This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2016.2635262, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. YY, MONTH 2016
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Uplink Scheduling and Power Allocation for M2M Communications in SC-FDMA based LTE-A Networks with QoS Guarantees Fayezeh Ghavimi, Student Member, IEEE, Yu-Wei Lu, and Hsiao-Hwa Chen, Fellow, IEEE
Abstract—Providing diverse and strict quality of service (QoS) guarantees is one of the most important requirements in M2M communications, which particularly need for appropriate resource allocation for a large number of M2M devices. To efficiently allocate resource blocks (RBs) for M2M devices while satisfying QoS requirements, we propose group based M2M communications, in which M2M devices are clustered based on their wireless transmission protocols, their QoS characteristics and requirements. To perform joint RB and power allocation in SCFDMA based LTE-A networks, we formulate a sum-throughput maximization problem, while respecting all the constraints associated with SC-FDMA scheme as well as QoS requirements in M2M devices. The constraints in uplink SC-FDMA air interface in LTE-A networks complicate the resource allocation problem. We solve the resource allocation problem by first transforming it into a binary integer programming (BIP) problem, and then formulate a dual problem using the Lagrange duality theory. Numerical results show that the proposed algorithm outperforms traditional Greedy algorithm in terms of throughput maximization while satisfying QoS requirements, and its performance is close to the optimal design.
Index terms—M2M communication; LTE-Advanced; Scheduling; Grouping; Power allocation; SC-FDMA; Resource allocation; QoS. I.
INTRODUCTION
Recently, wireless communications have been extensively used to exchange data among individuals. In addition to human-to-human (H2H) communications, the introduction of machine-to-machine (M2M) communications in cellular networks has extended the wireless connectivity to machines. In order to enable machine automation and thus to take full advantages of the opportunities created by a global M2M communications over cellular networks, the 3GPP LTE-A networks offer higher capacity and more flexible radio resource management (RRM) schemes than the existing packet access data technologies [1]. In LTE-A, various stations can be configured (e.g., evolved universal terrestrial radio access (E-UTRA) NodeBs (eNBs), home eNBs (HeNBs), and relay nodes (RNs)) to provide comprehensive wireless access in both outdoor and indoor environments. Via attaching to those Fayezeh Ghavimi (email:
[email protected]), Yu-Wei Lu (email:
[email protected]), and Hsiao-Hwa Chen (email:
[email protected]) are with the Department of Engineering Science, National Cheng Kung University, 1 Da-Hsueh Road, Tainan City, 70101, Taiwan. This work was supported in part by Taiwan Industrial Technology Research Institute (ITRI) research grant No. M0-10309-6, and Taiwan Ministry of Science and Technology grant No. 104-2221-E-006-081-MY2. The paper was submitted on May 16, and revised on Oct 1.
stations, higher-layer connections among all M2M devices can be provided, in which LTE-A was designed basically for wideband applications in order to support multimedia transmissions of a large amount of data with a high throughput. However, there are two important challenges in enabling M2M communications in LTE-A networks as described in the sequel. The first important challenge is that LTE-A networks were designed basically for H2H communications, where the amount of uplink (UL) traffic is normally lower than the downlink (DL) traffic. In contrast, M2M traffic is distinct from the H2H traffic and more traffic data can be generated in UL channels than that over DL channels. Thus, congestion could happen due to concurrent transmit messages from massive M2M devices, which leads to a low successful rate of random access (RA), and thus both M2M devices and UEs suffer continuous collisions in physical random access channel (PRACH) [2]-[3]. In the literature, some approaches have been studied for controlling PRACH overload problem [4]-[11], which will be explained in the next section. Another challenge is due to diverse quality of service (QoS) provision for M2M devices, which plays a critical role in M2M communication networks. Depending on their distinct QoS requirements, different M2M devices are expected to be sensitive to different QoS metrics. For instance, non-real time M2M applications, such as data transmissions, aim to maximize the reliability with a not-so-strict delay constraint. In contrast, for real-time M2M applications, such as video demand, a critical QoS metric is to ensure a stringent delaybound and rate requirement, rather than to achieve a high spectral efficiency. Furthermore, there also exist some M2M applications falling in between the aforementioned two situations (e.g., paging signals), which are delay-sensitive but do not require so stringent QoS requirements as real time M2M applications. Therefore, different M2M devices impose very much different and sometimes even conflicting QoS constraints, which are the challenges to the designs of efficient radio resource allocation algorithms for M2M communications in LTE-A networks. Current research efforts have been made to consider more sophisticated applications for extracting more realistic and precise information of highly unpredictable channels in the real world, and to deal with them in a responsive manner, where each M2M device performs various tasks ranging from sensing, decision making, and mission executing [1]. Wireless multimedia sensor networking (WMSN), as a powerful and intelligent class of M2M systems, has gained its popularity
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2016.2635262, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. YY, MONTH 2016
owing to its capability of ubiquitously retrieving multimedia information to support a large number of non-real time and real-time applications. In this paper, we consider the applications that have an intrinsic data rate and delay bound requirements, and the throughput may deteriorate rapidly when achievable data rate can not meet the requirements. To effectively deploy a large number of M2M devices with diverse QoS requirements, it turns out to be a very difficult task to design radio resource allocation algorithms for M2M devices. However, one may utilize common service features of M2M communications to deal with the issue, which implies that the average or maximum required radio resources of M2M devices could be easily calculated according to the service type or device type. In the next section, we will focus on this issue and take the advantages of this feature in order to implement our proposed algorithm. To satisfy certain QoS requirements, it is needed for appropriate resource allocation that can be applied to M2M communications. Therefore, first it is essential to design efficient radio resource allocation schemes in such networks. In the LTE networks, the radio resources are distributed in both time and frequency domains. In the time domain, radio resources are distributed over every transmission time interval (TTI), which consists of two slots and has a duration of 1 ms. 20 slots or 10 TTIs constitute one LTE frame. In the frequency domain, the available bandwidth is divided into a number of sub-channels each including 12 subcarriers. Every sub-channel has a bandwidth of 180 kHz and 7 symbols in the time domain constitute a resource block (RB) as shown in Fig. 1. Time Slot 0.5 msec LTE Symbol
Resource Block (RB)
Each RB is comprised of 12 Subcarriers along one time slot
12 Subcarriers
Resource Unit (RU)
Time
Fig. 1: Resource block in the LTE-A system. 3GPP uses single carrier frequency division multiple access (SC-FDMA) [12] as the uplink multiple access scheme. One of the principal advantages of SC-FDMA is its low peakto-average power ratio (PAPR), if compared to orthogonal frequency division multiple access (OFDMA), which reduces the processing power and battery requirements, and thus being well-suited for resource-constrained M2M devices. The issues on resource allocation in OFDMA systems have been extensively investigated in the literature. One of the well known approaches to solve OFDMA resource allocation prob-
2
lem is to exploit the time-sharing property [14]. Based on this property, the works in [13] and [14] indicated that for a given number of RBs, the resource allocation problem in an OFDMA system can be solved by the Lagrange multipliers method with zero duality gap. However, the proposed approaches for resource allocation in the context of OFDMA systems can not be utilized in SC-FDMA-based systems as RB allocation procedure is different if compared to OFDMA based systems. Unlike parallel transmission of orthogonal RBs in OFDMA, the RBs are transmitted sequentially in SC-FDMA, resulting in a low PAPR [12]. In this work, we need to address the problem of resource allocation for uplink of SC-FDMA based LTE-A networks with QoS guarantees. Our contributions in this paper are summarized as follows. 1) To address the aforementioned issues, we propose to use group-based radio resource allocation with identical transmission protocols and QoS requirements in order to ensure QoS guarantees for M2M devices and to efficiently tackle the overload problems for M2M communications in 3GPP LTE-A networks. To this aim, we propose an analytical model by utilizing an effective capacity concept to provide QoS guarantees (i.e., delay requirements) for M2M devices and to obtain statistical delay bound for M2M traffic. 2) To allocate radio resources for M2M devices, we focus on the uplink of SC-FDMA based LTE-A networks. We perform joint RB and power allocation together with given QoS requirements (i.e., rate requirement) for M2M devices. We formulate a framework as a sumthroughput maximization problem, while respecting all the constraints associated with SC-FDMA RB and power allocation in the LTE-A uplink networks. 3) In addition to the restriction of allocating a RB to one M2M device at most in a SC-FDMA system, multiple adjacent RBs should also be allocated to a M2M device. Furthermore, the transmit power in all RBs allocated to a M2M device should be the same. We first formulate the original problem into a binary integer programming (BIP) problem. As the BIP turns the problem into an extremely complex problem, also due to the aforementioned constraint in SC-FDMA (i.e., multiple RBs allocated to an M2M device should be adjacent), we provide an effective algorithm, which provides throughput maximization with a polynomial complexity, which is much more practical. 4) Finally, we propose a computationally feasible solution based on the Lagrange multiplier method, and then formulate its dual problem using the Lagrange duality theory to solve a near-optimal solution for power and RB allocation. The reminder of this paper is outlined as follows. Section II describes the system model in SC-FDMA resource allocation. In Section III, we formulate a sum-throughput maximization resource block allocation problem to maximize total throughput of the network subject to the QoS requirements of M2M devices. Then, we propose an algorithm to solve this problem.
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2016.2635262, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. YY, MONTH 2016
Simulation results are presented in Section IV, followed by the conclusion given in Section V. WiFi
Cluster member
ZigBee
ZigBee
WiFi
QoS(j)
support traffic flows with QoS guarantees. Thus, to facilitate an efficient support of QoS for M2M communications in LTEA networks, we utilize effective capacity concept [16] in order to model a wireless channel in terms of QoS metrics. The effective capacity [16] for the mth M2M device, defined as the maximum constant arrival rate that a given service process can support in order to guarantee a QoS requirement specified by θ, is given by m EC (θm ) = −
eNB
QoS(i)
3
QoS(k)
Fig. 2: Procedure of group formation for M2M devices based on their transmission protocols and QoS requirements.
II. S YSTEM M ODEL A. System Description Let us consider the uplink in a single cell of a multiuser 3GPP LTE-A network with SC-FDMA channel access. To satisfy diverse QoS requirements we deploy them in a wireless local area network (WLAN) (e.g., WiFi, Zigbee, SUN, and UWB) or wireless personal area network (WPAN) (e.g., Bluetooth). To this aim, M2M devices are grouped based on identical transmission protocols and clustered based on the same QoS characteristics and requirements. In this grouping scenario, the common service features of M2M devices are considered, and thus eNB can manage RBs on a cluster basis rather than an individual M2M device basis, with a reduced complexity. In this paper, we consider a WiFi group and focus on a cluster of this group, whose M2M devices have rate and delay bound requirements (i.e., the cluster with QoS(i) as shown in Fig. 2). Assume that there are M M2M devices in each cluster indexed by M = {1, 2, . . . , M } sharing K resource blocks (RBs) indexed by K = {1, 2, . . . , K} in the coverage area of the eNB. We assume a Poisson traffic generation rate for M2M traffic arrival intensity per device. The channel is assumed to exhibit block fading characteristics. Furthermore, the coherence time of the channel is considered to be greater than a transmission time interval (TTI), and thus the channel gain remains to be constant within a TTI. Since deterministic delay guarantees can not be provided in a wireless channel due to owning time varying nature. On the other hand, successful M2M communications in LTEA networks depend on how efficiently LTE-A networks can
1 ln E e−θm Rm , θm
(1)
where EC demonstrates the effective capacity, E(·) indicates the expectation operation, θm is statistical QoS exponent of the mth M2M device, and Rm is the data rate of the mth M2M device. Consider a queue of infinite buffer size due to a constant arrival rate λ. It can be shown that the QoS exponent θm indicates a steady-state delay violation probability of the mth M2M device, and this delay violation probability is given by δ = P rob Dm > Dmax ≈ ϕm e−θm Dmax , (2) where Dm is the delay experienced by a source packet of M2M device m, Dmax is a delay bound, ϕm (λ) = P r{Dm > 0} is the probability of non-empty buffer, and the pair of {ϕ(λ), θ(λ)} are to model the link. It is obvious that as the QoS requirement becomes more stringent, the arrival rate that a wireless channel can support with this QoS guarantee decreases. Thus, in order to guarantee a QoS requirement θm , we should satisfy the following condition. m EC (θm ) ≥ λm .
(3)
In order to obtain θm we need to solve Eqn. (3). Thus, using Shannon’s capacity formula, the maximum achievable transmission rate for M2M device m can be expressed as 2 Pm |hm | , Rm = B log2 1 + 2 σ
(4)
where B is the bandwidth of each RB, Pm is transmission power of the mth M2M device, |hm |2 is channel gain, σ 2 denotes the power of additive white Gaussian noise (AWGN), and Υm = (Pm |hm |2 /σ 2 ) is the signal to noise ratio (SNR) for the mth M2M device. v Using Eqn. (4), Eqn. (3) is converted to E[(1 + Υm ) ] ≤ −λm θm e , where E(·) indicates the expectation operation and v = (−θm B/ln 2). To calculate the expected value, we need the probability density function (PDF) of Υm , which is calculated as follows. Assume that channel coefficient hm is given by hm = p Fm 1/Zm , where Fm represents the channel fading coefficient and Zm is the path loss [17]. The channel fading coefficient, Fm , is modeled as complex Gaussian variable with zero mean and unit variance. The expected value of the channel 2 power gain is given by E(|hm |2 ) = σm = (1/ξdα m ), where ξ depends on the choice of path loss model, dm is the distance between M2M device m and eNB, and α is the path loss exponent. It follows that |hm |2 is exponentially distributed and 2 2 the PDF is given by (1/σm ) exp(−|hm |2 /σm ) for |hm |2 ≥ 0.
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Thus, the PDF of Υm is given by 2 2 (σ 2 /Pm σm ) exp(−σ 2 Υm /Pm σm ). Therefore, we have Z ∞ σ 2 Υm σ2 − θm B (1 + Υm ) ln 2 exp(− )dΥm ≤ e−λm θm . 2 2 Pm σm P m σm 0 (5) Via solving Eqn. (5), we can obtain θm . However, due to the computational complexity, we use an intuition given in [16] and extract the QoS exponent θ(λ) through the concept of following equation. θ(λ) =
ϕ(λ)λ . λτs (λ) + E[Q(t)]
(6)
Since the delay D is the sum of the delay due to the packets already in service and the delay due to the packets waiting in the queue Q(t), θ(λ) can be obtained as follows. Let us consider an interval of length T (e.g., T = 100000 TTI) and take a number of samples L = b TTa c, in which Ta is access grant time interval to the RBs, and can be interpreted as a representative for wireless link condition. In other words, in each Ta , the processor of the queue provides service to arrival traffic. Furthermore, for the cluster with a high priority, the access time to the RBs would be shorter in comparison with those in the other clusters. It should be noted that by adding other clusters, when access times of different clusters are arranged at the same time, the access time for the cluster with a lower priority is postponed to the next access time as shown in Fig. 3.
Cluster 1
Cluster 2
Cluster 3
The access time for the cluster with lower priorities are postponed to the next access time
Fig. 3: Priority-based cluster formation based on identical QoS requirements for M2M devices in order to allocate RBs among clusters. The figure shows that when access times of different clusters are aligned in time, the access time for a cluster with a lower priority is postponed to the next access time. To estimate ϕˆ and qˆ, based on the released time of the first RB and the number of samples L, we partition generated packets. Thus, to calculate ϕ, ˆ the number of packets in the lth sample are counted, given that the packet is in service. In other words, the packets in service are counted from the beginning of the partition till the starting time of the next partition. To this end, the indicator Il is utilized and it takes ”1” if the packet is in the service, and ”0” otherwise. The value of ϕˆ is obtained through summing up the values of Il divided by L. To estimate qˆ, first we count the packets generated before the released time of the first RB. Then, in each interval, the
4
packet in service is excluded and the number of packets in the queue in every sampling epoch, Ql , is counted. The value of qˆ is obtained through summing up the values of Ql divided by L. Finally, to estimate τˆs , given that there is one packet in service in every sampling epoch, the remaining service time, Tl , is calculated. Then, the value of τˆs is obtained through summing up the values of Tl divided by L. Therefore, the value of θ is obtained as follows. ϕλ ˆ . (7) θˆ = λτˆs + qˆ ˆ the QoS exponent θ can be obtained With the pair of {ϕ, ˆ θ}, while considering wireless channel condition. Hence, via this priority-based cluster forming approach and gathering M2M devices based on identical QoS requirements, we can simply utilize the common service features of M2M devices, in which the average or maximum radio resources required by M2M devices could be calculated according to the service type or device type. Thus, the eNB can manage RBs on a cluster basis that not only complexity is reduced, but also the difficulty of providing diverse QoS requirements of M2M devices could be significantly alleviated. After that, we can perform RB allocation for M2M devices, aiming to satisfy their rate requirements as demonstrated in the next part. B. SC-FDMA based Resource Allocation The use of SC-FDMA in the uplink of LTE-A networks imposes certain restrictions on power and RB allocation [12], which can be explained as follows. The first one is exclusive restriction, in which one RB can only be allocated to at most one M2M device. The second restriction is that multiple RBs allocated to an M2M device must be adjacent in order to retain the benefits of low PAPR. In terms of the power allocation, there are some constraints as follows. First, peak power transmitted by M2M device on each RB should be less than a given peak power level Ps . Second, the total power transmitted by each M2M device should be less than a given maximum power level PT . Third, the transmit power on all the RBs allocated to an M2M device should be equal. Due to the RB adjacency restriction, it is needed to partition K RBs into Θ ordered sets, in which each set has ki adjacent RBs such that K = k1 + k2 + . . . , kΘ [15]. The feasible RB allocation pattern matrix can be constructed by denoting a RB allocated to a M2M device by a ”1”, and not allocated by a m ”0”, thus forming the RB allocation pattern matrix Wk,j for M2M device m. The rows of this matrix correspond to the RB indexes, and the columns correspond to the feasible RB allocation patterns. Therefore, in general, the RB allocation pattern matrix including all of feasible RB allocation patterns for the case K = 4 RBs can be written as follows. 0 1 0 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 m Wk,j = (8) , 0 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 0 1 1 which is the same for all M2M devices. Note that when multiple RBs are assigned to a M2M device (i.e., the columns
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6-11), these RBs should be adjacent to each other. Thus, the RB allocation matrix is of order K × J, in which J denotes the total number of feasible allocation patterns given by J = 21 × (K 2 + K) + 1, which is 11 in this example. We associate each possible RB allocation for an M2M device m with a binary decision variable xm,j , {0, 1}, j = 1, . . . , J, which indicates whether a particular RB allocation pattern is chosen or not. We further denote a decision vector of length M J as X = [X1 , . . . , XM ]T , where Xm = [xm,1 , . . . , xm,J ]T . Suppose that we have K = 4 RBs and M = 2 M2M devices. Consider the case that k = 1 is allocated to m = 1 and k = 2, 3, and 4 are allocated to m = 2. Thus, RB allocation pattern matrix is given as follows. 0 1 0 0 0 0 0 0 0 0 0 m Wm,j = xm,j Wk,j = , 0 0 0 0 0 0 0 0 0 1 0 which represents j = 2 including k = 1 is allocated to m = 1; while for m = 2 the resource allocation pattern j = 10 is allocated, which includes the RBs k = 2, 3, and 4. Therefore, the aim to construct the RB allocation pattern matrix is that we want to allocate RB allocation pattern j to a M2M device m, assuring that in each j the adjacency of RBs are satisfied. Assume that a pattern j is allocated to M2M device m and each pattern includes some RB(s). Thus, using Shannon’s capacity formula, the maximum achievable transmission rate for M2M device m on RB k and pattern j can be expressed as 2 Pm,k(j) |hm,k(j) | , (9) Rm,k(j) = B log2 1 + σ2 where B is the bandwidth of each RB, Pm,k(j) is the transmission power of the mth M2M device on RB k(j) of the jth pattern, |hm,k(j) |2 is the channel gain, and σ 2 denotes the power of additive white Gaussian noise (AWGN). Consequently, the maximum achievable transmission rate for M2M device m on pattern j can be expressed as Rm,j =
K X
Rm,k(j) .
(10)
k=1
The total transmission power accumulated on pattern j is Pm,j =
K X
Pm,k(j) .
(11)
k=1
III. P ROBLEM F ORMULATION A. Sum-Throughput Maximization Design Problem with QoS Provisioning We aim to maximize sum-throughput of the whole network with M2M device QoS provisioning. Thus, the QoS requirement of each M2M device should be discussed first. The QoS requirements are indicated as the minimum transmission rate for each individual M2M device. The QoS rate requirement for M2M device m is described as follows. J X
min xm,j Rm,j ≥ Rm ,
(12)
j=1 min where Rm is the minimum rate requirement for the service required by M2M device m.
5
Let Ps denote the maximum power allocation for a M2M device m on RB k given by Pm,k(j) ≤ Ps . Thus, the transmission power an M2M device in the uplink is subject Pof J to the condition j=1 xm,j Pm,j ≤ PT , where Pm,j is the total transmission power accumulated on pattern j for the M2M device m and PT is the threshold indicating the M2M device total power constraint. Afterward, the sum-throughput maximization resource allocation problem is formulated as follows. T = max X,P
M X J X
xm,j Rm,j ,
m=1 j=1
subject to a)
J X
min xm,j Rm,j ≥ Rm , ∀m ∈ M,
j=1
b) 0 ≤ Pm,k(j) ≤ Ps , ∀m ∈ M, k ∈ K, c)
J X
xm,j Pm,j ≤ PT , ∀m ∈ M,
j=1
d) Pm,k(j) = Pm,l(j) , ∀m ∈ M, k ∈ K, l ∈ L, e) xm,j ∈ 0, 1, ∀m ∈ M, j ∈ J, f)
J M X X
m xm,j Wk,j = 1, ∀k ∈ K,
m=1 j=1
g)
J X
xm,j = 1, ∀m ∈ M.
(13)
j=1
The objective of the optimization problem given in (13) is power and RB allocation for M2M devices so that the sum-throughput of whole network is maximized, subject to QoS requirements provisioning for different M2M devices along with different constraints in a SC-FDMA system. As aforementioned, the constraint (13a) is the minimum rate requirement for every individual M2M device. The constraint (13b) indicates that the transmitted power for each M2M device in each RB should not exceed Ps , in which Ps is RB power constraint and it should be non-negative. The constraint (13c) ensures that the total transmit power for each M2M device in the allocation pattern should not exceed PT , where PT is the total power constraint of M2M device in allocation pattern j. The constraint (13d) ensures that the transmit power on all the RBs allocated to a M2M device should be equal. The constraint (13e) represents that it is a pure binary constraint and indicates whether a particular RB allocation pattern is chosen or not. The constraint (13f) ensures exclusive allocation of RB to each M2M device and also indicates that a RB should be allocated to one M2M device only. The constraint (13g) indicates that at most one allocation pattern should be assigned to each M2M device. Although the optimization problem (13) is more tractable, to obtain the optimal solution it is needed to exhaustively search over all feasible RB assignments with an exponential complexity O(M K ), which is impractical. Thus, we propose a computationally feasible solution based on the Lagrange dual method which is given as follows.
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B. Lagrange Dual Method Based Resource Block Allocation The Lagrangian function for our objective function (13) and its related constraints is L(X, P, µ, γ) =
M X
J X
xm,j Rm,j
+
µm
X J
m=1
+
M X
min xm,j Rm,j − Rm
j=1
γm PT −
m=1
J X
xm,j Pm,j ,
(14)
j=1
where µ = [µ1 , µ2 ,. . . ,µM ]T and γ = [γ1 ,γ2 ,. . . ,γM ]T are the vectors of dual variables for M2M device rate and transmission power constraints, respectively. Then, the Lagrange dual function [18] Ψ(µ,γ) can be obtained as max L(X, P, µ, γ), subject to m xm,j Wk,j = 1, ∀k ∈ K,
m=1 j=1 J X
xm,j = 1, ∀m ∈ M,
and the dual problem for (13) is min
Ψ(µ, γ) = min max L(X, P, µ, γ),
m xm,j Wk,j
= 1, ∀k ∈ K,
xm,j = 1, ∀m ∈ M,
xm,j ∈ 0, 1, ∀m ∈ M, j ∈ J, 0 ≤ Pm,k(j) ≤ Ps , ∀m ∈ M, k ∈ K, Pm,k(j) = Pm,l(j) , ∀m ∈ M, k ∈ K, l ∈ L. (16) After having elaborated how the Lagrange dual method can be used in our case, we utilize the Lagrangian dual decomposition (LDD) to decompose Ψ(µ, γ) into J subproblems, which can be solved independently for each RB. The jth subproblem for given (µ,γ) can be written as max Lj (Xj , Pj )
Xj ,Pj
M X
(1 + µm )xm,j Rm,j −
m=1
subject to
subject to 0 ≤ Pm,k(j) ≤ Ps , ∀m ∈ M, k ∈ K, Pm,k(j) = Pm,l(j) , ∀m ∈ M, k ∈ K, l ∈ L. (18)
m
given by Γj = [Γ1,j ,Γ2,j ,. . . ,ΓM,j ]T . To solve Γm,j for a given m on matrix allocation pattern j, we perform the following procedure. By substituting (9)-(11) into Γm,j , the objective of (18) turns into the specific form in (19), which is shown below. K X Pm,k(j) |hm,k(j) |2 ξm,j = (1 + µm )B log2 1 + σ2 k=1
K X
Pm,k(j) ,
(19)
k=1
j=1
=
where Xj and Pj are the vector of Xj = [x1,j , . . . , xm,j ]T and the matrix of Pm,k(j) at matrix allocation pattern j, respectively. From (17) it can be seen that Xj is an all zero vector except for one binary nonzero entry as every j can be allocated to only one M2M device. Hence, for a certain matrix allocation pattern j, we first obtain Γm,j = max (1 + µm )Rm,j − γm Pm,j ,
− γm
m=1 j=1 J X
xm,j = 1, ∀m ∈ M,
xm,j ∈ 0, 1, ∀m ∈ M, j ∈ J, 0 ≤ Pm,k(j) ≤ Ps , ∀m ∈ M, k ∈ K, Pm,k(j) = Pm,l(j) , ∀m ∈ M, k ∈ K, l ∈ L. (17)
µ,γ X,P
subject to µm ≥ 0, γm ≥ 0, ∀m ∈ M, J M X X
J X
Xj ,Pj
j=1
µ≥0,γ≥0
m=1 j=1
for each m and then solve the optimal value for subproblem j in (17) by max L(Xj , Pj ) = max Γj , where Γj is the vector
xm,j ∈ 0, 1, ∀m ∈ M, j ∈ J, 0 ≤ Pm,k(j) ≤ Ps , ∀m ∈ M, k ∈ K, Pm,k(j) = Pm,l(j) , ∀m ∈ M, k ∈ K, l ∈ L. (15)
Ω=
m xm,j Wk,j = 1, ∀k ∈ K,
Pj
X,P
J M X X
M X J X
j=1
m=1 j=1 M X
6
M X m=1
γm xm,j Pm,j ,
(1 + µm ) lnB2 ∂ξm,j = − γm = 0, (20) σ2 ∂Pm,k(j) Pm,k(j) + |hm,k(j) |2 + (1 + µm )B σ2 ∗ Pm,k(j) = min − , P s , (21) γm ln 2 |hm,k(j) |2 where (x)+ means max{x,0} and Γm,j is obtained by substituting P∗m,k(j) into (19) as following. ∗ Γm,j = ξm,j Pm,k(j) = Pm,k(j) . (22) Finally, the optimal vector X∗j to solve subproblem j in (17) can be given by ( 1, m = arg max Γj m xm,j = (23) 0, otherwise where max Γj means the maximum element in vector Γj , and m the corresponding optimal power allocation P∗j on allocation pattern j is ( ∗ Pm,k(j) , m = arg max Γj m Pm,k(j) = (24) 0, otherwise
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After solving all subproblems in (17), Ψ(µ, γ) can be obtained by (14) and (17) at given Ψ(µ, γ). To this aim, we first obtain the initial value of Lagrange multipliers µ and γ via Algorithm 1, which will be explained in detail later. Then, by utilizing Ellipsoid method [19], we update the dual vector (µ,γ) at each iteration and solve the dual problem (16) and achieve the dual optimum (µ∗ ,γ ∗ ). The sub-gradient of Ψ(µ, γ) is required by the Ellipsoid method at each iteration and can be readily given at the tth iteration by J X min d µm (t) = xm,j Rm,j − Rm , ∀m ∈ M,
all the sets accordingly. This process will be repeated until all RBs are allocated to the M2M devices. After the RB allocation, the power allocation is performed for the M2M devices in their corresponding RBs. In order to satisfy the rate and total transmit power requirements of M2M devices, the initial value of µm and fulfill these PJ γm are chosen tomin = 0 and conditions with equality ( j=1 xm,j Rm,j ) − Rm PJ PT − j=1 xm,j Pm,j = 0. Algorithm 1 Greedy Based Radio Resource Block Allocation Algorithm.
(25)
j=1 J X d γm (t) = PT − xm,j Pm,j , ∀m ∈ M.
7
(26)
j=1
The Ellipsoid method to update dual variables (µ∗ ,γ ∗ ) is given as follows [19]. An ellipsoid with a center z = [µ γ]T and a shape A−1 is defined as (27) E A−1 , z = y (y − z)T A−1 (y − z) ≤ 1 . Let di be the sub-gradient at the center of the ellipsoid zi . In each iteration, the half of the ellipsoid is eliminated based on di . A new ellipsoid that is the minimal-volume ellipsoid containing the other half, is formed. Mathematically, the update algorithm [19] is given as follows: di , (28) 1) d˜i = q T −1 di Ai di 1 2) zi+1 = zi − A−1 d˜i , (29) N +1 i 2 2 N A−1 A−1 d˜i d˜Ti A−1 , (30) 3) A−1 i − i i+1 = 2 N −1 N +1 i where, N = 2M and M is the number of M2M devices. Furthermore, A−1 can be obtained as shown in Eqn. (31). i C. QoS Assurance Sum-Throughput Maximization Resource Block Allocation We propose a method via utilizing the given analysis in order to solve problem (13) through the Lagrange dual method in Section III-B to obtain a resource allocation strategy with the dual optimum (µ∗ ,γ ∗ ). This resource allocation method satisfies both rate and total transmit power requirements of each M2M device. Thus, we propose a preprocessing procedure for the sub-channel assignment before conducting the ellipsoid method. The proposed algorithm includes two phases, which will be clarified in details as follows. 1) Phase A: Greedy Based Resource Block Allocation: First, we initialize the available sets of M2M devices and the RBs. The set Km is the resulting RB allocation for each M2M f device m and Km is a set of feasible RB indices for M2M device m at each iteration. We note that, all RBs are feasible for all the M2M devices in initialization step. However, when a RB is allocated to a M2M device, only the adjacent RBs to it are feasible. Then, for all the feasible RBs and all the M2M devices, we find maximum channel gain. Thus, the RB is allocated to that M2M device consequently, and we update
1: Initialize M ∈ {1,2,...,M}, K ∈ {1,2,...,K}, Km = ∅ ∀m ∈ M, and Kfm = K ∀m ∈ M 2: repeat 3: ∀m ∈ M T 4: ∀k ∈ Kfm K 5: for k = 1:K 6: for m = 1:M 7: Find (m∗ ,k∗ ) = arg maxm∈M, k∈K hm,k S ∗ 8: Km∗ = Km∗ k (f )
9: Km∗ = {min(Km∗ )-1, max(Km∗ )+1} 10: K = K\k∗ 11: end for 12: end for 13: until K = ∅
2) Phase B: QoS Assurance Sum-Throughput Maximization Resource Block Allocation: After preprocessing RB assignment and power allocation in Phase A, we obtain the initial value of µm and γm . As the resource allocation parameters (i.e., RB assignment and power allocation) are mutually dependent, the values of µm and γm should be updated jointly. We then conduct the ellipsoid method as discussed in Section III-B to maximize the objective function problem (13). The associated method is summarized in Algorithm 2. Algorithm 2 Proposed QoS Assurance Sum-Throughput Maximization Resource Block Allocation Algorithm. 1: Initialize (µ(0), γ(0)) and an Ellipsoid A−1 (0); 2: repeat 3: 4: 5: 6: 7: 8:
2
for each pattern j = 1 to ( K2 + K + 1) do 2 for each m if k ∈ j then Calculate P∗m,k(j) via (21) and obtain vector Γj by (22); Set xm,j and Pm,k(j) according to (23) and (24); For m = m∗ , set Pm,k(j) = P∗m,k(j) and xm,j = 1,
9: end if 10: end for 11: end for 12: Update dual variables (µ, γ) and ellipsoid A−1 by the ellipsoid method with sub-gradient in (25) and (26) 13: until converge to the dual optimum (µ∗ , γ ∗ )
IV. S IMULATION R ESULTS AND D ISCUSSIONS Our simulation model is established based on the uplink of a 3GPP LTE-A system. We consider a system with 5 MHz of bandwidth; thus 25 RBs are available per TTI, each having a bandwidth of 180 kHz. Assume that M = 10 uniformly
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A−1 i
=
N ( γ21 )2 0 .. .
0 N ( γ22 )2
0 0 0 .. .
.. . 0 0 0 .. .
0
0
8
... ... .. .
0 0 .. .
0 0 .. .
0 0 .. .
... ... .. .
0 0 .. .
... ... ... .. .
N ( γ2M )2 0 0 .. .
0 N ( µ21 )2 0 .. .
0 0
... ... ... .. .
0 0 0 .. .
...
0
0
...
N ( µ2M )2
distributed M2M devices exist in a cell of 500 m. The channel model accounts for small scale Rayleigh fading, large scale path loss, and shadowing (log-normally distributed). The power spectral density of noise is assumed to be -174 dBm/Hz. The RB peak power constraint is Ps = 10 mW, and per M2M device maximum power constraint is PT = 200 mW. We will present the simulation results in terms of delay violation probability for identical QoS-based grouping for M2M devices. Then, the performance of the proposed algorithm is evaluated via numerical simulations in terms of the sum-throughput maximization of the network. To this end, we first evaluate the optimality of our proposed algorithm. Then, we compare our scheme with exhaustive search by solving the binary-integer program, which is the optimal solution. Furthermore, we also compare the performance with the Greedy algorithm as provided in [15]. In identical QoS-based grouping scheme, the eNB allocates a set of RBs at each granted Ta ms while considering prioritization scheme based on the QoS exponent θ. Therefore, in one group, cluster with a higher θ than others is first granted access to the scheduled Ta . Thus, if Ta for different clusters are granted in the same subframe, Ta for the cluster with a lower θ is postponed to the subsequent subframe. The system bandwidth is 5 MHz, thus 25 RBs are available per TTI. An example setup is considered, where 100000 TTI are simulated for 10 M2M devices generating Poisson traffic with a packet arrival rate of λ = 1. As discussed earlier, in order to guarantee a QoS requirement θm , Eqn. (3) should be satisfied. Hence, if Eqn. (3) is held, it can be insured that for stationary arrival and service processes with the average arrival-rate less than the average service-rate as shown in Eqn. (3), the probability of delay Dm exceeding a certain threshold Dmax decays exponentially as the threshold Dmax increases, as shown in Figs. 4-6. As discussed earlier, the parameter θ plays an important role for the statistical QoS guarantees, which indicates decaying-rate of QoS violation probability. Based on Eqn. (2), a smaller θ corresponds to a slower delaying-rate, which implies that the system can only provide a less strict QoS requirement; while a larger θ leads to a faster delaying-rate, which means that a more stringent QoS requirement can be guaranteed. In Figs. 4-6 the delay-violation probability versus the delay bound Dmax are represented. It can be seen that the actual delayviolation probability decreases exponentially with the delay bound Dmax . Furthermore, Eqns. (1)-(7) insure that we can utilize this method in order to guarantee a QoS level that can
N ( µ22 )2 .. . 0
(31)
be satisfied, while considering the wireless channel condition we encounter in real applications. Thus, we could guarantee the statistical QoS requirements. It can be seen that by priority-based cluster formation process, gathering M2M devices based on identical QoS requirements, and granting access to the RBs for high-prioritized cluster with high QoS exponent θ first, the delay performance improves significantly as shown in Fig. 4. Also, as shown in Fig. 4, the proposed scheme improves the delay performance since high prioritized cluster with high QoS exponent θ is first granted to access the RBs. Fig. 5 shows that, for the cluster with identical QoS requirement, as θm decreases, the delay violation probability increases, which implies that the system can only provide a looser QoS guarantee. On the other hand, a larger θm yields a faster decaying rate, which means that a more stringent QoS requirement can be guaranteed. Furthermore, Fig. 5 demonstrates that by increasing the number of M2M devices from 10 to 30 and packet size from 8 byte to 24 byte, the delay violation probability increases, thus confirming Eqns. (2) and (7). Fig. 6 demonstrates the performance for non-identical QoS-based grouping. This figure shows that the delay performance becomes worse off by increasing the number of M2M devices from 10 to 30 and the packet size from 8 to 24 byte as well. Furthermore, in comparison of Fig. 6 with Fig. 5 it is obvious that the delay performance of proposed scheme significantly outperforms the non-identical one. Fig. 7 illustrate the sum-throughput of the system versus the number of M2M devices. In this figure the total number of M2M devices and RBs are assumed to be 10 and 25, respectively. As shown in the figure, the sum-throughput increases as the number of M2M devices increases, thus confirming the effect of multiuser diversity. This is due to the fact that as the number of M2M devices increases, the RBs are efficiently utilized, resulting in an increased sumthroughput. However, with the increasing number of M2M devices, the slope of the curve is decreasing. This happens due to the fact that as the number of M2M devices increases, the number of RBs allocated to each M2M device decreases. In addition, it is obvious from Fig. 7 that the proposed algorithm outperforms the Greedy scheme. Furthermore, it can also be observed that the results of the proposed algorithm are close to that obtained by solving the binary-integer program (BIP), which is the optimal solution. The sum-throughput of the system versus consumed power for different schemes is presented in Fig. 8. In this figure, the
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Fig. 4: Performance comparison versus packet delay distribution with and without identical QoS-based grouping when arrival traffic rate is λ = 1 and packet size is 8 bytes.
9
Fig. 6: Packet delay distribution performance without identical QoS-based grouping when arrival traffic rate is λ = 1 and packet size is 8 and 24 bytes, respectively. 7
x 10
Throughput versus Number of Users
16 14
Throughput (b/s)
12 10 8 6 4 Proposed Algorithm Optimal Algorithm Greedy Algorithm
2
Fig. 5: Packet delay distribution performance for identical QoS-based grouping when arrival traffic rate is λ = 1 and packet size is 8 and 24 bytes, respectively.
total number of M2M devices and RBs are considered to be 10 and 25, respectively. When the power increases, signal to noise ratio (SNR) increases, thus increasing the throughput of the system. By investigating Fig. 8, it is observed that the sumthroughput curve of the proposed algorithm is quite close to that obtained by optimal algorithm and also outperforms the Greedy scheme. Fig. 9 illustrates the fairness of the proposed algorithm in terms of RB allocation among M2M devices. The data rate requirements for M2M devices vary randomly from 640 kbps to 8.96 Mbps in multiples of 64 kbps; whereas 1 RB is assumed to be sufficient to fulfill the data rate requirements. As shown in Fig. 9, it can be observed that for the Greedy algorithm the RB allocation is performed for more M2M devices than proposed and optimal algorithms. However, in the Greedy scheme, the allocated power may not be an optimal one and this leads to the reduced sum-throughput of the total network. For the proposed algorithm the RB allocation is performed for more M2M devices than optimal algorithm.
2
4
6 Number of Users
8
10
Fig. 7: Sum-throughput versus number of users when total RB is K = 25 and the number of M2M users (M = 10) is uniformly distributed in a cell with its radius 500 m. The power spectral density of noise is assumed to be -174 dBm/Hz.
This is due to the fact that, in every pattern the RB(s) is/are allocated to an M2M device in a manner that by allocating the RBs in this way the throughput in that pattern will be maximized. Finally, let us discuss the complexity of the proposed resource allocation algorithms. It should be noted that the optimization problem (13) is difficult to solve due to its combinatorial nature. The cardinality of the feasible search space for PM M M2M devices and K RBs is given by i=1 Mi i! K−1 i−1 [20], which increases exponentially. For instance, for M = 10 and K = 24, a search across 5.26 × 1012 possible RB allocations is required, which is not practical. In the proposed algorithm, we will first analyze the complexity phase by phase and then the overall complexity of the proposed algorithm is estimated. In Phase A, M K comparison computations are required to find (m∗ , k ∗ ) and allocate RB
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7
Phase A are restricted by M2M device number M . Therefore, in Phase A, a fixed number of iterations rather than iterating until convergence is needed. Hence, the complexity of the proposed algorithm depends almost on Phase B, which is O(M K(2M )2 ). It is clear that our proposed algorithm has polynomial complexity with regard to the parameters M and K, which facilitates the practical implementation.
Throughput versus Consumed Power
x 10 16 14
Throughput (b/s)
12 10 8
V. C ONCLUSION
6 4 Proposed Algorithm Optimal Algorithm Greedy Algorithm
2 0.3
0.4
0.5
0.6 0.7 0.8 Consumed Power
0.9
1
1.1
Fig. 8: Sum-throughput versus consumed power when the number of RBs is K = 25, and M2M users (M = 10) are uniformly distributed in a cell with its radius 500 m. The RB peak power constraint is Ps = 10 mW and the per user maximum power constraint is PT = 200 mW. The power spectral density of noise is -174 dBm/Hz. 7
12
Fairness
x 10
Proposed Algorithm Optimal Algorithm Greedy Algorithm
10
Throughput (b/s)
8
This paper studied joint scheduling and power allocation issues for M2M communications in uplink SC-FDMA based LTE-A networks. Providing diverse and strict QoS guarantees is an important requirement in M2M communications. To efficiently allocate resource blocks for M2M devices while satisfying QoS requirements, we proposed group M2M devices based on their identical QoS requirements and characteristics. We formulated a framework as a sum-throughput maximization problem, while respecting all the constraints in SC-FDMA RB allocation in up-link LTE-A system. An optimization algorithm was proposed, and the optimization problem was converted into a Binary Integer Programming (BIP) problem by defining a RB allocation matrix, which ensures adjacent allocation of RBs for each M2M device. Then, we proposed a computationally efficient solution based on the Lagrange method to obtain a near-optimal solution for power and RB allocation. Numerical results have shown that the proposed algorithm not only outperforms Greedy algorithm in terms of sum-throughput maximization, but also its performance is very close to the optimal solution.
6
A PPENDIX D ERIVATION OF E QUATION (3)
4
As discussed in Section II, the effective capacity [16] for the mth M2M device to satisfy QoS requirement specified by θ is given by
2
0
1
2
3
4
5 6 7 Allocated User
8
9
10
Fig. 9: Fairness of the proposed algorithm in terms of RB allocation among M2M users when the total number of RBs is K = 25, and M2M users (M = 10) are uniformly distributed in a cell with its radius 500 m. The RB peak power constraint is Ps = 10 mW and the per user maximum power constraint is PT = 200 mW. The power spectral density of noise is -174 dBm/Hz. ∗
10
∗
k to M2M device m in each iteration. The associated ellipsoid method in Phase B has the largest impact on the complexity of the algorithm. Accounting for all subproblems in (13), it requires M K computations in total; Thus, the complexity for each iteration of the ellipsoid method is O(MK). With (2M ) dual variables in total, the ellipsoid method converges in O((2M )2 ) iterations [21]-[22]. From the given analysis, it is obvious that the iterations involved in
m EC (θm ) = −
1 ln E e−θm Rm . θm
(32)
Furthermore, as discussed earlier, in order to guarantee QoS requirement θm , the following condition should be satisfied: m EC (θm ) ≥ λm .
(33)
Substituting Eqn. (32) in Eqn. (33) we have E e−θm Rm ≤ e−θm λm . Using Eqn. (4), given that log2 x = following condition:
ln x ln 2 ,
(34) we obtain the
mB − θln 2 P .|h |2 ln(1+ m σ2m ) E e ≤ e−θm λm ,
(35)
in which Υm = (Pm |hm |2 /σ 2 ) and v = (−θm B/ln 2). The expanded expression of Eqn. (3) is given as follows: v E (1 + Υm ) ≤ e−θm λm . (36)
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TVT.2016.2635262, IEEE Transactions on Vehicular Technology IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. XX, NO. YY, MONTH 2016
R EFERENCES [1] F. Ghavimi and H. H Chen, ”M2M Communications in 3GPP LTE/LTE-A Networks: Architectures, Service Requirements, Challenges, and Applications”, IEEE Commun. Surveys & Tutorials, vol. 17, no. 2, pp. 525-549, 2015. [2] T. Taleb and A. Kunz, ”Machine Type Communications in 3GPP Networks: Potential, Challenges, and Solutions”, IEEE Commun. Mag. 50(3) (2012), pp. 178-184. [3] M. Hasan, E. Hossain, and D. Niyato, ”Random Access for Machineto-Machine Communication in LTE-Advanced Networks: Issues and Approaches”, IEEE Commun. Mag., vol. 51, no. 6, pp. 86-93, Jun. 2013. [4] A. Laya, L. Alonso, and J. Zarate, ”Is the Random Access Channel of LTE and LTE-A Suitable for M2M Communications? A Survey of Alternatives”, IEEE Communications Surveys & Tutorials, vol. 16, no. 1, pp. 4-16, 2014. [5] J. Seo and V. Leung, ”Approximate Queuing Performance of a Multipacket Reception Slotted ALOHA System with an Exponential Backoff Algorithm”, Fourth International Conference on Communications and Networking, China, 2009, pp. 1-5. [6] 3GPP TR 37.868 V11.0.0, ”Study on RAN Improvements for Machine Type Communications,” September 2011. [7] M. H. Cheung, H. Mohsenian-Rad, V. Wong, and R. Schober, ”UtilityOptimal Access for Wireless MUltimedia Networks”, IEEE Wireless Communications Letters, vol. 1, no. 4, pp. 340-343, Aug. 2012. [8] C. Joo, ”On Random Access Scheduling for Multimedia Traffic in Multihop Wireless Networks with Fading Channels”, IEEE Transactions on Mobile Computing, vol. 12, no. 4, pp. 647-656, App. 2013. [9] J.-P. Cheng, C. Lee, and T.-M. Lin, ”Prioritized random access with dynamic access barring for RAN overload in 3GPP LTE-A networks”, in Proc. IEEE BLOBECOM Workshops, Houston, TX, USA, Dec. 2011, pp. 368-372. [10] S.-Y. Lien, T.-H. Liau, C.-Y. Kao, and K.-C. Chen, ”Cooperative access class barring for machine-to-machine communications”, IEEE Trans. Wireless Commun., vol. 11, no. 1, pp. 27-32, Jan. 2012. [11] H. Wu, C. Zhu, R. J. La, X. Liu, and Y. Zhang, ”FASA: Accelerated SALOHA using access history for event-driven M2M communications”, IEEE/ACM Trans. Netw., vol. 21, no. 6, pp. 1904-1907, Dec. 2013. [12] H. G. Myung, J. Lim, and D. J. Goodman, ”Single carrier FDMA for uplink wireless transmission”, IEEE Veh. Technol. Mag, vol. 1, no. 3, pp. 30-38, 2006. [13] K. Seong, M. Mohseni, and J. Cioffi, ”Optimal resource allocation for OFDMA downlink systems”, In Proceeding of IEEE ISIT, Seattle, WA, Jul. 2006. [14] W. Yu and R. Lui, ”Dual method for non-convex spectrum optimization of multicarrier systems”, IEEE Trans. on Communications, vol. 54, no. 7, pp. 1310-1322, Jul. 2006. [15] I. Wong, O. Oteri, and W. McCoy, ”Optimal Resource Allocation in Uplink SC-FDMA Systems”, IEEE Trans. on Wireless Communications, vol. 8, no. 5, pp. 2161-2165, May 2009. [16] D. Wu and R. Negi, ”Effective capacity: A wireless link model for support of quality of service”, IEEE Trans. on Wireless Communications, vol. 2, no. 4, pp. 630-643, Jul. 2003. [17] M. K. Simon and M. S. Alouini, ”Digital Communication over Fading Channels: A Unified Approach to Performance Analysis”, New York: Wiley, 2nd Ed., 2005. [18] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004. [19] Lecture Slides on Class EE364b of Stanford Univ., S. Boyd, Ellipsoid Method. [Online]. Available: http://www.stanford.edu/class/ee364b/lectures.html [20] R. Merris, Combinatorics. Wiley-Interscience, 2003. [21] M. Tao, Y. Liang, and F. Zhang, ”Resource allocation for delay differentiated traffic in multiuser OFDM systems”, IEEE Trans. Wireless Commun., vol. 7, no. 6, pp. 2190-2201, Jun. 2008. [22] K. Seong, M. Mohseni, and J. M. Cioffi, ”Optimal resource allocation for OFDMA downlink systems”, in Proc. IEEE ISIT, Seattle, WA, USA, pp. 1394-1398, 2006.
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Fayezeh Ghavimi (S’13) received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Tabriz, Tabriz, Iran, in 2007 and 2012, respectively. She is currently working toward the Ph.D. degree in the Department of Engineering Science, National Cheng Kung University, Tainan, Taiwan. Her research interests include wireless communications, machine-to-machine communications, QoS provision for supporting next-generation wireless communications, and next-generation CDMA networks. Ms. Ghavimi received the Distinguished International Student Scholarship from the Department of Engineering Science, National Cheng Kung University, in 2012.
Yu-Wei Lu is currently a MSc student in the Department of Engineering Science, National Cheng Kung University, Taiwan. His major research interests include multiple access techniques, machine to machine communications, and MIMO systems.
Hsiao-Hwa Chen (S’89-M’91-SM’00-F’10) is currently a Distinguished Professor in the Department of Engineering Science, National Cheng Kung University, Taiwan. He obtained his BSc and MSc degrees from Zhejiang University, China, and a PhD degree from the University of Oulu, Finland, in 1982, 1985 and 1991, respectively. He is the founding Editor-in-Chief of Wiley?s Security and Communication Networks Journal (http://www.interscience.wiley.com/security). He is the recipient of 2016 IEEE Jack Neubauer Memorial Award. He served as the Editor-in-Chief for IEEE Wireless Communications from 2012 to 2015. He is a Fellow of IEEE, a Fellow of IET, and an elected Member at Large of IEEE ComSoc.
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