MASTER'S THESIS. Resource Allocation in Ka-band Satellite Systems. by Youyu Feng Advisor: John S. Baras CSHCN MS (ISR MS )

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1 MASTER'S THESIS Resource Allocaton n Ka-band Satellte Systems by Youyu Feng Advsor: John S. Baras CSHCN MS (ISR MS )

2 Report Documentaton Page Form Approved OMB No Publc reportng burden for the collecton of nformaton s estmated to average 1 hour per response, ncludng the tme for revewng nstructons, searchng exstng data sources, gatherng and mantanng the data needed, and completng and revewng the collecton of nformaton. Send comments regardng ths burden estmate or any other aspect of ths collecton of nformaton, ncludng suggestons for reducng ths burden, to Washngton Headquarters Servces, Drectorate for Informaton Operatons and Reports, 1215 Jefferson Davs Hghway, Sute 1204, Arlngton VA Respondents should be aware that notwthstandng any other provson of law, no person shall be subject to a penalty for falng to comply wth a collecton of nformaton f t does not dsplay a currently vald OMB control number. 1. REPORT DATE REPORT TYPE 3. DATES COVERED - 4. TITLE AND SUBTITLE Resource Allocaton n Ka-band Satellte Systems 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Army Research Laboratory,2800 Powder Mll Road,Adelph,MD, PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR S ACRONYM(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT Approved for publc release; dstrbuton unlmted 13. SUPPLEMENTARY NOTES The orgnal document contans color mages. 14. ABSTRACT see report 15. SUBJECT TERMS 11. SPONSOR/MONITOR S REPORT NUMBER(S) 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT a. REPORT unclassfed b. ABSTRACT unclassfed c. THIS PAGE unclassfed 18. NUMBER OF PAGES 98 19a. NAME OF RESPONSIBLE PERSON Standard Form 298 (Rev. 8-98) Prescrbed by ANSI Std Z39-18

3 ABSTRACT Ttle of Thess: RESOURCE ALLOCATION IN KA-BAND SATELLITE SYSTEMS Degree canddate: Youyu Feng Degree and year: Master of Scence, 2001 Thess drected by: Professor John S. Baras Department of Electrcal and Computer Engneerng The Ka-band satellte system s of ncreasng nterest around the world due to ts huge bandwdth. Ran fadng s one of the prmary factors affectng performance and avalablty of the Ka-band system. Extra power on the satellte can provde compensaton for ran attenuaton. In ths thess, we study the ran fade compensaton problem for downlnk transmsson n the Ka-band satellte by dynamc resource allocaton. The resources we consder nclude power and antennas onboard the satellte. The goal s to maxmze the aggregate prorty of packets arrvng at all downlnk spots as well as mantan farness among downlnks. We formulate the problem mathematcally n the framework of Knapsack Problems (KP). In partcular, we show the resource allocaton problem s equvalent to a Mult-choce Multple Knapsack Problem (MCMKP), whch, n general, s very hard to solve n a reasonable tme. By ntroducng the seedng theory nto the antenna schedulng, we decompose the orgnal MCMCP nto a sequence of Multple-choce Knapsack Problems (MCKP), whch are easer to solve.

4 The effectveness of our approach s demonstrated through smulatons n OPNET. Comparson wth the Multple Knapsack Problem (MKP) approach proposed by Brman s also provded.

5 RESOURCE ALLOCATION IN KA-BAND SATELLITE SYSTEMS by Youyu Feng Thess submtted to the Faculty of the Graduate School of the Unversty of Maryland, College Park n partal fulfllment Of the requrements for the degree of Master of Scence 2001 Advsory Commttee: Professor John S. Baras, Char Professor Armand Makowsk Professor Subramanan Raghavan

6 Copyrght by Youyu Feng 2001

7 DEDICATION To my famly

8 ACKNOWLEDGEMENTS I am grateful to my advsor Dr. John S. Baras for hs advce, support and encouragement. I would also lke to thank Dr. Armand Makowsk and Dr. S. Raghavan for agreeng to serve on my commttee and to revew ths thess. Ths thess was motvated by Vneet Brman s work. I am also grateful for hs valuable help n the start of ths work. Specal thanks are due to Mngyan Lu, Mansh Karr, Arvnd Man, Majd Rass-Dehkord and numerous other colleagues who contrbuted to constant help and support. The research reported n ths thess was supported through collaboratve partcpaton n Advanced Telecommuncatons/Informaton Dstrbuton Research Program (ATIRP) consortum sponsored by the U. S. Army Research Laboratory under the Federated Laboratory Program, Cooperatve Agreement DAAL Ths support s gratefully acknowledged.

9 TABLE OF CONTENTS LIST OF TABLES...v LIST OF FIGURES...v Chapter 1: Introducton Introducton to Ka-band Satellte Systems Motvaton for Resource Management Ran Fade Problem Revew of Ran Compensaton Approaches Contrbutons and Organzaton... 8 Chapter 2: Problem Descrpton and Formulaton System Confguraton Multmeda Servces Uplnk and Downlnk Onboard Swtch and Scheduler Network Operatons and Control Center (NOCC) Problem Descrpton Problem Formulaton Notaton Mathematcal Formulaton Chapter 3: Knapsack Problems: Some Background v

10 3.1 Introducton to Integer Programmng Overvew of 0-1Knapsack Problems Sngle Knapsack Problem Multple Knapsack Problem Multple-choce Knapsack Problem Chapter 4: Formulaton of Resource Allocaton as Knapsack Problems Mult-choce Multple Knapsack Model Multple Knapsack Model Stable Load Condton Unbalanced Load Condton Multple-choce Knapsack model Performance Metrcs A New Multple-choce Knapsack Scheme Chapter 5: Smulaton and Results OPNET Smulaton Model Traffc Models Web and Bulk Data Transfer Workload Connectonless Bursty Data Resource Allocaton Schemes Smulaton Results Aggregate Prorty Computng Tme Resource Utlzaton v

11 5.4.4 Servce Mssng Chapter 6: Conclusons and Future Work Conclusons Future Work Appendx A: Algorthms for Solvng Knapsack Problems Bblography v

12 LIST OF TABLES Table 5.1: Computng tme n seconds of three algorthms Table 5.2: Computng tmes of MCKP and MKP Table 5.3: Resource utlzaton and servce mssng v

13 LIST OF FIGURES Fgure 2.1: Typcal satellte network archtecture Fgure 2.2: Uplnk MF-TDMA scheme Fgure 2.3: The transmsson rate vs. power level and ran condton Fgure 2.4: Hysteretc relatonshp between sgnal level and ran fade condton Fgure 4.1: The standard method for seedng a tournament wth 16 teams Fgure 4.2: Illustraton of burst schedulng Fgure 5.1: OPNET smulaton model Fgure 5.2: Two-state MMPP OPNET model Fgure 5.3: Satellte onboard processor OPNET model Fgure 5.4: Aggregate prortes under no ran condton Fgure 5.5: Aggregate prortes wth ran fade area 2% Fgure 5.6: Aggregate prorty wth ran fade area 5% Fgure 5.7: Aggregate prorty wth ran fade area 8% Fgure 5.8: Aggregate prorty wth ran fade area 10% Fgure 5.9: Aggregate prorty wth ran fade area 12% Fgure 5.10: Aggregate prorty wth ran fade area 15% Fgure 5.11: Aggregate prorty under 18% ran condton Fgure 5.12: Advantage of MCKP over MCP vs. ran area Fgure 5.13: Number of out-of-servce downlnks vs. ran area Fgure 5.14: Hstogram of number of mssed rounds (12% ran area ) v

14 Fgure 5.15: Hstogram of number of mssed rounds (15% ran area) Fgure 5.16: Hstogram of number of mssed rounds (18% ran area) x

15 Chapter 1: Introducton 1.1 Introducton to Ka-band Satellte Systems There has been consderably ncreasng nterest n expandng the broadband ntegrated servces to nclude satellte communcaton lnks. Compared to conventonal terrestral networks, satellte communcatons have the followng attractve features: Ubqutous access: Servces are avalable to whole regons wthn satellte footprnts, ncludng locatons where terrestral wred networks are not possble or economcally nfeasble. Broadcast/multcast nature: Many multmeda applcatons beneft from ths feature of satellte networks. Hgh bandwdth: Satellte channels today can delver ggabts per second. Flexble bandwdth-on-demand capablty: Ths may result n maxmum resource utlzaton. To provde suffcent bandwdth to meet the growng demand for satellte transmsson capacty, people need to explot hgher frequency range and develop new technologes. In the late 1970 s, the Ka band (20/30GHz) was selected by many space agences around the world as the frequency band for the next generaton broadband satellte networks. Utlzng the Ka band and even hgher frequency bands has obvous advantages over the lower frequency ones: Large bandwdth: Huge bandwdth avalable n ths frequency range s the prmary motvaton for developng Ka band satellte systems. 1

16 Small antenna sze: The ncreasng rado frequency mples that we can decrease the sze of the antenna beam shape. Thus, ether the dstorton due to nterference from adjacent satellte systems s reduced, or antennas wth smaller dameter can be used. Smaller antenna sze makes broadband satellte servces affordable to mllons of personal and commercal end-users. Even larger system capacty: Usng many small spot beams n the Ka band systems ncreases the satellte power densty and permts large frequency reuse, whch leads to a much larger effectve bandwdth. Thousands of user termnals equpped wth nexpensve antennas can be served at the same tme wthout usng expensve hubs. As early as n 1970 s, researchers started to explore the Ka-band regon n the Unted States as well as n Europe and Japan. The frst Ka band satellte servces were ntroduced wth the basc technologes for transparent transponders n Japan. The frst operatonal regeneratve Ka-band system ntegrated wth terrestral networks, was mplemented n the Italan Ka-band program, ITALSAT. Snce ITALSAT- F1 was successfully launched n January 1991, satellte has been no longer a cable n the sky based on transparent transponders; nstead t has become a network node. Man features of the system ncluded: Italan coverage obtaned by means of sx very narrow spot beams; total capacty of 0.9 Gbt/s acheved wth 147 Mbt/s tme dvson multple access (TDMA) n the uplnk; nterspot connectvty provded by a synchronous baseband space-swtch matrx; TDM n the downlnk. ITALSAT system also provded operatonal experence for reallocaton of capacty n a fast and flexble way [1]. 2

17 In the Unted States, the Advanced Communcatons Technology Satellte (ACTS) program was formulated at the Natonal Aeronautcs and Space Admnstraton (NASA) n 1984 to contnue NASA s role of developng advanced space communcatons technology. The ACTS satellte was launched n September It created a revoluton n the satellte system archtecture by ntroducng the followng key dgtal technologes n Ka-band systems [2]: Fast hoppng multbeam antenna On-board baseband processor Wde-band mcrowave swtch matrx Adaptve ran fade compensaton Very small and ultra small aperture termnal Hgh data rate termnal and 900 MHz transponder These technologes have become the foundaton of the current nterests n the use of Ka band n global nteractve multmeda systems. Stmulated by the strong ndustral nterest, the Federal Communcatons Commsson (FCC) awarded 13 lcenses for the use of Ka band n the Unted States n Hughes SPACEWAY was among the frst fled systems. The SPACEWAY network s amed at provdng nteractve bandwdth-on-demand, cost-effectve, multmeda communcaton servces for hundreds of mllons of people wthn the contnuous vew of the satelltes. The state-of-the-art features of SPACEWAY network are lsted below [3]: Narrow (about 1 ) and wde (3 ) spot beams cover both populated and low populaton areas. 3

18 On board processors and swtches provde ndvdual customers wth mmedate access to the satellte, route packets wthn approprate spot beams, and nterconnect wth other satelltes n the network. Small, easly nstalled ground termnals brng satellte technology to the economc threshold of a greater unverse of customers. Varous dgtal transmsson bt rates can support a varety of applcatons. Also, through a unque arrangement of ntersatellte lnks, SPACEWAY, whch was proposed to launch n the tme wndow , wll create the frst truly nterconnected worldwde network. 1.2 Motvaton for Resource Management Most new generaton Ka-band satellte systems lke SPACEWAY are beng desgned to provde low-cost telecommuncaton servces to hundreds of mllons of users. Thus effcent management of varous satellte and spectrum resources s requred to meet the fast-growng servce demand. Some of these resources, lke the frequency spectrum, have been a lmted factor n most of the old and present day systems, so a lot of work has been done n desgnng good resource allocaton algorthms. Allocaton of satellte power and antennas ganed less attenton n the past. But t has become more and more mportant because of the specal ran fade problem and new technologes such as multbeam antennas n satellte systems operatng at Ka band. 4

19 1.2.1 Ran Fade Problem Havng the advantages of ncreased bandwdth and sgnfcantly smaller ground termnal equpment, Ka frequency band was long malgned as beng totally mpractcal for use by satellte. The bad mask was the degradaton due to atmospherc propagaton effects whch s much more severe than those found at lower frequency bands. The prmary propagaton factors that affect Ka-band earth-satellte channels nclude: Ran attenuaton Wet antenna Depolarzaton due to ran and ce Gaseous absorpton Cloud attenuaton Atmospherc nose Troposphere scntllaton Among all these factors, ran fade presents the most challengng mpedment to system desgners because sgnal attenuaton due to ran s the most severe propagaton effect at Ka band. Accordng to ACTS propagaton research, ran attenuaton at 20 GHz s almost three tmes that at 11 GHz and t can easly exceed 20 db n many areas of the world. Ran attenuaton s a functon of frequency, ran ntensty, randrop sze dstrbuton, randrop temperature, elevaton angle and polarzaton angle. For example, the relatonshp between frequency and ran attenuaton s approxmately as follows: 5

20 A1 f ( A f ) 2, where f, A (=1,2) represent the frequency and the correspondng attenuaton, respectvely. The followng ran fade characterstcs need careful consderaton n fade compensaton [5]: Ran tme: In general, the average ran tme that needs compensaton s less than 5%-10% of a year. Thus dynamc resource allocaton would be better than fxed lnk margns. Smultaneous ran fade over extended areas: A prelmnary analyss ndcates that fades at stes separated by dstances exceedng the average ran cell sze are uncorrelated. Fade rates: Ran fade rates rarely exceed 1 db/s for most locatons. Fade duraton: Fade duraton vares from several seconds to a few hours dependng on the system margn and ran condtons. Frequency scalng: Uplnk and downlnk fades are generally correlated. Thus accurate fade measurements n only one drecton are enough for fade compensaton. The downlnk ran attenuaton can be measured drectly by observng the power of the 20 GHz beacon sgnal receved at the earth staton. Frequency scalng technques then can be used to compute the fadng n the 30 GHz uplnk. When ran fade s determned, approprate methods can be mplemented to mtgate the fade. 6

21 1.2.2 Revew of Ran Compensaton Approaches Satellte communcaton systems operatng at Ka-band are subject to mparments produced by the troposphere, especally the ran attenuaton. As a consequence, fade compensaton schemes have to be mplemented to guarantee certan system performance and avalablty. Durng the past few years, consderable effort has been devoted to developng effectve fade mtgaton technques. Roughly speakng, there are four dfferent approaches. The most ntutve approach would be usng larger ground staton antennas and/or hgher power amplfers. But snce the current trend s to use small (< 20 nches apertures), low-cost ground termnals (< $1000) that are affordable by a great unverse of customers, ths form of compensaton would be too expensve to most end-users. In addton, snce the average ran tme for whch compensaton must be employed s usually short (< 10%), the added system margn wll be wasted for over 90% of the tme. Ste dversty s another effectve but expensve countermeasure n combatng ran fade. Ths technque nvolves tandem operaton of two earth statons located several klometers apart n dstance. As we mentoned before, ran fades at stes separated by dstances exceedng the average ran cell sze (several klometers) are expected to be uncorrelated. Ths enables a re-routng of the traffc va the less affected earth staton whenever a severe attenuaton occurs at the other ste. But the cost of two earth termnals makes ths approach not applcable to common customers budget. The thrd approach s to provde addtonal power to the transmt carrers at the satellte to compensate for ran attenuaton. As the downlnk ran fadng occurs n some beam, power control correcton of approxmately 1.5 tmes fade s requred to mantan 7

22 the carrer to nose rato. Transponders wth varous output power levels that are necessary for ths mtgaton method should be commanded nto hgh power modes under ran condtons and swtch back whenever the fadng s over. The most well known approach s ACTS adaptve ran fade compensaton. Ths protocol provdes 10 db of margn by reducng the burst by half and nvokng onehalf-rate forward error correcton codng durng a perod of sgnal loss caused by ran. Ths protocol also ncludes a decson process, whch makes use of the downlnk sgnal level together wth the FADED and CLEAR thresholds dentfed for each very small aperture termnal (VSAT) to determne the need for compensaton n real tme. The thrd and fourth compensaton technques both try to allevate ran mparments by settng asde an extra porton of system capacty. These resources wll be allocated to beams sufferng from ran attenuaton only when needed. For example, n Tme Dvson Multplex (TDM) systems, the addtonal tme slots wll provde adequate redundancy for mpared sgnals. Based on the thrd approach, Brman proposed a power allocaton and antenna schedulng scheme n hs thess [4]. The basc dea there was to boost the power of beams under ran condtons to mantan the normal bt rate, and then schedule bursts n such a way that the aggregate proft s maxmzed. In partcular, he posed the schedulng problem as a mult-knapsack problem (MKP). 1.3 Contrbutons and Organzaton Motvated by Brman s work, ths thess proposes an effectve and flexble ran fade compensaton scheme. We frst model the ran fade compensaton as a lnear nteger 8

23 programmng problem, and further formulate t n a framework of mult-choce multple knapsack problem (MCMKP). Ths framework subsumes Brman s MKP model as a specal sub-soluton. Completely solvng the MCMKP n reasonable tme s ntractable n consderaton of the number of varables nvolved. Then we present a sub-optmal scheme to the orgnal optmzaton problem, whch decomposes the MCMKP nto a sequence of mult-choce (sngle) knapsack problems (MCKP). The latter s solvable n real tme. To be specfc, our scheme conssts of two parts: schedulng antennas usng the seedng theory, and allocatng power by solvng MCKP. Essentally our approach decouples the orgnally coupled antenna schedulng problem and power allocaton problem. Compared to the MKP scheme, our MCKP scheme enjoys the followng advantages: farness, maxmum utlzaton of extra power, and low computaton complexty. The effectveness of our resource allocaton scheme s demonstrated by smulaton n OPNET. The remander of the thess s organzed as follows. Chapter 2 descrbes the system confguraton, states the problem we want to solve and gves the mathematcal formulaton. In Chapter 3, the classcal theory of knapsack problems (KP) s brefly revewed and several varants of KP relevant to our problem are ntroduced. We nvestgate the relatonshp between the ran fade compensaton and knapsack problems followed by the detaled descrpton of our mult-choce knapsack allocaton scheme n Chapter 4. Chapter 5 provdes the smulaton mplementaton and results. Fnally, conclusons and suggestons for future work are gven n Chapter 6. 9

24 Chapter 2: Problem Descrpton and Formulaton 2.1 System Confguraton In ths work, we wll focus on the geosynchronous Earth orbt (GEO) satelltes operatng at Ka band and provdng broadband servces. Fgure 2.1 below llustrates the typcal satellte network archtecture. Swtch Buffers S c h e d u l e r 30 Ghz U l 20 Ghz Downln NOCC VSAT PABX Multmeda LA Fgure 2.1: Typcal satellte network archtecture The consdered network scenaro s mesh confgured, comprsng a satellte wth on-board swtchng/processng, hundreds of low-cost earth statons generatng dfferent 10

25 types of traffc and a Network Operatons and Control Center (NOCC) that collects data, exchanges nformaton among the network components and controls the operatons of the satellte Multmeda Servces Usng Ka band satellte, nteractve multmeda servces can be provded globally to fxed and moble users wth nexpensve cost. Varous applcatons supported by the system nclude: nternet web browsng, bulk date transfer, nteractve on-demand and database consultaton, voce, vdeo conference, mage transmsson, etc. In the context of ntegrated servces networks, we consder four dstnct servce categores [6], [7]: Guaranteed Servce (GS): Ths category ncludes the real tme and long-lastng calls whch requre low packet loss and mnmum delay. ATM classes CBR (constant bt rate) and rtvbr (real-tme varable bt rate) can be mapped nto ths category. GS has the hghest prorty. Sustanable Servce (SS): Ths category requres only low packet loss. ATM class nrtvbr (non-real-tme varable bt rate) falls nto ths category. SS has lower prorty than GS. Controlled Servce (CS): ATM class ABR (avalable bt rate) belongs to ths famly. CS can tolerate slght packet loss and bounded delay. Its prorty s lower than SS. Best Effort (BE): Ths category corresponds to ATM UBR (unspecfed bt rate) servce class. It requres no guarantee and has the lowest prorty. 11

26 Accordng to the dfferent QoS (Qualty of Servce) requrements of the above categores, we assgn prortes 4, 3, 2, 1, to the traffc belongng to GS, SS, CS and BE respectvely Uplnk and Downlnk The number of downlnk spots n the system s about four tmes that of uplnk spots. Consequently, the downlnk cell sze s much smaller than that of the uplnk. Thus, downlnk power s concentrated and small antennas are allowed. The earth statons share the 30GHz uplnk (earth to satellte) channel n a Multple Frequency TDMA manner (MF-TDMA) [7], whch combnes Frequency Dvson Multple Access (FDMA) and Tme Dvson Multple Access (TDMA). The total bandwdth allocated to each spot beam s frst dvded nto a number of non-overlappng carrers, as the rows n Fgure 2.2. Ths allows for the smaller sze of the ground statons due to the lower transmsson rates. Then each sub-channel s further dvded nto nonoverlappng tme slots, as the columns n Fgure 2.2. Ths combnaton of FDMA and TDMA makes the bandwdth utlzaton more flexble and effcent. Tme Frequency Fgure 2.2: Uplnk MF-TDMA scheme 12

27 On the 20 GHz downlnk (satellte to earth), the access mechansm nsde every spot s tme dvson multplex (TDM). In ths thess, we wll focus on the resource allocaton problem n the downlnk transmsson. There are tens of antennas and hundreds of downlnk buffers on the satellte. Downlnk transmsson to the ground spots s organzed nto bursts, each of whch occupes a fxed tme nterval. Each antenna serves one and only one downlnk spot durng a burst. To guarantee certan Bt Error Rate (BER) performance, the maxmum downlnk transmsson rate B allowed s a functon of the transmsson power and the weather condton: B = f ( power, ran), as llustrated n Fgure 2.3. To be specfc, for a fxed transmsson power level, we need to reduce the transmsson rate to satsfy the BER requrement when ran condton gets worse. On the other hand, under the same weather condton, wth a hgher power level, we can rase the transmsson rate wthout affectng the BER performance. no ran lght ran heavy ran power level Fgure 2.3: The transmsson rate vs. power level and ran condton 13

28 For convenence of dscusson, we wll fx certan BER requrement n the sequel. Also we defne certan transmsson rate as the standard rate. The correspondng standard power for each downlnk s thus defned to be the power requred servng ths downlnk at the standard rate under clear weather condton. We assume the satellte has some extra power n addton to the sum of standard power needed by downlnk spots n a burst, whch provdes compensaton when some downlnks suffer from ran fade. In partcular, we wll assume that wth the extra power, the standard rate can stll be mantaned f the ran area s less than 10%. The antennas can adjust power levels and thus transmsson rates to accommodate weather condtons. The earth statons are also capable of dong approprate adjustment Onboard Swtch and Scheduler Due to the large number of beams, an onboard swtch s requred to route traffc among the end spot beams. Snce the number of uplnk beams s dfferent from the number of downlnks, the swtch matrx would be asymmetrc, that means, the swtch has unequal number of nput and output ports. The onboard scheduler wll receve control nformaton from the Network Operatons and Control Center (NOCC), pck the approprate downlnk beams, allocate power to these beams and schedule the bursts Network Operatons and Control Center (NOCC) NOCC s the core of ths network scenaro. It nstructs the satellte to operate n dfferent modes accordng to the nformaton t collects. The resource allocaton work wll be done manly n NOCC. 14

29 The typcal msson lfetme for a Ka band satellte wll be years. Durng ths perod of tme, the Internet traffc wll grow even faster and the types of applcatons wll change unpredctably. A preprogrammed algorthm onboard the satellte wll not be able to provde effcent capacty allocaton and utlzaton, thus mplementng the resource management algorthms (whch maybe change as the tme evolves) n NOCC on the ground would be a better choce. For ran fade compensaton, each earth termnal measures the downlnk sgnal level and transmt t to the NOCC. Takng the reported sgnal level as an nput, we determne the correspondng ran fade condton through a hysteretc operator [8], as llustrated n Fgure 2.4. The ran fade condton takes value from {Heavy ran, Lght ran, No ran}. If the sgnal level s between the predefned CLEAR1 and FADE2 thresholds, the earth termnal s clamed to be under lght ran condton. The ran condton remans Lght ran untl the sgnal ncreases and passes CLEAR2, or t decreases and passes FADE1. In the frst case, we say the ran fade s over; whle n the second case, we clam the termnal s sufferng from heavy ran fade. Smlarly, we can determne the fade levels for varous other cases. Usng both CLEAR and FADE thresholds we can cope wth the nose n sgnal level measurement and add stablty to the decson system. These thresholds are set ndvdually for every earth termnal based on ther BER performance. NOCC also collects the traffc data, such as traffc type and traffc load, from the ground statons and the satellte. Whenever substantal change n traffc occurs or an earth termnal requres ran fade compensaton, NOCC wll call the resource allocaton 15

30 algorthm and transmt the resultng operatonal schedule to the satellte. The scheduler onboard the satellte thus manages ts next burst accordng to the new schedule. Ran fade level Heavy ran Lght ran No ran FADE1 FADE2 CLEAR1 CLEAR2 Sgnal level Fgure 2.4: Hysteretc relatonshp between sgnal level and ran fade condton 2.2 Problem Descrpton In ths secton, we wll state the resource allocaton problem n the scenaro descrbed n the prevous secton. We have defned prortes for dfferent types of servces n Subsecton Thus every uplnk packet has a prorty set n ts header. Every downlnk spot beam s assgned an ndvdual buffer on the satellte. After recevng the packets, the onboard swtch wll route them nto approprate downlnk buffers accordng to the destnaton addresses specfed n ther headers. As we mentoned earler, the number of downlnks s many (say 30) tmes that of antennas, and each antenna serves one downlnk spot durng a burst. The resources we 16

31 consder here nclude antennas and the total power of antennas. By resource allocaton, we mean two thngs: Burst schedulng: Assgnment of antennas to downlnks for each burst perod; Power allocaton: Allocaton of power to each antenna under the constrant that the total power of antennas does not exceed a specfed lmt. Our objectve n the resource allocaton s two-folded: hgh proft and farness, whch are made clear below. Hgh proft: We defne the proft by the aggregate prorty collected at all earth statons durng a fxed tme nterval (to be specfed soon),.e., the sum of prortes of all packets receved at all termnals. Farness: We want to prevent the followng stuaton from happenng: one or more downlnks do not get servce for a relatvely long tme. In consderaton of ths farness requrement, we defne the tme nterval durng whch hgh proft s sought, to be the tme t takes to serve every downlnk one and only one burst wth no antenna dlng. In the sequel, we call ths tme nterval a round, and t s the tme horzon for our resource allocaton problem. If there were no ran fade or traffc varaton, the soluton s straghtforward: servng the downlnk buffers n a round robn manner wth a fxed data rate. Ths scheme s very smple and far to every downlnk. Unfortunately, ths s not the real case. When ran fades occur n some spot beams, those spots may not be able to be served wth the fxed rate due to the lmted total transmsson power n satellte. In 17

32 Subsecton 2.1.2, we have descrbed the relatonshp between the transmsson rate, the transmsson power, and the ran fade level for a certan BER performance. Under certan ran condton and BER requrement, f there s extra power avalable, we can rase the transmsson power to hold the fxed rate, otherwse we have to reduce the transmsson rate. In other words, when the ran condton and requred BER performance are gven, there s only one freedom left, ether power or rate, for each downlnk. Snce the transmsson power s the actve factor n these two, we vew t as a power allocaton problem. From the above analyss, we can see that the antenna assgnment and power allocaton problems are coupled n that antenna assgnment cannot be done wthout consderng the power settngs for the selected downlnk buffers and vce versa. Thus these two problems must be consdered together to acheve hgh proft. In short, the resource allocaton problem can be stated as follows: For each burst perod n one round, we want to select downlnks to be served and allocate assocated transmsson power to them wthn the constrant of total avalable power, so that under varous weather condton dstrbutons, the aggregate proft s maxmzed and the farness requrement s satsfed. 2.3 Problem Formulaton In ths secton, we wll gve the mathematcal formulaton of the resource allocaton problem. 18

33 2.3.1 Notaton Frst, we ntroduce the notatons that wll be used n the remander of the thess. N number of antennas; M number of downlnk spots (buffers); L number of bursts n a round, L = M / N ; R number of transmsson power levels for every downlnk spot; P tot total avalable power for each burst; w mr transmsson power of level r for downlnk m, wth hgher r ndcatng hgher power level. m = 1,2,, M, r = 1, 2,, R ; d mr number of packets that can be transmtted n downlnk m n one burst tme usng transmsson power condton. m = 1,2,, M, r = 1, 2,, R ; w mr under current ran p mr prorty sum of the frst d mr packets n buffer m, m = 1,2,, M, r = 1, 2,, R ; x lmr ndcator of whether the mth downlnk spot wth power level r s allocated to the lth burst, l = 1, 2,, L, m = 1,2,, M, r = 1, 2,, R, x lmr 1 = 0 f spot m wth O. W. power level r s put n burst l 19

34 The followng constrants regardng the above parameters and varables are satsfed n practce: (1) M >> N and M s nteger dvsble by N. (2) Consder the power matrx as follows: w w P = w M 1 w w 12 w 22 M 2 w 1R w 2R w MR The dfferences of w, m = 1,2,, M nsde each column are much smaller mr than the dfferences of w, r = 1, 2,, R nsde each row. mr M (3) wm 1 < LPtot < wmr. As we mentoned n Subsecton 2.1.2, the total system m= 1 M m= 1 power s enough to provde standard power (whch s hgher than the mnmum power w m1 ) to every downlnk n a burst, whle t cannot supply everybody wth the hghest power power). w mr (whch s hgher than the standard Mathematcal Formulaton The coupled resource management problem of antenna schedulng and power allocaton s formulated as follows: gven the ran fade condton of every downlnk spot and the BER requrement, maxmze L M R l= 1 m= 1 r= 1 x lmr p mr, subject to M R m= 1 r= 1 x lmr w mr P tot, l = 1,2,, L, (1) 20

35 M R m= 1 r= 1 L R l= 1 r= 1 x lmr N, l = 1,2,, L, (2) x = 1, m = 1,2,, M, (3) lmr { 0, 1} x, l = 1, 2,, L, m = 1,2,, M, lmr r = 1, 2,, R. The frst constrant ensures that the system power s enough to serve the selected spots wth ther respectve power n each burst. The lmt of antenna number s represented n constrant (2). Constrant (3) guarantees farness among downlnk spots by servng every spot once and only once n a round. All the numbers p mr, w mr, N and P tot are postve ntegers. And also the objectve functonal and the constrants are lnear n x lmr, thus the above problem falls nto the class of (lnear) nteger programmng. In partcular, t has the smlar structure as the well-known 0-1 knapsack problems, whch we wll dscuss n detal n the next two chapters. 21

36 Chapter 3: Knapsack Problems: Some Background 3.1 Introducton to Integer Programmng A lnear program s a mathematcal model desgned to fnd a set of decson varables to maxmze (or mnmze) a lnear objectve functon whle satsfyng some lnear constrants. If the restrcton that decson varables must take nteger values s added, we have a (lnear) nteger program (IP) [9], [10], [11]. An nteger programmng problem can be formulated as: maxmze cx, subject to Ax b, x 0, and x nteger, where A s an m by n matrx, c an n-dmensonal row vector, b an m-dmensonal column vector, and x an n-dmensonal column vector of decson varables. And f all varables are further restrcted to 0-1 values, we have a 0-1 or bnary nteger program (BIP): maxmze cx, subject to Ax b, x } n {0, 1. A wde varety of practcal problems can be formulated as or converted to nteger programs. Included n these are schedulng, plannng, locaton, network, cuttng and selecton problems that arse n ndustry, mltary, educaton, health, and other 22

37 envronments. In the past ten years, there has been a remarkable advance n the nteger programmng feld due to mproved modelng, faster computers, new cuttng plane theory, branch-and-cut and other advanced algorthms. So more complex problems can be modeled and solved usng nteger programmng n a reasonable computng tme [9]. 3.2 Overvew of 0-1Knapsack Problems An mportant class of bnary nteger programmng problems s the famly of 0-1 knapsack problems (KP). The name s n reference to packng a knapsack (or knapsacks) by choosng a subset of the gven n tems such that the correspondng proft sum s maxmzed wthout exceedng the capacty of the knapsack(s). The decson varable x j s ether 1 (tem j s selected) or 0 (tem j s not selected). Knapsack problems have been extensvely studed durng the last three decades wth a rch lterature (see Psnger [14], Martello and Toth [12] and Ln [13] for great surveys). The KP famly s one of the wdely dscussed topcs n nteger programmng manly because of the followng two reasons: Ther mmedate applcatons n ndustry and fnancal management such as budget control, project selecton, cargo loadng, and cuttng stock. They appear as sub-problems n varous nteger programmng algorthms. Many complex combnatoral optmzaton problems can be reduced to knapsack problems and they beneft from mprovements n the feld of knapsack problems. 23

38 Dfferent types of 0-1 knapsack problems occur whle varous dstrbutons of the knapsacks and tems arse: In the 0-1 Sngle Knapsack Problem (SKP) only one knapsack needs to be flled and each tem may be chosen at most once; Specal case of Subset-sum Problem arses when for each j, the proft c j equals the weght a j ; If the tems should be chosen from dsjont classes and exactly one tem from each class, we obtan the Multple-choce Knapsack Problem (MCKP); The Multple Knapsack Problem (MKP) occurs when several knapsack of (maybe) dfferent capactes are to be packed smultaneously. The generalzatons of 0-1 knapsack problems nclude the Bounded Knapsack Problem, Unbounded Knapsack Problem and Bn-packng Problem. If the amount of tems chosen from each tem type s unlmted or bounded by a fnte number, we get the Unbounded or bounded Knapsack Problem respectvely. The Bn-packng problem, whch s desgned to pack all tems nto mnmum number of equally szed bns, s an example of mnmzaton problem. The most general form of a knapsack problem s the Multdmensonal Knapsack Problem, also known as Mult-constraned Knapsack Problem. Whle t has the formulaton of general nteger programmng, all the coeffcents n the object functon and constrants are requred to be nonnegatve. All Knapsack problems belong to the NP-hard famly (see Garey and Johnson [15]), therefore t s very unlkely that polynomal tme algorthms can be devsed for them. The only way to get an exact soluton s an enumeraton n the soluton space. If the enumeraton s complete, unacceptable solvng tme s expected. Fortunately, several 24

39 effectve enumeratve technques have been developed durng the past decades of research to save qute a lot of efforts [9], [16], [17]: Branch and bound: buld an enumeraton tree, and remove the nodes whch cannot produce mproved solutons by usng bounds derved from the ntegralty, nonnegatvty, and other constrants. Ths s also called mplct enumeraton. Preprocessng: before solvng the program, quckly check the sensblty of the formulaton, detect and elmnate redundant constrants and varables, and tghten bounds where possble. Dynamc programmng: calculate the optmal soluton recursvely from the optmal values of slghtly dfferent problems. State space relaxaton: Scale the coeffcents by a fxed value. In ths way the tme and space complexty of an algorthm may be consderably decreased, at the loss of optmalty. Several effcent algorthms arse from state space relaxaton. In the next several sectons, we wll gve more detaled descrptons of some welldeveloped knapsack problems whch are most related to our work Sngle Knapsack Problem The most fundamental knapsack problem s the 0-1 sngle knapsack problem (SKP). Gven n tems, each wth weght w j and proft p j, and a knapsack wth capacty c, the problem s to fll the knapsack so that the proft sum of the chosen tems s 25

40 maxmzed and the weght sum of these tems does not exceed the knapsack capacty. 0-1 sngle knapsack problem can be descrbed mathematcally as: maxmze z = n j= 1 p j x j, subject to n j=1 w j x j c, where x j = 1 0 f tem j s selected OW.. j = 1,2,, n. Wthout loss of generalty, we make the followng assumptons about the coeffcents p w, and c: j, j (1) All coeffcents are nonnegatve ntegers; fractonal case can be transformed by multplyng some factor. (2) p > 0 : Otherwse t can be removed from the tem set. j (3) 0 < w j < c : 0-weght tem can be drectly put nto the optmal solutons and tems wth weght exceedng c can be deleted. n (4) 0 < c < w j : We can get trval solutons by settng all x j = 0 for case j= 1 n w j j= 1 c = 0 and all x j = 1 for case c. SKP s representatve of many ndustral stuatons such as budget control, cuttng stock and project selecton. It also appears as a sub-problem n many algorthms of other nteger programmng and knapsack problems: the multple knapsack problem, to menton an example. 26

41 SKP s NP-hard, but t can stll be solved n pseudo-polynomal tme. The problem has been ntensvely studed snce 1966 due to ts wde applcablty and theoretcal nterest. See Dudznsk and Walukewcz [18] (the theoretcal framework of exact algorthms), Martello and Toth [12] (elaboraton and mplementatons of these algorthms) and Gerasch and Wang [19] (parallel computng methods) for thorough revews. 3.4 Multple Knapsack Problem The multple knapsack problem (MKP) deals wth packng m dstnct knapsacks wth n gven tems. The m knapsacks have (maybe) dfferent capactes c, = 1,2,, m. Each tem has a proft p j and the assocated weght w j, and the problem s to choose m dsjont subsets from the n tems, such that the total proft sum of the selected tems s maxmzed whle the weght sum of subset does not exceed the capacty of knapsack, for each { 1,2,, m}. The multple knapsack problem thus can be formulated as: maxmze z = m n = 1 j= 1 p j x j, subject to n w j xj j=1 c, = 1, 2,, m, m = 1 x 1, j = 1,2,, n, j where x j 1 = 0 f tem j s assgned to knapsack OW.. = 1, 2,, m, j = 1,2,, n. 27

42 Wthout loss of generalty, we wll make smlar assumptons as n sngle knapsack problems to avod trval cases: (1) All the coeffcents p w, j, j and c are postve ntegers. n (2) w > max{ c = 1, 2,, m}. Ths avods the trval soluton of puttng all j= 1 j tems n one knapsack. (3) w max{ c = 1,2,, m} for j = 1,2,, n. Ths ensures that every tem can j ft nto at least one knapsack as otherwse t can be removed from the tem set. (4) c mn{ w j = 1, 2,, n} for = 1, 2,, m. The knapsack volatng ths j assumpton can be taken out as t cannot contan any tem. MKP has an mmedate applcaton n cargo loadng problems, e.g., loadng m vessels/contaner wth an optmal plan such that maxmum beneft s acheved. MKP s NP-hard n the strong sense, thus dynamc programmng approaches cannot be appled to MKP. As a result, most reported algorthms n the lterature focused on branch and bound technques: Hung and Fsh [20], Martello and Toth [12], and Psnger [14] to menton a few examples. Among these, the algorthm presented n Psnger [14] s more effcent for large problem nstances and s selected to solve MKP n our work (see Chapter 5). 3.5 Multple-choce Knapsack Problem The last well-known knapsack problem we wll descrbe here s the multplechoce knapsack problem (MCKP). We consder the problem of packng tems from k 28

43 nto dsjont sets N, N, 2, N 1 k some knapsack of capacty c. Each tem j n class N has proft p j and weght w j. We want to select exactly one tem from each set to pack n the knapsack such that the total proft sum of the chosen tems s maxmzed, and the weght sum does not exceed the knapsack capacty. The multple-choce knapsack problem thus may be formulated as: maxmze z = k = 1 j N p j x j, subject to k = 1 j N w j x j c, j N x = 1, = 1, 2,, k, j where x j = 1 0 f tem j n classs selected OW.. = 1, 2,!, k, j N. Smlarly, we make the followng assumptons: (1) All coeffcents p w, j, j and c are postve ntegers. (2) The k classes are mutually dsjont wth sze n, k = 1, 2, ", k. (3) mn{ w j N } c < max{ w j N }. Ths avods nfeasble stuatons = 1 or trval solutons. j k = 1 MCKP has many applcatons: captal budgetng, menu plannng, etc. An applcaton n KP theory s transform of nonlnear KP to MCKP. j MCKP s also NP-hard snce t contans SKP as a specal case: each tem n SKP can be vewed as a two-element class by addng a dummy tem (p,w)=(0,0). However, 29

44 due to ts specal structure, Dudznsk and Walukewcz [18] showed that MCKP s solvable n pseudo-polynomal tme. The problem has been ntensvely nvestgated durng the last two decades and a number of algorthms were presented n lterature. We menton several here as examples: Nauss [20], Snha and Zoltners [21], Dyer, Rha and Walker [22], and Psnger [14], among whch we use the mnmal algorthm n [14] to solve the MCKP n our work. 30

45 Chapter 4: Formulaton of Resource Allocaton as Knapsack Problems 4.1 Mult-choce Multple Knapsack Model In Chapter 2, we descrbed the resource allocaton problem we want to nvestgate and gave the mathematcal formulaton as follows: maxmze z = L M R l= 1 m= 1 r= 1 x lmr p mr, subject to M R m= 1 r= 1 x lmr w mr P tot, l = 1, 2, #, L, M R m= 1 r= 1 L R l= 1 r= 1 x lmr N, l = 1,2, $, L, x = 1, m = 1,2, %, M, lmr where = 1 f spot m wth power level r s assgned toburst l x lmr, 0 OW.. l = 1, 2, &, L, m = 1,2, ', M, r = 1, 2, (, R, L, M, R, and N are the numbers of bursts n a round, downlnk spots, transmsson power levels, and antennas, respectvely, w mr stands for the transmsson power of level r for downlnk spot m and p mr denotes the correspondng prorty, and P tot s the total avalable power for each burst. 31

46 Ths problem s a bnary nteger program (BIP) as we defned n Secton 3.1. We can further relate t to the famly of knapsack problems by makng the followng observaton: L bursts can be vewed as L knapsacks wth the same capacty P tot, and every downlnk spot wth ts dfferent power levels and assocated prortes as ndvdual tem class. To be specfc, each tem r n class weght N m (downlnk spot m) has a proft p mr and w mr. Thus the problem s to choose exactly one tem from each class to pack n L knapsacks, such that the proft sum s maxmzed wthout exceedng any knapsack s capacty. From the above dscusson, the resource allocaton problem s equvalent to a non-standard knapsack problem, whch we shall call Mult-choce Multple Knapsack Problem (MCMKP). The mult-choce part s responsble for selectng an approprate power lever for each spot, so ths accounts for the power allocaton aspect; whle the multple knapsack part corresponds to pckng at most N spots for every burst n the round, so t accounts for the burst schedulng aspect. The resource allocaton problem s thus reformulated as mult-choce multple knapsack problem n the followng form: maxmze z = L M l= 1 m= 1r Nm p mr x lmr, subject to M m= 1 r Nm w mr x lmr P tot, l = 1, 2, ), L, L lmr l= 1 r Nm x = 1, m = 1,2, *, M, M x lmr m= 1 r Nm N, l = 1, 2, +, L, 32

47 where = 0 f tem r nclass ms assgned to knapsack l x lmr, 1 OW.. l = 1, 2,,, L, m = 1,2, -, M, r N m. All the assumptons for knapsack problems lsted n Chapter 3 are naturally satsfed by ths problem s engneerng background descrbed n Subsecton MCMKP subsumes MKP and MCKP as two specal cases: settng L = 1and M = N results n MCKP; whle lettng R = 1 reduces MCMKP to MKP (wth slght modfcaton). As we mentoned n Chapter 3, MKP s NP-hard n the strong sense, so s MCMKP. Therefore t rules out the exstence of pseudo-polynomal algorthms or fully polynomal approxmaton schemes. There has been lttle effort devoted to the partcular structure lke MCMKP n the lterature. The best algorthms publshed up-to-date take about a fracton of second to solve relatvely large MKP nstances and pseudopolynomal tme for MCKP. MCMKP s a combnaton of these two problems, thus t s very unlkely that an exact algorthm wth a reasonable computng tme (lke seconds) can be devsed based on today s technques of nteger programmng. Snce our work s more engneerng rather than theoretcal, we are more nterested n fndng a feasble sub-optmal soluton than a tme-consumng optmal soluton. Therefore, we wll adopt some approprate reductons and smplfcatons to the orgnal problem and make t easer to solve. In the next two sectons, we wll provde two schemes for solvng the problem, whch may be vewed as modfcatons of the above MCMKP model. In Secton 4.2, we ntroduce and dscuss Brman s work [4], where he modeled the problem as MKP. In Secton 4.3, we frst state the performance measures for resource allocaton schemes n 33

48 Ka-band satellte systems, then we present our new approach of MCKP, whch s the man contrbuton of the thess. 4.2 Multple Knapsack Model In hs master thess, Brman proposed a set of schemes to solve the resource allocaton problem for Ka-band satellte systems. The system confguraton n hs thess s very smlar as that n ths thess except that the transmsson rate for downlnk spots s fxed to some standard rate rather than tunable as n our settng. As a consequence, there s only one power level assocated wth each downlnk under certan ran condton. Compared to the MCMKP model formulated n last secton, ths smpler confguraton removes the tems wth non-standard transmsson rates from each tem set, elmnates the multple-choce part of MCMKP, and reduces the problem to MKP structure whch s more tractable. We wll elaborate ths below. Brman nvestgated allocaton schemes for the two lmted resources, power and antenna, separately. In consderaton of dfferent weather and traffc condtons, he dscussed two cases, namely stable load condton and unbalanced load condton respectvely, and proposed dfferent burst schedulng and power allocaton algorthms for each load condton Stable Load Condton By Brman s defnton, stable load condton means that the transmsson system on the satellte can serve all the traffc arrvng at the satellte wthout overfllng the buffers and the whole system s stable. 34

49 By ths stablty assumpton, the total system power s enough to meet the demand. So the power allocaton scheme s very smple: allottng the approprate power to the downlnks so that they can mantan the standard transmsson rate under ther ran condtons. For burst schedulng, Brman utlzed one of the smplest generalzed processor sharng schemes, whch s a varant of Weghted Round Robn (WRR). The weght assocated wth a downlnk queue s defned to be the prorty sum of packets n that queue up to a search depth, whch s equal to the number of packets that can be sent out n one burst by an antenna wth the standard transmsson rate. As soon as the weght of every queue s determned, all the queues can be ranked n the decreasng order of weghts and the antennas wll serve these queues n a round robn manner. WRR and the power-on-demand descrbed above formed Brman s resource allocaton scheme under stable condton. Ths scheme has two obvous advantages: (1) smple to mplement; (2) effectve n allocatng power and antennas to downlnks under stable load condton. But the dsadvantage s also obvous: the system capacty s not fully used. As we mentoned before, the satellte systems are usually desgned to carry extra power n addton to that requred by downlnks under the clear weather condton. So under stable condton, the extra backup power s wasted Unbalanced Load Condton Unbalanced load condton, on the other hand, refers to the stuatons whenever stable load condton s not satsfed. In ths case, the system cannot provde suffcent capacty to transmt all the arrvng traffc and overflows n buffers occur. 35