We consider an optimal power and rate scheduling problem for a single user transmitting to a base station on a fading wireless link with the objective of minimizing the mean delay subject to an average power constraint. The base station acts as a controller which, depending upon the transmitter buffer lengths and the signal power to interference ratio (SIR) on the uplink pilot channel, allocates transmission rate and power to the user. We provide structural results for an average cost optimal stationary policy under a long run average transmitter power constraint. We obtain a closed form expression relating the optimal policy when the SIR is the best, to the optimal policy for any other SIR value. We also obtain lower and upper bounds for the optimal policy. Keywords: Power and rate control in wireless networks, Quality of service in wireless networks In communication systems, many fundamental problems involve the optimal allocation of resources subject to performance objectives. In a wired network, the crucial resources are the transmission data rates available on the link. Techniques such as flow control, routing and admission control are all centered around allocating these resources. We consider a resource allocation problem that arises in mobile wireless communication systems. Several challenging analytical problems arise because of the special limitations of a wireless link. One is the time varying nature of the multipath channel, and another is the limited battery power available at a typical wireless handset. It is desirable to allocate transmission rates to a user such that the energy used to transmit the information is minimized while keeping errors under control. Most applications, however, also have quality of service (QoS) objectives such as mean delay, delay jitter, and throughput. Thus there is a need for optimal allocation of wireless resources which provides such QoS guarantees subject to the above said error and energy constraints. Various methods for allocating transmission resources are part of most third generation cellular standards. They include adjusting the transmission power, changing the coding rate and varying the spreading gain in a CDMA based system. The system model in our work is given in Fig. 1 and is explained below. We assume a slotted system where the higher layer presents the data, that arrives over a slot, to the link layer at the end of each slot. The link layer is assumed to have an infinite capacity buffer to hold the data. We assume that the channel gain and any other interference to the system remain fixed over a slot and vary independently from slot to slot. Over a mini-slot (shown as shaded in Fig. 1 ), the buffer length information is communicated to the receiver/controller, and the user transmits pilot bits at a fixed power level which we refer to as a pilot channel. The receiver estimates the signal to interference ratio (SIR) on the pilot channel. We assume that the estimates are perfect. Depending on the SIR estimates and the buffer length information, the receiver evaluates the optimal transmission rate and power for the current slot and communicates it back to the transmitter. In practice, there are some restrictions on how much these controls can vary. In this paper we assume that the transmitter can transmit at any arbitrary rate and power level. The transmitter removes that much amount of data from the buffer and encodes it at the allocated rate. All this exchange of information and the encoding is assumed to be completed within the time slot shown as shaded in the Fig. 1 . After this the transmitter starts to transmit the encoded data. Goldsmith and Varaiya [3] are probably the first to obtain the optimal power allocation policy for a single link fading wireless channel. Their emphasis was on the optimal physical layer performance, while ignoring the network layer performance such as queueing delay. In recent work, Berry and Gallager [1] have considered a problem similar to ours. They obtained structural results exhibiting a tradeoff between the network layer and physical layer performance, i.e. the optimal power and mean delay. They show that the optimal power vs; the optimal delay curve is convex, and as the average power available for transmission increases, the achievable mean delay decreases. They also provide some structural results for the optimal policy that achieves any point on the power delay curve. In this work, we improve upon the results obtained in [1] . We prove the existence of a stationary average optimal policy, and give a closed form expression for the optimal policy for any SIR value in terms of the optimal policy when the SIR is one, i.e., the best SIR. We also provide lower and upper bounds for the optimal rate allocation policy, not obtained by Berry and Gallager. This paper is organized as follows. In Section III, we give the model of the system under consideration and formulate 0-7803-7753-2/03/$17.00 (C) 2003 IEEE 311
While the existence of a stationary optimal policy for the average cost problem has been considered in REF when the packet arrival process is independent and identically distributed (i.i.d.), the problem becomes much more difficult when the arrival process is Markovian.
Power constrained and delay optimal policies for scheduling transmission over a fading channel
IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428)
IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428)
Computer Science