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Modeling and Analysis of Wireless Communication Systems Using Automatic Retransmission Request Protocols

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Modeling and Analysis of Wireless Communication Systems Using Automatic Retransmission Request Protocols Modeling and Analysis of Wireless Communication Systems using Automatic Retransmission Request Protocols vorgelegt von Diplom-Ingenieur Anastasios Giovanidis aus Athen, Griechenland Von der Fakultat¨ IV - Elektrotechnik und Informatik der Technischen Universitat¨ Berlin zur Erlangung des akademischen Grades Doktor der Ingenieurwissenschaften - Dr.-Ing. - genehmigte Dissertation Promotionsausschuss: Vorsitzender: Prof. Dr.-Ing. Klaus Petermann Berichter: Prof. Dr.-Ing. Dr. rer. nat. Holger Boche Berichter: Prof. Dr. Leandros Tassiulas Berichter: PD Dr.-Ing. habil. Sławomir Stanczak´ Tag der wissenschaftlichen Aussprache: 12.04.2010 Berlin 2010 D 83 Zusammenfassung Der Schwerpunkt der aktuellen Arbeit ist die Modellierung, Analyse und Regelung von au- tomatischen Wiederholungsanfrage (Automatic Retransmission reQuest - ARQ) Protokollen, die als Teil eines drahtlosen Kommunikationssystems betrachtet werden. Die Aufgabe von solchen Protokollen ist die Detektion und Korrektur vom Fehlern. Um dies zu erreichen, informiert der Empfanger¨ den Sender uber¨ das Ergebnis der Decodierung jedes Pakets mit Hilfe eines binaren¨ Steuersignals ACK / NACK. Das NACK Signal steuert eine Wiederhol- ung der Ubertragung¨ fur¨ das fehlerhaften Paket an. Das ACK Signal informiert den Sender, dass das Paket korrekt empfangen wurde, woraufhin das nachste¨ wartende Paket im Puffer fur¨ die neue Ubertragung¨ vorbereitet wird. Eine bedeutsames Performanzmass fur¨ solche Protokolle ist der goodput, der definiert ist als die Rate der korrekt uber¨ die drahtlose Verbindung ubertragenen¨ Pakete. Typis- cherweise wird der goodput beschrieben als Produkt der Ubertragungsrate¨ mal der Er- folgswahrscheinlichkeit. Dieses folgt aus der Renewal-Reward Theorie, die eine feste Wahrscheinlichkeitsverteilung sowie Ergodizitat¨ des Fading-Prozesses annimmt. Alter- native Masse fur¨ den goodput fur¨ Kommunikation zeitlich eng begrenzter Dauer werden vorgeschlagen, die besser geeignet sind fur¨ den Fall einer endlichen Anzahl von zuubertra-¨ genden Paketen. Legt man die Werte fur¨ die Erfolgswahrscheinlichkeit pro wiederholter Ubertragung¨ durch a priori Auswahl der Wiedrholung-Strategie fest, kann die Entwicklung des ARQ Protokolls als success run beschrieben werden. Eine Definition fur¨ die Zuverlassigkeit¨ der Kommunikation wird vorgestellt, die verwandt ist zur Idee der Delay-limited Kapazitat.¨ Es wird bewiesen, dass ein ARQ Protokoll dann und nur dann zuverlassig¨ ist, wenn seine Ubergangswarscheinlichkeitsmatrix¨ ergodisch ist. Bedingung fur¨ Ergodizitat¨ und Nicht- Ergodizitat¨ fuhren¨ zu einer Kategorisierung der ARQ Protokolle (und entsprechend der Leistungszuteilungs-Strategien pro Wiederholung) in zuverlassige¨ und unzuverlassige.¨ Weil bei der praktischen Ubertragung¨ die ARQ Protokolle immer zusammengeschnit- ten werden und ein Paketverlust auftritt, sobald die maximale Zahl an Wiederholungen i ii Zusammenfassung erreicht wurde, untersucht diese Arbeit das Problem des optimalen Zuschnitts der Anzahl der Wiederholungen. Die Methode verwendet Argumente des optimalen Abbruchs (optimal stopping), wobei eine erfolgreiche Ubertragung¨ eines Pakets mit einer Belohnung ausgeze- ichnet wird, wohingegen Verzogerungen¨ und Leistungsverbrauch als generalisierte Kosten modelliert werden. Das System vergibt außerdem eine Strafe, wenn eine Paket fallenge- lassen wird. Aus der sequentiellen Analyse folgt die optimale Zuschnittlange,¨ woraus man eine Regel erhalt,¨ die alle oben genannten Kosten und Belohnungen in eine einfache Ungle- ichung uberf¨ uhrt.¨ ARQ Protokolle sind naturlich¨ verwandt mit Queuing. Die Integration eines Wieder- holungsprotokolls auf dem Server einer Queue verursacht eine zusatzliche¨ Verzogerung¨ fur¨ die gepufferten Pakete, so dass die Zuverlassigkeit¨ der Ubertragung¨ gewahrleistet¨ werden kann. Um die Verzogerung¨ zu reduzieren, konnen¨ bestimmte Pakete durch Unterbrechung des Wiederholungsprozesses fallengelassen werden. Durch Anwendung von dynamischer Programmierung wird die optimale Abbruchstrategie hergeleitet. Die Entscheidung zum Fallenlassen hangt¨ von dem Systemzustand ab, der das Paar aus Queue-Lange¨ und ak- tuellem Aufwand fur¨ die Wiederholung bildet. Die daraus folgende Strategien sind optimal im Sinne der Minimierung des zeitlichen Mittelwerts eine Linearkombination von Queue- Lange¨ und der Anzahl der verlorenen Pakete. Ein nachster¨ Schritt in der Analyse ist die Leistungssteuerung von ARQ Protokollen in einem Downlink-System. Daten, die fur¨ eine bestimmte Anzahl von Nutzern vorge- sehen sind, werden an der Basisstation gepuffert. Jeder Puffer benutzt das Wiederhol- ungsprotokoll, um Zuverlassigkeit¨ zu erzielen, wahrend¨ die Basisstation ein spezifisches Gesamt-Leistungsbudget zur Verfugung¨ hat, um dieses an alle Nutzer in jedem Zeitschlitz zu verteilen. Bei Betrachtung von festen Ubertragungsraten¨ pro Nutzer und unter Beruck-¨ sichtigung von Interferenzen wird die Stabilitatsregion¨ des Systems hergeleitet. Es wird gezeigt, dass eine Leistungszuteilungsstrategie diese Stabilitatsregion¨ erreichen kann, und Algorithmen zur Berechnung der Leistung pro Nutzer werden angewendet und verglichen. Die Arbeit schließt mit einer Untersuchung eines drahtlosen Ad-Hoc Netzwerks, bei dem Daten an verschiedenen Quell-Knoten eingespeist werden, die dann uber¨ die System- knoten zu ihren Zielen geroutet werden. Fehler treten pro Hop durch Fading und Interferenz auf. Jeder Knoten is wieder mit einem ARQ Protokoll fur¨ Fehlerkorrektur versehen. Die Stabilitatsregion¨ des Systems wird hergeleitet. Jeder Datenfluß wird in Beziehung gesetzt zu einer Utility-Funktion, woraus ein Netzwerk Utility Maximierungsproblem unter Sta- bilitatsbedingungen¨ formuliert wird. Seine Losung¨ liefert die optimale Strategie fur¨ die per-Slot congestion control, routing sowie Leistungszuweisung, mit der die Summe der Zusammenfassung iii Utilities maximiert wird, wahrend¨ alle Puffer im System beschrankt¨ gehalten werden. Die Anforderung, dass die Leistungszuweisungsstrategien in einer dezentralisierten Weise im- plementierbar sein sollen, kann erfullt¨ werden, wenn Kooperation zwischen Knoten erlaubt wird und gleichzeitig jeder Knoten Messungen durchfuhren¨ kann, um die Starke¨ seiner Interferenz zu schatzen.¨ Bei Anwendung der Spieltheorie und Benutzung der obigen Infor- mation, kann jeder Knoten die optimale Leistung fur¨ die Ubertragung¨ wahlen.¨ Abstract The focus of the current thesis is on the modeling, analysis and control of Automatic Re- transmission reQuest (ARQ) protocols as part of a wireless communications system. The function of these protocols is the detection and correction of errors. To achieve this the receiver informs the transmitter over the result of packet decoding using a binary control signal ACK/NACK. The NACK triggers a retransmission of the erroneous packet, while an ACK informs the transmitter that the packet has been correctly received and the next packet awaiting in the buffer is prepared. A significant performance measure related to such protocols is the goodput, defined as the rate of correctly transmitted packets over the wireless link. Typically goodput is expressed as the product of scheduled transmission rate times the success probability, which results from renewal-reward theory assuming fixed probability distribution and ergodicity of the fading process. Alternative goodput measures for short term communications are suggested which are more appropriate in case the number of packets to be transmitted is finite. Fixing the success probability values per retransmission, by selecting a priori a retrans- mission policy, the evolution of an ARQ protocol can be described as a success run. A definition of reliability in communications is provided, which is related to the notion of delay limited capacity. It is proven that an ARQ protocol is reliable if and only if its tran- sition probability matrix is ergodic. Conditions for ergodicity and non-ergodicity result in a categorization of ARQ protocols (and subsequently of power allocation policies per retransmission), into reliable and unreliable. Since in practical communications the ARQ protocols are always truncated and a packet dropping occurs when the maximum number of retransmissions is exceeded, the problem of optimal truncation has been investigated. The method utilizes optimal stopping arguments where the successful transmission of a packet is related to a reward, whereas the delay and power consumption are modeled as generalized costs. The system incurs additionally a penalty when the packet is dropped. Optimal truncation length has resulted from the v vi Abstract sequential analysis which provides a rule combining all the above costs and rewards into a simple inequality. ARQ protocols are of course related to queuing. Incorporating a retransmission proto- col at the server of a queue brings additional delay to the buffered packets so that reliability of transmission can be guaranteed. To reduce delay certain packets can be dropped by inter- rupting the retransmission process. Applying dynamic programming the optimal dropping policy is derived. The decision to drop depends on the system state which is the pair of queue length and current retransmission effort. The resulting policies are optimal in the sense of minimizing the time average of a linear combination of queue length and number of dropped packets. A next step in the analysis is the power control of ARQ protocols in a downlink system. Data destined to a certain number of users are buffered at the base station. Each buffer uses the
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