Power control for wireless data

With cellular phones mass-market consumer items, the next frontier is mobile multimedia communications. This situation raises the question of how to do power control for information sources other than voice. To explore this issue, we use the concepts and mathematics of microeconomics and game theory. In this context, the Quality of Service of a telephone call is referred to as the "utility" and the distributed power control problem for a CDMA telephone is a "noncooperative game". The power control algorithm corresponds to a strategy that has a locally optimum operating point referred to as a "Nash equilibrium." The telephone power control algorithm is also "Pareto efficient," in the terminology of game theory. When we apply the same approach to power control in wireless data transmissions, we find that the corresponding strategy, while locally optimum, is not Pareto efficient. Relative to the telephone algorithm, there are other algorithms that produce higher utility for at least one terminal, without decreasing the utility for any other terminal. This paper presents one such algorithm. The algorithm includes a price function, proportional to transmitter power. When terminals adjust their power levels to maximize the net utility (utility price), they arrive at lower power levels and higher utility than they achieve when they individually strive to maximize utility. I. BACKGROUND AND MOTIVATION The technology and business of cellular communications systems have made spectacular progress since the first systems were introduced fifteen years ago. With new mobile satellites coming on line, business arrangements, technology and spectrum allocations make it possible for people to make and receive telephone calls anytime, anywhere. The cellular telephone success story prompts the wireless communications community to turn its attention to other information services, many of them in the category of "wireless data" communications. To bring high-speed data services to a mobile population, several "third generation" transmission techniques have been devised. These techniques are characterized by user bit rates on the order of hundreds or thousands of kb/s, one or two orders of magnitude higher than the bit rates of digital cellular systems. One lesson of cellular telephone network operation is that effective radio resource management is essential to promote the quality and efficiency of a system. One component of radio resource management is power control, the subject of this paper. An impressive set of research results published since 1990 documents theoretical insights and practical techniques for assigning power levels to terminals and base stations in voice communications systems [1-4]. The principal purpose of power control is to provide each signal with adequate quality without causing unnecessary interference to other signals. Another goal is to minimize the battery drain in portable terminals. An optimum power control algorithm for wireless telephones maximizes the number of conversations that can simultaneously achieve a certain quality of service (QoS) objective. There are several ways to formulate the QoS objective quantitatively. Two prominent examples refer to a QoS target. In one example, the target is the minimum acceptable signal-to-interference ratio and in the other example the target is the maximum acceptable probability of error. In turning our attention to data transmission, we have discovered that this approach does not lead to optimum results. This is because the QoS objective for data signals differs from the QoS objective for telephones. To formulate the power control problem for data, we have adopted the vocabulary and mathematics of microeconomics in which the QoS objective is referred to as a utility function. The utility function for data signals is different from the telephone utility function. Our research indicates that when all data terminals individually adjust their powers to maximize their utility, the transmitter powers converge to levels that are too high. To obtain better results, we introduce a pricing function that recognizes explicitly the fact that the signal transmitted by each terminal interferes with the signals transmitted by other terminals. The interference caused by each terminal is proportional to the power the terminal transmits. This leads us to establish a price (measured in the same units as the utility function) to be calculated by terminals in deciding how much power to transmit. Terminals adjust their powers to maximize the difference between utility and price. In doing so, they all achieve higher utilities than when they aim for maximum utility without considering the price. II. UTILITY FUNCTIONS FOR VOICE AND DATA A utility function is a measure of the satisfaction experienced by a person using a product or service. In the wireless communications literature the term Quality of Service (QoS) is closely related to utility. Two QoS objectives are low delay and low probability of error. In telephone systems low delay is essential and transmission errors are tolerable up to a point. By contrast, data signals can accept some delay but have very low tolerance to errors. In establishing a minimum signal-to-interference ratio for telephone signals, engineers implicitly represent utility as a function of signal-to-interference ratio in the form of Figure 1. We consider systems to be unacceptable (utility = 0) when the signal-to-interference ratio ( ) γ is below a target level, 0 γ . When 0 γ γ >= , we assume that the utility is constant. Our power control algorithms implicitly assume that there is no benefit to having a signal-to-interference ratio above the target level. In cellular telephone systems, the target, γ0 is system dependent. For example analog systems aim for dB 18 0 = γ . In GSM digital systems the target can be as low as 7 dB, and in CDMA it is on the order of 6 dB [5]. In each case 0 γ is selected to provide acceptable subjective speech quality at a telephone receiver. 0 2 4 6 8 10 12 14 16 18 20 0 0.2 0.4 0.6 0.8 1