Power Control for Ad-Hoc Wireless Networks Using Sliding-Mode Control Theory Mihaela R. Cistelecan Department of Automation Technical University of Cluj-Napoca, Romania Email: mihaela.cistelecan@aut.utcluj.ro Dimitrie C. Popescu Department of Electrical Engineering University of Texas at San Antonio, USA Email: dimitrie.popescu@utsa.edu Abstract— In this paper we present a theoretical approach to power control for ad-hoc wireless networks using sliding mode control theory. We derive a dynamic system based on the signal- to-interference ratio (SIR) of links in the network whose control input is related to the transmitted power, and show how sliding mode control theory is used to derive the power equations that lead to an equilibrium point where the link SIR are optimized. I. I NTRODUCTION Transmitter power control is one of the components of radio resource management at the physical layer of a wireless net- work which contributes to minimizing interference, increasing network capacity, and extending the battery life of active nodes in the wireless network by ensuring that these transmit at the minimum power level necessary to achieve a specified quality of service (QoS) usually defined in terms of the SIR. A good power control mechanism should balance several conflicting requirements which can be summarized as follows: • The SIR of any node in the wireless network can be increased by increasing its transmitted power. • Increasing the transmitted power for one node will in- crease the interference experienced by all the other nodes in the network, which may increase their transmitted powers as well to overcome the increased interference. • Increasing the transmitted power consumes more energy and shortens the battery life of nodes in the wireless network. When all nodes keep increasing their transmitted power to meet specified SIR values, they will end up transmitting at their maximum allowed power level which will exhaust their battery energy rapidly. This can create instability in the wireless network which may experience rapid deactivation of nodes due to battery failure. We note that numerous power control algorithms have been developed over the past decade [6], which are presently imple- mented in cellular telephone systems or wireless networking applications that combine wireless access with the existence of a fixed wired infrastructure. However, there is increasing interest in ad-hoc wireless networks with network topology that is no longer dependent on a fixed wired infrastructure. Rather, ad-hoc networks are based on multihop connectivity, with information being transmitted over a set of nodes that is dynamically reconfigurable in response to mobility or quality of the radio link [1]. In our paper we present a new approach to power control for ad-hoc networks based on the theory of sliding mode control [2], [4], [5]. This is a robust control technique that is applicable to nonlinear systems, systems with varying parameters, or systems that are subject to external disturbances. We derive the dynamic equation of the SIR error function corresponding to mobile terminals in the ad-hoc network, and apply sliding mode control theory to obtain a sliding mode control law that will bring the error to the origin by appropriately changing the transmitted power. II. SYSTEM MODEL AND PROBLEM STATEMENT We consider an ad-hoc wireless network consisting of N pairs of transmitter and receiver nodes that make up distinct wireless links which interfere with each other [1]. The SIR of a given link i in the networks is expressed as γ i = G ii p i  j=i G ij p j + η i i, j =1,...,N (1) where p i is the power of transmitter for link i, G ii is channel gain of link i (between link i transmitter and receiver), G ij is the channel gain of between the transmitter of a different link j and link i receiver, and η i is the power of the additive white Gaussian noise (AWGN) that corrupts the received signal at link i receiver. We assume that gains may vary in time between known lower and upper bounds, and that a minimum SIR value is required for each link’s operation, that is γ i ≥ γ m i ∀i (2) When the actual SIR of link i is below the specified lower bound γ m i the link is not functional as a communication link, but acts as a disturbance for all functional links in the ad-hoc network [1]. When the actual SIR of link i is above γ m i but below an optimal value γ M i required by the QoS for link i, then it is necessary to increase it using appropriate changes in transmitted power. Our goal in this paper is to use sliding mode control theory to identify the variation of transmitted power that will bring the network to a stable equilibrium point corresponding to the vector of optimal SIRs ( γ M 1 ... γ M N ) T for a given link configuration described by the gain values {G ij } along with their variation in time { ˙ G ij }. Assuming a standard pathloss model in which gains are related to the distance between the corresponding transmitter and receiver, these values can be obtained from the network topology and mobility patterns. Sliding mode control [5] is a robust control technique that 335 1-4244-0359-6/06/$20.00 ©2006 IEEE.