A Game-Theoretic Approach to Energy-Efficient Modulation in CDMA Networks with Delay QoS Constraints
📝 Abstract
A game-theoretic framework is used to study the effect of constellation size on the energy efficiency of wireless networks for M-QAM modulation. A non-cooperative game is proposed in which each user seeks to choose its transmit power (and possibly transmit symbol rate) as well as the constellation size in order to maximize its own utility while satisfying its delay quality-of-service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. The best-response strategies and Nash equilibrium solution for the proposed game are derived. It is shown that in order to maximize its utility (in bits per joule), a user must choose the lowest constellation size that can accommodate the user’s delay constraint. This strategy is different from one that would maximize spectral efficiency. Using this framework, the tradeoffs among energy efficiency, delay, throughput and constellation size are also studied and quantified. In addition, the effect of trellis-coded modulation on energy efficiency is discussed.
💡 Analysis
A game-theoretic framework is used to study the effect of constellation size on the energy efficiency of wireless networks for M-QAM modulation. A non-cooperative game is proposed in which each user seeks to choose its transmit power (and possibly transmit symbol rate) as well as the constellation size in order to maximize its own utility while satisfying its delay quality-of-service (QoS) constraint. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. The best-response strategies and Nash equilibrium solution for the proposed game are derived. It is shown that in order to maximize its utility (in bits per joule), a user must choose the lowest constellation size that can accommodate the user’s delay constraint. This strategy is different from one that would maximize spectral efficiency. Using this framework, the tradeoffs among energy efficiency, delay, throughput and constellation size are also studied and quantified. In addition, the effect of trellis-coded modulation on energy efficiency is discussed.
📄 Content
Wireless networks are expected to support a variety of applications with diverse quality-of-service (QoS) requirements. Because of the scarcity of network resources (i.e., energy and bandwidth), radio resource management is crucial to the performance of wireless networks. The goal is to use the network resources as efficiently as possible while providing the required QoS to the users. Adaptive modulation has been shown to be an effective method for improving the spectral efficiency in wireless networks (see for example [1]- [4]). However, the focus of many of the studies to date has been on maximizing the throughput of the network, and the impact of the modulation order on energy efficiency has not been studied to the same extent. Recently, the authors of [5] have studied modulation optimization for an energy-constrained time-division-multiple-access (TDMA) network. For such a network, they have used a convex-optimization approach to obtain the best modulation strategy that minimizes the total energy consumption under throughput and delay constraints.
Game-theoretic approaches to power control have recently attracted considerable attention (see, for example, [6]- [16]). In [6], the authors provide motivations for using game theory to study communication systems, and in particular power control. In [7], power control is modeled as a non-cooperative game in which users choose their transmit powers in order to maximize their utilities, where utility is defined as the ratio of throughput to transmit power. A game-theoretic approach to joint power control and receiver design is presented in [13], and power control for multicarrier systems is studied in [14]. The authors in [8] use pricing to obtain a more efficient solution for the power control game. Similar approaches are taken in [9]- [12] for different utility functions. Game-theoretic approaches to power control in delay-constrained networks are proposed in [15], [16].
In this work, we use a game-theoretic approach to study the effects of modulation on energy efficiency of code-divisionmultiple-access (CDMA) networks in a competitive multiuser setting. Focusing on M-QAM modulation, we propose a noncooperative game in which each user chooses its strategy, which includes the choice of the transmit power, transmit symbol rate and constellation size, in order to maximize its own utility while satisfying its QoS constraints. The utility function used here measures the number of reliable bits transmitted per joule of energy consumed, and is particularly suitable for energy-constrained networks. We derive the bestresponse strategies and Nash equilibrium solution for the proposed game. In addition, using our non-cooperative gametheoretic framework, we quantify the tradeoffs among energy efficiency, delay, throughput and modulation order. The effect of coding on energy efficiency is also studied and quantified using the proposed game-theoretic approach. In addition, our framework allows us to illustrate the tradeoff between energy efficiency and spectral efficiency.
The remainder of this paper is organized as follows. The system model and definition of the utility function are given in Section II. We then present a power control game with no delay constraints in Section III and derive the corresponding Nash equilibrium solution. A delay-constrained power control game is proposed in Section IV and the corresponding best-response strategies and Nash equilibrium solution are derived. The analysis is extended to coded systems in Section V. Numerical results and conclusions are given in Sections VI and VII, respectively.
We consider a direct-sequence CDMA (DS-CDMA) wireless network in which the users’ terminals are transmitting to a common concentration point (e.g., a cellular base station or an access point). The system bandwidth is assumed to be B Hz. Let R s,k and p k be the symbol rate and the transmit power for user k, respectively. In this work, we focus on M-QAM modulation. Hence, each symbol is assumed to be complex to represent the in-phase and quadrature components. For the M-QAM modulation, the number of bits transmitted per symbol is given by b = log 2 M.
Since there is a one-to-one mapping between M and b, we sometimes refer to b as the constellation size. We focus on square M-QAM modulation, i.e., M ∈ {4, 16, 64, • • • } or equivalently b ∈ {2, 4, 6, • • • }, since there are exact expressions for the symbol error probability of square M-QAM modulation (see [17]). We can easily generalize our analysis to include odd values of b by using an approximate expression for the symbol error probability. We define the utility function of a user as the ratio of its throughput to its transmit power, i.e.,
This utility function is similar to the one used in [7] and [8]. Throughput in (1) is defined as the net number of information bits that are transmitted without error per unit time (it is sometimes referred to as goodput), and is expressed as
where
is the tran
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