Radio resource allocation problems for OFDMA cellular systems

Abstract

Orthogonal frequency division multiple-access (OFDMA) manages to efficiently exploit the inherent multi-user diversity of a cellular system by performing dynamic resource allocation. Radio resource allocation is the technique that assigns to each user in the system a subset of the available radio resources (mainly power and bandwidth) according to a certain optimality criterion on the basis of the experienced link quality. In this paper we address the problem of resource allocation in the downlink of a multi-cellular OFDMA system. The allocation problem is formulated with the goal of minimizing the transmitted power subject to individual rate constraint for each user. Exact and heuristic algorithms are proposed for the both the single-cell and the multi-cell scenario. In particular, we show that in the single-cell scenario the allocation problem can be efficiently solved following a network flow approach. In the multi-cell scenario we assume that all cells use the same frequencies and therefore the allocation problem is complicated by the presence of strong multiple access interference. We prove that the problem is strongly NP-hard, and we present an exact approach based on an MILP formulation. We also propose two heuristic algorithms designed to be simple and fast. All algorithms are tested and evaluated through an experimental campaign on simulated instances. Experimental results show that, although suboptimal, a Lagrangian-based heuristic consisting in solving a series of minimum network cost flow problems is attractive for practical implementation, both for the quality of the solutions and for the small computational times.

Introduction

Wireless cellular networks provide mobile radio access to an ever-increasing number of users with seamless coverage for voice and data services. Nonetheless, the great commercial success of mobile services has pushed to the limit the capacity of existing networks and poses great demands on the deployment of future systems based on new technologies. As a result, regulator bodies are undergoing an active standardization phase [1], [2], [3], [4] to define next generation cellular networks, which are expected to provide rich and diverse multimedia services with very high data rates, possibly greater than 100 Mbps. Most of the candidate technologies of future generation broadband wireless networks employ a multi-carrier multiple access scheme based on the orthogonal frequency division modulation (OFDM) [5], [6]. Among the attractive features of multi-carrier technology [7], there is its robustness to channel distortions and its granular resource allocation capability [8], [9], [10], [11]. In a multi-carrier system the transmitted data flow is divided into several substreams that are modulated over different sub-channels, called sub-carriers. Typically, the system is designed so that the sub-carriers remain orthogonal also when the propagation channel is severely frequency selective.

In an OFDMA system a different subset of sub-carriers is assigned to each user in a cell. If the transmitter possesses full knowledge of the propagation channel, an intrinsic advantage of OFDMA over other multiple access methods is its capability to exploit the multi-user diversity embedded in diverse frequency-selective channels. In recent years resource allocation has been envisaged as one of the most efficient techniques to increase the performance of multi-carrier systems. In fact, propagation channels are independent for each user and thus the sub-carriers that are in a deep fade for one user may be good ones for another. Following the path open by the seminal article by Wong et al. [12], many resource allocation algorithms have been proposed to take advantage of both the frequency selective nature of the channel and the multi-user diversity. Most of the works in literature follow either the margin adaptive approach, formulating dynamic resource allocation with the goal of minimizing the transmitted power with a rate constraint for each user [13], [14] or the rate adaptive approach aiming at maximizing the overall rate with a power constraint [15], [16], [17]. In this latter case, the optimal solution for resource allocation in the downlink is often found as an application of the well-known water-filling algorithm. In particular, in [16] the authors show that OFDMA is the optimal multiple access scheme in a multiuser multi-carrier downlink system. Capacity is maximized by assigning each subcarrier to the user with the maximum channel gain on it and distributing the power over subcarriers using the water-filling solution with respect to the allocated channel gains. In such scenarios, enforcing some sort of fairness among users might become a critical issue and therefore some authors consider the joint scheduling-allocation problem following a cross-layer approach [18], [19]. All these works only consider allocation in a single cell. Because of its complexity, resource allocation in multi-cellular systems has not been fully studied yet and only few works tackle the problem [20], [21], [22], [25].

In this paper we focus on the downlink of both a single-cell and a multi-cellular system with universal frequency reuse. Allocation is performed following a margin adaptive approach so as to minimize the overall transmission power while providing a given transmission rate to each user. One of the major advantages of implementing an efficient resource allocation strategy in the multi-cellular scenario is the mitigation of multiple-access interference (MAI). Since the frequency reuse factor is set to one, all cells transmit on same spectrum and minimizing the overall transmission power results also in a minimization of interference. To simplify the allocation problem we follow the same assumptions made in [19] and adopt just one transmission format per user. The performance loss due to the use of a single transmission format is partially compensated by the so called multi-user diversity. In fact, as a consequence of resource allocation, the mean value of the gains of the assigned channels is larger than in the case of channel-independent allocation. The larger the number of users, the larger is the set of channels over which to perform the allocation and the larger is the multi-user diversity gain. Thus, link adaptation becomes progressively a less effective measure. For the given allocation problem, exact and heuristic algorithms are proposed. Performance of the proposed allocation algorithms are given in terms of requested transmission power for a given system throughput, and comparisons with an approach from the literature is given as well. Even if we focus on the allocation problem without tailoring specific applications, the proposed schemes may have many and important practical implementations in real systems, e.g., in WiMAX OFDMA point to multi-point (PMP) broadband wireless access networks [23], as it will be discussed in the next section.

The paper is organized as follows. Section 2 describes the system model. Section 3 introduces the single-cell scenario, i.e., a scenario where no extra cell interference is present, and proposes a polynomial algorithm which is based on a network flow formulation. Section 4 introduces the multi-cell scenario and addresses the computational complexity of the problem. In particular, we show that the multi-cell sub-carrier allocation problem is strongly NP-hard. In 5 A MILP formulation for MCRRAP, 6 Heuristic algorithms for MCRRAP, a MILP formulation and heuristic algorithms are, respectively, presented for the multi-cell case. In Section 7, experimental results are presented and discussed. Finally, Section 8, provides conclusive remarks.