Residual Self-Interference Mitigation in Full-Duplex Two-Way MIMO Relaying Network

Transcription

1 Residual Self-Intefeence Mitigation in Full-Duplex Two-Way MIMO Relaying Netwok Thesis submitted in patial fulfillment of the equiements fo the degee of Maste of Science in Electonics and Communications Engineeing by Reseach by Nachiket Ayi Intenational Institute of Infomation Technology Hydeabad , India May 2018

2 Copyight c Nachiket Ayi, 2018 All Rights Reseved

3 Intenational Institute of Infomation Technology Hydeabad, India CERTIFICATE It is cetified that the wok contained in this thesis titled Residual Self-Intefeence Mitigation in Two- Way Full-Duplex MIMO Relaying Netwok by Nachiket Ayi has been caied out unde my supevision and is not submitted elsewhee fo a degee. Date Adviso: D. P. Ubaidulla

4 To My Family and Fiends

5 Acknowledgements It has been almost thee yeas since I joined IIIT Hydeabad. Fom stating as a student who was clueless about what eseach is, to submitting my MS thesis now, I feel I ve leaned a lot duing this time. I would like to offe my gatitude to eveyone who has been a pat of my jouney. Fist and foemost, I would like to thank my adviso D. P. Ubaidulla fo his guidance not only in selecting the eseach topic, but also fo tips on pape witing, pape eading and most impotantly about eseach ethics. I also thank him fo giving me an oppotunity to be a teaching assistant fo two of his couses, which gave me a fist hand expeience of teaching and inteacting with some of the bightest minds of this county. It was tuly an amazing expeience. Also, I am extemely gateful to him fo allowing me to attend the VTC Sping I am gateful to the othe faculty membes of SPCRC: D. Lalitha Vadlamani, D. Sachin Chaudhai, D. Pasad Kishnan, D. G. Ramamuthy fo thei guidance and suppot. Special thanks to D. Lalitha Vadlamani fo guiding me with the student tavel gants pocess of IEEE Hydeabad section, and fo he effots duing the R&D showcase I would like to thank Ms. Sailaja fo the administative suppot. I had an amazing time hee thanks to the fiends I made. Special thanks to Upende, Rhishi, Maneesh, Mahesh, Pakash, Patik fo the bainstoming sessions duing the post-dinne walks, the lone outing, and the numeous Biyani paties! I am gateful to my senios: Sumit, Deepa, Kunal, Chandan fo thei academic guidance, and to my fellow lab mates Pudhvi and Shubham. Best wishes to the new eseaches in SPCRC: Zaki, Kali Kishna, Anish. Special thanks to PEC committee fo oganizing the spots events and fo poviding the spots facilities. I owe my inteest, and the subsequent pogess, in Maathon unning to you folks. I would like to thank ou Diecto D. P. J. Naayanan fo poviding us with an envionment conducive to eseach. His simplicity is an inspiation. Last but not the least, I am thankful to my family fo thei constant suppot and motivation. Looking back at the day of the inteview at IIIT-H, when I was asked to choose between MS and MTech, I am happy that I made the ight decision. My tenue hee has ignited my inteest in eseach. Apat fom the academics, I have tuly enjoyed my stay in Hydeabad. v

6 Abstact In-band full-duplex (FD) communication that enables concuent tansmission and eception in a single fequency-time channel holds the pomise of nealy doubling the spectal efficiency compaed to the cuent half-duplex and out-of-band FD communication systems. The main hudle in the pactical implementation of such a full-duplex system is the loopback self-intefeence (LSI), which aises due to the FD opeation of the communicating nodes. In such an FD tansceive, the tansmit signal geneally ovepowes the intended eceive signal making its detection extemely difficult. Howeve, with the ecent advancements in the LSI cancellation techniques, FD systems have finally become viable. Hence, it is no wonde that FD has been envisaged as one of the pomising technologies fo the next geneation wieless netwoks, viz., 5G and beyond. In pactice, the LSI cancellation pocess cannot eliminate the LSI completely due to vaious easons, chief among them the difficulty in obtaining the pefect channel state infomation of the loopback channel. As a esult, we ae still left with a esidual LSI, which would degade the pefomance of an FD system. In this wok, we conside the design of optimal tansceive and elay pocessing algoithms fo FD multiple-input multiple-output (MIMO) coopeative netwoks. Specifically, we popose the algoithms fo FD communication in thee diffeent scenaios: (i) a cognitive adio netwok, (ii) secue communication using physical laye secuity techniques, and (iii) a cellula netwok. In the cognitive adio setup, we conside the FD tansceives and the FD elay to be a pat of the seconday netwok. The tansceive and the elay pecodes ae designed so as to ensue that the intefeence caused to the pimay use is always below a specified theshold. We have consideed the maximization of the eceive signal-to-noise atio (SNR) as the citeion fo the design of the tansceive pecodes. We have futhe extended this poblem to the case whee multiple elays ae available fo selection. A cental contol unit selects the elay that povides the highest eceive SNR. In the next scenaio, a passive eavesdoppe ties to decode the data of the two legitimate FD tansceives. In this case, we conside secue communication between the legitimate tansceives using physical laye secuity techniques. The pecode and eceive filte matices ae designed to ensue secue communication between the legitimate uses. The sececy pefomance of this system in the pesence of a passive eavesdoppe is analyzed by consideing the elay signal as atificial noise fo the eavesdoppe. The effectiveness of the poposed design is evaluated in tems of the sum-sececy-ate of the system. Finally, we conside a futuistic FD cellula netwok scenaio whee an FD base station communicates with two FD tansceive nodes, whee one of the tansceives is assisted by an FD amplify-and-fowad elay. In each of the scenaios, ou pime vi

7 vii focus is on mitigating the esidual LSI and its detimental effect on the pefomance of the system. The pecodes at the tansceive nodes ae designed to mitigate the LSI based on the equiements of thei opeating envionment. The LSI at the elay is mitigated by incopoating it into the sum of meansquae-eo (SMSE) minimization poblem. The elay pecode and the tansceive eceive filtes ae designed based on the minimization of the SMSE of the end-to-end communication. The esulting optimization poblem is non-convex and hence a globally optimal solution is not guaanteed. We apply the coodinate descent method and the Kaush-Kuhn-Tucke (KKT) conditions to obtain sub-optimal solutions. The complexities of the poposed algoithms ae lowe than that of the state-of-the-at algoithms, in tems of both numbe of computations and memoy equiements. The vaious simulation esults demonstate the efficacy of ou poposed designs in tems of LSI mitigation, powe efficiency, numbe of iteations, and sum-ate pefomance.

8 Contents Chapte Page 1 Intoduction Poblem Oveview Contibutions Oganization of the Thesis Full-Duplex Relaying - A Suvey Full-Duplex Wieless Communication Relay-assisted Full-Duplex Self-Intefeence Cancellation Techniques Popagation-Domain LSI Cancellation Analog-Cicuit-Domain LSI Cancellation Digital-Domain LSI Cancellation Channel Modeling fo the LSI Channel MIMO in Relaying Summay Low-Complexity Residual LSI Mitigation Intoduction System Model Iteative Estimation of the Popagating Eo Tem Summay Full-Duplex Two-Way Relaying in a Cognitive Netwok Intoduction System Model Design of Optimal Tansceive Pecodes and Relay Selection Tansceive Pecode Design Optimal Relay Selection Design of Seconday Relay Pecode and Tansceive Receive Filtes Simulation Results Summay Design and Analysis of a Secue Full-Duplex Two-Way Relaying System Intoduction System Model viii

9 CONTENTS ix 5.3 Design Tansceive Pecode Design Relay Pecode and Tansceive Receive Filte Design Analysis of the Sececy Pefomance of the Poposed Design Simulation Results Summay Low-Complexity Tansceive Designs fo a Relay-Assisted Full-Duplex Cellula Netwok Intoduction System Model Design of Optimal Pecodes and Receive Filtes Pecode and Receive Filte Design fo UE, Base Station Pecode Design fo UE and Base Station Simulation Results Summay Conclusions Summay and Conclusion Scope fo Futue Wok Bibliogaphy

10 List of Figues Figue Page 2.1 Global mobile data taffic fom 2016 to 2021 [1] A cellula towe equipped with massive MIMO tansceive [2] A mmwave cellula netwok [3] Self-intefeence in a full-duplex system [4] Schematic of a ciculato A egula ciculato and a CMOS ciculato [4] Relay-assisted communication Relaying schemes An in-band full-duplex two-way elaying system System diagam of an FD two-way MIMO elaying netwok System diagam of a cognitive FD two-way elaying netwok with M cognitive elays Relay selection fo vaying values of intefeence theshold θ Vaiation of tansmit powe vesus θ fo diffeent values of path loss Numbe of iteations equied to obtain optimal U, F, fo diffeent values of INR, fo θ = -92 dbm and SNR = 5 db Vaiation of SMSE ove time, fo diffeent values of INR, at θ = -92 dbm and SNR = 10 db SMSE vesus SNR fo diffeent values of INR and θ Sum-ate vesus SNR fo diffeent values of INR and θ System diagam of secue full-duplex two-way elaying system Tansmit powe of tansceive T 1, in the 8 th time slot, vesus SNR, with P1 max = Convegence of SMSE at each time slot Evolution of SMSE ove time at SNR=10 db SMSE pefomance at diffeent values of SNR, INR Sum sececy ate, in the 8 th time slot, vesus SNR, fo diffeent values of INR System diagam of a elay-assisted two-way FD MIMO cellula netwok Vaiation of esidual LSI vesus eo vaiance σei 2 at σ2 ni = 90 dbm fo: (a) base station B, (b) use U Convegence of SMSE at each time slot at SNR = 10 db fo diffeent INR values Evolution of SMSE ove time at SNR=5dB fo diffeent INR values SMSE pefomance at diffeent SNR and INR x

11 LIST OF FIGURES xi 6.6 Sum-ate vesus SNR fo diffeent values of INR

12 List of Tables Table Page 3.1 Computational complexity of Λ (t) z xii

13 List of Abbeviations 3G 3GPP 4G 5G Thid Geneation Mobile Technology. 3d Geneation Patneship Poject. Fouth Geneation Mobile Technology. Fifth Geneation Mobile Technology. AF AN Amplify-and-Fowad. Atificial Noise. BER Bit Eo Rate. CCI CF CMOS CU Co-Channel Intefeence. Compess-and-Fowad. Complementay Metal-Oxide-Semiconducto. Contol Unit. DF DTH Decode-and-Fowad. Diect-To-Home. EF Estimate-and-Fowad. FD Full-Duplex. HD Half-Duplex. IEEE INR IoT IUI ITU Institute of Electical and Electonics Enginees. Intefeence-to-Noise Ratio. Intenet of Things. Inte-Use-Intefeence. Intenational Telecommunication Union. xiii

14 KKT Kaush-Kuhn-Tucke. LAN LSI LTE LTE-A Local Aea Netwok. Loopback Self-Intefeence. Long Tem Evolution. Long Tem Evolution-Advanced. MAC MIMO MMSE mmwave Media Access Laye. Multiple-Input-Multiple-Output. Minimum Mean Squaed Eo. millimete Wave. PU Pimay Use. RF Radio Fequency. SINR SLNR SMS SMSE SNR SR SU Signal-to-Intefeence-plus-Noise Ratio. Signal-to-Leakage-plus-Noise Ratio. Shot Message Sevice. Sum of Mean Squae Eo. Signal-to-Noise Ratio. Seconday Relay. Seconday Use. UE Use Equipment. WiFi WLAN Wieless Fidelity. Wieless Local Aea Netwok.

15 List of Symbols L t α Loopback channel. Cuent time slot. fee-space path loss H, G, K MIMO channel gains Ω (i) AF N T N R U i U i s i x i y i M T i σ ni Ψ i θ P i n i estimate of loopback esidual self-intefeence powe at i (th) time slot. Numbe of antennas at the tansceives. Numbe of antennas at the elay node. Pecode employed at i (th) node. Receive filte employed at i (th) tansceive. Symbol vecto at i (th) tansceive. Tansmit vecto at i (th) tansceive. Receive vecto at i (th) tansceive. Numbe of seconday elays. i (th) full-duplex tansceive node. Noise powe at the i (th) node. Eo is knowledge of CSI of L i at the i (th) node. Pimay use intefeence theshold. Tansmit powe of the i (th) node. Ciculaly symmetic complex Gaussian noise vecto at i (th) node. xv

16 List of Notations x A scala at cuent time t. x A vecto at cuent time t. X A matix at cuent time t. X T Tanspose of matix X. X Complex conjugate of matix X. X H Complex conjugate tanspose of matix X. X 1 Invese of matix X. X Deteminant of matix X. t(x) Tace of matix X. vec(x) Vectoization of matix X. X Fobenius nom of matix X. X Y Konecke poduct of X and Y. E{ } Expectation opeato. x 2-nom of vecto bfx. mat( ) Pefoms the invese opeation of vec( ). x (j) A scala at any time j. x (j) A vecto at any time j. X (j) A matix at any time j. x if x = 1, then x = 2 and vice vesa. xvi

17 Chapte 1 Intoduction Wieless communication has become an integal pat of ou daily lives. Wieless technologies such as WiFi, bluetooth, cellula access have had a significant impact in the way we communicate, especially in the fom of data tansfe of late. Bluetooth is one of the fist wieless technologies to be standadized in the late 1990s. Bluetooth is known fo its simple, secue connectivity fo data exchange ove small distances. It opeates in the GHz fequency band. Bluetooth vesion 4.0 offes a maximum speed of 25 Mbps ove a maximum ange of 60 metes. WiFi o the Wieless Local Aea Netwoks (WLANs) povide much faste connectivity ove a small ange. WiFi is based on the IEEE standad and opeates in both the 2.4 GHz and 5 GHz bands at a maximum data tansfe ate of 600 Mbps. WiFi is cuently the most popula option fo high speed and cheap intenet access to uses. The ecent suge in mobile data consumption ove the intenet can be accedited to the wide-spead deployment of WiFi stations. With the advent of mobile applications that suppot audio and video calls ove WiFi, the WLAN technology is poving to be an altenative to cellula access in aeas of decent WiFi coveage. Howeve, the cellula access o mobile communication still emains the most pefeed option fo on-the-go wold-wide connectivity. Cellula communication systems have gained immense populaity fo poviding ubiquitous coveage and high-speed data access. Even though the data speeds ae still petty much slowe as compaed to the wied ethenet o optical fibe standads, it is the hassle-fee mobility that has been a diving foce fo the wide acceptance of cellula access. Cellula communication systems have come a long way since the humble beginning in 1980s which offeed only voice connectivity and elied on analog modulation techniques. The digital evolution in cellula communication systems began in the 1990s with intoduction of digital modulation techniques. This was known as the second geneation of mobile sevices o the 2G standad and offeed digital sevices such as SMS and low ate data. Till then, the cellula communication systems wee pimaily used fo voice calling pupose. The paadigm shifted to mobile data usage with the intoduction of the thid geneation of mobile sevices o the 3G standad in ealy The 3G communication systems povided maximum data speeds of about 144 Kbps fo mobile uses, 384 Kbps fo pedestian uses, and 2 Mbps indoo uses. The next evolution in cellula communication systems aived with the intoduction of the fouth geneation of mobile sevices o the 1

18 4G/ Long Tem Evolution (LTE) standad in The 4G standad allowed theoetical speeds of 100 Mbps in downlink and 75 Mbps in uplink. The LTE netwok is optimized fo heavy data taffic and suppots data-intensive applications such as online high definition TV steaming, high definition video confeencing, online gaming, etc. The next step fowad in cellula communication systems was the intoduction of the LTE-Advanced standad which offeed downlink speeds of up to 1 Gbps using the caie aggegation technology on top of LTE. Wieless communication has taditionally been half-duplex (HD), wheein the two-way communication equies sepaate time, and/o fequency esouces. The eason fo the wide acceptance of HD technology in wieless communication systems is its simplicity of implementation. Howeve, the main dawback with HD systems is that they have poo spectal efficiency since two sepaate fequency channels ae equied fo tansmission and eception. Theoetically, HD systems can achieve only half of the maximum possible spectal efficiency. Also, this excess spectum usage esults in eduction in the numbe of uses that can be simultaneously seved by a netwok. These dawbacks ae ovecome by full-duplex (FD) communication. In full-duplex wieless, o in-band full-duplex wieless, all the communicating nodes eceive and tansmit on the same fequency band at the same time! As a esult, an in-band full-duplex adio can achieve bette spectal efficiency, viz., twice the efficiency of half-duplex wieless. Along with enhanced data ates, full-duplex would also fee up a lot of spectum, which would esult in incease in numbe of suppoted uses. Despite having such benefits, thee ae some challenges that have hampeed the feasibility of FD wieless systems in eal-wold applications. The most pominent amongst them is loopback self-intefeence (LSI)! The poblem of LSI is inheent to the opeation of any FD system. Since, the communicating node is simultaneously tansmitting and eceiving on the same fequency, the node will eceive its own tansmit signal along with the intended eceive signal. This unintended eceived signal which was tansmitted by the node itself is called the LSI. In pactice, the powe of the tansmit signal is much geate than the intended eceived signal fom othe nodes. The LSI is usually 80 db to 100 db stonge than the intended eceived signal. As a esult, the LSI at the node due to its own tansmit signal can completely ovewhelm the intended eceived signal fom othe nodes. So, canceling this LSI at the node is the majo challenge in pactical adoption of FD wieless. 1.1 Poblem Oveview The pefomance of any FD system is detemined by the effectiveness with which it mitigates o eliminates the LSI. This equies complete knowledge of the loopback channel, which is difficult to estimate accuately. As a esult, the LSI cancellation pocess at a FD node is impefect and leaves a esidual LSI. We conside a next geneation wieless netwok compising FD two-way elaying netwok consisting of an amplify-and-fowad (AF) full-duplex elay node. Now, the poblem of esidual LSI becomes even moe sevee. Hee, the AF opeation of the FD elay popagates the esidual LSI ove 2

19 time. As a esult, the esidual LSI keeps accumulating ove time and can advesely affect the pefomance of the FD system. Hence, this esidual LSI needs to be mitigated even futhe until it no longe has an impact on system pefomance. 1.2 Contibutions In this thesis, we popose the designs of tansceive pecodes and eceive filtes fo a full-duplex two-way multiple-input multiple-output (MIMO) coopeative netwoks. Specifically, we conside the following thee design scenaios: (i) A cognitive netwok compising two FD tansceives and multiple FD elays, (ii) A FD netwok compising two legitimate tansceives, a FD elay, and a passive eavesdoppe, and (iii) A futuistic cellula netwok compising two FD tansceives, a FD base-station, and a FD elay. In each scenaio, we develop the tansceive and elay pocessing algoithms to mitigate the esidual LSI at each of the nodes. We assume the communication between the tansceives occu only via the elay node. This is the case when the diect path is unavailable due to path loss, shadowing, etc. In the fist scenaio, we conside a cognitive netwok whee the two seconday tansceives communicate with the assistance of a seconday elay. The seconday netwok compises multiple elays and a cental contol unit. This cental unit selects the optimal elay fo communication between the tansceives. We design the tansceive and elay pecodes and the tansceive eceive filtes such that the intefeence to the pimay use is always below a specified theshold and the esidual LSI is mitigated. In the second scenaio, we design a secue netwok and eview its pefomance in the pesence of an eavesdoppe. Hee, the tansceive pecodes ae designed by nullifying the effect of the tansceiveelay channel. The elay pecode and the tansceive eceive filtes ae designed to mitigate the esidual LSI at the elay. Hee, we conside the pecoded elay signal to act as noise to the passive eavesdoppe and evaluate the sum-sececy ate of the system. In the thid scenaio, we popose the design of pecodes and eceive filtes fo a futuistic FD cellula netwok. The netwok compises a FD base-station simultaneously communicating to two uses in a FD manne at the same time! The uses ae selected by the base-station in such a way that they ae geogaphically fa apat and hence don t cause intefeence to each othe. One of the uses is assisted by a FD elay. Hee again, the tansceive pecodes ae designed by nullifying the effect of the tansceive-elay channel as well as by equalizing the signal-to-intefeence-plus-noise atio (SINR) of the tansceive-elay link. The elay pecode and the tansceive eceive filtes ae designed to mitigate the esidual LSI. In each scenaio, the LSI at the elay is assimilated in the sum of mean squae eo (SMSE) of the end-to-end communication and is subsequently minimized. We popose an iteative algoithm to mitigate this esidual LSI. The algoithm has both low computational complexity as well as high efficiency. 3

20 1.3 Oganization of the Thesis The est of the thesis is oganized as follows. Chapte 2 pesents the suvey of the latest advancements in full-duplex technology, descibing the advancements in hadwae and signal pocessing techniques that have made FD MIMO tansceive a eality. We also discuss vaious elaying techniques and the motivation to select a elay woking on AF potocol. Chapte 3 pesents the main wok of this thesis. We develop an iteative algoithm to mitigate the esidual LSI in a FD two-way elaying MIMO system. We compae it with the state-of-the at and analyze its pefomance. Chapte 4 pesents the fist scenaio. Hee, we addess the poblem of elay selection, and design of tansceive and elay pocessing algoithms fo a FD two-way MIMO elaying system in a cognitive setup, with a limit on the maximum toleable pimay use intefeence theshold. Chapte 5 pesents the second scenaio. Hee, we addess the poblem of designing a secue FD twoway elaying system. We pesent the design of tansceive and elay pecodes, and tansceive eceive filtes to mitigate the esidual LSI. We also analyze the sececy pefomance of the poposed designs in the pesence of a passive eavesdoppe, in tems of the sum-sececy ate. Chapte 6 pesents the thid scenaio. Hee, we design a futuistic FD cellula netwok. We popose the design of pecodes and eceive filtes fo the tansceives, base-station and the elay with an aim to mitigate the esidual LSI. The efficacy of the designs is demonstated by compaing the sum-ate pefomance of the poposed system with taditional HD and one-way FD systems. Chapte 7 pesents the conclusions of the wok in this thesis and the scope fo futue wok on this topic. 4

21 Chapte 2 Full-Duplex Relaying - A Suvey With the advent of 3G and 4G LTE wieless sevices, the consumption of intenet data ove the wieless medium has inceased apidly. Such has been the ise in mobile data consumption that the global mobile data taffic which amounted to 7 exabytes pe month in 2016 is expected to each 49 exabytes pe month in 2021 at a compound annual gowth ate of 47 pecent [1]. Most of the mobile data taffic is expected to be consumed by online video steaming sevices. Fig. 2.1 shows the expected gowth in mobile data taffic ove the yeas 2016 to With moe and moe uses accessing intenet sevices on thei handheld devices, intenet access will soon be dominated by wieless devices such as smatphones, tablets, laptops, intenet of things (IoT) devices, etc. Mobile data taffic (exabytes/month) mobile data gowth Figue 2.1: Global mobile data taffic fom 2016 to 2021 [1]. With such a emakable incease in demand fo wieless data sevices, the eseach on next geneation wieless netwoks has ganeed significant inteest in ecent yeas [5]. These eseach woks ae mainly focused on poviding highe data ates, bette spectal efficiency, enhanced enegy efficiency, as well as lowe latency. The fifth geneation (5G) of cellula technology evolution aims to povide these featues. 5

22 The enabling technologies fo 5G includes massive MIMO, full-duplex, mmwave, and softwae defined netwoking. Each of these have gained significant eseach inteest in ecent yeas. Figue 2.2: A cellula towe equipped with massive MIMO tansceive [2]. Massive MIMO compises hundeds of antennas at the tansmitte and eceive which togethe enhance the diectional gain of the oveall antenna system. These antennas opeate coheently to povide benefits like enhanced data ates and impoved spectal efficiency, lowe latency, simplification of media access contol (MAC) laye, etc. Accoding to IEEE, moving fom MIMO to massive MIMO involves making a clean beak with cuent pactice though the use of a lage excess of sevice antennas ove active teminals and time-division duplex opeation. Exta antennas help by focusing enegy into eve smalle egions of space to bing huge impovements in thoughput and adiated enegy efficiency [6, 7, 8]. Howeve, Massive MIMO also bought along a lot of eseach poblems like synchonization between the antennas, efficient use of exta degees-of-feedom, optimizing the intenal powe consumption at the tansceives, and educing the numbe of adio fequency (RF) chains [9]. Also, eseach is being caied out to find its optimal use in cellula netwok scenaio [10]. A typical massive MIMO base station is illustated in Fig It seves multiple uses in the uplink and downlink simultaneously using a lage aay of antennas. The beamfoming at the base station using the massive MIMO antennas helps segegate diffeent uses in space. Millimete-wave wieless communication efes to RF communication in the millimete wave spectum between 30 GHz and 300 GHz. Taditionally used fo ada communications, mmwave spectum in the ange of 24 GHz to 86 GHz is cuently being consideed fo cellula and IoT opeations in 5G as pe the ecommendations of Intenational Telecommunication Union (ITU) [11]. In this spectum, the two bands of paticula inteest ae the 28 GHz and the 60 GHz ones. The high fequency mmwaves would povide highe data ates as compaed to cuent cellula o wieless local aea netwok (WLAN) standads. Howeve, the attenuation at these fequencies ae also high. As a esult, mmwaves cannot 6

23 Figue 2.3: A mmwave cellula netwok [3]. penetate though high density objects like walls, glass, humans, etc., thus leading to educed coveage aea. As a esult, mmwave communication is cuently been envisioned to be used in pico cells o femto cells. The feasibility of mmwave cellula communication, in tems of the steeable antenna equiements, methodology, and channel measuements wee put foth in [12]. An illustation of a mmwave cellula system is shown in Fig. 2.3 whee a base station seves uses with the assistance of mmwave elay links and mmwave backhaul. Due to the millimete length wavelengths at these fequencies, the spacing between adjacent antennas in an aay equied to achieve spatial isolation is also vey less. So the tansceives of a mmwave system usually have antenna aays with lage numbe of elements to achieve diectional gain, so as to incease the coveage aea of the system. The topics of eseach in mmwave communications include pecoding techniques such as hybid beamfoming [13, 14], spase pecoding [15], channel estimation [16], antenna design [17], etc. In-band full-duplex (FD) wieless is one of the emeging technologies fo 5G that has gained massive inteest among the eseach community in ecent yeas. In this chapte, we will pesent a bief suvey of in-band FD wieless communication in Section 2.1 followed by the eview of vaious elaying techniques fo a two-way FD elaying netwok in Section 2.2. Vaious LSI cancellation techniques ae descibed in Section 2.3. We then pesent the channel modeling fo the LSI channel in Section 2.4. A bief oveview of MIMO elaying systems in pesented in Section 2.5. Finally, we summaize in Section Full-Duplex Wieless Communication In most of cuent systems, communication is in half-duplex (HD) mode, i.e., tansmission and eception happen in diffeent times slots and/o in diffeent fequency bands. In in-band FD wieless, all the communicating nodes eceive and tansmit on the same fequency band at the same time! An in-band FD adio can achieve bette spectal efficiency, viz., twice the efficiency of HD o out-of-band FD wieless. Along with enhanced data ates, full-duplex would also fee up a lot of spectum, which 7

24 Figue 2.4: Self-intefeence in a full-duplex system [4]. would esult in incease in numbe of suppoted uses. In spite of such benefits, FD wieless was not ealized pactically until ecently [18]. The main eason was the taditional belief among the eseach community that tansceive adios can only opeate eithe as a tansmitte o a eceive at a given time and on a given fequency simultaneously [19]. Tying to opeate in FD mode esults in stong loopback self-intefeence (LSI) fom the tansmitte to the eceive. This phenomenon is illustated in Fig. 2.4 whee two FD nodes ae communicating with each othe. It can be obseved that the signal fom node 1 attenuates due to path loss as it eaches node 2. As a esult, the powe of the intended eceived signal at node 2 is vey much less, usually of the ode of 80 db-110 db, than the powe of node 2 s own tansmit signal. At the eceive of node 2, both these signals ae eceived collectively. Hee, the LSI signal of node 2 can completely ovewhelm the intended signal fom node 1 due to the huge diffeence in magnitude, and can also dive the eceive cicuity into satuation. Until ecently, it was believed that the LSI signal cannot be mitigated, hence the belief. With the ecent advancements the LSI cancellation techniques [20, 21, 22, 23, 24], in-band FD has finally been shown to be feasible. Even MIMO FD pototypes have been developed in eseach labs [18]. The authos in [20] claim to be successful in educing the LSI down to the noise floo, thus making thei system viable fo commecial applications. The FD MIMO system shown in Fig. 2.4 compises nodes that use sepaate antennas fo tansmission and eception of signals. Since the intoduction of FD systems, eseaches have been tying to find ways to use the same antenna fo both tansmission and eception of signals. This equies use of a device called ciculato. Ciculato has been used in ada systems fo long, howeve its use in mobile communication systems is quite nascent. A ciculato is a thee-pot device in which signal can flow only in one diection, eithe clockwise o counte-clockwise. To use a common antenna fo both tansmission 8

25 Figue 2.5: Schematic of a ciculato. and eception, the configuation used is as shown in Fig The ciculato povides isolation of about 15 db between the tansmitte and eceive cicuit paths [18]. The use of ciculato educes the antenna equiement in a FD node by a facto of two! Such ciculatos wee used in the initial expeiments in [18, 20] whee a FD WLAN was consideed. Figue 2.6: A egula ciculato and a CMOS ciculato [4]. The ciculato [4] used in these setups is a bulky component. The size of the ciculato had to be educed dastically in ode to ealize the LSI mitigation in handheld FD devices such as smatphones o tablets. Also most of the off-the-shelf ciculatos ae feite based, which make them unsuitable fo chip fabication pocess. So, a new type of non-feite ciculato was needed fo integating in today s handheld devices. This feat was achieved by the eseaches at Columbia univesity [25]. They wee able to fabicate a non-ecipocal ciculato using tansistos on a silicon chip. Fig. 2.6 shows a egula ciculato and a CMOS ciculato chip on top of it. With these developments, it can be safely assumed that the commecial poduction of FD MIMO handheld devices is not a distant goal. Though the LSI cancellation techniques available in liteatue 9

26 claim to educe the LSI below the noise floo, the assumptions they make while doing so may not be applicable in cellula netwok scenaios. As a esult, thee is always some esidual LSI that emains afte the LSI cancellation pocess. In this thesis, ou main aim is to mitigate this esidual LSI. Next we pesent a bief oveview of the vaious elaying techniques. 2.2 Relay-assisted Full-Duplex Figue 2.7: Relay-assisted communication. Coopeative communications using elays is yet anothe emeging technology fo next-geneation wieless communication. In fact, the suppot fo elay nodes has been included in elease 10 of 3GPP LTE-Advanced (LTE-A) [26]. In elay assisted communication, the souce node (S) and the destination node (D) communicate with the help of a elay node (R). Thee can be two cases as shown in Fig. 2.7, eithe the diect path between S and D is pesent, o it is not. The fist case is what is geneally temed as coopeative communications whee the destination node eceives the same infomation fom multiple nodes by coopeation amongst souce and elay nodes. The latte case depicts the scenaio wheein the diect path between S and D isn t available due to effects such as high path loss, shadowing, etc. In such cases, the elay node basically extends the coveage of the souce node. In addition to this, elays also povide bette quality of sevice, impoved link capacity, etc. Pesence of multiple elays in paallel between S and D helps to take advantage of multipath divesity, wheeas multiple elays in seies between S and D helps take educe the path loss. Based on the mode of opeation, elaying can be classified as: (i) tanspaent elaying and (ii) egeneative elaying. In tanspaent elaying, the elay node amplifies the eceived signal befoe etansmitting it. In addition to this, the elay may also pefom some linea opeations such as phase shifting, beamfoming. Amplify-and-Fowad (AF) elaying [27, 28, 29, 30] is an example of tanspaent elaying. It must be noted that in tanspaent elaying, the elay does not decode the eceived symbols o change them and hence is unaffected by the modulation type of the tansmitted signal [31]. The majo dawback of tanspaent elaying is that it amplifies and popagates the noise and intefeence signals as well [32]. So, as a pecautionay measue, the amplification facto needs to be monitoed to pevent 10

27 any oscillations. In egeneative elaying, the elay may modify the infomation content of the eceived signal by employing digital signal pocessing in baseband. Opeations such as decoding, estimation, compession, encoding ae included in egeneative elaying. Examples of egeneative elaying potocols include decode-and-fowad (DF), compess-and-fowad (CF), estimate-and-fowad (EF), etc. [33, 34, 35, 36]. Fom an implementation pespective, the hadwae complexity in ascending ode is AF, EF, DF, CF. AF elays also have the lowest pocessing time since they do not decode the data symbols and e-encode them. Pocessing times ae vey citical in today s ulta-fast wieless systems. It has been shown that spatial divesity enhances the capacity of AF elays moe than DF elays when the elay link is poo [37]. So, both fom hadwae and softwae complexity point of view, as well as capacity wise, AF elays seem to be a bette choice fo use in next-geneation wieless netwoks. Figue 2.8: Relaying schemes. Based on elaying schemes, we have the classification as shown in Fig One-way elaying coesponds to unidiectional flow of infomation between S and D via R. The oveall communication equies two time slots. In the fist time slot, the souce tansmits the infomation signal to the elay. Then in the second time slot, the elay pocesses the eceived data based on its mode of opeation and tansmits the esultant signal towads the destination. In two-way elaying scheme, thee is bi-diectional flow of infomation between the uses. So, the use nodes behave as both tansmittes and eceives, viz., tansceives. In the fist time slot of communication, both the tansceives tansmit thei signal towads the elay. The elay eceives the combined data of the uses. In the second time, based on its mode of opeation, the elay pocesses the combined data and tansmits it back towads the tansceives. In a HD system, the tansceives and the elay tansmit in altenate time slots. This esults in loss of spectal efficiency but makes the system design simple. In the case of a FD system, the tansceives as well as the elay tansmit in each time slot. This povides double the spectal efficiency of a HD system [18], but the nodes ae then plagued with self-intefeence caused by the FD opeation which makes the system design complicated. Figue 2.9: An in-band full-duplex two-way elaying system. 11

28 Two-way in-band full-duplex elaying [5] incopoates the meits of both in-band FD communication and two-way elaying. In a two-hop two-way FD AF elaying system, the tansceives tansmit and eceive simultaneously on the same fequency in each time slot, with the assistance of a FD elay. We conside two MIMO tansceives and a MIMO elay. As mentioned ealie, due to the FD opeation, all the nodes in the system suffe fom self-intefeence. A schematic fo such a system is shown in Fig We conside the elay to be opeating on AF potocol. The end-to-end communication equies two time slots. In the second time slot of communication, the tansceives eceive the amplified signal fom the elay. This signal contains the data fom the othe tansceive as well as the data tansmitted by the same tansceive in the fist time slot. This tansmitted data when eceived back afte amplification acts as self-intefeence fo a tansceive. Good channel estimation is equied at the tansceives to cancel out this self-intefeence [38]. Apat fom this, thee is anothe fom of self-intefeence, which aises because of the FD opeation of the nodes. We call it as loopback self-intefeence (LSI) hencefoth. As shown in Fig. 2.9, LSI is intefeence caused at a FD node because of its own tansmission. As explained ealie, this LSI can completely ovewhelm the desied signal at the eceive hence needs to be mitigated. Both these foms of SI need to be suppessed to make any two-way FD elaying system design feasible. A bief oveview of the vaious LSI cancellation technologies is pesented next. 2.3 Self-Intefeence Cancellation Techniques As explained ealie, mitigating the stong self-intefeence fom the tansmitte to the eceive is pivotal fo any FD system. In this section, we shall povide a bief oveview of the thee LSI cancellation techniques, namely, popagation-domain LSI cancellation, analog-cicuit-domain LSI cancellation and digital domain LSI cancellation Popagation-Domain LSI Cancellation Since the powe of the tansmit signal is aound db highe than that of the intended eceived signal, the LSI can completely ovewhelm the desied signal at the FD eceive and may also dive the eceive cicuity into satuation. Popagation-domain LSI suppession technologies ae essential to avet these poblems. Popagation-domain LSI suppession technologies act as the fist line of defense against LSI. The techniques used hee involve use of the duplexe, antenna spacing, path loss, diectional antennas, tansmit beamfoming, coss-polaization etc., to mitigate the LSI electomagnetically befoe it entes the eceive cicuity. A moe detailed desciption of each of these techniques is available in [5]. Popagation-domain LSI suppession is known to mitigate the LSI by as much as 65 db in existing FD systems, such as the one in [39]. The popagation-domain LSI suppession techniques ae vey effective in mitigating the diect paths of LSI passively. Howeve, these techniques ae sensitive to device size and antenna placement. The authos in [40] have shown that the amount of passive suppession 12

29 feasible is limited by envionmental eflections. Channel-awae technologies ae desiable to combat the eflected paths of LSI caused by neaby scattees. One majo dawback with popagation-domain LSI suppession techniques is that they also mitigate the desied signal fom the intended eceive Analog-Cicuit-Domain LSI Cancellation Analog-cicuit-domain LSI cancellation technologies act as the second line of defense. Hee, we obtain a copy of the tansmit signal fom the analog tansmit-chain cicuity which is then subtacted fom the eceived signal befoe it is digitized [21]. By doing so, the non-linea distotions in the tansmit signal intoduced by analog components in the RF chain can be effectively mitigated. A dawback with analog-cicuit-domain LSI cancellation is that the pocess equies analog signal pocessing, which is difficult to achieve in case of wideband eflected LSI [41] Digital-Domain LSI Cancellation Digital-domain LSI mitigation technologies act as the last line of defense against the LSI. These ae adopted afte digitizing the eceived signal. Once in digital-domain, the sophisticated signal pocessing of the LSI becomes elatively easy by utilizing the advanced digital signal pocessing techniques. The techniques used hee involve using a digital LSI cancele and eceive beamfoming. A Digital LSI cancele fist estimates the esidual LSI afte the initial two stages of LSI cancellation, and then the estimate is subtacted fom the eceived baseband samples [21]. Receive beamfoming is widely used in MIMO FD systems wheein the signal eceived at each of the antenna is multiplied by a complex numbe afte which the eceive takes a linea combination of all these signals in an attempt to mitigate the esidual LSI. 2.4 Channel Modeling fo the LSI Channel It s impeative to assume cetain channel models fo the LSI chennel in a FD elaying system. The pefomance of such a system hugely depends on the accuacy in the estimation of the assumed channel model. Some of the woks in the liteatue assume pefect LSI cancellation and hence ignoe the esidual LSI [42, 43]; while some studies assume LSI to follow Gaussian distibution [44], Rayleigh distibution [45] o Nakagami-m distibution [46]. The expeiment-diven chaacteization of the full-duplex LSI channel has been caied out in [21, 23]. A pecise and adequate channel model is necessay while designing the LSI cancellation techniques. Such a model needs to ecod featues such as the esidual LSI, and linea and non-linea tansceive distotions. An efficient channel estimation algoithm is equied fo this pupose in an FD system. The authos in [20] popose dynamic algoithms to estimate the linea and non-linea distotions intoduced by analog cicuity of the tansceive and accuately model the actual LSI being expeienced by the eceived signal. The hybid analog-digital design fo LSI cancellation poposed in [20] successfully models all these distotions along with the tansmitte noise. 13

30 2.5 MIMO in Relaying A MIMO elay system povides the high capacity of MIMO communication along with the coveage extension capability of elay tansmission [47]. Also, a MIMO elay channel is moe obust to channel outages. Moeove, the multiple antennas at the elay can also be utilized to beamfom the signal towads the end uses. Most of the pevious wok on a FD two-way elaying systems compising two use tansceives communicating with the assistance of a elay consideed a single antenna at each of the thee nodes [48, 49, 50, 51]. The authos in [48] consideed the poblem of powe allocation at the souce teminals fo maximizing the ate of communication. They assumed pefect LSI cancellation at the nodes. A moe pactical appoach was consideed in [49] whee LSI cancellation at the nodes was assumed to be impefect, giving ise to esidual LSI. In such a scenaio, the poblem of powe allocation at the nodes was studied unde a constaint on the total powe. In a simila scenaio, the authos in [50] consideed the poblem of sum-ate maximization in the pesence of esidual LSI subject to powe constaint at each node. In addition to this, the poblem of elay mode selection, among one-way HD, two-way HD, one-way FD, and two-way FD was also studied. Residual LSI seveely degades the pefomance of a FD system. Tackling this issue with only single antenna at the FD nodes has shotcomings. In such a scenaio, having multiple antennas at a MIMO FD device poves to be advantageous. Beamfoming using multiple antennas could help to mitigate the esidual LSI. This motivated the study of a FD two-way elaying system with multiple antennas at the elay node. Howeve, thee have been vey few woks which conside such a scenaio [52, 53]. In [52], the authos studied a two-way FD AF elay system with multiple antennas at the elay and single antenna at the tansceives. Hee, the elay pecode matix and the souce powe allocation wee jointly optimized with an objective to maximize the sum-ate, unde a zeo focing (ZF) constaint such that the esidual LSI is pefectly canceled at the elay. An iteative algoithm was poposed since a closed fom solution was not achievable. Contay to the beamfoming matix which pefectly cancels out the esidual SI with a ZF constaint, beamfoming at a FD elay is equied to balance between the esidual SI suppession and the desied signal tansmission. Contay to [52], the system model consideed in [53] compises multiple antennas even at the souce teminals. With the aid of multiple antennas, the authos poposed eceive filtes at the two tansceives to addess the inte-steam intefeence in the MIMO channels. 2.6 Summay In this chapte, we stated with the motivation fo FD wieless. We then pesented at the challenges that delayed the development of FD nodes and the technological advancements in ecent yeas that can make handheld FD device a eality vey soon. We gave an oveview of the vaious elaying techniques, elaying potocols, and intoduced two-way in-band FD AF elaying. We also gave a bief intoduction 14

31 to the vaious LSI cancellation techniques available in liteatue followed by the suvey of channel modeling fo the LSI channel. Finally, we povided a bief intoduction to MIMO in elaying systems. In the next chapte, we will pesent the design of ou low-complexity algoithm fo esidual LSI mitigation. 15

32 Chapte 3 Low-Complexity Residual LSI Mitigation 3.1 Intoduction Self-intefeence mitigation is a majo challenge in the pactical adoption of full-duplex elaying systems. In this chapte, we descibe the esidual loopback self-intefeence (LSI) and pesent the poposed low complexity computation of its effect in an in-band full-duplex MIMO two-way elaying system. We employ pecoding and eceive filteing in ode to mitigate the LSI at each of the FD nodes. These pecode and eceive filte matices need to be updated at each time slot to cope up with the dynamic wieless envionment. A two-way FD amplify-and-fowad (AF) MIMO elaying system is studied in [53], wheein the beamfomes at elay and eceive filtes at the tansceives wee jointly designed fo minimizing the sum of mean-squae-eo (SMSE) at the two tansceives. This wok consides only the LSI at the elay but not at the tansceives. Also, some of the pevious woks on full-duplex system design assume that the LSI can be completely emoved. As discussed in the pevious chapte, thee ae two types of self-intefeences in a full-duplex twoway elaying netwok. One aising due a node eceiving its own signal along with the data fom the othe use in the second time slot and the othe aising due to a node s own tansmission being eceived at its eceive in the same time slot. We designated the latte one as the LSI. We assume pefect cancellation of the fist type of self-intefeence due to availability of channel state infomation (CSI) at all the nodes. Also, we assume the available CSI of the loopback channels to be impefect and that the LSI is not completely mitigated, just as in eal wold FD systems. We ae then left with some esidual LSI. The pesence of esidual LSI esults in subsequent degadation in pefomance of a FD two-way elaying system. Mitigation of this esidual LSI at the nodes is the main focus of this thesis. Fo mitigating the esidual LSI at the two tansceives, we employ pecodes at tansceives; wheeas to mitigate the esidual LSI at the AF elay node, we shall employ pecode at the elay and also eceive filtes at the tansceives. In the poposed scheme, we incopoate the esidual LSI in the sum of meansquae-eo (SMSE) of the end-to-end communication and then use the SMSE as a pefomance metic 16

33 to obtain the pecode and eceive filte matices. The pecode design is dependent on the scenaio in which the system is opeating, and is dealt with accoding to the scenaio. The amplify-and-fowad opeation of the FD elay leads to the appeaance of intefeence in a moe complicated way. It amplifies the self-intefeence signal along with othe signals and etansmits them. As a esult, the self-intefeence keeps popagating with time in the system and can eventually build up to hampe the communication itself. We shall call this as the popagating eo tem. As such, it is vey impotant to accuately estimate and eliminate this popagating eo tem. As the name suggests, this eo tem keeps evolving ove time and hence it needs to be estimated continuously. The wok in [53] poposed the computation of this continuously evolving eo tem. Howeve, thei solution was computationally inefficient and does not scale well with time. A sub-pa altenative to compute the eo tem was also poposed by the authos in [53]. The main focus of this chapte is to povide a low complexity solution to estimate this popagating eo tem The est of this chapte is oganized as follows. Section 3.2 descibes the system model and Section 3.3 pesents the iteative estimation of the popagating eo tem. The summay of this chapte is pesented in Section System Model We conside a MIMO FD two-way elaying system shown in Fig. 3.1, which consists of FD tansceives T 1 and T 2, and a MIMO FD AF two-way elay R that assists the communication between T 1 and T 2. The communication between T 1 and T 2 is assumed to occu only via an FD AF elay R due to high path loss in the diect link. The tansceives ae equipped with N T antennas each and the elay has N R antennas of which N T ae used fo signal eception wheeas all the N R antennas ae used fo tansmission (N R N T ). We assume that the channel gain matices H m C N T N T, G m C N T N R, m {1, 2} ae pefectly known wheeas the LSI channel gain matices L i C N T N T, i {1, 2, }, ae impefect such that L i = L i + Ψ i, (3.1) whee L i is the available channel estimate and Ψ i is the coesponding eo with zeo mean and covaiance E{Ψ i Ψ H i } = N T σei 2 I N T. All the channels ae modeled as independent and fequency-flat Rayleigh fading channels that ae static fo a time slot duation and ae assumed to incopoate the fee space path loss between the coesponding nodes. The noise vecto n m, m {1, 2, }, is ciculaly symmetic complex Gaussian with zeo mean and covaiance E{n m n H m} = σnmi 2 NT. The infomation exchange between between tansceives T 1 and T 2 takes two time slots. In the fist time slot, the two tansceives tansmit thei pecoded data towads the elay. In the second time slot, the elay pecodes the data eceived in the fist time slot and etansmits it back to the two tansceives. Also, in the second time slot, each tansceive etieves the data tansmitted by the othe tansceive fom the signal eceived fom the elay. The following events occu duing each time slot t: 17

34 Figue 3.1: System diagam of an FD two-way MIMO elaying netwok. (i) Tansceive T m, m {1, 2} pecodes its symbol vecto s m C N T 1, which has covaiance E{s m s H m} = I NT and is meant fo T m, with pecode matix U m C N T N T and tansmits the esulting vecto x m = U m s m, (3.2) to the elay node R. The combined signal fom the two tansceives at the elay is given by y =H 1 x 1 + H 2 x 2 + L x + n, =H 1 U 1 s 1 + H 2 U 2 s 2 + L x + n, (3.3) whee L x epesents the LSI at the elay node, and n epesents the ciculaly symmetic complex Gaussian with zeo mean and covaiance E{n n H } = σ 2 ni NT. Afte impefect LSI cancellation at R, we get the esultant signal at R, fom (6.1), as ỹ = H 1 U 1 s 1 + H 2 U 2 s 2 + Ψ x + n, (3.4) whee the tem involving Ψ epesents the esidual LSI esulting fom impefect LSI cancellation. (ii) At the AF elay R, the signal eceived in the pevious time slot t 1 is pecoded with matix U C N R N T and fowaded as x = U y (t 1), t 2, (3.5) (iii) Each tansceive eceives the signal tansmitted by the elay R. The eceived signal is given as y m =G m x + L m x m + n m, =G m U y (t 1) + L m x m + n m, =G m U [H (t 1) m U (t 1) m s (t 1) m + H (t 1) m U (t 1) m s (t 1) m + Ψ (t 1) x (t 1) + n (t 1) ] + L m x m + n m, (3.6) whee L m x m epesents the LSI at the tansceive T m, m {1, 2}, and n m epesents the ciculaly symmetic complex Gaussian with zeo mean and covaiance E{n m n H m} = σ 2 nmi NT. Afte impefect LSI cancellation at T m, we get the esultant eceived signal at the tansceives, fom (6.1), as ỹ m = G m U [H (t 1) m U (t 1) m s (t 1) m + H (t 1) m U (t 1) m s (t 1) m + Ψ (t 1) x (t 1) + n (t 1) ] + Ψ m x m + n m, (3.7) 18

35 (iv) Each tansceive also cancels out its own tansmit signal x (t 1) m fom the pevious time slot t 1 and then multiples with eceive filte F m C N N to estimate data ŝ (t 1) m tansmitted by T m as ŝ (t 1) m =F H mỹm =F H m { G m U [H (t 1) m U (t 1) m s (t 1) m + Ψ (t 1) x (t 1) + n (t 1) ] + Ψ m x m + n m }. (3.8) 3.3 Iteative Estimation of the Popagating Eo Tem If we obseve (3.8), it compises two tems that coespond to LSI. The tem Ψ m x m coesponds to esidual LSI due to the tansceive T m s own tansmit signal, wheeas Ψ (t 1) x (t 1) epesents the esidual LSI due to elay R s tansmission. As can be seen fom (3.8), elay s esidual LSI popagates to the tansceives as well. This LSI also continues to build up ove time, which can be explained as follows. Conside (3.5) x =U y (t 1), t 2, { =U H (t 1) 1 x (t 1) 1 + H (t 1) 2 x (t 1) } + n (t 1) 2 + Ψ (t 1) x (t 1) { =U Ψ (t 1) x (t 1) + U H (t 1) 1 x (t 1) 1 + H (t 1) 2 x (t 1) 2 + n (t 1) } (3.9) Let Z (j) = H (j) 1 x(j) 1 + H (j) 2 x(j) 2 + n (j). So (3.9) can we witten as x =U Ψ (t 1) x (t 1) whee we set =U Ψ (t 1) =U Ψ (t 1) =U Ψ (t 1) U Ψ (t 1) { (t 1) =U k=1 U (t 1) U (t 1) U (t 1) + U Z (t 1) { Ψ (t 2) x (t 2) Ψ (t 2) x (t 2) Ψ (t 2) U (t 2) U (t 1) Z (t 2) + U Z (t 1) ( (t 1 k) j=1 Ψ (t j) + Z (t 2)} + U Z (t 1) + U Ψ (t 1) Ψ (t 3) x (t 3) U (t 1) Z (t 2) + U Z (t 1) + U Ψ (t 1) U (t 1) Ψ (t 2) U (t 2) Z (t 3) + ) U (t j) Z (k)}, (3.10) b ( ) = 1, if b < a. i=a A close look at (3.10) will eveal that the cuent tansmit signal of the elay R compises the esidual LSI tems fom t = 2 onwads! This shows how the esidual LSI keeps popagating in a FD two-way AF elaying system. It needs to be estimated accuately to be able to eliminate its effects on the system pefomance. 19

36 Next, we ty to estimate the aveage powe of this LSI tem at the elay. Its significance will be explained in futue chaptes when we design the tansceive and elay pocessing algoithms. Fo now, we shall deive an equation to estimate the aveage powe of the esidual LSI of the elay. Let us conside the aveage powe given by E{ Ψ (t 1) x (t 1) 2 } =E{t(Ψ (t 1) =t(e{ψ (t 1) x (t 1) x (t 1) x (t 1)H Ψ (t 1)H )} x (t 1)H Ψ (t 1)H }). (3.11) Let Ω f = Ψ (t 1) x (t 1) x (t 1)H Ψ (t 1)H. (3.12) Now using (3.10), (3.12) can be witten as Ω f =Ψ (t 1) = U (t 1) U (t 1)H Ψ (t 1)H (t 2) k=1 ( (t 1 k) j=1 [ (t 2) k=1 Ψ (t j) ( (t 2 k) j=1 U (t j) whee we have used the popety that Ψ (t j) )Λ U (t j) )Z (t 1 k) (k)( j=1 (t 2) (k)][ U (k+j)h k=1 ( (t 2 k) j=1 ) Ψ (k+j)h E{Z (i) Λ (k), if i = k. Z (k)h } = 0 N, othewise. Ψ (t j) U (t j) ) Z (k)] H t 3, (3.13) Now, we pesent the Lemma 1 fom [54] and the Theoem 1 fom [53] which ae equied to get a simplified expession fo the aveage powe of LSI at the elay. Lemma: Let K be a n n andom matix with E{KK H } = σ 2 I n 2, and A and B be matices of appopiate dimensions. Then E{t(KAK H B)} = σ 2 t(a)t(b). Poof: E{t(KAK H B)} =E{t(K H BKA)} ( ) =E{vec(K) H vec(bka)}... t(xy) = vec(x H ) H vec(y) ( ) =E{vec(K) H (A T B)vec(K)}... vec(xyd) = (D T X)vec(Y) n ( ) = σ 2 E{(A T B) i,i }... E{KK H } = σ 2 I n 2 i=1 =σ 2 E{t(A T B)} ( =σ 2 E{t(A)}E{t(B)}... ) t(x T Y) = t(x)t(y). 20

37 Theoem: Let K be a n n andom matix with E{KK H } = σ 2 I n 2, and Z be a matix of appopiate dimensions. Then { E t fo v 3. [Z (v)( v 1 K (v j) Z (v j))( v 1 ) ]} Z (j)h K (j)h Z (v)h = σ 2(v 1) j=1 j=1 v t(z (j) Z (j)h ), Poof: This theoem is poved by the pinciple of mathematical induction. The detailed poof is available in [53] { E t { = E t [Z (v)( v 1 K (v j) Z (v j))( v 1 ) ]} Z (j)h K (j)h (v)h Z j=1 [( v 1 j=1 K (v j) Z (v j))( v 1 ) Z (j)h K (j)h Z (v)h Z (v)]} j=1 j=2 j=1 { = E t [K (v 1) Z (v 1)( v 1 K (v j) Z (v j))( v 2 ) Z (j)h K (j)h Z (v 1)H K (v 1)H Z (v)h Z (v)]} = E{t(K (v 1) AK (v 1)H B)} whee, j=1 j=1 A = Z (v 1)( v 1 K (v j) Z (v j))( v 2 ) Z (j)h K (j)h Z (v 1)H, j=2 B = Z (v)h Z (v). Using the afoementioned Lemma, we have { E t [Z (v)( v 1 j=1 j=1 j=1 K (v j) Z (v j))( v 1 ) ]} Z (j)h K (j)h (v)h Z = σ 2 E{t(A)}E{t(B)} = σ 2 E{t (Z (v 1)( v 1 K (v j) Z (v j))( v 2 ) ) Z (j)h K (j)h Z (v 1)H } t(z (v)h Z (v) ) j=2 Repeating the above steps, we have { E t [Z (v)( v 1 { = (σ 2 ) 2 E t j=1 (Z (v 2)( v 1 j=1 j=1 K (v j) Z (v j))( v 1 ) ]} Z (j)h K (j)h (v)h Z K (v j) Z (v j))( v 3 ) )} 2 Z (j)h K (j)h Z (v 2)H t(z (v k+1) Z (v k+1)h ) j=3 j=1 k=1 21

38 { = (σ 2 ) 3 E t { = (σ 2 ) 4 E t.. (Z (v 3)( v 1 K (v j) Z (v j))( v 4 ) )} 3 Z (j)h K (j)h Z (v 3)H t(z (v k+1) Z (v k+1)h ) j=4 (Z (v 4)( v 1 j=1 K (v j) Z (v j))( v 5 ) )} 4 Z (j)h K (j)h Z (v 4)H t(z (v k+1) Z (v k+1)h ) j=5 j=1 { = σ 2(v 2) E t(z (2) K (1) Z (1) Z (1)H K (1)H Z (2)H ) } v 2 v 1 = σ 2(v 1) t(z (1) Z (1)H ) t(z (v k+1) Z (v k+1)h ) k=1 v = σ 2(v 1) t(z (v k+1) Z (v k+1)h ) k=1 v = σ 2(v 1) t(z (k) Z (k)h ) k=1 k=1 k=1 t(z (v k+1) Z (v k+1)h ) Using the above Theoem, we can expess the aveage powe of LSI at the elay as t 2 ( Ω AF E{Ω f } = (σe) 2 k t k=1 U (t k) k=1 Λ (t k 1) U (t k) H ) k 1 I NT l=1 ( t U (t l) U (t l) H ) t 3. (3.14) We shall see in futue chaptes that the vaiable Ω AF plays a pivotal ole in the design of pecodes and eceive filtes at the tansceives and the elay, which in tun ae equied to mitigate the esidual LSI at the nodes. Hence, accuate estimation of Ω AF is necessay. Howeve, a close examination of (3.14) eveals that the cuent fom of Ω AF is highly inefficient in tems of the computational complexity and also the memoy equiements. Using (3.14), the cuent value of Ω AF depends on all the pevious matices stating fom t = 3 onwads. This makes the computation of Ω AF highly inefficient as the system evolves ove time. Memoy management fo such a computation is infeasible ove time. An altenative method to compute Ω AF was poposed in [53] whee only the n latest time slot values of Ω (j) AF wee used to compute Ω AF. This method is computationally efficient but that efficiency is achieved at the expense of accuacy in estimating Ω AF. Now, let us ty to detemine if we can do bette in tems of both computational efficiency as well as accuacy. Conside (3.14) at vaious time slots Ω (3) AF =σ2 et(u (2) Λ (1) U (2) H ), Ω (4) AF =σ2 et(u (3) Λ (2) U (3) H ) + (σ 2 e ) 2 t(u (2) Λ (1) U (2) H )t(u (3) Ω (5) AF =σ2 et(u (4) Λ (3) U (4) H ) + (σ 2 e ) 2 t(u (3) Λ (2) U (3) H )t(u (4) (σe) 2 3 t(u (2) Λ (1) U (2) H )t(u (4) U (4) H )t(u (3) U (3) H ), U (3) U (4) H ), H )+ 22

39 Ω (6) AF =σ2 et(u (5) Λ (4) U (5) H ) + (σ 2 e ) 2 t(u (4) Λ (3) U (4) H )t(u (5) U (5) H )+ (σe) 2 3 t(u (3) Λ (2) U (3) H )t(u (5) U (5) H )t(u (4) U (4) H )+ (σe) 2 4 t(u (2) Λ (1) U (2) H )t(u (5) U (5) H )t(u (4) U (4) H )t(u (3) U (3) H ),.. Ω (8) AF =σ2 et(u (7) Λ (6) U (7) H ) + (σ 2 e ) 2 t(u (6) Λ (5) U (6) H )t(u (7) U (7) H )+ (σe) 2 3 t(u (5) Λ (4) U (5) H )t(u (7) U (7) H )t(u (6) U (6) H )+, (σe) 2 4 t(u (4) Λ (3) U (4) H )t(u (7) U (7) H )t(u (6) U (6) H )t(u (5) U (5) H )+, (σe) 2 5 t(u (3) Λ (2) U (3) H )t(u (7) U (7) H )t(u (6) U (6) H )t(u (5) U (5) H )t(u (4) (σe) 2 6 t(u (2) Λ (1) U (2) H )t(u (7) U (7) H )t(u (6) U (6) H )t(u (5) U (5) H )t(u (4) t(u (3) H ),.. and so on... U (3) U (4) U (4) H )+, H ) (3.15) The equations in (3.15) exhibit ecuing pattens which can be exploited to ewite these equations moe effectively in a ecusive fom as follows: Ω (4) AF =σ2 e[t(u (3) Λ (2) U (3) H (3) ) + Ω AF t(u(3) Ω (5) AF =σ2 e[t(u (4) Λ (3) U (4) H (4) ) + Ω AF t(u(4).. Ω (8) AF =σ2 e[t(u (7).. Ω (t) AF =σ2 e[t(u (t 1) Λ (6) U (7) Λ (t 2) U (t 1) H ) + Ω (7) AF t(u(7) U (3) U (4) U (7) H )IN + Ω (t 1) AF H )], H )], H )], t(u(t 1) U (t 1) H )]. (3.16) The final equation in (3.16) epesents the iteative expession fo Ω AF. With this expession, the cuent value of the tem Ω AF only depends on its pevious value Ω (t) AF and a few othe matices. This ensues that the computation time as well as the memoy equiement fo estimating Ω AF is minimal. Also as compaed to the altenative solution in [53], expession (3.16) would pefom bette since it incopoates the effect of all the pevious Ω (j) AF stating fom t = 3 onwads! The compaison of the computational complexity of the algoithm in [53] with ou poposed iteative algoithm is shown in 3.1. It compaes the numbe of addition and multiplication opeations equied to 23

40 Refeence algoithm Poposed algoithm iteative No. of Additions No. of Multiplications 1 2 (t 1)(2 + t + t N ) (t 1)(t + 4) 3 + 2N 8 Table 3.1: Computational complexity of Λ (t) z. compute Ω AF at the cuent time slot t. As can be seen fom the table, the complexity to compute Ω AF in [53] inceases exponentially with time, while it is independent of time with ou iteative appoach. 3.4 Summay In this chapte, we intoduced the issue of esidual LSI at the FD nodes in a two-way FD MIMO elaying system. We consideed the poblem of esidual LSI mitigation at the elay node and deived an expession to estimate the aveage powe of this esidual LSI. We obseved that this expession fo computing the estimate was highly inefficient in tems of the computational complexity and memoy equiements. We then analyzed this expession and pesented an iteative expession fo computing the estimate of the aveage powe of the esidual LSI at the elay. The effectiveness of the poposed expession was demonstated by the computational complexity compaisons. Next chapte onwads, we shall pesent the designs of pecodes and eceive filtes fo a two-way FD MIMO elaying system fo diffeent opeating scenaios. We shall use ou iteative expession to design these matices. 24

41 Chapte 4 Full-Duplex Two-Way Relaying in a Cognitive Netwok 4.1 Intoduction The communicating nodes in wieless communications utilize a fequency band. This fequency band is usually allocated to the nodes in advance befoe beginning the communication. These nodes ae temed as the pimay uses (PUs) since they ae licensed to utilize the fequency band duing the couse of thei communication. Taditionally, only the PUs wee allowed to use thei allocated fequency band so that they didn t intefee, o eceive intefeence fom, othe nodes pesent in thei vicinity. Howeve, thee is a majo dawback with this scheme. Using spectum sensing techniques, it was ealized that the PUs do not utilize the allocated spectum at all times leading to wastage of the pecious spectum. Cognitive adio is a technology which is useful in such a scenaio. In an undelay cognitive adio netwok, multiple unlicensed uses, temed as the seconday uses (SUs), shae the spectum with a licensed pimay use (PU). The SUs can eithe tansmit when the PU is inactive o even when the PU is tansmitting. In the latte case, the SUs need to opeate unde a tansmit powe constaint in ode to limit the intefeence to the PU. In this case, we achieve bette spectal efficiency since both the PU and the SUs ae utilizing the spectum, but unde stict tansmit powe constaints. We conside such a scenaio in this chapte. In such a scenaio, FD two-way elaying, having bette efficiency than one-way elaying, will be beneficial to enhance the ange as well as the ate of communication. In [55], an FD MIMO cognitive cellula system was studied whee only the elay station opeates in FD. The authos pesented an MMSE-based obust tansceive design fo this system. A elaying netwok with multiple elays is moe obust to channel outages than a single elay netwok. In such a scenaio, elay selection, wheein only one elay is selected, enhances the system pefomance while having low complexity [56]. Most of the pevious woks on elay selection fo a two-way FD AF elaying netwok, including [57, 58], conside the outage pobability, symbol eo pobability, aveage channel capacity, and/o the outage capacity as the citeia fo optimal elay selection. To the best of ou knowledge, thee is no pevious wok which consides the poblem of elay selection and esidual LSI mitigation fo a cognitive two-way FD AF MIMO elaying netwok. In the pevious chapte, we deived an expession to compute the estimate of the aveage powe of popagating 25

42 esidual LSI tem at the full-duplex AF elay. In this chapte, we shall use that expession to design the pecodes and eceive filtes fo a two-way AF full-duplex MIMO elaying netwok in a cognitive adio envionment. We begin by designing the tansceive pecodes fo the SUs and addessing the optimal elay selection poblem. We then conside the design of elay pecode and tansceive eceive filtes to mitigate the esidual LSI at the nodes. We evaluate the pefomance of the poposed designs in a LTE cellula cognitive netwok scenaio. The est of this chapte is oganized as follows. Section 4.2 descibes the system model. The poblems of pecode design fo SUs, and optimal seconday elay (SR) selection ae consideed in Section 4.3. The design of SR pecode and SU eceive filte is discussed in Section 4.4. Simulation esults ae pesented in Section 4.5 and the conclusions ae dawn in Section System Model The cognitive FD two-way elaying netwok shown in Fig. 4.1 consists of a PU, two seconday tansceives T 1 and T 2, and M seconday AF elays. Tansceives T 1 and T 2, and PU have N T antennas each. Each SR has N R antennas, out of which N T ae eceiving antennas while all N R ae tansmitting antennas, such that N R N T. All the nodes in the netwok tansmit and eceive simultaneously in the same fequency band which is allocated to the licensed PU. We assume that thee is no diect communication link between the SUs due to high path loss and so they communicate only via the optimally selected SR. The matix H ij epesents the MIMO channel matix between tansmitte i and eceive j. So, H k C N T N T, H k C N T N R, H lp C N T N T and H pl C N T N T, k {1, 2, p}, l {1, 2}, epesent the MIMO channels as shown in Fig. 1. All the channel links ae modeled as independent and fequency-flat Rayleigh fading channels and ae assumed to be static fo one time slot. The channel state infomation (CSI) fo these channels is assumed to be pefectly known. The matices L C N T N R and L k C N T N T, k {1, 2, p}, epesent the LSI MIMO channels. As in the pevious chapte, we assume the available CSI fo the loopback channels to be impefect, such that L l = L l + Ψ l, l = 1, 2, p,, (4.1) whee L l is the available channel estimate and Ψ l is the eo in the CSI with zeo mean and covaiance E{Ψ l Ψ H l } = N T σej 2 I N T. The symbol α ij epesents the path loss between nodes i and j; i, j {1, 2, p, }, such that α ij = α ji. We conside the loopback path loss α ii = 1 and it won t be explicitly mentioned hencefoth. The following events occu duing each time slot t: (i) The PU tansmits signal x p C NT 1. Since all nodes opeate on the same fequency, x p will cause intefeence at the seconday nodes. (ii) Based on the knowledge of tansceive - elay channels, an optimal elay is selected by the cental contol unit and notified to the SUs using contol channels. 26

43 Figue 4.1: System diagam of a cognitive FD two-way elaying netwok with M cognitive elays. (iii) Each of the SUs pecodes symbol vecto s m C N T 1, having covaiance E{s m s H m} = I NT, with matix U m C N T N T and tansmits x m, m {1, 2} towads the selected elay. Using (4.1), the signal at the optimal SR afte impefect LSI cancellation can be expessed as y = α 1 H 1 U 1 s 1 + α 2 H 2 U 2 s 2 + Ψ x + α p H p x p + n, (4.2) whee the noise n is a ciculaly symmetic complex Gaussian andom vecto with zeo mean and covaiance E{n n H } = σ 2 ni NT. The thid tem in (4.2) efes to the esidual LSI due to impefect LSI cancellation as modeled in (4.1). (iv) The selected SR pecodes the signal eceived in the pevious time slot, y (t 1), using the pecoding matix U C N R N T and tansmits the esulting signal x = U y (t 1), t 2. (4.3) 27

44 (v) Each of the SUs eceives signals fom the selected SR and PU. Afte canceling its tansmitted signal and impefect loopback SI cancellation using (6.1), we have y m = α m H m U { α m H (t 1) m U (t 1) m s (t 1) m + n (t 1) + Ψ (t 1) x (t 1) } + Ψ m U m s m + α pm H pm x p + n m, m = 1, 2, (4.4) whee noise n m is a ciculaly symmetic complex Gaussian andom vecto with zeo mean and covaiance E{n m n H m} = σnmi 2 NT. The esidual LSI is epesented by the tems containing Ψ m, Ψ. The estimate of the data tansmitted by the othe seconday use, ŝ m, is obtained by applying a eceive filte F m C N T N T to y m, (vi) The signals tansmitted by the selected SR and the SUs cause intefeence at the PU given as I p = I 1 + I 2 + I, (4.5) whee I k = α kp t(h kp x k x H k HH kp ), k = 1, 2,. (4.6) The end-to-end communication equies two time slots. 4.3 Design of Optimal Tansceive Pecodes and Relay Selection In this section, we pesent the design of the tansceive pecodes U 1 and U 2, and the optimal selection of the SR, both of which ae done in the fist time slot of end-to-end communication Tansceive Pecode Design The aims of designing pecodes fo SUs ae: (i) to nullify the effect of the SU SR channel link, and (ii) to limit the intefeence to the PU below a theshold. To addess the fist sub-poblem, we do the QR-decomposition of the Hemitian of the channel matix H k as: H H k = Q kr k, whee Q k is an othogonal matix, and R k is an uppe tiangula matix. The pecode matices ae given by U k = µ k Q k V k, k = 1, 2. (4.7) and the coesponding tansmit powe is given as P k = E{ U k s k 2 } = µ 2 k t(v kvk H ), k = 1, 2, (4.8) 28

45 whee, the scaling facto µ k will be deived in the sequel. To undestand how the matix V k is obtained, conside the following H k U k = µ k H k Q k V k = µ k (H H k )H Q k V k = µ k (Q k R k ) H Q k V k = µ k R H k (QH k Q k)v k = µ k R H k I N T V k = µ k R H k V k So, the matix V k is given by (R H k ) 1 so that H k U k = µ k I NT. (4.9) Since R H k too. is a lowe tiangula matix, computation of its invese is simple and computationally efficient Optimal Relay Selection Optimal elay selection aims at selecting the SR that esults in the eceive signal-to-noise atio (SNR) at the SU, such that the total intefeence to PU fom the SUs and the selected SR is below the intefeence limit, θ. Apat fom the tansceive-elay channel conditions, the two main factos that affect the elay selection pocess ae: (i) the distance of the SR fom SU and PU, and (ii) the theshold θ. The cental contol unit (CU) has pefect knowledge of CSI fo all the M tansceive-elay channel links. Fo each such link, the CU selects optimal scaling factos µ k, k {1, 2} such that they maximize the eceive SNR at the coesponding SR while keeping the total intefeence powe, I p, at the PU below θ. The CU then selects the SR having the highest SNR and notifies it to SUs using the contol channel. Fo a given intefeence theshold θ, the intefeence constaint is given by Using (4.5), (4.6), (4.7), (4.8), (4.9), we expess (4.10) as I p θ. (4.10) θ α 1p H 1p x α 2p H 2p x α p H p x 2 = α 1p µ 2 1d 1 + α 2p µ 2 2d 2 + α p p H p 2 F, (4.11) whee d k = t(h kp Q k V k V H k QH k HH kp ), k {1, 2}, E{x x H } = p I NT, and p is the powe tansmitted by each antenna of the SR. We pove in next section that the SR always tansmits at maximum powe, such that p = P max /N R = p max. (4.12) 29

46 As a consequence, equation (4.11) can be expessed as α 1p µ 2 1d 1 + α 2p µ 2 2d 2 θ α p p max H p 2 F = θ. (4.13) Since the SR will always tansmit at the maximum powe, we can only optimize the tansmit powe of the SUs to limit I p. Hence, we choose SNR at the SR, which is dependent on the tansmit powes P 1, P 2, as the function to be maximized. Fom (4.2), (4.9), the SNR at the i th SR is SNR Ri = α 1 i µ 2 1 i N T + α 2i µ 2 2 i N T σ 2 n i N T, i = 1, 2,.., M, (4.14) whee µ ji, j {1, 2}, is the scaling facto fo i th SU SR channel. Fom (4.14), we obseve that maximizing the SNR at SR is same as maximizing the signal powe, fo a given noise powe. We assume the noise powe at all elays to be the same without loss of geneality. So, to obtain the optimal µ 1, µ 2, SR, we fomulate the following optimization poblem: max k I,µ 2 1 k,µ 2 2 k α 1k µ 2 1 k + α 2k µ 2 2 k subject to α 1p µ 2 1 k d 1 + α 2p µ 2 2 k d 2 θ P min m P m P max m, m = 1, 2. (4.15) whee I is the set of elay indices. This is a joint optimization poblem ove elay indices and scaling factos. As such it is a mixed-intege pogam and had to solve. Howeve, since only one elay will opeate at any given time, this optimization can be pefomed in two steps; fist ove the scaling factos µ 2 1 k, µ 2 2 k and then ove the elay indices as max k 1,2,...,M max µ 2 1 k,µ 2 2 k α 1k µ 2 1 k + α 2k µ 2 2 k subject to α 1p µ 2 1 k d 1 + α 2p µ 2 2 k d 2 θ P min m We begin with the inne optimization poblem given by max µ 2 1 k,µ 2 2 k α 1k µ 2 1 k + α 2k µ 2 2 k P m P max m, m = 1, 2. subject to α 1p µ 2 1 k d 1 + α 2p µ 2 2 k d 2 θ P min m P m P max m, m = 1, 2. (4.16) (4.17) The optimization poblem in (4.17) is a linea optimization poblem in µ 2 1 k, µ 2 2 k and can be solved by a optimization tool such as linpog in MATLAB. The optimal values thus obtained ae µ 2 1 k, µ 2 2 k. We now poceed to the poblem of optimal SR selection. The optimization poblem can be fomulated as k = agmax k I α 1k µ 2 1 k + α 2k µ 2 2 k, (4.18) 30

47 whee the function to be maximized is the signal powe with optimal scaling factos µ 2 1 k, µ 2 2 k. Denoting the scaling factos coesponding to the optimal SR as µ 1, µ 2, the infomation conveyed to the SUs is (k, µ 1, µ 2 ). The SUs then tansmit thei data to the optimal SR in the fist time slot itself using the data channel. The coesponding optimal pecode matices and tansmit powes ae given by (4.7), (4.8), espectively. 4.4 Design of Seconday Relay Pecode and Tansceive Receive Filtes In the second time slot of communication, the selected SR pecodes the signal eceived fom the SUs with U and fowads it, fom which the SUs extact the equied data using eceive filtes F 1 and F 2. Hencefoth, we will denote the optimal scaling factos as simply µ 1, µ 2. Due to the FD mode of opeation, the AF elay eceives its own signal as LSI, epesented by Ψ x in (4.2). This LSI also gets popagated to the SUs as Ψ (t 1) x (t 1) in (4.4) and keeps accumulating ove time. To mitigate it, we design pecode U and eceive filtes F 1, F 2 by minimizing the SMSE of end-to-end communication, with a constaint on the tansmit powe of SR. To obtain closed fom solution, matix U is decomposed as U = βu, whee β is a positive scaling facto and U F = 1. Fo the same eason, tem β 1 is intoduced in (4.20). The following optimization poblem gives the optimal design: min β,u,f 1,F 2 subject to SMSE E{ x 2 } P max, (4.19) whee the SMSE can be expessed in tems of the optimization vaiables β, U, F 1 and F 2 Fo convenience we ll denote (α 1 µ 2(j) 1 +α 2 µ 2(j) 2 +σn)i 2 NT +α p p (j) p H (j) p H (j)h p by Λ (j) thoughout this chapte, whee p p is the pe antenna tansmit powe at the PU. The SMSE of the two tansceives is given by SMSE = = 2 i=1 2 i=1 E{ s (t 1) i β 1 ŝ i 2 } E{ s (t 1) i 2 } + β 2 E{ F H i y i 2 } β 1 [t(e{f H i y i s (t 1)H i }) + t(e{s (t 1) i yi H F i })]. (4.20) We now expess each tem of SMSE equation in tems of the elevant optimization vaiables. Thus, we have E{s (t 1) i yi H F i } = µ (t 1) i αi α i t(u H H H i F i ), E{ s (t 1) i 2 } = N T. (4.21) 31

48 Futhe, using (4.4) and (4.9), we have E{ F H i y i 2 } =α i t[f H i H i U (E{Ω f } + α i µ (t 1)2 i I NT + σni 2 NT + α p p (t 1) p H (t 1) p H (t 1)H p )U H H H i F i ] + σnit(f 2 i F H i ) + E{ F H i Ψ i U i s i 2 F + α pi p p F H i H pi 2 F, i = 1, 2, (4.22) whee, E{Ω f } is the aveage powe of the LSI tem at the elay. We defined this aveage powe as Ω AF in Chapte 3, whee we deived a ecusive equation to compute Ω AF which is expessed as Ω (t) AF E{Ω f } =σe[t(u 2 (t 1) Λ (t 2) U (t 1) H )INT + Ω (t 1) AF t(u(t 1) U (t 1) H )]. (4.23) Due to the ecusive stuctue of Ω AF, the nodes need not stoe all the pevious elay pecode matices, but only U (t 1) to compute U. This geatly educes the memoy equiement at the elay and also esults in low complexity and educed computation time fo Ω AF. Moeove, the pecode designed using (4.23) will lead to bette pefomance than that poposed in [53] whee only the n latest time slots ae used fo computing Ω AF. Again, using the Lemma fom Chapte 3 and (4.8), we can expess Using (4.2), (4.3), (4.9), we expess elay s tansmit powe as E{ F H i Ψ i U i s i 2 F = σ2 eip i t(f i F H i ). (4.24) E{ x 2 } = t[u (Ω AF + Λ (t 2) )U H ] = t(u B U H ), (4.25) Having expessed the tems of SMSE and elay tansmit powe in tems of the optimization vaiables, we now tun to the solution of the poblem in (4.19). The Lagangian coesponding to this poblem is given by L(β, U, F 1, F 2, λ) =f(β, U, F 1, F 2 ) + λ[q 2 + E{ x 2 } P max ], (4.26) whee λ is the lagangian vaiable and q is the slack vaiable. On substituting the esults of (4.20), (4.21), (4.22), (4.25), (4.23),(4.24) in (4.26) and putting U = βu, we get L = 2 i=1 {N T + β 2 (σ 2 ni + σ 2 eip i )t(f i F H i ) µ (t 1) i αi α i t(f H i H i U + U H H H i F i )+ α pi p p F H i H pi 2 F + α it(f H i H i U B i U H H H i F i )} + λ[q 2 + β 2 t(u B U H ) P max ], (4.27) whee B i = Λ f + (α i µ (t 1)2 i + σ 2 n)i NT + α p p (t 1) p H (t 1) p H (t 1)H p. The optimization poblem in (4.27) can be solved using the Kaush-Kuhn-Tucke (KKT) conditions [59]. Since the SMSE function is not jointly convex in the optimization vaiables, we use the coodinate 32

49 descent method. Thus, the optimal values of U, F i, i {1, 2}, ae obtained iteatively. Fist, keeping F i fixed, we apply the KKT conditions as follows whee L β =0 λβt(u B U H ) = β 3 (c 1 + c 2 ), (4.28) L =0 NR N T λβ 2 U B + α 1 H H 1F 1 F H 1 H 1 U B 1 + α 2 H H 2F 2 F H 2 H 2 U B 2 U L λ =0 L q =0 = α 1 α 2 (µ (t 1) 1 H H 2F 2 + µ (t 1) 2 H H 1F 1 ), (4.29) t(u B U H ) = β 2 (P max q 2 ). (4.30) λ[β2 t(u B U H ) P max ] = 0, (4.31) c i = (σ 2 ni + σ 2 eip i )t(f i F H i ). Fom (4.28), (4.31), we obseve that at the optimal point, λ 0. So, the constaint in (4.19) becomes equality, i.e., the SR tansmits at full powe P max. So, (4.30) becomes: t(u B U H ) = β 2 (P max ). (4.32) Fom (4.28), (4.32), we get: λβ 2 = (c 1+c 2 ) P. Substituting this in (4.29) and following Theoem 2 of max [53], we get U opt β opt = = mat ([ 2 (B T k α kh H k F kf H k H k) + (B T (c 1 + c 2 ) I NR ) ] 1 k=1 α1 α 2 vec [ 2 P max t(u opt k=1 B U H ). µ (t 1) k H H k F k]), Theefoe, optimal elay pecode is given by U opt = β opt U opt L compute optimal eceive filtes by applying the KKT condition: F c i the optimal eceive filte as F opt i =[c i I NT + α i H i U opt B i U H P max. Now, using the optimal U opt, we = 0 NT, i {1, 2}, which gives H H i ] 1 β opt α 1 α 2 µ (t 1) i H i U opt. It must be noted that the optimal matices U opt, F opt 1 and F opt 2 ae obtained by iteatively computing each othe s filte until the SMSE conveges. The initial value of F i fo computing U can be any andom N T N T matix. The sum-ate fo the designed system is 2 R = E{log 2 I NT + SINR m } m=1 (bits/sec/hz), 33

50 whee, with, SINR m =[α 1 α 2 µ (t 1)2 m F H mh m U U H H H mf m ][F H m(σnmi 2 NT + α m σnh 2 m U U H H H m+ µ 2 mψ m Q m V m V H mq H mψ H m + α 1p p p H p1 H H p1 + α 1 α p p p H m U H p H H pu H H H m+ α m H m U Λ z U H H H m)f m ] 1, m = 1, 2, Λ z =Ψ (t 1) Simila to Ω AF, Λ z = 0 Ns fo t < 3. U (t 1) (Λ (t 2) + Λ (t 1) z )U (t 1)H Ψ (t 1)H. 4.5 Simulation Results We conside the following values fo the paametes in the simulations: N T = 2, N R = 4, M = 3 elays, p max = 1, Pk min = 0.6, Pk max = 2, k {1, 2}. We conside the path loss as defined by the 3GPP LTE fo outdoo maco cells [60], viz., α = log 10 (d ij ) db, (4.33) 3 Relay selected θ (dbm) Figue 4.2: Relay selection fo vaying values of intefeence theshold θ. whee d ij is the distance between nodes i and j, in metes, at 2 GHz fequency. Unless othewise specified, we conside the sepaation, in metes, between the nodes to be as follows: d 1R1 = 800, d 1R2 = 1600, d 1R3 = 1000, d 1p = 1400, d 2R1 = 900, d 2R2 = 750, d 2R3 = 650, d 2p = 1400, d pr1 = 850, d pr2 = 700, d pr3 = The distances wee selected andomly. The coesponding path loss is given by (4.33). We assume all the channel matices and channel estimation eo matices to follow Rayleigh fading and thei elements to be independent and identically distibuted complex Gaussian andom vaiables, each with zeo mean and unit vaiance. We aveaged the esults of 1000 Monte Calo simulations to aive at each of the following esults. 34

51 Tansmit powe P 1 (W) d 1 =1000, d 2 =650, d p =1200 d 1p =900, d 2p =1300 d 1p =700, d 2p = θ (dbm) Figue 4.3: Vaiation of tansmit powe vesus θ fo diffeent values of path loss. Fig. 4.2 shows the esult fo simulating optimal SR selection pocess fo the afoementioned sepaation values. It shows the elay selected fo vaying values of intefeence theshold θ. We obseve thee distinct ange of θ values fo which a paticula elay is selected. Fo example, elay 1 is selected fo θ = -45dBm o highe. Fig. 2(a) clealy signifies the effect of θ and sepaation between nodes on optimal SR selection pocess. Fig. 4.3 shows the vaiation in tansmit powe of the tansceive 1 vesus θ fo two sets of sepaation values of d 1p, d 2p, which coespond to path loss given by (4.33). As seen, the tansmit powe of tansceive vaies fom P min 1 to P max 1 as θ vaies fom -105 dbm to -80 dbm. As expected, the tansceive tansmits moe powe when the intefeence toleance limit of the PU inceases. 3.5 SMSE θ = -92dBm INR=0.1 INR=0.5 INR=1.0 INR= Numbe of iteations Figue 4.4: Numbe of iteations equied to obtain optimal U, F, fo diffeent values of INR, fo θ = -92 dbm and SNR = 5 db. 35

52 The pactical feasibility of the poposed algoithm fo U and F m, m {1, 2}, design is depicted by the esult in Fig It shows the numbe of iteations equied to obtain the optimal value of U, F m, at SNR = 5 db, fo vaying INR and θ = -92 dbm. The optimal matices ae obtained when the SMSE conveges. We obseve that beginning with any andom 2x2 matix F m, the SMSE conveges afte 6 iteations fo all the INR values. 3 SMSE 2.5 θ = -92dBm INR=0.1 INR=0.5 INR=1.0 INR= time slots Figue 4.5: Vaiation of SMSE ove time, fo diffeent values of INR, at θ = -92 dbm and SNR = 10 db. Fig. 4.5 exhibits the significance of the effect of feedback tem Ω AF, on the pefomance of the system ove time. It shows the vaiation of SMSE, fo diffeent INR values, with θ = -92 dbm. As seen, the SMSE begins to stabilize fom 3 th time slot due to the effect of feedback tem Ω AF, which stats fom t = 3. SMSE INR / θ 0.1/-92dBm 1.0/-92dBm 0.1/-97dBm 1.0/-97dBm SNR (db) Figue 4.6: SMSE vesus SNR fo diffeent values of INR and θ. 36

53 SUM-RATE (bits/sec/hz) INR / θ 0.1/-92dBm 1.0/-92dBm 0.1/-97dBm 1.0/-97dBm SNR (db) Figue 4.7: Sum-ate vesus SNR fo diffeent values of INR and θ. Fig. 4.6 and Fig. 4.7 illustate the SMSE and sum-ate pefomance of the designed system, espectively vesus SNR fo diffeent INR and θ. The poposed designs demonstate good pefomance at low INR with the pefomance degading slightly as INR inceases. This signifies the need fo pecoding with multiple antennas to suppess esidual LSI. Also, it can be obseved fom these figues that the pefomance at high SNR is bounded by the intefeence theshold θ. This is because θ contols the tansmit powe of tansceives as seen in Fig Summay In this chapte, we consideed a cognitive full-duplex two-way elaying netwok with multiple elays. We pesented an optimal elay selection scheme based on SNR maximization at the elay, while limiting the intefeence to the pimay use. The pecodes at the seconday tansceives wee designed to nullify the effect of the tansceive-elay channel link. To account fo the pepetuating esidual selfintefeence caused by AF opeation of the FD elay, we poposed the design of optimal elay pecode and tansceive eceive filtes. These matices wee obtained by SMSE minimization of end-to-end communication. An iteative technique having low computational complexity, low memoy equiement fo computing the feedback tem was pesented. The simulation esults validated the pactical feasibility of the poposed algoithms. The esults also veified, in a cognitive adio envionment, that the SMSE and sum-ate pefomance of the system ae capped by the intefeence theshold of the pimay use. 37

54 Chapte 5 Design and Analysis of a Secue Full-Duplex Two-Way Relaying System 5.1 Intoduction In the pevious chapte, we consideed the poblem of elay selection and tansceive design in a cognitive adio envionment. We analyzed the pefomance of ou poposed pecode and eceive filte designs and concluded that thei pefomance is uppe bounded by the intefeence theshold of the pimay use. In this chapte, we shall conside the design of tansceive and elay pocessing algoithms in the pesence of a passive eavesdoppe. Also, we shall analyze the inheent physical laye secuity povided by a two-way FD elaying netwok. Owing to the boadcast natue of wieless communication, wieless netwoks ae always pone to eavesdopping. With the eve inceasing adoption of wieless netwoks fo pesonal and official puposes, the issues of secuity and pivacy in wieless netwoks have become pivotal. Secuity in communication netwoks has been taditionally consideed to be taken cae of by cyptogaphic techniques implemented above the physical laye of the OSI model. Advanced Encyption Standad (AES) is one of the most fequently used and most secue encyption algoithms available today. Howeve, the ole of physical laye in encyption was not studied well until ecently [61]. Physical laye secuity employs channel coding techniques that take advantage of the andomness of the wieless channels to secue the data tansmission fom an unwanted eavesdoppe pesent in the vicinity of the intended eceive. A ich scatteing envionment is assumed so that the eavesdoppe and the intended eceive will have distinct channels. Such a scenaio involving secue communication between two legitimate nodes in the pesence of an eavesdoppe was intoduced in [62] as a wietap channel. The aim of physical laye secuity is to pevent the eavesdoppe fom decoding the data of the legitimate uses. The pefomance of physical laye secuity is chaacteized in tems of sececy ate, which is the diffeence between the data ate fom tansceive to legitimate destination and tansceive to eavesdoppe. In [63], a secue tansmission scheme fo a HD two-way elaying MIMO system based on diection otation alignment is poposed. Hee, the otation matix is designed based on the the singula value decomposition of the uplink channel matix. Eavesdopping in the downlink has been ignoed in this wok. In [64], a secue one-way elaying FD system has been studied fom a physical laye secuity pespective wheein, the 38

55 FD elay simultaneously eceives data fom the souce and sends jamming signals to the eavesdoppes. Hee, sececy is achieved at the expense of eduction in data ate, while implementing physical laye secuity, and having data ate same as that of a half-duplex (HD) system. In [65], a two-way FD amplifyand-fowad (AF) elaying system is consideed with MIMO elay, legitimate tansceives and a passive eavesdoppe with single antenna. Hee the elay does two sepaate tasks, viz., geneating beamfoming matix fo legitimate channel and geneating atificial noise (AN) fo the eavesdoppe. Hee, sececy is achieved at the cost of eduction in data ate. To the best of ou knowledge, thee is no pevious wok which consides the poblem of esidual LSI mitigation simultaneously at the tansceives and at the elay in the pesence of an eavesdoppe. The FD opeation of a two-way AF elaying system makes it inheently secue due to the pesence of multiple signals combined on the same fequency. This makes it difficult fo the eavesdoppe to extact a signal fom a paticula use. Howeve, this inheent sececy has not been analyzed yet in liteatue. In this chapte, we mainly addess these two poblems. Conside a two-way in-band FD AF MIMO elaying system with two tansceives, one eavesdoppe, and one elay. Pecoding with multiple antennas is necessay fo suppessing the dominant LSI at the nodes. Fist, we jointly design the tansmit pecode at the elay and the eceive filtes at the tansceives by minimizing the SMSE at the tansceives. The poblem is non-convex and is solved by coodinate descent method. Next, we design tansmit pecode at the tansceives by a QR-decomposition of the fowad tansceive-elay channel. Finally, we eview the physical laye secuity aspect of the poposed design in tems of the achievable sum-sececy-ate as defined in [65]. 5.2 System Model As shown in Fig. 5.1, the system compises two FD tansceives T 1 and T 2, each equipped with N T antennas, an eavesdoppe E with N E antennas, and a FD AF elay R with N R antennas, of which N T ae used as eceives while all N R antennas ae used as tansmittes, such that N R N T. Node E is a passive eavesdoppe. We assume that thee is no diect link between the nodes T 1 and T 2. The matices H m C N T N T, G m C N T N R, K m C N E N T, K C N E N R, m {1, 2}, epesent the MIMO channel gains as shown in Fig These matices ae assumed to be pefectly known. The matices L C N T N R, L m C N T N T, m {1, 2}, epesent the LSI MIMO channel gains. We assume that the available channel state infomation (CSI) of the loopback channels is impefect such that L j = L J + Ψ j, j = 1, 2,, (5.1) whee L j is the available estimate and Ψ j is the CSI eo with zeo mean and covaiance E{Ψ j Ψ H j } = N T σ 2 ej I N T. All the above channel links ae modeled as independent and fequency-flat Rayleigh fading channels assumed to be static fo the duation of a time slot. The vecto n k, k {1, 2,, e} epesents a ciculaly symmetic complex Gaussian andom noise vecto with zeo mean and covaiance E{n m n H m} = σ 2 nmi NT, k {1, 2, }, E{n e n H e } = σ 2 nei NE. The symbol α i epesents path loss fo 39

56 Figue 5.1: System diagam of secue full-duplex two-way elaying system. S i R link. i {1, 2}, while α 3, α 4, α 5 epesent path loss fo S 1 E, R E, S 2 E links, espectively. We assume unity pathloss fo loopback channels. The following events occu duing each time slot t : (i) Each tansceive pecodes data vecto d m C Ns 1 of covaiance E{d m d H m} = I NT with pecoding matix U m C N T N T to geneate x m, m {1, 2}, and tansmits it to the elay node. The signal at the elay afte impefect LSI cancellation is given by ỹ = α 1 H 1 U 1 d 1 + α 2 H 2 U 2 d 2 + Ψ x + n. (5.2) Since the available loopback CSI is eoneous as modeled in (5.1), pefect LSI cancellation is not possible and the consequent esidual LSI is given by the thid tem in (5.2). (ii) The elay pecodes the signal eceived in the pevious time slot, y (t 1), using matix U C N R N T and tansmits signal x = U ỹ (t 1), t 2. (5.3) (iii) Each tansceive eceives elay s tansmit signal. Afte canceling out its own signal and also impefect LSI cancellation, we get ỹ m = α m G m U [ α m H (t 1) m U (t 1) m d (t 1) m + Ψ (t 1) x (t 1) + n (t 1) ] + Ψ m x m + n m. (5.4) The esidual LSI is given by the tems containing Ψ and Ψ m. Each tansceive then applies a eceive filte F m C N T N T to ỹ m to obtain an estimate of the data, d m, tansmitted by the othe tansceive. The oveall end-to-end communication equies two time slots. 40

57 5.3 Design We addess the design of tansceive pecodes U 1, U 2 at cuent time slot t, followed by the design of the elay pecode U and the tansceive eceive filtes F 1 and F 2 in the second time slot of end-toend communication Tansceive Pecode Design The pecode matices U 1, U 2 ae designed to essentially nullify the effect of tansceive-elay channel apat fom balancing the signal-to-intefeence-plus-noise atio (SINR) at the elay and tansceive nodes. Moeove, the tansceives opeate unde a tansmit powe constaint P m Pm max. We begin with the QR-decomposition of hemitian of the channel matices given by H H m = Q m R m, m = 1, 2. Thus, U m is given by and the esultant tansmit powe is given by U m = β m Q m W m, m = 1, 2, (5.5) P m = E{ U m d m 2 } = β 2 mt(w m W H m), m = 1, 2, (5.6) whee the scaling facto β m will be deived in the sequel and W m is deived fom R m such that H m U m = β m I NT. (5.7) Apat fom its othe benefits [66], channel invesion also simplifies the design of the pecode in the following way. Fom (5.5), it s clea that fo a given H m, Since SINR R is an inceasing function of β 2 m wheeas SINR m is a deceasing function of β 2 m, the optimal value of β m is obtained by solving: Using (5.7), (5.2) and (5.4), we equate them as: SINR R = SINR m. α m β 2 m + α m β 2 m σ 2 n + P σ 2 e = α mα m β (t 1)2 m t[f H mg m U U H G H mf m ] X m, (5.8) whee P =E{ x 2 } X m =t[f H m{α m G m U (Ω c + σ 2 ni NT )U H G H m}f m ] + σ 2 nmt(f m F H m)+ β 2 mσ 2 emt[f m F H m]t[w m W H m]. Let u =β 2 m, z 1 = α 1 m α m β 2 m, z 2 = α 1 m (σ 2 n + P σ 2 e), z 3 =α m α m β (t 1)2 m t[f H mg m U U H G H mf m ], z 4 =t[f H m{σ 2 nm + α m G m U (Ω c + σ 2 ni NT )U H G H m}f m ], z 5 = σ 2 emt[f m F H m]t[w m W H m]. 41

58 So (5.8) becomes α m u + z 1 z 2 = z 3 z 4 + u z 5, u = (z 4 + z 1 z 5 ) ± (z 4 + z 1 z 5 ) 2 + 4z 5 (z 1 z 4 z 2 z 3 ) 2z 5, β m = u, whee β m is the smallest positive solution. The optimal value of β m is chosen as β opt m whee β max m is obtained by putting P m = P max m in (5.6). = min(β m, β max m ), Relay Pecode and Tansceive Receive Filte Design The optimal design is obtained by solving the following sum of mean squae eo (SMSE) optimization poblem: min f(ρ, U, F 1, F 2 ) ρ,u,f 1,F 2 subject to E{ x 2 } P max. The elay pecode matix U is decomposed as U = ρu, whee ρ is a positive scaling facto and U F = 1. This decomposition simplifies the deivation of F in closed fom. Fo the same eason, the tem ρ 1 is intoduced in the SMSE equation. Due to space constaints, we ll denote (σn 2 + α 1 β (j) α 2 β (j) 2 2 )INT by Λ (j) hencefoth. The SMSE of the two tansceives is given by f(ρ, Ū, F 1, F 2 ) = = 2 i=1 2 i=1 E{ d (t 1) i ρ 1ˆdi 2 } E{ d (t 1) i 2 } ρ 1 t(e{f H i (t 1)H ỹid i }) + ρ 1 t(e{d (t 1) i ỹi H F i })+ (5.9) ρ 2 E{ F H i ỹi 2 }. (5.10) We now expess each tem of (5.10) in tems of the elevant optimization vaiables. Thus, we have Futhe, using (5.4) and (5.7), we have E{ d i 2 } = N T, E{d i ỹ H i F i } = α i α i β i t(u H G H i F i ). (5.11) E{ F H i ỹi 2 } =α i t[f H i G i U (E{Ω f } + α i β (t 1)2 i I NT + σ 2 ni NT )U H G H i F i ] + σ 2 nit(f i F H i )+ E{t(F H i Ψ i U i d i d H i U H i Ψ H i F i )}, (5.12) whee, E{Ω f } is the aveage powe of the LSI tem at the elay. We defined this aveage powe as Ω AF in Chapte 3, whee we deived a ecusive equation to compute Ω AF which is expessed as 42

59 Ω AF E{Ω f } = σ 2 e[t(u (t 1) Λ (t 2) U (t 1) H )INT + Ω (t 1) AF t(u(t 1) U (t 1) H )]. (5.13) This ecusive stuctue of Ω AF assues that the nodes need not stoe all the pevious elay pecodes and tansceive eceive filte matices. This geatly educes the memoy equiement at the elay as well as the computation time fo Ω AF. Moeove, the filtes designed using (5.13) will lead to bette pefomance than that of the system poposed in [53] whee only the n latest time slots ae used fo computing Ω AF. Using Lemma 1 fom [54] and equation (5.6), we can ewite E{t(F H i Ψ i U i d i d H i U H i Ψ H i F i )} = σ 2 eip i t(f i F H i ). (5.14) Using (3.4), (5.3), (5.5), (5.13), we expess the elay tansmit powe as Now, the Lagangian fo the poblem in (6.7) is given by E{ x 2 } =t[u (Ω AF + Λ (t 1) )U H ]. (5.15) L =f(ρ, U, F 1, F 2 ) + λ(e{ x 2 } P max + b 2 ), (5.16) whee λ is the lagangian vaiable and b is the slack vaiable. On substituting the esults of (5.10), (5.11), (5.12), (5.15), (5.13),(5.14) in (5.16) and putting U = ρu, we get L(ρ, U, F 1, F 2, λ) =λ[ρ 2 t(u B U H ) P max + b 2 ] + 2N T + whee 2 { α i α i βi (t 1) t(f H i G i U + U H G H i F i ) + ρ 2 σ 2 niρ 2 σ 2 eip i t(f i F H i + α i t(f H i G i U B i U H G H i F i }, B i = Ω AF + (α i β (t 1)2 i + σ 2 n)i NT, B = (Ω AF + Λ (t 1) ). i=1 (5.17) The optimization poblem in (5.17) can be solved using the Kaush-Kuhn-Tucke (KKT) conditions [59]. Since the SMSE function is not jointly convex in the optimization vaiables, we use the coodinate descent method, wheein the minimization is pefomed with espect to one vaiable while keeping the othe vaiables fixed. Fist, keeping F i fixed, we apply the KKT conditions L ρ 0 NR N T, L L λ = 0, b = 0 to espectively get: L = 0, U λρt(u B U H ) = ρ 3 (w 1 + w 2 ), (5.18) α 1 G H 1 F 1 F H 1 G 1 U B 1 + α 2 G H 2 F 2 F H 2 G 2 U B 2 + λρ 2 U B = α 1 α 2 (β (t 1) 1 G H 2 F 2 + = β (t 1) 2 G H 1 F 1 ), (5.19) t(u B U H ) = ρ 2 (P max b 2 ), (5.20) λ[ρ 2 t(u B U H ) P max ] = 0, (5.21) 43

60 whee, w i = (σ 2 ni + σ 2 eip i )t(f i F H i ), i = 1, 2 Now, fom (5.18) and (5.21), we obseve that at optimal point, λ 0 and so the constaint on E{ x 2 } becomes equality constaint, i.e., the elay R tansmits at full powe P max. So, (5.20) becomes: t(u B U H ) = ρ 2 (P max ). (5.22) Fom (5.18) and (5.20), we get: λρ 2 = (w 1+w 2 ) P. Substituting this value in (5.19) and following Theoem max 2 of [53], we get: whee U opt = mat(m 1 α 1 α 2 vec[β (t 1) 1 G H 2 F 2 + β (t 1) 2 G H 1 F 1 ]), ρ opt P = max t(u B U H ). (5.23) M =(B T (w 1 + w 2 )I NR P max ) + 2 (B T m α m G H mf m F H mg m ). m=1 The optimal tansmit pecode fo elay R is given by U opt = ρ opt U opt L compute optimal eceive filtes by applying the KKT condition: F i the optimal eceive filte: F opt i = [w i I NT + α i G i U opt B i U H. Using the optimal U opt, we = 0 NT, fo i {1, 2}, which gives G H i ] 1 ρ opt αi α i β (t 1) i G i U opt. The matices U opt, F opt ae obtained by iteative computation until a stable value of SMSE is eached. The initial value of F fo computing U can be any andom N T N T complex matix. 5.4 Analysis of the Sececy Pefomance of the Poposed Design In this section, we eview the sececy pefomance of ou poposed system. We conside the wost case scenaio whee E is able to decode the signals fom tansceives using blind channel estimation techniques. Even in this case, E will not have CSI of elay-tansceive channels G m and hence, it won t be able to decode the signal eceived fom R, which is pecoded with F. Relay pecode F is a function of elay-tansceive channels G m. So, even in the wost case scenaio, the elay signal acts as AN fo E. Also, as seen in the pevious section, the elay always tansmits at full powe P max. This makes the elay signal a stong intefee fo E. The signal eceived by E at time t is given by y e = α 3 K 1 x 1 + α 5 K 2 x 2 + α 4 K x + n e, (5.24) We eview the pefomance of this system using the sum-sececy-ate [65] given by [R S1 + R S2 R E ] +, whee R m is the ate of the m th tansceive node, R E is the ate of eavesdoppe, in bits/sec/hz, m {1, 2} and [z] + = max(z, 0). We can expess the sum-sececy-ate as 44

61 whee [( 2 R s = m=1 ) +, E{log 2 I NT + SINR m } E{log 2 I NE + SINR E }] SINR m =[β (t 1)2 m (F H mg m U U H G H mf m ][F H m(σ 2 nm + σ 2 nb G mu U H G H m+ β 2 mψ m Q m W m W H mq H mψ H m + G m U Ω U H G H m)f m ] 1, m = 1, 2, SINR E =(α 3 K 1 x 1 x H 1 K H 1 + α 5 K 2 x 2 x H 2 K H 2 )(α 4 K x x H K H + σ 2 nei NE ) 1, with Ω =Ψ (t 1) U (t 1) Simila to Ω AF, Ω is also 0 NT fo t < 3. (Λ (t 2) + Ω (t 1) )U (t 1)H Ψ (t 1)H. 5.5 Simulation Results Fo the simulation expeiments descibed in this chapte, we set the following value fo the paametes: N T = 2, N R = 4, P1 max = P2 max = N T watt, P max = N R watt, We conside the path loss as defined by the 3GPP LTE fo outdoo maco cells [60], viz., α = log 10 (d) db, whee d is the distance between nodes, in metes, at an opeating fequency of 2 GHz. We conside α 1 = α 2 = 92 dbm, α 3 = α 4 = α 5 = 101 dbm. All the channel matices and estimation eo matices ae assumed to follow Rayleigh fading and thei elements ae independent and identically distibuted complex Gaussian andom vaiables with zeo mean and unit vaiance. Each esult was obtained by aveaging 1000 Monte Calo simulations. Powe Tansmitted (W) without pecoding at souce with SI based pecoding at souce σ e 2 / σ n 2 Figue 5.2: Tansmit powe of tansceive T 1, in the 8 th time slot, vesus SNR, with P max 1 = 2. Fig. 5.2 shows the tansmit powe of T 1 vesus σ 2 em/σ 2 nm, m {1, 2}. We compae ou design with that of [53], whee no pecoding is done at the souces. The system in [53] is designed to mitigate the esidual LSI at R and doesn t conside the esidual LSI at T 1 and T 2. As seen fom Fig. 5.2, the tansceive in [53] always tansmit at full powe iespective of the vaiations in esidual LSI. This will 45

62 lead to poo system pefomance at medium and high values of σem. 2 The pecode design poposed in this pape accounts fo this esidual LSI, hence the tansmit powe is optimized accoding to the amount of esidual LSI. Also, in the case of no esidual LSI (σem 2 = 0), the tansmit powe with the poposed design is much lesse than that in [53] SMSE INR=0 INR=0.1 INR=1 INR= Numbe of iteations Figue 5.3: Convegence of SMSE at each time slot. Fig. 5.3 depicts the convegence behavio of the poposed iteative algoithm. As seen fom the figue, the algoithm fo iteative computation of U, F m conveges in about 5 iteations fo all values of INR. Such a fast convegence advocates the pacticality of the poposed algoithm, endeing it deployable in eal-wold systems SMSE INR=0 INR=0.5 INR=1 INR= time slots Figue 5.4: Evolution of SMSE ove time at SNR=10 db. Fig. 5.4 shows the vaiation of SMSE ove time at SNR = 10 db, fo diffeent values of INR. It can be obseved fom the figue that the SMSE stats to stabilize fom the 3 d time slot. This is due to the 46

63 effect of feedback tem Ω AF which begins fom t = 3. So, we can conside any time slot afte t = 3 fo evaluation of futhe esults. We consideed the 8 th time slot INR=0 INR=0.1 INR=0.5 INR=1 SMSE SNR (db) Figue 5.5: SMSE pefomance at diffeent values of SNR, INR. Fig. 5.5 shows the vaiation of SMSE vesus SNR fo diffeent values of INR. The poposed design is found to show good pefomance at low esidual INR and it degades with inceasing INR. This may be accedited to the contibution of the feedback tem Ω AF in suppessing the esidual LSI. This again highlights the need fo pecoding and eceive filteing with multiple antenna nodes to suppess the LSI. Sum sececy ate (bits/sec/hz) INR=0 INR=1.0 INR=2.0 INR= SNR (db) Figue 5.6: Sum sececy ate, in the 8 th time slot, vesus SNR, fo diffeent values of INR The esults fo sum sececy-ate analysis of the system ae as shown in Fig It shows the vaiation of sum-sececy ate vesus SNR fo vaying INR. It can be obseved that, with sufficient suppession of esidual LSI, this system achieves good sum-sececy ate. The high ate is also due the stong intefeence fom the elay signal to E. 47

64 5.6 Summay We pesented the design of optimal pecodes and eceive filtes fo a FD two-way MIMO elaying system opeating unde tansmit powe constaints in the pesence of a passive eavesdoppe. The enduse pecodes optimize the tansmit powe to mitigate the esidual LSI. We consideed the use of elay signal as atificial noise fo the pupose of physical laye secuity. By analyzing the sum-sececy ate pefomance, we conclude that with pope LSI cancellation, this system povides good physical laye secuity even in the wost case scenaio without equiing any additional expenditue of powe, computation, o loss of data ate fo sepaate AN geneation. 48

65 Chapte 6 Low-Complexity Tansceive Designs fo a Relay-Assisted Full-Duplex Cellula Netwok 6.1 Intoduction In the pevious chapte, we pesented the design of pecodes and eceive filtes fo a two-way FD AF elaying system in the pesence of a passive eavesdoppe. We also analyzed the physical laye secuity povided by the elay signal, without any additional expenditue of antenna esouces o powe. In this chapte, we conside a FD cellula scenaio and pesent the design of tansceive and elay pocessing algoithms. A majo hudle in the adoption of FD fo cellula access is the cancellation of the LSI. Vaious selfintefeence cancellation (SIC) techniques have been epoted in liteatue fo a cellula netwok. The authos in [67] popose a signal-to-leakage-plus-noise atio (SLNR) based pecoding, with equal powe allocation, fo downlink channel and self-intefeence-plus-noise covaiance matix-awae SLNR pecoding fo the uplink channel. The system consideed theein is compised MIMO half-duplex (HD) uses and a FD base station. A simila system was studied in [68] with focus on tansmit beamfoming fo the base station, and the uplink uses based on maximizing the sum-ate of the system while suppessing the LSI and co-channel intefeence (CCI). The joint design of linea hybid pecode and equalize fo a FD base station with single antenna HD uses was studied in [69]. The pecode and equalize wee designed to achieve minimum mean squaed eo (MMSE) fo FD massive MIMO cellula systems. A MIMO FD cellula netwok in a cognitive envionment was consideed in [70]. Theein, the pecodes and eceive filtes ae designed based on SMSE minimization along with LSI and CCI suppession. The poblem was iteatively solved by semidefinite pogamming (SDP) algoithm. The system compised a FD base station and HD uses. The authos in [71] conside a two-way FD cellula netwok with both the base station and the uses opeating in FD mode. The wok focuses on asymptotic analysis with vey lage numbe of antennas at the base station to eliminate the LSI completely. As such, thee is vey limited published eseach wok which consides a tuly FD cellula netwok with all nodes opeating in FD. Moeove, the use of elays in such a FD cellula netwok is not vey 49

66 thooughly investigated. In this context, we popose the design of optimal pecodes and eceive filtes fo a elay-assisted two-way FD cellula netwok with multiple-antenna nodes. We design pecodes and eceive filtes fo the use equipments (UEs), the base station, and the elay. The poposed design mitigates the effect of esidual LSI by making use of multiple antennas and appopiately taking the LSI effect into account in the design objective function. The pecodes and the eceive filtes ae designed by minimizing the SMSE of the system unde a constaint on the tansmit powe. This tuns out to be a non-convex optimization poblem. Moeove, the LSI at the nodes vaies continuously and hence the optimal filtes need to be updated at each time slot. The main contibutions of this pape ae twofold: (i) Pecode and eceive filte design fo esidual LSI mitigation at the nodes in a cellula netwok, and (ii) iteative calculation of cumulative effect of esidual LSI based on tempoal feedback with low computational complexity. Futhemoe, we analyze the pefomance of the poposed designs in a LTE maco cell envionment in tems of the esidual LSI suppession, thei computational complexity, and sum-ate. The est of this chapte is oganized as follows. Section 6.2 descibes the system model. The design of sub-optimal pecodes and eceive filtes is discussed in Section 6.3. Simulation esults ae pesented in Section 6.4 and the conclusions ae dawn in Section System Model We conside a elay-assisted two-way FD cellula netwok as shown in Fig The base station B allocates the same fequency to uses T 1 and T 2. The base station selects T 1 fom its vicinity while T 2 neae to the cell edge to avoid CCI. The cell edge use T 2 is assisted by a two-way AF elay R. We assume R is located fa fom T 1 and thee is no CCI between them. All nodes in the system opeate in FD mode. The nodes R, T 1, and T 2 ae each equipped with N T antennas, while the base station B has N B antennas such that N B > 2N T. The base station uses 2N T antennas fo downlink communication and N B antennas fo uplink communication fom uses T 1 and T 2. All the MIMO channel links ae modeled as independent and fequency-flat Rayleigh fading channels and ae assumed to be static fo the duation of one time slot. As shown in Fig. 6.1., the matices G i, H i, i {1, 2, } epesent the downlink and uplink MIMO channel matices, espectively, such that H i C N T N T, i {1, 2, }, G j C N T 2N T, j {1, }, and G 2 C N T N T. These channel matices ae assumed to be pefectly known. The matices L b C N T 2N T and L m C N T N T, m {1, 2, }, epesent the LSI MIMO channels. The tansmitte signal can eflect off neaby objects and follow seveal paths that aive at the eceive. This makes accuate estimation of the loopback channel a vey difficult task. Hence, we assume that the available CSI of the loopback channels to be impefect. The actual loopback channel matix can be modeled as L j = L j + Ψ j, j = 1, 2, b,, (6.1) 50

67 Figue 6.1: System diagam of a elay-assisted two-way FD MIMO cellula netwok. whee L j is the available channel estimate and Ψ j is the eo in CSI having zeo mean and covaiance E{Ψ j Ψ H j } = N Tσej 2 I N T. The channel matices also incopoate the path loss. In a cellula netwok, the uplink data ate is usually lowe than the downlink date ate. Also the tansmit powe of a use device is much lowe (about 250 mw) than that of the base station (10-20 W). Due to these easons, we employ tansmit divesity in the uplink fo eliable communication. So, each use device tansmits the same data symbol fom all of its N antennas. The complex data symbols at T 1 and T 2 ae denoted by d 1 and d 2, espectively, such that E{ d 1 2 } = E{ d 1 2 } = 1. In the downlink, howeve, the base station B tansmits 2N T diffeent symbols, N T symbols fo each use, fom 2N T out of its N B antennas. Thus, the tansmit data vecto fo B is given as s b = [s 11, s 12,..., s 1NT, s 21, s 22,..., s 2NT ] T C 2NT 1 having covaiance E{s b s H b } = I 2N T. The data vectos s 1 = [s 11, s 12,..., s 1NT ] T, s 2 = [s 21, s 22,..., s 2NT ] T ae downlink data fo T 1 and T 2, espectively. The following events take place duing each time slot t: (i) Each use pecodes its data vecto d i C NT 1, with pecoding matix U i C N T N T and tansmits x i, i {1, 2}, whee d 1 = 1 NT /2 [d 1 d 1 ] T and d 2 = 1 NT d 2, with 1 NT denoting a column vecto consisting of N T 1 s. Let D 1 = E{d 1 d H 1 } and D 2 = E{d 2 d H 2 }. (ii) The base station B pecodes data vecto s b with pecoding matix U b C 2N T 2N T and tansmits x b. (iii) The AF elay R eceives the signal tansmitted by B and U 2. The signal at the elay afte impefect LSI cancellation is given by y =G U b s b + H 2 U 2 d 2 + Ψ x + n, (6.2) 51