Fairness is based on criteria like max-min that do not consider the notion that ... theory in OFDMA RRM have been proposed by Han, Ji and Liu in [4] and by Noh ...
QoS-driven Radio Resource Allocation for OFDMA Networks based on a Game Theoretical Approach Claudio Sacchi, and Fabrizio Granelli University of Trento Department of Information Engineering and Computer Science (DISI) Via Sommarive 14, I-38050, Povo (Trento), Italy
{sacchi,granelli}@disi.unitn.it
Abstract. In this paper, we propose a cooperative strategy for OFDMA radio resource allocation based on game theory. The main novelty with respect to state-of-the-art is that the utility function considers the application-oriented Mean Opinion Score (MOS) rather than the gross data rate attributed to each user flow. In such a scenario, data flows compete in cooperative way in order to maximize the perceived Quality-of-Service (QoS). Experimental results show that the MOS achievable by the proposed resource allocation strategy is better than that one provided both by uncoordinated strategies based on water-filling and by cooperative strategies based on pure data rate maximization. Keywords: OFDMA, Radio Resource Allocation, Game theory, QoS measurements
1. Introduction Orthogonal Frequency Division Multiplexing (OFDM) is a very promising solution to design high performance physical layer in digital radio communications. Some well-known wireless standards adopt OFDM as radio interface, namely: IEEE 802.11a, IEEE 802.11g, and IEEE 802.16e (WiMAX). One of the best features of OFDM is the increased flexibility in radio resource management with respect to single-carrier systems. Radio resource management (RRM) is made adaptive with respect to channel conditions with the objective of providing controlled QoS levels [1]. In a single-user OFDM system, RRM essentially consists of dynamically adapting modulation constellation and transmit power on each subcarrier. In a multi-user OFDM context, there is a need for a multiple access scheme to allocate subcarriers, bit loading and transmit power to the various users. The problem of optimal allocation of power and subcarriers in OFDM and OFDMA systems has been widely dealt by literature. The tradeoff between efficiency (i.e.: maximum attainable data rate) and fairness (i.e.: equity in radio resource assignment) is one of the most challenging aspect of OFDMA RRM. State-of-the-art solutions look suboptimal from this viewpoint. Efficiency trends to privilege users with good channel conditions (that are generally closer to the base-station – BS).
Fairness is based on criteria like max-min that do not consider the notion that different users might have different requirements [1]. In some recent works, some solutions have been proposed for OFDMA RRM based on “negotiation” strategies inspired to everyday life. RRM resembles to a marketplace where transmitting users can exchange goods (i.e.: power and/or subcarriers) and negotiate transactions so that people can be satisfied through bargaining. In a single-cell multi-user OFDMA system, the BS acts as the market and the distributed users can negotiate via the BS to cooperate in making decision on the subcarrier usage [2]. This fact fully motivates the application of game theory [3] to this specific problem. Game theory can achieve fairness while maximizing the overall system rate [2]. The Nash Bargaining Solution (NBS) is considered in [2] together with coalition in order to find an optimal agreement among negotiating users. Other approaches considering the use of game theory in OFDMA RRM have been proposed by Han, Ji and Liu in [4] and by Noh in [5]. In [4] a non-cooperative resource competition game is proposed in opposition to the cooperative approach of [2]. Non-cooperative game can solve the issue of some undesirable Nash equilibrium that sometimes affects cooperative strategies. In [5], an iterative resource control algorithm for distributed OFDMA systems using an auction game is proposed. Users and BS control transmitting power and bidding to maximize their utility. These controls are aimed at maximizing system capacity and fairness. In this paper, we propose a novel approach for OFDMA RRM that intrinsically maximizes the fairness in terms of user’s satisfaction. Saul and Auer in [6] show the advantage to optimize cross-layer between application and MAC layer by considering user-centric metrics linked to the perceived quality-of-service (like e.g. Mean Opinion Square – MOS), rather than network-centric metrics like bit-rate or bit-error-rate. Therefore, we propose a cooperative game theoretic approach, where user data flows cooperate to achieve the best possible perceived QoS. In particular, the considered utility function is the maximization of the minimum MOS. In such a way, the RRM should increase fairness in order to allow users to be as much as possible satisfied with respect to their specific QoS requirements. The rest of the paper is organized as follows: section 2 will describe the proposed OFDMA RRM algorithm, section 3 will present some selected experimental results, and finally section 4 will draw paper conclusions.
2. The proposed OFDMA RRM strategy
2.1 Problem statement Let’s consider an OFDMA transmission system sharing among K users a fixed bandwidth B spanned around a transmission frequency fc. The available bandwidth is partitioned into N subcarriers, each one of bandwidth B / N [Hz]. As usually done in literature (see e.g. [1]) the channel is assumed flat over each assigned subcarrier; therefore the signal-to-noise ratio measured by user k on its subcarrier n is given by:
γ n ,k =
pn ,k g n, k
σ2
(1)
being pn , k the power allocated to the user k on the subcarrier n, g n , k the channel power gain, and σ 2 the Guassian noise variance. The objective of RRM in OFDMA systems is to maximize the system data rate with a constraint on bit-error-rate (BER). The general problem can be summarized as follows [1]:
α gap p n,k g n,k B N −1 K maxck ,n , pk ,n ∑∑ cn,k log2 1 + σ2 N n=0 k =1 K N c = 1 ∀n, ck ,n pk ,n ≤ Ptot ∀k ∑ k ,n ∑ k =1 n =1
(2)
where cn , k ∈ {0,1} is the subcarrier allocation coefficient, and αgap is the signal-tonoise ratio gap [1], expressed as a function of the desired BER. In the presence of constraints on the total available power, the resource allocation strategy maximizing the total system throughput is water-filling [1]. Water-filling tends to maximize power allocation on those subcarriers having the highest signal-to-noise ratio γ n, k , while, on the other hand, to penalize those subcarriers having lowest SNR values by minimizing power allocation on them. This strategy is simple to be implemented, but it privileges users with highest channel gains and penalizes users experimenting worse channel response. Therefore, strategies to counteract this issue and support “fairness” in radio resource allocation should be established [1]. A thorough overview of rate maximization scheduling schemes has been presented in [7]. Proportional fairness has been proposed in [7] as feasible sub-optimal approach for uplink OFDMA. This algorithm requires the knowledge of the target rate and the available transmit power of each user, together with the knowledge of γ n,k values. Substantially, the algorithm compares the normalized ratios of each user and assigns more carriers to users whose proportional rates are the least met. It is shown in [7] that, although decreasing the total data rate, proportional fairness makes the rate distribution significantly fairer as compared to other schemes based on global data-rate maximization.
2.2 The MOS-based utility function The key concept underlying the proposed approach is to consider as utility function of the cooperative game the Mean Opinion Score (MOS) of users competing for the access in a mixed traffic configuration (audio, video, best-effort data download). In the classical OFDMA RRM problem, expressed in (1), the cost function that is maximized is the total system data-rate. Although fairness is introduced in the RRM (see e.g. [1] and [7]), the optimization with respect to “gross” data rate may not match with the QoS requirements of users transmitting differentiated data streams. Therefore, in this paper, we propose a cost function directly quantifying the QoS
effectively perceived by the competing users. Each user is represented by a data flow, with the related quality target. The MOS is expressed by a real number ranging from 1 (very dissatisfied user) to 4.5 (very satisfied user). The user’s satisfaction threshold is commonly set to 4. In the present paper, we consider three different classes of users (i.e.: players): “video streamers”, “audio streamers” and “best effort”, the latter indicating users requiring file transfer. For audio and file transfer applications, a suitable expression of MOS can be given as follows [6]:
MOS audio , BE = a log bR (1 − PEP )
(3)
R being the transmission rate and PEP the packet-error-probability. The constants a, b are computed by fixing the MOS at a given rate value R, in the absence of packet errors (PEP=0). Considering the QoS requirements of WiMax applications expressed in [8], we can regard as fully satisfactory data rates (corresponding to MOS=4.5): rb=200 Kb/s for audio streamers, and rb=2 Mb/s for video streamers and best-effort users. As far as video streaming is concerned, the following MOS model has been considered [9]:
MOSvideo
PSNR ≤ PSNR 1.0 1.0 = d log PSNR + e PSNR 1.0 < PSNR < PSNR 4.5 4.5 PSNR ≥ PSNR 4.5
(4)
The parameters PSNR 1.0 and PSNR 4.5 denote the Peak-Signal-to-Noise-Ratio (PSNR) at which the perceived QoS drops to “not acceptable” (MOS=1.0) and exceeds “very satisfied” (MOS=4.5), respectively. The constants d and e are derived according to this. The simple model that relates PSNR with the data-rate of the video stream proposed in [9] has been considered also in this paper:
PSNRdB = u + v
R w 1 − w R
(5)
The parameters u, v, and w characterize a specific video sequence (see in Fig.1 three sample frames corresponding to different MOS values).
2.3 The cooperative RRM algorithm based on game theoretical approach Game theory is mainly applied in Economics in order to provide a reliable model for company competition [3]. Nevertheless, other applications in the field of information science and networking are considered by literature [10]. Game theory represents a formal method that analyzes conflict situations, searching for competitive
(a) (b) (c) Fig.1. Sample frame of “Foreman” sequence corresponding to three different MOS: (a): MOS=3, (b): MOS=3.5, and (c): MOS=4.5
and/or cooperative solutions obtained by means of specific models. A game substantially consists of three elements: • A set of players; • A set of strategies or actions available for each player; • A utility function that rewards the player for its strategy combination. In the OFDMA case, the users competing for access share limited radio resources (i.e.: a finite subcarrier set). Each user tries to allocate the “best” subcarriers, i.e.: those subcarriers that are not severely attenuated by the frequency selective fading. In such a way, user conflicts are unavoidable. The aim of the cooperative game is to manage these conflicts in order to allow users to achieve a satisfactory agreement. The equilibrium point of a cooperative game is represented by the so-called Nash equilibrium [3]. If all players reach Nash equilibrium, none of them can improve their performance by modifying its own strategy. Nash equilibrium is substantially a sort of “optimal agreement” that is not necessarily the optimal solution of the game. Players are represented by data flows, with the corresponding resource requirements. User profiles in terms of data-rates and BER are derived according to [8] and shown in Tab.1. Table 1. BER and data-rate requirements for different user typologies Video Audio Best Effort streamers streamers users 10-6 10-4 BER ≤ 2·10-4 384 24.6 56 Rate [kbps] for MOS=4 2000 200 2000 Rate [kbps] for MOS=4.5
In order to enable negotiation of available resources, the game is organized like a “championship” in several rounds, with challenges or negotiations between pairs of users. Negotiation is targeted to identify the partitioning of available resources maximizing the joint utility function. The following pseudo code provides additional information on the proposed algorithm: %Algorithm initialization • Assign N1=floor(N/K) subcarriers to each users • Perform water-filling over the assigned subcarriers
• Computation of utility function: U(1)=min(MOS(P(0),C(0))) %minimum MOS after initial assignment: P(0), and C(0) are the power and subcarrier allocation matrices computed by initial water-filling %Competition among user pairs for i=1:K*(K-1) %for the no. of user pairs • The subcarrier sets of the selected users pair i are merged; %Min-MOS based user pair negotiation • Subcarrier indexes j are ordered in decreasing order with respect to the ratio gj1(i)/gj2(i) • for j=1:N(i) %N(i)=cardinality of subcarrier set related to pair i Subcarriers from 1 to j are associated to user 1 of pair i and water-filling is performed on these subcarriers Subcarriers from j+1 to N(i) are attributed to user 2 of pair i and water-filling is performed on these subcarriers Computation of utility function: U(i)=min(MOS1(i),MOS2(i)) Return index j that maximizes U(i) End %end of user pair negotiation • Return power allocation matrix P(i) and bit allocation matrix C(i) updated after the challenge (negotiation) i • Computation of utility function U(i+1)=min(MOS(P(i),C(i)) for all users • If U(i+1)>4 %all users are satisfied break End End %end of competition
The user pair negotiation is similar to that one proposed in [2], but using a different utility function (the minimum MOS achieved by the two negotiating users). On the other hand, the multi-user negotiation methodology is different. In [2], random coalitions of user pairs and the Hungarian algorithm for optimal coalition selection are considered. The first methodology is clearly sub-optimal; the second one may be computationally expensive. Moreover, the challenge is interrupted when the minimum MOS, computed for all users, trespasses the satisfaction threshold. Resulting complexity is in the order of O(KN log N), while exhaustive search would lead to O(KN). The sub-optimal RRM algorithm based on proportional fairness of [7] has a complexity of order O(KN). Therefore, the proposed RRM algorithm looks computationally affordable. The most significant novelty with respect to state-of-the-art yielded by the proposed approach is represented by the refereed competition for reciprocal maximization of perceived quality of service, instead of a competition for maximizing the gross data-rate as shown e.g. in [2]. Practically speaking, the proposed game aims at partitioning the available resources in order to allocate enough capacity to each data flow to achieve a satisfactory MOS level. In the next section, the proposed scheme is numerically validated, demonstrating that this kind of competition can turn onto a substantial performance improvement, impacting on measurable perceived QoS.
3. Experimental results Intensive simulation trials have been performed in MATLAB environment in order to test the effectiveness of the proposed RRM methodology. K=30 users of mixed typology (10 video streamers, 10 audio streamers and 10 best-effort users) are sharing a set of 256 subcarriers distributed over a 4MHz bandwidth. The frequency-selective Stanford University Interim (SUI) channel model of type 5 has been considered for simulations [11]. Fig.2 shows the minimum MOS vs. SNR obtained by the different RRM algorithms assessed in this paper, i.e.: a) the proposed approach based on game theory and perceived QoS, b) an approach based on game theory and rate maximization (similar to that one proposed in [2]) and c) an OFDM-FDMA approach with static allocation of users’ subcarriers and waterfilling inside each user’s group with fairness constraint [12]. The improvement of MOS index achieved by the proposed RRM strategy is evident both with respect both to OFDM-FDMA strategy and to game theoretical rate-maximization algorithm. In Figs.3-5, MOS bar plots related to the different RRM strategies for SNR=20dB clearly underline that the proposed algorithm provides a satisfactory QoS both for audio streamers and best-effort users, while video streamers are in any case very close to the satisfaction threshold. On the other hand, game theoretical rate maximization RRM severely penalizes some classes of users while satisfying other ones. Finally, Fig.5 shows that OFDM-FDMA RRM is more in favor of audio streamers (that require the lowest rate), while all best-effort users are close around the satisfaction threshold, and video streamers are clearly below the satisfaction threshold. Bar plot results shown in Figs.3-5 are condensed in empirical Cumulative Distribution Functions (CDFs) of MOS drawn in Fig.6. One can note from graphs of Fig.6 that the statistical spread of MOS values is very large when considering cooperative RRM based on rate maximization. On the other hand, the proposed cooperative RRM strategy, based on minimum-MOS maximization, is characterized by the smallest statistical spread of MOS values. This is a further confirmation of the fairness introduced by users’ cooperation targeted at reciprocally enhancing perceived QoS. It is interesting to note that the MOS index is not directly related with the overall system data-rate – which is the usual indicator of effectiveness of RRM strategies in wireless networks (see Fig.7). This happens as max-rate strategies merely maximize the overall system data rate, without considering the impact on the effective QoS perceived by the users. Other interesting results have been shown in Fig. 8, where the impact of the number of users on the proposed RRM algorithm is shown. One can note that for high transmission SNR, the achievable utility values are substantially invariant with respect to the number of users, as all the available subcarriers are characterized by a satisfactory signal-to-noise ratio. On the other hand, for lower SNR and larger user number, the role of the negotiation becomes relevant. This is expectable, because the competing users have to share radio resources that cannot provide to the overall community a satisfactory QoS. If SNR drops below 15dB, larger user communities (i.e. K=15 and K=30) cannot reach a satisfactory QoS.
4. Conclusion and future works In this paper, a cooperative RRM strategy, based on game theory, has been studied with the clear objective of maximizing the perceived QoS of OFDMA users. The proposed approach, explicitly including users’ perceived quality (measured in terms of Mean Opinion Score – MOS), may ensure the right balance between efficiency and fairness, resulting in a perceived QoS increase with respect to state-of-the-art noncooperative RRM strategies. Future works may concern with the impact on performance of channel estimation (in this paper, we assumed that CSI is ideally known) and novel cooperative strategies involving all competing users together, rather than to make them negotiating in couples.
Acknowledgements Authors wish to thank Dr. Fabrizio Vicari of University of Trento (Italy) for his valuable help in collecting paper results. This work has been partially supported by the Italian Ministry of University and Scientific Research, under the framework of SALICE (COFIN 2007RFTYY7_002) and WORLD (project code: COFIN 2007R989S) research projects.
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Fig.2. Minimum MOS achieved by the different RRM strategies considered in the paper: cooperative min-MOS maximization, cooperative rate maximization, not-cooperative FDMAOFDM with water-filling (channel: SUI-5, bandwidth 4 MHz)
Fig.3. MOS achieved by cooperative RRM based on minimum-MOS maximization (bar plot), K=30 users, SNR=20dB
Fig.4. MOS achieved by cooperative RRM based on rate maximization (bar plot), K=30 users, SNR=20dB
Fig.5. MOS achieved by RRM based on not-cooperative FDMA-OFDM (bar plot), K=30 users, SNR=20dB
Fig.6. Empirical CDF of MOS related to different RRM strategies proposed in this paper, obtained using MOS values drawn in bar plots of Figs.3-4 and 5.
Fig.7. Overall data rate achieved by the different RRM strategies considered in the paper: theoretical game-based min-MOS maximization, theoretical game rate maximization, static FDMA-OFDM with water-filling (channel: SUI-5, bandwidth 4 MHz)
Fig.8. MOS achieved by the proposed cooperative Max-min MOS RRM strategy vs. SNR and user number (channel: SUI-5, bandwidth 4 MHz)
