A New Modeling Approach for Utility-Based Resource Allocation in OFDM Networks Mehri Mehrjoo ∗ , Somayeh Moazeni ∗∗ , Xuemin (Sherman) Shen ∗ ∗ Department of Electrical and Computer Engineering ∗∗ School of Computer Science University of Waterloo Waterloo, Ontario, Canada N2L 3G1 Email:{mmehrjoo, smoazeni, xshen}@uwaterloo.ca Abstract— A new modeling approach is proposed for utility- based resource allocation in orthogonal frequency division mul- tiplexing (OFDM) networks with heterogeneous traffic. The spectrum and power of a base station (BS) are allocated to users, in a point to multi-point manner, to maximize the users’ aggregate utility. We first model the problem of assigning sub-carriers to the users and the power allocation to the sub-carriers as a mixed integer nonlinear programming (MINLP) problem. The MINLP problem is maximizing a non-concave objective function over a non-convex feasible region that includes some integer variables. We then eliminate integer variables and propose a continuous nonlinear programming (NLP) model for the problem. The obtained model is suitable for heuristic and search algorithms. Genetic algorithm (GA) is applied to obtain the near optimal solution of the NLP model. Numerical results are presented to illustrate the convergence of the GA and utilization performance of the network. I. I NTRODUCTION Resource allocation is a fundamental issue in wireless networks due to the scarce resources and fading channel. OFDM is a well accepted technology that combats the deficits of fading channel by converting a frequency selective fading channel into several flat fading channels. Dynamic sub-carrier assignment and adaptive power allocation techniques can improve the performance of resource allocation schemes for OFDM networks. In practice, the procedure of allocating resource is modeled as an optimization problem whose objective function and constraints can be determined based on the users’ requirements and network specifications. Depending on the definition of the objective functions, different utilization performance, such as fairness or maximum throughput, are expected. One common form of objective function is to maximize aggregate utility functions of all users in the network. A utility function characterizes a user’s satisfaction of an application level QoS requirement [1]. For example, a utility function of rate defined as U (r)= r represents that the user’s satisfaction increases linearly by allocating more rate to the user, while a step utility function of rate represents that the user expects a threshold rate, allocating less rate is not useful at all, and allocating more rate is wasteful. Commonly obtained application level utility functions for real-time and non-real-time traffic are sigmoid and logarithm functions. While a logarithm function is concave 1 , sigmoid functions (and most of application level utility functions of real-time traffic) are not concave. Such utility functions yield maximization problems whose objective functions are not concave. When the set of feasible solutions that satisfy all of the constraints, i.e., feasible region, is a convex set, and the objective function is concave, any local optimum will be a global optimum. Moreover, for many concave utility functions, the utility-based resource allocation optimization problem can be solved efficiently and very reliably, using interior-point methods or other special methods for convex optimization [2]. Therefore, most works in the literature have considered only the concave utility functions. On the contrary, in case of utility maximization for heterogeneous traffic, some of the utility functions are not concave, and the traditional local scope search methods can only offer a local solution which depends on the starting point of the search algorithm. In order to find the global optimum of the problem, a global optimization strategy is needed. In this paper, we use GA as a global search algorithm to find near optimal solution of the utility-based OFDM sub-carrier and power allocation problem, respecting the users’ channel status and quality of service (QoS). We assume that the real- time and non-real-time traffic with sigmoid and logarithm utility functions, respectively, are present in the network. Due to the discrete nature of sub-carriers and continuous nature of power, the problem is modeled as an MINLP problem, i.e., a mathematical programming problem including integer and continuous variables as well as nonlinear constraints and objective function. The feasible region of the MINLP model contains integer variables representing sub-carriers allocated to the users and continuous variables representing the power al- located to the sub-carriers. We prove that the integer variables are redundant and can be eliminated. Accordingly, we propose an NLP model that unifies the sub-carrier and power allocation in a rate allocation problem. The NLP model provides a new insight into the OFDM resource allocation problem and sheds some light on applying other continuous optimization techniques in the future. Also, the NLP model with one set of 1 A function f is concave if the domain of f , D f , is a convex set, i.e., (1 - t)x + ty ∈ D f for every x, y ∈ D f and t ∈ [0, 1], and f (θx + (1 - θ)y) ≥ θf (x) + (1 - θ)f (y) for every x, y ∈ D f and 0 ≤ θ ≤ 1. This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings. 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