رویکرد تئوری بازی اکتشافی ـ آب پرکردن ترکیبی در تخصیص منابع MC-CDMA

This paper discusses the power allocation with fixed rate constraint problem in multi-carrier code division multiple access (MC-CDMA) networks, that has been solved through game theoretic perspective by the use of an iterative water-filling algorithm (IWFA). The problem is analyzed under various interference density configurations, and its reliability is studied in terms of solution existence and uniqueness. Moreover, numerical results reveal the approach shortcoming, thus a new method combining swarm intelligence and IWFA is proposed to make practicable the use of game theoretic approaches in realistic MC-CDMA systems scenarios. The contribution of this paper is twofold: (i) provide a complete analysis for the existence and uniqueness of the game solution, from simple to more realist and complex interference scenarios; (ii) propose a hybrid power allocation optimization method combining swarm intelligence, game theory and IWFA. To corroborate the effectiveness of the proposed method, an outage probability analysis in realistic interference scenarios, and a complexity comparison with the classical IWFA are presented.

In the last years the telecommunication scenario has been passing through a huge increase in traffic demand due to the arrival of new devices and services. In this context, the multiple access networks represent an important solution, once these systems can admit more users and, at the same time, achieve a higher throughput than other technologies. Thus, a specific multiple access system draws the attention of many researchers nowadays: the MC-CDMA networks. Even with all these avails, since all users transmit at the same time and in the same spectrum a resource allocation scheme must be adopted in order to guarantee acceptable quality of service (QoS) requirements, associated with minimum rates, maximum allowed delay, maximum permitted bit error rate (BER) and so forth. 1.1. Motivation The study of resource allocation problems in wireless networks has been discussed for many years due to its impacts in company profits and user satisfaction. Additionally, current technologies do not provide enough bandwidth at low operational costs for corporations which also affects their customers. So, a practical resource allocation scheme is desirable in order to save power,1 increase the throughput and guarantee the QoS. 1.2. Related work Several studies have been conducted in recent years in order to find good resource allocation algorithms. Within this context, some works may be highlighted [1], [2], [3], [4], [5], [6], [7], [8] and [9]. The distributed power control algorithm (DPCA) proposed in [1] is considered the base of many well known DPCAs. In [2] a multi-objective resource allocation scheme is presented. The algorithm considers three different non-linear parameters that weight the procedure goals: minimize the power, guarantee the QoS (in terms of target rate) and maximize the rate. In addition, a DPCA for single-rate [3] and multi-rate networks [4] inspired on Verhulst equilibrium analytical-iterative model is proposed in order to solve the power allocation with rate constraints problem in DS/CDMA networks. On the other hand, heuristic approach based on swarm intelligence was applied to solve the power allocation with rate constraints [5] and the rate maximization problem [6]. Besides, the total network power minimization problem subject to multi-class information rate constraints, as well as the problem of throughput maximization constrained to power limitation was analyzed in [7] applying swarm intelligence. The motivation to use heuristic search algorithms is due to the nature of the NP complexity posed by the wireless network optimization problems. The challenge is to obtain suitable performances in solving those hard complexity problem in a polynomial time. Previous results indicated that the application of heuristic search algorithm in several wireless optimization problems have been achieved excellent performance-complexity tradeoffs, particularly the use of genetic algorithm, evolutionary program, particle swarm optimization (PSO), and local search algorithm. Concerning the resource allocation issue, there are several challenging single- or multi-objective optimization problems associated, such as the total network power minimization subject to multi-class information rate constraints, as well as the throughput maximization while minimizing the total transmitted power. Multi-rate users associated with different types of traffic can be aggregated to distinct classes of users, with the assurance of minimum target rate allocation per user and quality of service (QoS). In order to achieve promising performance-complexity tradeoffs, both continuous or discrete PSO search algorithms have been successfully employed in the resource allocation problems [7]. A game theoretic approach for power control with rate constraints in Gaussian parallel interference channels using water-filling algorithm is proposed in [8], while in [9] a multi-linear fractional programming approach is used to solve the weighted throughput maximization problem in multiple access systems. However, under strong interference density configurations, iterative water-filling algorithm (IWFA) is unable to offer promising solutions to power allocation with fixed rate constraint in multi-carrier code division multiple access (MC-CDMA) networks. Hence, in this work the existence and uniqueness of the solution are studied and shown by numerical results that a new method combining swarm intelligence and IWFA is more promising and suitable for realistic MC-CDMA scenarios. 1.3. Organization This paper is organized as follows: Section 2 presents the system model and description; the game theoretic approach is presented in Section 3. Section 3.3 discusses the iterative water-filling algorithm (IWFA); moreover, in Section 4 the scenarios are characterized and further the game theoretic plus IWFA approach are applied in orde to solve the power-rate allocation problem. Finally, the proposed hybrid approach is discussed in Section 5 and conclusions in Section 6.

The paper pointed out the main flaws of the game theoretic approach alone. In most cases the game does not have a GNE and, thus, the IWFA does not truly converge, either by using more than the maximum allowed transmitted power or by not satisfying QoS requirements. Therefore, a method combining PSO and IWFA is proposed in order to find a solution in the situations that there are no GNE present. Tested through different scenarios, the game theoretic approach does not have a GNE for scenarios with low interference density, e.g. in scenario three a interference density of 3.75 interf/Km2 is observed, which is considered still low, and yet simulations results manage to find no GNE. A huge improvement was achieved combining the heuristic approach with IWFA, such that for more realist scenarios the IWFA was able to find solutions to the power control problem. Moreover, it is important to highlight that, asymptotically, the computational complexity of the proposed method did not increased. Since IWFA can be implemented in a totally distributed way, this is an important result once mobile terminals are restricted in terms of computational power. Finally, future work includes finding a way to redistribute the average power found by the PSO algorithm into the N sub-channels of the system, reducing even more the computational complexity. Besides other simpler heuristic methods and a reformulation of the game may be tested.