A Fuzzy Logic Based Scheduling Approach to Improve Fairness in Opportunistic Wireless Networks Hakkı Soy
¨ ur Ozdemir ¨ Ozg¨
Department of Electrical and Electronics Engineering Necmettin Erbakan University, Konya, Turkey Email:
[email protected]
Department of Electrical and Electronics Engineering Fatih University, ˙Istanbul, Turkey Email:
[email protected]
Abstract—In the design of wireless scheduling policies, the fairness criterion plays an important role in upgrading the performance of network. This paper concentrates on how the channelaware opportunistic scheduler can improve both throughput and fairness in cellular wireless networks. In order to improve the fairness, we propose an adaptive fair scheduling algorithm by using fuzzy logic model. Proposed scheduler operates on Time Division Multiple Access (TDMA) fashion and calculates the priority index of each user according to channel quality fed back and fairness of channel assignment. We evaluate its performance via statistical simulations. The obtained results show that our strategy can improve the fairness but at the expense of slight throughput loss compared to well-known opportunistic scheduling methods. Keywords—opportunistic scheduling, throughput, fairness, fuzzy logic.
I.
multiuser
diversity,
I NTRODUCTION
Scheduling plays an important role in quality-of-service (QoS) provision over wireless fading channels [1]. For realtime applications, the scheduler is designed with the goal of providing high performance in terms of the throughput, delay and fairness [2], [3]. Recently, opportunistic approaches have drawn much research attention due to its throughput advantage [4]. In a cellular wireless network, the channel conditions of users have time-varying behavior due to the fading effect. Therefore different users experience independent channels at the same time, which is referred as multiuser diversity [5]. Opportunistic scheduling exploits the multiuser diversity to maximize system throughput by granting higher priority to users with better channel quality. But, always giving priority to the powerful users causes unfairness in access to the shared channel at a certain moment. Therefore, the achievable gain of opportunistic schedulers is generally restrained with fairness considerations [6]. Since the fairness criterion plays an important role in the performance improvement of the system throughput, there are several fair opportunistic scheduling schemes that have been proposed to reflect different trade-off scenarios [7]. The presence of fading is crucial in order to realize the multiuser diversity because it increases the dynamic range of the channel fluctuations and also the probability that one of the users experiences a good channel gain. Especially in slow fading environments, the multiuser diversity gain is amplified by opportunistic beamforming method that induces larger and faster fluctuations on the fading channel [8].
Traditional opportunistic scheduling algorithms take decisions based only on favorable wireless link conditions. The base station (BS) needs to obtain information of each user’s channel condition at a given time-slot to make the scheduling decision. The users continuously estimate their own channel quality measurements (e.g., signal-to-noise ratio (SNR) or alternative channel quality metric) based on the common pilot signal broadcast from BS in the downlink and then feed it back to the BS in the uplink. The BS decides which user should be scheduled to transmit/receive in the current time-slot [9]. In this work, unlike existing opportunistic scheduling algorithms, we present an adaptive fair scheduling algorithm that will be maintaining fairness in term of channel assignment by considering the number of channel access besides the instantaneous channel quality information. Fuzzy logic can offer a simple presentation and a good framework to arrive at right decision in the design of scheduling algorithm. Our aim is to investigate the possible throughput and fairness gains by using proposed method for downlink transmission. The rest of this paper is organized as follows: In Section II, the underlying system model and its assumptions are explained. This section also details the scheduling algorithms studied. Section III describes the proposed scheduling technique. Section IV shows the performance evaluation of the proposed fuzzy scheduler in terms of throughput and fairness. Finally, Section V concludes the paper. II.
S YSTEM M ODEL
The system of interest is a single cell of the cellular wireless network in which the BS serves K users. As shown in Figure 1, the BS is equipped with M antennas whereas each user is equipped with single antenna. The channel vector between the kth user and the BS is denoted by M × 1 vector hk = [hk,1 hk,2 . . . hk,M ]T and the elements of hk are independent and identically distributed (i.i.d.) adopting circularly symmetric, complex, Gaussian distribution whose mean is zero and variance which is γ¯ , hk,i ∼ CN (0, γ¯ ). It is assumed that the channel is frequency flat, block-Rayleigh fading and the channel vector hk is considered to be constant over a fixed number of time slots called one frame and changes between different frames independently. The BS forms the beam by choosing the M × 1 random beamforming vector w whose distribution is identical to the distribution of hk but normalized to keep the transmit power fixed, w ∼ h/h. The pilot signal x(n) with power
matched with the beamforming vector (wp ≈ hk /hk ), this user will attain its maximum possible SNR or NSNR value. We consider a time-slotted wireless network with multiple users in which a centralized scheduler runs at the BS and controls the downlink packet transmission. It is assumed that only a single user can access the channel at a given timeslot. If K represents the number of users in the network, the simple TDMA scheme which uses non-opportunistic roundrobin (RR) scheduling provides the highest fairness among the users when the time slots are allocated in rounds of K time-slots [6]. The TDMA scheme with opportunistic scheduling takes advantage of favorable channel conditions in assigning timeslots to the users [7]. Several algorithms may be found in the literature for scheduling users in an opportunistic way. In maximum SNR scheduling, the BS assigns the current timeslot to the user with the highest SNR. From a practical point of view, average SNR of the users is different due to differences in distances to the BS. Therefore, giving priority to the users with the highest SNR causes unfairness in the network. On the other hand, maximum NSNR scheduling achieves fairness among all users at the expense of throughput loss [10].
Fig. 1.
The downlink system model of the wireless network.
E[x2 (n)] = εx is transmitted from the BS to the users. Hence, the received signal yk (n) at the kth user may be written as yk (n) = (wH hk )x(n) + zk (n)
(1)
where zk (n) is the circularly symmetric, complex, additive white Gaussian noise (AWGN) with distribution CN (0, σ 2 ). Note that, by randomly changing the beamforming vector w at each time slot, the observed composite channel process of the kth user (wH hk ) changes from time slot to time slot due to time-varying beamforming vector. In order to simplify the analysis, we assume that the channel statistics of all the users are the same and the ratio of the transmit energy to the noise variance (εx /σ 2 ) is 1. So, without loss of generality, the path loss together with all the other powers is lumped into the channel process. With these assumptions, the SNR of the kth user can be written as γk = wH hk hH k w.
(2)
An alternative channel quality metric can be considered that is normalized SNR (NSNR). It is defined as the ratio of the received SNR to the maximum SNR. The NSNR of the kth user can be computed as ηk =
wH hk hH kw . hH h k k
(3)
Note that the NSNR value is in [0, 1] interval. We can take advantage of the multiuser diversity technique over the large network, in which there will be one of the users that experience good channel quality compared with the others on formed random beam. If the channel vector of kth user is
To increase the short-term fairness between the users, opportunistic RR (ORR) scheduling algorithm is introduced in [4]. ORR algorithm is different from the traditional RR scheduling, the best user among all users is chosen for the first time-slot in a round. In the next time-slot, this user taken out of the competition and the best out of the remaining users is selected for channel assignment. This procedure is repeated until the last round, where the latter user is scheduled. ORR scheduling ensures the constraint that the K users should get exactly one time-slot each within the same round as well as RR scheduling. The ORR scheduling algorithm can be combined with maximum NSNR scheduling to achieve higher throughput than ORR, by scheduling the user with highest NSNR. This algorithm is denoted as the normalized ORR (N-ORR) [11]. Fairness is measured by how equally the channel assignments are allocated to users. The Jain’s fairness index (JFI) is frequently used to measure fairness of different scheduling algorithms in wireless networks. By considering the time-slot allocation (instead of the throughput allocation) JFI is defined as follows: K | k=1 xk |2 IJFI = (4) K K k=1 x2k where xk is the number of allocated time-slots to user k in a round [12]. III.
P ROPOSED F UZZY S CHEDULER
In this section the essential details of the proposed adaptive fuzzy scheduling scheme are given. Proposed scheduler aims to enhance the temporal fairness and avoid starving users falling outside this prioritization. Fuzzy logic implements human experiences and preferences via membership functions and fuzzy rules. It can be used as a general methodology to incorporate knowledge into decision makers. The general steps involved in designing a fuzzy model are fuzzification, decisionmaking and defuzzification [13].
domain expert’s knowledge and stored in fuzzy rule base. The rule base used to schedule users can be imagined to be a two dimensional matrix. Table 1 shows the fuzzy conditional rules for proposed scheduler. The Mamdani type fuzzy model is used for decision-making stage in the rule base. The input variables have 12 combinations and the corresponding output is shown from the tabulation. TABLE I.
Fig. 2.
Input membership functions for NSNR metric. TSA
RULE BASE OF THE PROPOSED SCHEDULER
Rare Middle Dense
Bad Medium Very Low Very Low
NSNR Ordinary Good High Very High Low Medium Very Low Low
Favorable Very High High Medium
C. Defuzzification
Fig. 3.
Input membership functions for time-slot allocation.
A. Fuzzification The fuzzy scheduler has two input variables and one output variable. The input variables are channel quality information and time-slot allocation (TSA). The output variable is user priority index. Channel quality is measured by NSNR metric due to its suitability to the fuzzification and TSA is measured by number of channel access. There are four linguistic terms that are used for NSNR: Bad (B), Ordinary (O), Good (G) and Favorable (F) and three linguistic terms that are used for TSA: Rare (R), Middle (M) and Dense (D). Membership functions of input variables are shown in Figure 2 and Figure 3, respectively. Similarly, five linguistic variables are used for the user priority index: Very Low (VL), Low (L), Medium (M), High (H) and Very High (VH). The membership functions of output variable are shown in Figure 4. B. Decision-making The main purpose of the designed scheduler decides the channel assignment of users. The control action in the fuzzy scheduler is determined by a set of fuzzy rules. Fuzzy rules are written based on the empirical knowledge obtained from
Fig. 4.
Output membership functions for user priority index.
Our objective in wireless scheduler design is to ensure fairness while simultaneously employing opportunistic scheduling strategy to increase the total throughput by selecting users with high channel quality as much as possible. Since our algorithm will exploit the users’ channel access in making the scheduling decision, proposed scheduler tries to improve the fairness performance of the network. The fuzzy scheduler calculates the priority index of each user according to input variables. The weighting-mean method of defuzzification [14] is adopted to obtain the crisp value of priority index. The scheduler selects the user with the largest value of priority index among all users in the network. IV.
P ERFORMANCE E VALUATION
Fairness and throughput are important performance metrics that are often used to analyze and compare the effectiveness of different scheduling algorithms in wireless networks. We evaluated the performance of the proposed fuzzy scheduler with statistical (Monte Carlo) simulation under Rayleigh fading channel. In order to validate obtained results, the proposed scheduling algorithm is compared with several algorithms as introduced in Section II. In simulation, the number of iteration is chosen as 1000 to achieve an acceptable convergence and the number of time slots in iteration is taken as the number of users in the network. We also assume that the γ¯ = 1 to eliminate the effect of average SNR on the simulation results. Figure 5 plots the fairness performance of considered algorithms by using JFI. It means that the higher value of JFI implies higher fairness in channel assignment. Note that, the RR based algorithms have the best fairness index. Proposed algorithm has better fairness than the maximum SNR/NSNR algorithms and its performance close to the RR based algorithms. It is clearly shown that the maximum SNR scheduling has the worst fairness performance among all evaluated algorithms. The throughput performance of proposed algorithm against other approaches is shown by Figure 6. As seen from the plot, maximum SNR/NSNR algorithms improve the throughput compared with the others. However, proposed algorithm has better throughput than the RR based algorithms. Contrary to the fairness comparison, the maximum SNR scheduling has the best throughput performance among all evaluated algorithms.
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Similarly, Figure 8 shows the throughput performance of considered algorithms for M = 8. As seen from this plot, the throughput performance of proposed algorithm remained almost the same, as well as maximum SNR and RR algorithms. However, the throughput of the maximum NSNR, ORR and NORR scheduling algorithms increases with increasing number of antennas at the BS. C ONCLUSION
R EFERENCES
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Fig. 7.
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In this paper, we design a fuzzy logic based scheduler to determine the priority of the users in a cellular wireless network. The proposed scheduling algorithm allocates the shared channel among the users adaptively. It aims to balance the throughput and fairness objectives by using channel quality and time-slot allocation of users. According to obtained results, we can say that our proposed scheduling algorithm has throughput advantage over RR based algorithms and also has fairness advantage over maximum SNR/NSNR algorithms.
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Throughput versus number of users in the network for M = 8.
V. Fig. 6.
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In order to see the effect of the different antenna numbers at the BS over the performance, we test the proposed algorithm for M = 8 and compare results with other algorithms. Figure 7 shows the fairness performance of considered algorithms for M = 8. According to obtained results, the fairness of proposed scheme approximates to the maximum level. Similarly, the maximum SNR algorithm offers better fairness performance toward higher antenna numbers.
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