver . . . 51
3.4 Summary . . . 56
3.A The Proof of Proposition 3.2.1 . . . . 57
3.B The proof of Proposition 3.3.1 . . . . 58
3.C The proof of Corollary 3.3.1 . . . . 60 ix
3.D The Proof of Proposition 3.3.2 . . . . 61
3.E The Proof of Proposition 3.3.3 . . . . 62
4 K-user SISO Interference Networks: Pilot-assisted Interfer- ence Alignment 65 4.1 Multi-user SISO Interference Network . . . 66
4.2 Pilot-assisted Ergodic Interference Alignment . . . 67
4.2.1 Pilot Transmission Phase . . . 67
4.2.2 Feedback Transmission Phase . . . 67
4.2.3 Data Transmission Phase . . . 69
4.3 Analog Feedback . . . 70
4.3.1 Achievable Rate Region . . . 70
4.3.2 The Optimum Power Allocation . . . 72
4.3.3 Achievable Degrees of Freedom Region . . . 73
4.3.4 Numerical Evaluation . . . 74
4.4 Digital Feedback . . . 76
4.4.1 Power Control Problem . . . 78
4.4.2 Throughput Maximization Problem . . . 86
4.5 Summary . . . 96
4.A The Proof of Proposition 4.3.2 . . . . 98
4.B The Proof of Theorem 4.4.3 . . . . 98
4.C The Proof of Theorem 4.4.4 . . . . 100
5 K-user MIMO Interference Networks: Transceiver Design and Power Control 101 5.1 Multi-user MIMO Interference Network . . . 102
5.1.1 Transmitter Structure . . . 102
5.1.2 Receiver Structure . . . 103
5.2 Transceiver Design and Power Control . . . 103
5.2.1 CSI Acquisition, Transceiver Design, and Power Control . 104 5.2.2 Distributed Power Control . . . 107
5.3 Performance Evaluation . . . 118
5.4 Test-bed Implementation . . . 123
5.5 Summary . . . 124
5.A The Proof of Theorem 5.2.1 . . . . 126
5.B The Proof of Theorem 5.2.2 . . . . 126
6 Multi-cell Interference Networks: Pilot-assisted Opportunis- tic User Scheduling 129 6.1 Multi-cell Interference Network . . . 131
6.2 Pilot-assisted Opportunistic User Scheduling Scheme . . . 131
6.2.1 Pilot Transmission Phase . . . 131
6.2.2 Feedback Transmission and User Selection Phase . . . 132
6.2.3 Data Transmission Phase . . . 133
6.3 Achievable Rate Region . . . 134
6.3.1 Achievable Total Degrees of Freedom . . . 135
6.3.2 Numerical Evaluation . . . 136
6.4 Summary . . . 137
6.A The Proof of Theorem 6.3.1 . . . . 139
7 Conclusion 141 7.1 Concluding Remarks . . . 141
7.2 Future Work . . . 143
Bibliography 147
1.1 Operations in a wireless communication network. . . 5
2.1 K-user wireless interference network . . . . 22
2.2 Interference management schemes . . . 24
2.3 Interference alignment in a three-user MIMO interference network . 28 3.1 Two-user interference network. . . 36
3.2 Solution of the power control problem for the NOT1 scheme. . . 42
3.3 The outage probability of the NOT1scheme . . . 43
3.4 The ǫ-outage achievable rate region of the NOT1 scheme . . . 45
3.5 Solution of the power control problem for the NOT2 scheme . . . 48
3.6 The outage probability of the NOT2scheme . . . 50
3.7 The ǫ-outage achievable rate region of the NOT2 scheme . . . 52
3.8 Solution of the power control problem for the NOT3 scheme. . . 54
3.9 The outage probability of the NOT3scheme in a symmetric network 55 3.10 The outage probability of the NOT3scheme in a asymmetric network 56 3.11 The ǫ-outage achievable rate region of the NOT3 scheme . . . 57
4.1 Transmitted symbols’ format in a K-user interference network. . . . 66
4.2 The optimum power allocation factor. . . 75
4.3 The achievable rate of the PAEIA and TDMA schemes. . . 76
4.4 The achievable sum-rate versus the number of users. . . 77
4.5 Feasibility probability versus transmission rate of each user . . . 82
4.6 Average transmission power versus transmission rate of each user . . 85
4.7 Feedback bits trade-off in a three-user interference network . . . 86
4.8 Throughput versus power . . . 92
4.9 Feedback bits allocation trade-off . . . 93
4.10 Throughput of a K-user interference network. . . . 94
4.11 Delay-limited throughput of a three-user network . . . 95
4.12 Delay-limited throughput of a K-user interference network . . . 97
5.1 The structure of a transmitter and receiver pair . . . 102 xiii
5.2 CSI acquisition, transceiver design, and power control procedure . . 104
5.3 Feasibility probability versus transmission rate. . . 110
5.4 Feasibility probability in a network with maximum power constraint. 112 5.5 The mutual information of the source-destination pairs versus iterations 119 5.6 Transmission power of a source versus number of iterations . . . 120
5.7 The mutual information of the source-destination pairs versus iterations 121 5.8 The computed transmission power versus the number of iterations . 122 5.9 The mutual information of the different streams versus iterations . . 123
5.10 Transmission powers versus the number of iterations . . . 124
5.11 Computed power versus the number of iterations . . . 125
6.1 Schematic representation of different phases of the PAOUS scheme . 130 6.2 Transmitted symbols within one fading block. . . 133
6.3 The achievable sum-rate versus power. . . 136
6.4 The achievable sum-rate versus the decision threshold. . . 137
6.5 The achievable sum-rate versus the power allocation factor. . . 138
|x| Absolute value of x
CN (m, σ2) Complex Gaussian distribution with mean m and variance σ2 f′(x) Derivative of function f (x)
∅ Empty set
νi[X] Eigenvector corresponding to the ith lowest eigenvalue of matrix X
Element-wise vector inequality
≻ Element-wise strict vector inequality E[X] Expectation of random variable X
λmax(X) The largest absolute eigenvalue of matrix X.
N (m, σ2) Gaussian distribution with mean m and variance σ2 X−1 Inverse of matrix X
ℑ[x] Imaginary part of x
span(X) Linear span of columns of matrix X Nf Number of feedback bits
fX Probability density function of random variable X Q(x) Q-function
∆ Quantization step-size rank(X) Rank of matrix X ℜ[x] Real part of x
ρ(X) Spectral radius of matrix X Tr[X] Trace of matrix X
XT Transpose of matrix X
X∗ Transpose conjugate of matrix X
xv
AWGN Additive white Gaussian noise CoMP Coordinated multi point CSI Channel state information
CSIR Channel state information at receiver CSIT Channel state information at transmitter DoF Degrees of freedom
DSM Discrete superposition model EIA Ergodic interference alignment
EIA-PC Ergodic interference alignment with power control EIA-RA Ergodic interference alignment with rate adaptation FDD Frequency-division duplex
FDMA Frequency-division-multiple-access
KKT Karush-Kuhn-Tucker
LICQ Linear independent constraint qualification M2M Machine-to-machine communications MMSE Minimum mean square error
MIMO Multiple-input multiple-output OT Orthogonal transmission
PAEIA Pilot-assisted ergodic interference alignment
PAEIA-US Pilot-assisted ergodic interference alignment with user selection PAOUS Pilot-assisted opportunistic user scheduling
pdf Probability density function QoS Quality of service
RHS Right hand side
SNR Signal-to-noise ratio
SIC Successive interference cancelation SINR Signal-to-interference-plus-noise ratio SISO Single-input single-output
TDD Time-division duplex
TDMA Time-division-multiple-access USRP Universal software radio peripheral WBAN Wireless body area networks
xvii
Introduction
A
NETWORKED SOCIETY in which everyone and everything, everywhere, have the potential to benefit from connectivity, will shape the future of hu- man life [Sac03]. Wireless communication systems are expected to play an important role in the development of the networked society. Fore example, wire- less networks will provide ubiquitous access to information, while wireless health monitoring systems will decentralize medical treatments. Vehicular communication networks will help make future transportation systems more efficient and safe, and networked control systems will take advantage of global information fusion in order to make intelligent decisions.The trend towards massive usage of wireless technology has led to an explo- sion in the number of connected devices, and tremendous growth in wireless traffic volume [Eri12]. However, the scarcity of radio resources and the inherent char- acteristics of the wireless transmission medium make handling communication in these conditions a formidable task. The radio spectrum is scarce and is consid- ered to be among the most expensive natural resources [Her85, ZKAQ01]. In ad- dition, the energy budget of mobile terminals is restricted and there are serious concerns regarding the vast energy consumption of wireless communication sys- tems [CHA+11, DCG+13]. Consequently, spectral and energy efficient design is es- sential for emerging wireless technologies. Wireless transmission is generally subject to two phenomena: fading and interference [PL]. The former is a consequence of reflectors scattered in the environment surrounding a transmitter and a receiver, such that the receiver observes a superposition of multiple copies of the transmitted signal. The superposition of the signals can be either constructive or destructive depending on the phase shift and the attenuation of received signals from differ- ent paths. The randomness of fading may degrade communication quality. Several effective techniques have been devised in recent decades to overcome the adverse effects of random fading. For instance, multiple-antenna transmission techniques have been proposed to realize spatial diversity and to improve the performance of wireless systems [TJC99, JSO02, GSDs+03, LS03].
Another, even more challenging, obstacle in the operation of wireless networks
1
is interference. Because of the broadcast nature of wireless transmission medium, a user can interfere with the communication of any other user. This occurs in some existing and emerging wireless communication scenarios, including inter-cell interference in cellular networks; ad-hoc networks; interference between neighbor- ing access points in wireless local area networks; inter-user interference between neighboring devices in machine-to-machine (M2M) communication scenarios; inter- ference between implanted medical sensors in wireless body area networks (WBAN);
and interference between licensed and unlicensed users in cognitive radio networks.
These communication systems, usually composed of multiple information sources and destinations, can be modelled as an important class of wireless networks: inter- ference networks. In an interference network, each source intends to communicate with its dedicated destination and all sources share the same transmission medium.
Inter-user interference makes communication of different users interrelated, and if not properly managed, it can severely degrade communication quality. For in- stance, in a two-user interference network in which two sources intend to com- municate with their respective destinations simultaneously in the same frequency band [Ahl74], the transmission power of each source affects the signal detection, not only at its desired destination, but also at the other destination. Therefore, op- timizing the performance of each source-destination pair becomes interrelated with that of the other pair, and it becomes challenging to characterize the performance limits [AC78,HK81,ETW08,JLD08,LJ08,MK09]. The situation becomes even more complicated, when the number of users exceeds two.
Wireless devices must carefully coordinate the use of the radio resources in order to effectively manage interference and enable successful communication [GKGI07].
The term coordination has been widely used in various disciplines, including com- puter science, sociology, management science, systems theory, and economics [MC90].
The broad definition of coordination according to the American Heritage Dictio- nary [Dic81] is
“the act of working together harmoniously.”
In the context of wireless interference networks, this implies that the terminals work together in order to design their transmit signals in such a way that the interference can be managed properly. Although, they may have conflicts of interest in using the available radio resources, they intend to cooperate with each other in order to achieve a reasonably good performance.
Conventional interference management strategies (such as time division multiple access (TDMA) or frequency division multiple access (FDMA)) tend to divide the available radio resources and orthogonalize the transmissions of different source–
destination pairs. This requirement causes the subspaces of different interference signals to be orthogonal to those of the desired signal at each destination, and also orthogonal to each other. Interference is avoided at the cost of low spectral efficiency.
However, it has been shown recently that transmitters can shape their transmit- ted signals in an appropriate domain, such as space (by using multiple antennas),
time (by coding across time-varying channels), or frequency (by coding across dif- ferent carriers in frequency-selective channels) [MAMK08, CJ08, MGMAK14], or they may perform opportunistic scheduling in dense networks [JwJS09, YSJP13], in order to manage interference and conduct communication more efficiently. For instance, the interference alignment concept [MAMK08, CJ08] reveals that, with proper coordinated transmission signaling design, different interference signals can be aligned together, such that more radio resources can be assigned to the de- sired transmission. Consider a multi-user interference network with more than two source–destination pairs. At each destination, the interference signals can be aligned so that so that up to half of the signal space can be left to its desired signal [CJ08].
This means that each user may achieve half of the interference-free transmission rate, regardless of how many interferers exist. Moreover, in dense communication networks in which a massive number of users should be served, an opportunistic scheduling scheme can be deployed to schedule only those users that experience less interference. This scheme can take advantage of the crowd of users to manage the interference [JwJS09, YSJP13].
However, the realization of such coordinated transmission schemes can be con- siderably more challenging than in the case of the conventional orthogonal transmis- sion strategies. For instance, global channel state information (CSI) must usually be perfectly available at all sources and destinations to conduct the coordinated ac- tions (for example, beamforming, scheduling, and resources allocation). Acquiring such perfect global CSI is clearly a difficult problem in time-varying environments.
In practice, no CSI is a priori available at terminals and proper channel learning schemes thus must be applied. The destinations can obtain an estimation of the CSI through a pilot-based channel training scheme in which each source allocates a portion of the total transmission time and energy for transmitting pilot symbols, and the rest for data transmission. The quality of estimated CSI determines how accurately the coordinated transmission scheme can be conducted and therefore af- fects the performance of each decoder. In general, each transmitter shares its radio resources between pilot transmission and data transmission. More accurate channel estimation can be obtained by allocating more resources for pilots. This implies that fewer resources are left for data transmission. In such scenarios, the achievable performance of the network needs to be analyzed carefully and the optimum radio resource allocation is an important problem to be investigated.
One possible way for other terminals to obtain the CSI is to require the des- tination to share its estimated channel knowledge with others via channel state feedback signals. [NJGV09, BT09, KV10, AH12] showed that as long as the capacity of the feedback channel is sufficiently large – such that the CSI regarding the whole network obtained by each terminal is accurate enough – interference alignment can be realized as if perfect global CSI is available. Clearly, this requirement is not usu- ally practical. In most existing systems, the capacity of feedback channels would be strictly limited. Each terminal can attain only erroneous global CSI (for example, the quantized global CSI if digital feedback is used [BT09, KV10, KG13], or noisy global CSI if analog feedback is deployed [AH12]) or the CSI regarding only a part
of the network (local CSI, for example [GCJ08]). Therefore, it may not be possi- ble to perform interference alignment perfectly. Ideally, the interference signals at each destination should be aligned together in the same subspace, which is distin- guishable from the subspace for its desired signals, so that they can be completely canceled. However, the limited CSI at each terminal means that it may no longer be straightforward to perfectly separate these two subspaces. In other words, some non-negligible interference would leak into the desired signal subspace and it would not be possible to eliminate it. The communication performance is certainly affected by such interference leakage. Similar to the above-mentioned case of two-user in- terference networks, the transmission power of each source influences the signal detection at all destinations. Optimizing the performance of all source–destination pairs is interrelated and is a challenging problem.
The objective of this thesis is to investigate the performance limits of wireless interference networks and to design efficient coordinated transmission schemes to achieve these limits. These schemes include employing channel training and chan- nel feedback to acquire CSI, and using the estimation of CSI to coordinate data transmission. We also address the optimum radio resource allocation for channel training and data communication, and study the existing tradeoff on this matter.
In our designs, we mainly consider two types of networks in terms of the qual- ity of service (QoS) requirements. For the first type, each source must commu- nicate with its destination at a fixed transmit data rate. A power control prob- lem [Zan92, JBS04, FM93a, Yat95, RFLT98, SB04, CHLT08, TCS11, Ngu09]) is stud- ied in order to properly assign transmission power (normally the minimum) to each source in order to guarantee the transmission’s success. For the second type, each source’s transmission power is fixed. We investigated a throughput maximization problem that performs rate adaptation in order to maximize network throughput.
Since interference management and power control (or rate adaptation) are gener- ally highly intertwined in the context of wireless interference networks, our aim is to efficiently address joint design of transmission strategy and power control (or rate adaption). Below, we first provide an overview of the operation of wireless communication systems, and then discuss in more detail how the abovementioned objectives are investigated in the thesis.
Channel training CH4 CH5 CH6
Channel feedback CH3 CH4 CH6
Beamforming and Filtering CH5 Power Control
CH4 CH5
Rate Adaptation CH4
Scheduling CH6
Data transmission CH3 CH4 CH5 CH6
Figure 1.1: Operations in a wireless communication network.
1.1 Wireless Network Operations Overview
In wireless communication systems, propagation environment is continuously chang- ing and channels are time-varying. As mentioned in the previous section, coor- dinated communication techniques (such as interference alignment, coordinated multi-point (CoMP) transmission, and opportunistic scheduling) usually require certain CSI to be known at terminals in order to adapt their transmission and conduct communication [LHL+08, MLES13]. Therefore, a mechanism is required to acquire CSI at terminals and adapt transmission strategy, accordingly. An il- lustrative representation of this mechanism is shown in Fig. 1.1. In order to esti- mate the local CSI at each terminal, a channel training scheme can be applied (see e.g. [HH03,CJKR10,KJC11,ALH12,KRB+13,FKS14,Sha14]). One possible way for the other terminals to acquire such estimated CSI is to share this channel knowl- edge to the other terminals via channel state feedback schemes (see e.g. [LHL+08, BT09,FWS11,ALH12]). The terminals can then use this estimated CSI to adapt the appropriate transmission strategy. For instance, in multiple-antenna systems, termi- nals can compute their beamforming and filtering [LHL+08], while in single-antenna systems they may perform opportunistic transmission (e.g. using the ergodic inter- ference alignment scheme [NGJV12], or user scheduling) in order to manage the in- terference. Moreover, depending on the system requirements, the transmitters may apply power control (see e.g. [SB06,CHLT08,FWS14b]) or rate adaptation [FWS11]
in order to minimize transmission power or maximize throughput, respectively. In large wireless interference networks with many users, a user scheduling can be ap- plied to opportunistically serve a subset of the users that experience the acceptable channel condition [LTYF03, SN07a, SN07b, SBM09, JwJS09, FGS14]. The decisions can be made based on available CSI and the terminals then conduct data transmis- sion. In this thesis, these items are investigated for wireless interference networks.
Table 1.1: Thesis outline.
Network size Antennas CSI CSIR CSIT
Chapter 3 2× 2 SISO global perfect perfect
Chapter 4 K× K SISO global noisy quantized
Chapter 5 K× K MIMO local perfect perfect
Chapter 6 K× KN SISO local noisy quantized
1.2 Thesis Scope and Contributions
This thesis investigates coordinated transmission schemes for wireless interference networks and their performance limits. The thesis is presented in six chapters. A summary of the system considered in each chapter and the underlying assump- tions is shown in Table 1.1. Below, we briefly present the contents along with the contributions in each chapter.
Chapter 2
This chapter is a review of results, concepts, and definitions that are required for the presentation of the materials in the following chapters. The presentation starts from the definition of wireless interference networks in this thesis. We then briefly review the main research results on seeking the capacity region (i.e., the largest rate region in which reliable communication is possible) of the two-user interference networks.
For networks with more than two users, we introduce the concept of interference alignment and some techniques to realize it. The contents of this chapter are in part based on
• [Far12] H. Farhadi, “Interference alignment and power control for wireless interference networks,” Licentiate Thesis, KTH Royal Institute of Technology, Stockholm, Sweden, Sep. 2012.
• [MFZ+14] N. N. Moghadam, H. Farhadi, P. Zetterberg, M. Khormuji and M. Skoglund, “Interference alignment: Practical challenges and test-bed im- plementation,” book chapter in Contemporary Issues in Wireless Communi- cations, INTECH Open Access Publisher, Nov. 2014.
Chapter 3
In this chapter, we study a two-user single-input single-output (SISO) interference network in which each source communicates at a given fixed rate to the intended destination.
Background
The optimal solution to the throughput maximization problem and the power control problem for two-user interference networks in general case is unknown.
Indeed, these have been the subject of extensive research. For instance, refer- ences [Tun08, WT11, RV11, AB12, EK12] have studied the throughput maximiza- tion problem for a two-user fading interference network, in which they deployed the Han-Kobayashi coding scheme [HK81]. However, the recent development of capac- ity achieving codes for point-to-point communications has made it attractive to use such codes for network communications (even though they might be sub-optimal in these scenarios). Applying point-to-point code between each transmitter–receiver pair is important from a practical viewpoint as the design and operations of these codes are relatively less complexity that those designed for multi-user scenarios.
For fading interference networks, the throughput maximization problem – subject to using Gaussian point-to-point codes – has been addressed in [BGT11] and the capacity region has been characterized. The power control problem has been studied only for a class of fading interference networks in which transmitters simultaneously send their messages and each receiver decodes its message by treating the interfer- ence as noise (see e.g. [CHLT08, SWB06] and references therein). Various iterative power control algorithms have been proposed (see e.g. [Zan92,Yat95,CHLT08]) that assign power to the transmitters so that every transmitter–receiver pair meets a desired signal-to-interference-plus-noise ratio (SINR). This keeps the instantaneous mutual information within each fading block at a value larger than the desired transmission rate. However, only a few studies have been conducted on the feasi- bility of the solutions for the power control problems. Specifically, for each fading block in which channel gains remain constant, [CHLT08, Zen92, HC00a, MDEK10]
have shown whether the power control problem has feasible solutions. Indeed, re- gardless of how large the powers are, for some channel gains, the power control problem may not have any solution. When there is no power constraint, a feasi- bility criteria was derived in [Zen92], [HC00a]. It is possible to use this criteria to determine whether, for specific channel gains, the power control problem has any solution to support transmission at desired rates. Nevertheless, the solutions may require large powers. Reference [MDEK10] has extended the results to the case in which there are linear power constraints. For a fading channel, when there is a short-term power constraint in the system, due to the random nature of fading, for some channel realizations there is no choice of power control that satisfy power constraint and can guarantee successful communication at the desired rate. In this case, we define the power control problem to be infeasible, and the system to be in
outage. At a given transmission rate, the probability that an outage event occurs is defined as outage probability. In many communication systems, a small value of outage probability is tolerable. In these cases an ǫ-outage achievable rate region is defined as the supremum of transmission rates for which the outage probabil- ity is less than ǫ [CTB99, VH94, TV05]. The outage probability and the ǫ-outage achievable rate region for random continuously distributed channels is unknown (e.g. Rayleigh fading).
Contributions
Chapter 3 considers a two-user Rayleigh block-fading interference network. Each transmitter utilizes a fixed-rate point-to-point Gaussian code to communicate with its dedicated receiver. Perfect CSI is globally available at all terminals. Each trans- mitter is subject to a short-term power constraint. We consider five different trans- mission schemes. When the two transmitter-receiver pairs are orthogonally acti- vated, inter-user interference can be completely eliminated, possibly at the cost of spectral inefficiency. When both users non-orthogonally access the available chan- nel, inter-user interference must be taken into account during the decoding process.
This leads to the four following schemes: (1) both receivers directly decode their desired messages by simply treating interference as noise; (2) both receivers conduct successive interference cancellation (SIC); (3) the first receiver performs direct de- coding and the second receiver performs SIC; and (4) the first receiver performs SIC and the second receiver performs direct decoding. For each of these five schemes, we start by finding the solution to the power control problem. Next, we derive a lower bound and an upper bound on the outage probability, as functions of channel statistics, desired transmission rates, and power constraints. These results are then used to find an outer bound and an inner bound on the ǫ-outage achievable rate region. The contributions of this chapter are based on
• [FWS14a] H. Farhadi, C. Wang, M. Skoglund, “Delay-limited constant-rate transmission over fading interference channels using point-to-point Gaussian codes,” submitted to IEEE Trans. Commun., 2014.
• [Far12] H. Farhadi, “Interference alignment and power control for wireless interference networks,” Licentiate Thesis, KTH Royal Institute of Technology, Stockholm, Sweden, Sep. 2012.
Chapter 4
In this chapter, we study a time-varying K-user SISO interference network. We assume that no CSI is a priori available at terminals, and devise a coordinated schemes to acquire CSI and also to conduct communication.
Background
The performance limits of K-user interference networks have attracted a great deal of interest for decades; for example, the capacity region of the two-user interference networks has been the subject of extensive research. Although various inner bounds and outer bounds on the capacity region of the two-user interference network have been proposed, the exact capacity region is still unknown in general [EK11]. Ex- tension of the results to general K-user interference networks is even more com- plicated. It has been shown that when channels are time-varying, applying an in- terference management technique called interference alignment [MAMK08, CJ08], at a given signal-to-noise-ratio (SNR) the sum-rate K2 log(SNR) + o(log(SNR)) can be achieved, where limSNR→∞o(log(SNR))/SNR = 0 [CJ08]. This achievable sum- rate linearly scales with the number of users and is substantially higher than the sum-rate log(SNR) + o(log(SNR)) achieved by the conventional TDMA and FDMA schemes. Furthermore, an ergodic interference alignment scheme has been devel- oped in [NGJV12] so that, when channel gains are symmetrically distributed, the sum-rate K2E[log(1 + 2|h|2SNR)] is achievable under an ergodic setting. Such a re- sult implies that the interference network in time-varying fading environments may not be interference-limited at any SNR. The outstanding performance promised by the aforementioned schemes is based on underlying assumptions that the CSI is perfectly known at all terminals, and an asymptotically long delay in transmis- sion (due, for example, to the symbol extension technique in [CJ08], or the channel pairing technique in [NGJV12]) can be tolerated.
Regarding the delay issue, it has been shown through studying the delay-rate tradeoff for the ergodic interference alignment scheme [KWG10,MM12,JAP12] that the delay can be reduced by sacrificing transmission data rate. In general, however, an asymptotically long delay in transmission is still required in order to exhibit the advantage of the ergodic interference alignment scheme. It is not known whether the scheme is capable of providing performance gains over orthogonal transmissions under finite delay constraint.
Moreover, in practice no CSI is a priori available at terminals. They can deploy a pilot-based channel training scheme to acquire an estimate of CSI at receivers, and a channel state feedback scheme to obtain an estimate of CSI at transmitters. Chan- nel training schemes for point-to-point communication systems have been studied extensively (see, e.g., [HH03, BLM03, LSD04, ZCLB07, Sha14]). However, in multi- user scenarios they are even more challenging and the underlying performance limits of pilot-based channel training for these systems are less known. Channel training schemes for broadcast channels have been studied in [CJKR10, KJC11],
for multiple-access systems in [HKD11], and for certain interference networks in [ALH12, MGL13, FKS14]. [ALH12] studied channel training for multiple antenna interference networks and also the impact of the allocated time for channel train- ing on the system performance. Transmission power for pilot transmission was as- sumed to be the same as that for data transmission. In general, however, they can certainly be different. A more accurate channel estimation can be obtained by allocating more power for pilot transmission, which implies that less power is left for data transmission. The interesting problem of optimum power allocation to pilot symbols and data symbols in point-to-point communication scenarios was investigated in [HH03]. In interference networks, finding the solution to this opti- mum power allocation problem is even more important because the quality of CSI estimation not only affects the performance of each decoder, but also determines how accurately the interference alignment can be performed. It is also important to characterize the performance limits of the pilot-assisted channel training schemes for interference networks.
Regarding acquiring CSI at the transmitter-side, several references (e.g. [BT09, KV10, FWS11, NGJV12, RG12, LK12, KMLL12, KLC11, NWHC12, CY14]) have in- vestigated cases in which each destination provides only the quantized version of its incoming channel gains to the other terminals through channel state feedback.
It has been shown that when the number of quantization bits is proportional to log (SNR), the achievable rate of interference alignment with perfect CSI at the high-SNR regime can be preserved [BT09]. However, the capacity of feedback chan- nels is limited in practice and terminals may not be able to attain a sufficiently accurate CSI estimation. Applying interference alignment based on the imperfect CSI, inter-user interference can be only partially eliminated so that some residual interference remains at each destination. This residual interference, if not appropri- ately managed, will degrade the system performance. On the other hand, instead of exploiting the available (even imperfect) CSI to solely conduct interference align- ment, the sources can also adapt their transmission strategies; for example, by controlling transmission data rate or power, to compensate for the aforementioned performance loss and fulfil service requirements.
Contributions
In this chapter, we propose a pilot-assisted ergodic interference alignment scheme.
This scheme deploys pilot-based channel training in order to acquire an estimate of CSI at destinations. Each destination obtains a noisy estimate of its local CSI and sends an un-quantized (quantized) version of the estimated CSI to the other terminals via analog (digital) feedback signals. The ergodic interference alignment scheme is then applied to perform data transmissions. Each transmitter shares available radio resources between pilot transmission and data transmission phases.
If analog feedback is deployed, we compute an achievable rate region and investi- gate the optimum power allocation between channel training and data transmission phases. We also address the scenario in which digital feedback is used to send quan-
tized CSI with limited resolution. Two problems are studied in this case. The first is a power control problem in which each user wishes to successfully transmit infor- mation at a fixed rate using minimum power. We use a power control scheme that adapts transmission power values such that the mutual information corresponding to each source–destination pair is always larger than the transmission rate, which means that transmitted codewords can be successfully decoded at the desired des- tination. We then study a throughput maximization problem in which each source has a fixed transmission power value and the network throughput is desired to be maximized [FWS11]. Since each source only knows quantized CSI, it is not aware of the exact value of mutual information between itself and its intended destination.
Therefore, for some channel realizations, the mutual information may fall below the transmission rate and communications fail, which leads to an outage event. The out- age probability can be used to quantify throughput as a measure of the amount of information that can be successfully transmitted. We propose a rate adaptation scheme to maximize network throughput. As noted earlier, most existing works on ergodic interference alignment assume that the system can tolerate asymptot- ically long delays. To understand how the considered schemes perform in realistic situations, we extend our results to communication systems with finite delay con- straint, and quantify network throughput in these delay-constrained systems. The contributions of this chapter are based on
• [FWS14c] H. Farhadi, C. Wang, and M. Skoglund, “Interference alignment with limited feedback: Power control and rate adaptation,” submitted to IEEE Trans. Wireless Comm., 2014.
• [FWS11] H. Farhadi, C. Wang, and M. Skoglund, “On the throughput of wire- less interference networks with limited feedback,” in Proc. IEEE Int. Symp.
Info. Theory (ISIT’11), St. Petersburg, Russia, Jul. 2011.
• [FWS12] H. Farhadi, C. Wang, and M. Skoglund, “Power control in wire- less interference networks with limited feedback,” in Proc. IEEE Int. Symp.
Wireless Comm. Sys. (ISWCS’12), Paris, France, Aug. 2012.
• [FKWS13] H. Farhadi, M. N. Khormuji, C. Wang, and M. Skoglund, “Ergodic interference alignment with noisy channel state information,” in Proc. IEEE Int. Symp. Info. Theory (ISIT’13), Istanbul, Turkey, Jul. 2013.
• [FKS14] H. Farhadi, M. N. Khormuji, and M. Skoglund, “Pilot-assisted er- godic interference alignment for wireless networks,” in Proc. IEEE Int. Conf.
Acoustics, Speech and Signal Processing (ICASSP’14), Florence, Italy, May 2014, [Best Student Paper in Signal Processing for Communications and Net- working].
• [Far12] H. Farhadi, “Interference alignment and power control for wireless interference networks,” Licentiate Thesis, KTH Royal Institute of Technology, Stockholm, Sweden, Sep. 2012.
Chapter 5
In Chapter 5, we study a K-user multiple-input multiple-output (MIMO) inter- ference network. Each source intends to send multiple independent data streams to its corresponding destination where the number of data streams coincides with the achievable DoF of the network. Each data stream is encoded at a fixed data rate while different streams can have different rates. Only local CSI (that is, the knowledge related to the channels directly connected to a terminal) is available at each terminal. We propose iterative algorithms to perform distributed power control and transceiver design. Transmitter beamforming matrices and receiver fil- tering matrices are designed to maximize the SINR at each receiver corresponding to each stream. Power control is conducted to assign the minimum power to each encoded data stream to guarantee successful communication.
Background
Characterizing the performance limits of K-user MIMO interference networks and designing efficient interference management schemes to achieve the limits have both generated a great deal of interest among researchers. As already noted, it is a challenge to find the capacity region of interference networks even with only two source-destination. Instead, degrees of freedom (DoF)– defined as the asymptotic scaling factor of the capacity with respect to the logarithm of SNR– has been in- vestigated recently [CJ08,MAMK08,Jaf11]. Intuitively, DoF represents the number of independent streams that can be transmitted interference-free in the asymptot- ically high-SNR regime. The total achievable DoF of the conventional interference management schemes (for example, TDMA or FDMA) in which the transmissions of different source-destination pairs are orthogonalized, does not increase with the number of users. However, as we already mentioned the interference alignment concept [MAMK08, CJ08] reveals that, with proper transceiver design, different interference signals at each destination can be aligned together, such that more radio resources can be assigned to the desired transmission. In certain cases (such as a three-user MIMO interference network), applying interference alignment can achieve a total DoF equal to half of the total achievable DoF in the interference- free network. To do so, the sources perform linear beamforming to simultaneously transmit multiple independent streams in such a way that, at each destination, in- terference signals align and span only half of the available signal space (in the spatial domain). Consequently, the interference can be eliminated with linear zero-forcing filter at each destination [CJ08]. Thus, a total DoF proportional to the number of users in the network can be achieved. This idea has inspired several linear beam- forming and filtering design solutions for interference networks. For instance, it has been shown that the beamforming and filtering matrices can be further optimized to achieve a larger sum-rate at the finite-SNR regime [SPLL10]. Also, for MIMO interference networks with finite alphabet channel inputs, a linear beamforming design is proposed in [WXG+13] to maximize sum-rate.
Although interference alignment can achieve a larger DoF than that achieved by orthogonal transmission strategies, several challenges must be addressed to enable the deployment of this technique in future wireless networks [APH13, MET13]. To compute transmitter beamforming matrices and receiver filtering matrices, global CSI must usually be perfectly known at all terminals [CJ08, SPLL10]. Acquiring such channel knowledge is clearly a challenging problem in practice. In most cases, it is more convenient for each terminal to obtain only the CSI corresponding to the links directly connected to it (that is, the local CSI). For instance, the local CSI can be the exact channel matrices corresponding to the local links or some function of these matrices. Accordingly, distributed interference alignment have been proposed in the literature (e.g., [GCJ11, PH11]).
Consider a MIMO interference network in which each user may send multiple independent data streams. An iterative algorithm for distributed interference align- ment, referred to as the DIA algorithm, is proposed in [GCJ11]. Since only local CSI is available at terminals, interference signals cannot be perfectly aligned at each receiver. Therefore, zero-forcing filtering cannot perfectly eliminate the interference and some leakage interference remains at the receivers. This algorithm iteratively minimizes the power of the leakage interference. The solution computed by the DIA algorithm achieves the DoF of the network in the high-SNR regime. However, prac- tical systems have finite SNR and the solutions intended for the high-SNR regime may not be efficient in this case. Therefore, another iterative algorithm is proposed in [GCJ11] to maximize the signal-to-leakage interference-plus-noise ratio for each transmitted data stream. This algorithm, which is referred to as the Max-SINR algorithm, achieves a larger sum-rate than the DIA algorithm at the finite-SNR regime while achieving the same DoF at high SNR.
In practical wireless environment, channel variations mean that the equivalent SINR corresponding to each transmitted data stream changes over time. Thus, adaptive transmission is required for reliable communication. Depending on the objectives and the constraints, two different types of adaptive schemes can be ap- plied. In a class of communication systems where the maximum throughput is desired, similar to the one considered for the DIA algorithm and Max-SINR algo- rithm in [GCJ11], an adaptive coding and modulation scheme is required to adjust the data rate based on channel state [GC98]. In such systems, transmission pow- ers might be fixed or can be adapted (for instance, by using an algorithm similar to the one proposed in [QZH09]) to maximize the throughput. In another group of applications, such as voice/video communications, or control over communica- tion networks, a fixed-rate data transmission is desired instead [WGM07,CHLT08].
Therefore, a power control problem should be solved. Several iterative power control algorithms have been proposed for the uplink and downlink transmissions of cellu- lar systems (see e.g. [Zan92, FM93b, Yat95, FJC12]). [Yat95] introduced the family of standard power control problems and showed the convergence of the correspond- ing iterative power control algorithm. Furthermore, joint beamforming design and power control has been studied in some MIMO communication systems (such as the MIMO downlink channel) where the power control problem is intertwined with the
transceiver design problem [RFLT98,SB04,CHLT08,TCS11,HZB+11,HZB+12]. In interference networks, the SINR corresponding to each source-destination pair de- pends on the transmission powers of all sources. The solution of the power control problem for each user is coupled to that for the other existing users. This depen- dency leads to conflicting goals. Specifically, when each source tries to increase the transmission power to compensate interference at its intended destination, it also increases the interference to the other destinations. Ignoring this dependency in signaling design may cause unnecessarily power demand or unsatisfactory commu- nication quality. With regard to MIMO interference networks, directly applying conventional power control strategies when multiple source-destination pairs are non-orthogonally activated is highly likely to be infeasible or lead to large power requirements. Thus, to guarantee successful fixed-rate transmission for each source- destination pair, power control is conventionally carried out when the transmissions of different sources are orthogonalized. According to the recent intuitions from the interference alignment concept, this may not be a spectrally efficient transmission strategy as shown in [Far12, FWS13].
Contributions
In this chapter, we aim to address the problem of transceiver design and power con- trol for MIMO interference networks by further taking into account the achievable DoF of the network. Specifically, we consider a network where each source sends multiple data streams: the same number as the corresponding DoF achieved by interference alignment. We propose two iterative algorithms that compute trans- mitter beamforming matrices and receiver filtering matrices to maximize the SINR for each stream, and allocate the minimum powers to realize the desired fixed-rate communications. In both algorithms, the required power values are computed in a distributed fashion at each destination and the associated source is informed via a feedback link. In the first algorithm, the exact value of the computed power is sent, while only a one-bit feedback signal is transmitted in the second algorithm, via feedback. The proposed algorithms can provide reliable communication when mul- tiple streams are transmitted, as each is encoded with potentially different rates.
This is particulary useful in wireless networks in which each user intends to com- municate multiple multimedia data with diverse contents, each with possibly dif- ferent QoS requirements. Numerical evaluations confirm that these algorithms re- quire substantially smaller power values compared to the conventional orthogonal transmission strategies. These algorithms are implemented on KTH’s four-multi test-bed, which consists of three source-destination pairs of USRP-based termi- nals [MFZS14, MFZ+14]. The experimental measurements in indoor environment also confirm the promised performance of the proposed algorithms. The contribu- tions of this chapter are based on the following publications.
• [FWS14b] H. Farhadi, C. Wang, and M. Skoglund, “Distributed transceiver design and power control for wireless MIMO interference networks,” accepted
for publication in IEEE Trans. Wireless Commun., Oct. 2014.
• [FWS13] H. Farhadi, C. Wang, and M. Skoglund, “Distributed interference alignment and power control for wireless MIMO interference networks,” in Proc. IEEE Wireless Commun. and Networking Conf. (WCNC’13), Shanghai, China, Apr. 2013.
• [FZF+13] H. Farhadi, A. Zaidi, C. Wang, and M. Skoglund, “Distributed interference alignment and power control for wireless MIMO interference net- works with noisy channel state information,” in Proc. Int. Black Sea Conf.
Commun. and Networking (BlackSeaCom’13), Batumi, Georgia, Jul. 2013.
• [Far12] H. Farhadi, “Interference alignment and power control for wireless interference networks,” Licentiate Thesis, KTH Royal Institute of Technology, Stockholm, Sweden, Sep. 2012.
• [MFZ+14] N. N. Moghadam, H. Farhadi, P. Zetterberg, M. Khormuji and M. Skoglund, “Interference alignment: Practical challenges and test-bed im- plementation,” book chapter in Contemporary Issues in Wireless Communi- cations, INTECH Open Access Publisher, Nov. 2014.
Chapter 6
In Chapter 6, we consider a multi-cell interference network with multiple cells, each of which has a base station and multiple mobile terminals. Each base station communicates to mobile users in the corresponding cell. We assume that no CSI is a priori available at terminals. We propose a low-complexity scheme to conduct channel training and data communication in these networks.
Background
It has been predicted that one of the most typical scenarios in 5G communica- tions systems will be to support an exponentially increasing demand for data rate, in ultra-dense deployments. Such communication scenarios are characterized by a high data rate requirement that needs to be sustained, irrespective of the harsh urban propagation conditions [OBB+14, JMZ+14]. Moreover, the relatively high user density in such settings implies that channel training and feedback overhead is a major challenge. Consequently, spectrally efficient transmission techniques with low-overhead are greatly desired.
In order to enhance spectral efficiency, the time-varying characteristics of wire- less transmission medium can be effectively exploited. It has been shown that opportunistic transmission can benefit from the time variations of propagation environment and enhance system performance. These schemes schedule a subset of the users depending on the instantaneous CSI. Several opportunistic transmis- sion schemes have been developed in the literature; these include opportunistic scheduling [XCS01, LTYF03, TW08, SBM09], opportunistic beamforming [VTL02], random beamforming [SH05], and opportunistic interference alignment [PDLC08, JNPS12, YSJS14, LGLL14]. The early opportunistic schemes were mainly designed to exploit multi-user diversity in single-cell communication scenarios (e.g. [XCS01, VTL02,LTYF03,SH05,TW08]). Studies have shown that opportunistic transmission schemes can also mitigate inter-cell interference, thereby achieving multiplexing gain in multi-cell communication scenarios (e.g. [PDLC08, JNPS12, YSJS14, LGLL14]).
However, the aforementioned schemes exhibit several characteristics that hinder their application in dense cellular deployments. For instance, the proposed schemes in [XCS01, LTYF03, PDLC08] require CSI to be perfectly known at mobile termi- nals and base stations. while the schemes proposed in [VTL02,SH05,TW08,SBM09, JNPS12, YSJS14, LGLL14] require only finite rate feedback to acquire CSI at base stations, they also need CSI to be a priori known at mobile terminals. This effec- tively limits their scalability since the overhead required for channel estimation at mobile terminals may degrade the expected delivered performance gains. In prac- tice, CSI is not a priori available at mobile stations and they may only obtain imperfect CSI via channel training schemes. This has a twofold impact: Firstly, base stations need to allocate part of their radio resources for channel training, which means that fewer resources will be available for data transmission; Secondly, the performance of opportunistic transmission schemes degrades as a consequence
of imperfect scheduling and erroneous decoding at mobile terminals. Less is known about how to perform opportunistic transmission when no a priori CSI is available at terminals, and the performance limits of networks in such scenarios is a high priority for investigation.
Contributions
We consider a dense cellular communication scenario in which one base station in each cell serves a large number of mobile terminals, with no a priori CSI available.
We propose a pilot-assisted opportunistic user scheduling (PAOUS) scheme con- sisting of low complexity channel training and one-bit feedback transmission. We compute the achievable rate region for the proposed scheme and characterize the achievable DoF region. Our results reveal that, in a multi-cell network with B base stations and a coherence time T , the achievable sum-rate increases as the number of mobile terminals scales and the total DoF Bopt(1− Bopt/T ) is achievable, given that the number of mobile terminals in each cell scales is proportional to SNR. This result indicates that, to maximize the achievable sum DoF only a subset of base stations should be activated, where the optimum number of active base stations is Bopt= min{B, T/2}. The contribution of this chapter is based on
• [FGS14] H. Farhadi, H. Ghauch, and M. Skoglund, “Pilot-assisted oppor- tunistic user scheduling for wireless multi-cell networks,” submitted to IEEE Int. Conf. Commun. (ICC’15), London, UK, Oct. 2014.
Chapter 7
In the last chapter, we summarize our contributions in the thesis, and discuss potential directions for future research.
Contributions Outside the Scope of the Thesis
In addition to the contributions listed above, the author of this thesis has also contributed to some other related works, which are published in the papers listed below. For consistency of the thesis structure, these are not included in the thesis.
Test-bed Implementation of Transceiver Design and Power Control Algorithm
We implemented our proposed iterative transceiver design and power control algo- rithm (presented in Chapter 5) on the KTH four-multi test-bed (see [Zet, ZM12, Zet14] for more details about this test-bed). The test-bed is composed of three base stations and three mobile stations. All base stations were transmitting simultane- ously and on the same frequency band. The baseband processing at the terminals was implemented on universal software radio peripheral (USRP) platforms. Each terminal has two antennas, each of which is connected to one dedicated USRP. The indoor measurements reveal that, the proposed algorithm can achieve at least 4 dB reduction in transmission power in 90% of the experiments compared to the case where MaxSINR algorithm was implemented. The power saving gains as high as 13 dB was also observed in 10% of the measurements. This implementation and the measurement results are presented in the following publications:
• [MFZS14] N. N. Moghadam, H. Farhadi, P. Zetterberg and M. Skoglund,
“Test-bed implementation of iterative interference alignment and power con- trol for wireless MIMO interference networks,” in Proc. IEEE Int. Work- shop on Signal Proc. Advances in Wireless Commun. (SPAWC’14), Toronto, Canada, June 2014.
• [MFZ+14] N. N. Moghadam, H. Farhadi, P. Zetterberg, M. Khormuji and M. Skoglund, “Interference alignment: Practical challenges and test-bed im- plementation,” book chapter in Contemporary Issues in Wireless Communi- cations, INTECH Open Access Publisher, Nov. 2014.
Multi-user Relay Networks
We have studied the achievable sum DoF of a class of multi-user SISO relay net- works. In these networks, the communications between K unconnected source–
destination pairs are provided by a large number of half-duplex relays. When the number of relays is sufficiently large, we show that the sum DoF of this network is K. This can be achieved through the combination of spectrally efficient relay- ing and interference alignment. This result implies that allowing only distributed processing and half-duplex operation can provide performance that is similar to permitting joint processing and full-duplex operation in wireless relay networks at a high-SNR regime. This material has been published in:
