# Seminar: Reliability by Retransmissions in the Wireless World

Anastasios Giovanidis - Technical University of Berlin

Mobile Communications

**Date:** July 27, 2010

**Location:** Eurecom - salle des conseils

The talk focuses on the modeling, analysis and control of Automatic Retransmission reQuest (ARQ) protocols as part of a wireless communications system and provides an overview of several recent results of the speaker. A significant performance measure related to ARQ protocols is the goodput, which is typically expressed as the product of scheduled transmission rate times the success probability. We initially propose alternative goodput measures for short term communications - more appropriate in case the number of packets to be transmitted is finite. 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 transition probability matrix is ergodic. Conditions for ergodicity and non-ergodicity result in a categorization of ARQ protocols 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 is next investigated using optimal stopping arguments. ARQ protocols are of course related to queuing. Incorporating a retransmission protocol 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 interrupting the retransmission process. Applying dynamic programming the optimal dropping policy is derived. A next step 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 retransmission protocol to achieve reliability, while the base station has a specific total power budget to divide among users at each time slot. Considering fixed transmission rate per user and taking interference into account, the stability region of the system and power control algorithms to achieve this are derived. The talk concludes with an investigation of an ad hoc wireless network, where data enter in different source nodes and should be routed through the system nodes to their destination. Errors occur per hop due to fading and interference. Each node is again equipped with an ARQ protocol for error correction. The stability region of the system is derived. Each data flow is related to a utility function and a network utility maximization problem with stability constraints is formulated. Its solution provides the optimal per slot congestion control, routing and power allocation policy to maximize the sum of utilities while keeping all buffers in the system finite. The requirement that the power allocation policies should be implemented in a decentralized manner can be fulfilled if cooperation between nodes is allowed and at the same time each node performs measurements to estimate its interference level. Applying game theory and using the above information, each node can choose an optimal power to transmit.

**Permalink:** http://www.eurecom.fr/seminar/353

*Reliability by Retransmissions in the Wireless World*