This paper focuses on the cross-layer issue of joint multiuser detection and resource allocation for energy efficiency in wireless CDMA networks. In particular, assuming that a linear multiuser detector is adopted in the uplink receiver, the case considered is that in which each terminal is allowed to vary its transmit power, spreading code, and uplink receiver in order to maximize its own utility, which is defined as the ratio of data throughput to transmit power. Resorting to a game-theoretic formulation, a non-cooperative game for utility maximization is formulated, and it is proved that a unique Nash equilibrium exists, which, under certain conditions, is also Pareto-optimal. Theoretical results concerning the relationship between the problems of SINR maximization and MSE minimization are given, and, resorting to the tools of large system analysis, a new distributed power control algorithm is implemented, based on very little prior information about the user of interest. The utility profile achieved by the active users in a large CDMA system is also computed, and, moreover, the centralized socially optimum solution is analyzed. Considerations on the extension of the proposed framework to a multi-cell scenario are also briefly detailed. Simulation results confirm that the proposed non-cooperative game largely outperforms competing alternatives, and that it exhibits a quite small performance loss with respect to the socially optimum solution, and only in the case in which the users number exceeds the processing gain. Finally, results also show an excellent agreement between the theoretical closed-form formulas based on large system analysis and the outcome of numerical experiments.
the joint multiuser detection and channel equalization problem, have been tackled and thoroughly investigated. Results regarding these research issues are surveyed, among the others, in the textbooks [1], [2]. In the recent past, a new trend has emerged, i.e. the so-called cross-layer approach. Roughly speaking, the basic idea here is to perform joint optimization of procedures that are implemented in different layers of the network protocol stack, so as to outperform solutions based on single optimization of the procedures of each network layer. Regarding CDMA systems, the cross layer approach has mainly focused on the problem of integrating physical layer issues, such as multiuser detection and channel estimation, with network level issues, such as call admission control, power control, and, more generally, resource allocation [3]. In keeping with this recent trend, this paper focuses on the issue of joint multiuser detection and resource allocation in order to achieve energy efficiency in wireless CDMA networks. The results of this paper are mainly based on two powerful mathematical tools, namely game theory and large system analysis.
Game theory [4] is a branch of mathematics that has been applied primarily in economics and other social sciences to study the interactions among several autonomous subjects with contrasting interests. More recently, it has been discovered that it can also be used for the design and analysis of communication systems, mostly with application to resource allocation algorithms [5], and, in particular, to power control [6]. As examples, the reader is referred to [7]- [9]. In these papers, for a multiple access wireless data network, noncooperative and cooperative games are introduced, wherein each user chooses its transmit power in order to maximize its own utility, defined as the ratio of the throughput to transmit power. While the above papers consider the issue of power control assuming that a conventional matched filter is available at the receiver, the recent paper [10] considers the cross-layer problem of joint linear receiver design and power control so as to maximize the utility of each user: it is thus shown in [10] that the inclusion of receiver design in the considered game brings remarkable advantages. This same utility function is also used in [11] for energy-efficient power control in ultra-wideband (UWB) communications, while the survey paper [12] reviews recent advances in the application of a game-theoretic framework for energy-efficient resource allocation.
Large system analysis (LSA) is a relatively new mathematical tool, first introduced in [13], that has recently emerged in the analysis of CDMA systems. In summary, [13] has revealed that in a CDMA system with processing gain and number of users both increasing without bound but with their ratio fixed, and with randomly chosen, unit-norm, spreading codes, the Signal-to-Interference plus Noise Ratio (SINR) of each user for the case in which a linear minimum mean square error (MMSE) receiver is adopted converges in probability to a non-random constant. In particular, denoting by K the number of active users, by N the system processing gain, by N 0 /2 the additive thermal noise power spectral density (PSD) level, and by E P [•] the expectation with respect to the limiting empirical distribution F of the received powers of the interferers, the SINR of the MMSE receiver for the k-th user, say γ k , converges, for K, N → ∞, K/N = α = constant, in probability to γ * k the unique solution of the equation
with P k the received power for the k-th user. Interestingly, the limiting SINR depends only on the limiting empirical distribution of the received powers of the interferers, the load α, the thermal noise level and the received power of the user of interest, while being independent of the actual realization of the received powers of the interferers and of the spreading codes of the active users. LSA is now a well-established mathematical tool for design and analysis of communication systems (see, e.g., [14]- [16], to cite a few).
This paper is the first in this area that considers the crosslayer issue of utility maximization with respect to the choice of linear multiuser detector, spreading code and transmit power. Using game theory and LSA, the following contributions are given here.
-We generalize the non-cooperative game considered in [10] by considering utility maximization with respect to the linear uplink multiuser receiver, transmit power and spreading code assignment. We will show that the newly considered non-cooperative game admits a unique Nash equilibrium, which, for the case in which the number of users does not exceed the system processing gain, is also Pareto-optimal. -As an introductory step to the previous item, we also formulate a non-cooperative game for SINR maximization with respect to linear multiuser detector and spreading code choice, and show that this game admits a unique Nash equilibr
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