Power-Aware Scalable Video Multicast in 4G Wireless Systems

This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.

Power-Aware Scalable Video Multicast in 4G Wireless Systems Ya-Ju Yu

Pi-Cheng Hsiu

Ai-Chun Pang and Chi-Ping Lai

Graduate Institute of Networking and Multimedia Department of Computer Science and Information Engineering National Taiwan University Taipei, Taiwan 106, R.O.C.

Research Center for Information Technology Innovation Academia Sinica Taipei, Taiwan 115, R.O.C.

Graduate Institute of Networking and Multimedia Department of Computer Science and Information Engineering National Taiwan University Taipei, Taiwan 106, R.O.C.

[email protected]

{acpang,d93944005}@csie.ntu.edu.tw

[email protected]

Abstract Scalable video coding with adaptive modulation and coding is a promising technique to provide real-time multicast services for heterogeneous mobile devices. Nevertheless, as the rapid growth of data communication for emerging applications, energy consumption is an critical challenge of mobile devices. This paper targets the problem of resource allocation for scalable video multicast with adaptive modulation-coding schemes in next generation cellular wireless networks, with an objective to minimize the total energy consumption of all mobile devices for reception. We show the N P -hardness of the target problem and propose a 2-approximation algorithm. Extensive simulations are conducted to compare the proposed algorithm with a brute-force optimal algorithm and a conventional approach, which provides some useful insights into power-aware scalable video multicast in 4G wireless systems. Keywords Energy efficiency, scalable video multicast, adaptive modulation and coding, 4G wireless systems

1.

Introduction

With the popularity of mobile devices and online multimedia applications, such as live video streaming, the provision of realtime multicast services is specified in next generation cellular wireless systems, such as WiMAX [5] and LTE [1]. In a multicast system, multiple users may desire to access the same video streaming, and the base station providing the video content can adaptively change modulation-coding schemes based on the channel conditions at the users. In order to provide the users with different video quality, scalable video coding (SVC) [3], which divides a raw video into multiple layers, is a promising technique employed to accommodate users having different quality requirements or channel conditions. One essential challenging issue in the design of such a system is to determine which video layer should be transmitted with which modulation-coding scheme so that the user requirements can be satisfied, and to allocate appropriate radio resources for carrying the video layers, especially when there are many multicast groups competing limited resources. To solve above mentioned challenging issue, extensive studies have been conducted on the resource allocation problem for scalable video multicast in wireless networks, e.g., [2, 6, 7, 11, 13, 15]. The concept of introducing layered encoding to wireless multicast services was first raised in [2], where only two modulation-coding schemes were available for consideration. In the past years, researchers mainly considered scalable video multicast with adaptive modulation-coding schemes and devel-

oped efficient heuristic algorithms to allocate limited radio resources for multiple multicast groups (or video sessions), with a purpose of optimizing various objective functions they defined as the system performance metrics. Popular performance metrics include the peak signal-to-noise ratio [6], the utility function defined as the number of video layers received at a user [15], and the utility function defined as the total data rate of video layers received at a user [7,11,13]. In recent years, several algorithms with theoretical analysis were proposed. Among them, a polynomial-time algorithm of a constant approximation ratio was proposed in [13], and a pseudo-polynomial-time optimal algorithm based on dynamic programming was proposed in [11], for the maximization of the data rates received at users. However, the algorithms did not take energy consumption of mobile devices into consideration. The resource allocation problem is further complicated by the consideration of energy efficiency which is always a concern of mobile devices, in particular, as the rapid growth of data communication for emerging applications in cloud computing. Both WiMAX [5] and LTE [1] specify that power-saving mechanisms should be supported to allow mobile devices to minimize their energy consumption in multicast services. A typical approach is to turn the transceiver into sleep mode during the duration of communication intended for others [16]. Consequently, resource allocation designed for multicast systems should consider the reduction of reception time as a primary objective. Such an observation motivates our study on poweraware scalable video multicast. In recent years, power-aware resource allocation in orthogonal frequency division multiplexing (OFDM) systems started receiving attention. Kim et al. [8,9] appropriately allocated radio resources in OFDM multicast systems, with an objective to reduce the total energy consumption of all mobile devices for reception, where the energy consumed by a device is proportional to the number of OFDM symbols it receives. Given an amount of data to be transmitted to each device [8] or multicast group [9], heuristic algorithms were proposed to reduce the number of symbols all the devices need to receive. However, the algorithms did not consider SVC and were designed for systems without adaptive modulation and coding, which has been employed in nearly all wireless networks. In this paper, we consider the power-aware scalable video multicast problem with adaptive modulation and coding in 4G wireless systems. The objective is to minimize the total energy consumption of all mobile devices for the reception of OFDM symbols, provided the video quality required by every user is satisfied. The contributions of this paper start with the funda-

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mental but negative result on the N P -hardness of the target problem. We then propose a two-stage greedy algorithm for the problem and prove that the greedy strategy leads to an approximation ratio of 2, in the sense that it always derives a feasible resource allocation such that the total energy consumption of all mobile devices for reception is no more than twice that of any feasible allocation. For performance evaluation, we used real video sequences encoded with SVC [3] and conducted extensive simulations with parameters set based on IEEE 802.16m [5]. The algorithm was compared with an optimal algorithm (with exhaustive search) and a conventional approach revised based on that in [9] to provide more useful insights into power-aware scalable video multicast. The rest of this paper is organized as follows: Section 2 describes the system model and provides formal formulation of the problem. In Section 3, the N P -hardness of this problem is presented. A two-stage greedy algorithm is proposed and its essential properties are proved. Simulation results and analysis are reported in Section 4. Section 5 concludes this paper.

2.

System Model and Problem Definition

2.1

System Model

All next generation cellular wireless systems employ orthogonal frequency division multiple access (OFDMA) based multicarrier technology. An OFDMA frame consists of symbols in the time domain and subchannels1 in the frequency domain, as shown in Figure 1. A symbol and subchannel combination, referred to as a tile, is the minimum allocable unit that can be individually modulated and coded2 . In a multicast system, the available tiles in a frame are shared by multiple video groups (and other non-real-time application services [4]), and users requesting the same video simply join the corresponding group. Consequently, the users in a multicast group may experience different channel conditions because of the distances to the base station or other factors. In both WiMAX and LTE, the base station is allowed to adaptively change modulation-coding schemes (modulation for short) based on the channel conditions at the users. A user with good channel conditions (e.g., when it is close to the base station) can potentially receive the video with a higherrate modulation (such as 64-QAM) or, certainly, with lowerrate ones (such as QPSK). Contrarily, a user must receive the video with a lower-rate modulation (for tolerating the bit error rate) when faced with poor channel conditions. Because users shall report the information on their channel conditions (such as signal-to-noise ratios) when requesting multicast services, the base station is aware of the channel conditions of every user and able to determine the modulation for each video. Note that the same amount of video data with a lower-rate modulation needs more tiles to carry. Therefore, which users can receive a video and how many tiles needed depend on the modulation adopted by the base station for the video. When users requesting the same video experience different channel conditions, an issue is that the base station shall either adopt a robust modulation to accommodate all the users or sacrifice users with poor channel conditions to provide the others 1 Sub-carriers

are usually grouped into subchannels for resource allocation. There are two subchannelization schemes: contiguous and distributed. The latter is recommended for use in multicast systems [13] and considered in this paper. 2 The terminology is mostly based on WiMAX but the concept also applies to LTE. To enforce the WiMAX requirement, saying that all the tiles in one burst must use the same modulation-coding scheme, a tile can be defined as a larger allocable unit and treated as a burst [11].

S u b ch an n el

Figure 1. An example of resource allocation related to receiving power. with better video quality. The issue was addressed by introducing scalable video coding to multicast services [2, 11, 13]. SVC divides a raw video into a base layer and multiple enhancement layers. The base layer is essential for the reception of the video with minimal quality, while the enhancement layers are to improve the video quality. Note that an enhancement layer is useful only if the base layer and all the other lower enhancement layers are received. With SVC, the base station can apply different modulations to different layers so that users with different channel conditions can obtain different video quality. Note that an entire layer must use the same modulation and the number of tiles it needs relies on the modulation used. Therefore, for an OFDMA frame, the base station shall determine which layer of which video should be transmitted and with which modulation. In addition to selecting video layers to be transmitted and their corresponding modulations, the base station shall also determine how to allocate tiles for the layers. In an OFDMA-based multicast system, only some of the symbols in a frame may carry the video layers a user needs. It is simply wasting of energy for a user to receive the whole frame, and the transceiver is usually turned into sleep mode during the transmission of symbols that are intended for others [16]. Therefore, an appropriately arranged frame is helpful in reducing energy consumption. The energy consumption of a user for reception is proportional to the number of symbols it receives [9]. Note that a symbol must be received in an atomic manner even if only a partial symbol carries the desired data. Figure 1 shows two possible allocations for a simple example, where each of the two groups contains two users with different quality requirements. In allocation 1, users U1, U2, U3, and U4 need to consume energy for receiving one, three, three, and three symbols, respectively, so as to receive the video data requested. In allocation 2, each user only needs to receive one or two symbols. As the result, allocation 2 is considered 2 times more energy efficient than allocation 1. 2.2

Problem Definition

In this paper, we are interested in the minimization of the total energy consumption for video reception, provided the minimum quality requirement of every user is satisfied. For the sake of brevity, we shall omit “∀” when there is no ambiguity in the context. The system model under consideration can be formulated as follows. An OFDMA frame consists of S · C tiles, where S and C are the numbers of symbols and subchannels, respectively. The possible modulations are denoted by m = 1, 2, ..., M, where a lager index indicates a higher-rate modulation. A user is called

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an m-modulation user if modulation m is the highest modulation that can be received by the user. There are G multicast groups. g For each group g, there are N g users, Nm users of which are mg M modulation users. Note that ∑m=1 Nm = N g . Every user could have its minimum data rate requirement (i.e., the video quality it requires), but the m-modulation users in group g must receive the same video layers, so we assume, for the simplicity of g presentation, they have the same data rate requirement Rm . The g video of group g is split into L layers, and each layer is of data rate λ(g,) . Let γm be the data rate provided by a single tile (g,) with modulation m. Then, the layer needs tm = λ(g,) /γm (g,) tiles if it is transmitted with modulation m. We use χ(m,s,c) as an indicator function that is 1 if layer of group g is selected to transmitted with modulation m in the tile combined by symbol s and subchannel c, and 0 otherwise. In other words, the indicator function denotes whether a user needs to receive the video data (g,) carried in a specific tile. To ease the notation, we use χm to S C (g,) represent s=1 c=1 χ(m,s,c) , which is 1 if layer of group g is selected to transmitted with modulation m, and 0 otherwise. Note that an m-modulation user can also receive modulation m if m ≤ m. Therefore, the data rate received by an m-modulation g Lg (g,) ·χ(g,) , user in group g can be represented as τm = Σm i i=1 Σ=1 λ g g and τm ≥ τm if m > m . An allocation is feasible if it satisfies the following constraints: Resource constraint: The first two constraints are respectively to ensure that, for each subchannel, the allocated tiles cannot exceed the available symbols, and for each symbol, the allocated tiles cannot exceed the available subchannels. G

Lg

M

∑∑∑

S

M possible modulations. There are G multicast groups. Each g g group g has Nm m-modulation users that require data rate Rm . g The video for group g is split into L layers, and each layer is of data rate λ(g,) . A single tile can carry data rate γm with modulation m. Our objective is to find a feasible resource allocation (g,) χ(m,s,c) such that the total energy consumption of all users for reception is minimized (i.e., the summation of the symbols received by all the users). The problem is formally formulated as follows: G

min ∑

G

M

L

C

m C Lg (g,)

i=1 =1 c=1

χ(i,s,c)

(7)

g

(g,)

Table 1. Summary of Main Notations S C M G Lg g Nm γm λ(g,)

Number of available symbols Number of available subchannels Number of possible modulation-coding schemes Number of multicast groups Number of video layers for group g Number of m-modulation users in group g Data rate carried by a single tile with modulation m Data rate of layer of group g

tm

Number of tiles required for layer of group g with modulation m Data rate received by an m-modulation user in group g Data rate required by an m-modulation user in group g

(g,) g

τm g Rm χm

An indicator function which is 1 if layer of group g is transmitted with modulation m and 0 otherwise

(g,)

An indicator function which is 1 layer of group g is transmitted with modulation m in the tile combined by symbol s and subchannel c and 0 otherwise

χ(m,s,c)

(g,)

∑

s=1

(1)

∑ ∑ ∑ ∑ χ(m,s,c) ≤ C, ∀ s

S

L C subject to constraints (1)-(6), where m i=1 =1 c=1 χ(i,s,c) g indicates if the Nm m-modulation users of group g need to receive symbol s or not.

g=1 m=1 =1 s=1 g

∑

Nmg ×

g=1 m=1

(g,)

(g,)

∑ χ(m,s,c) ≤ S, ∀ c

M

(2)

g=1 m=1 =1 c=1

Modulation constraint: The third constraint dictates that the number of tiles allocated for a layer with any modulation must be no less than that it needs. The fourth reflects a physical constraint of SVC, where a video layer of any group can be modulated with at most one modulation. S

C

(g,)

(g,)

∑ ∑ χ(m,s,c) ≥ tm

s=1 c=1 M

∑

(g,)

χm

, ∀ g, , m

(3) (4)

Requirement constraint: The fifth constraint states that any user must be satisfied with the data rate it receives. To avoid ung g solvable or trivial situations, we assume Rm ≤ ∑L=1 λ(g,) , ∀g, m. τgm ≥ Rgm , ∀ g, m

(5)

Dependence constraint: In SVC, the decoding of an enhancement layer relies on the base layer and all the other lower enhancement layers. It means that if layer − 1, for some > 1, of group g is transmitted with modulation m , the m-modulation users cannot receive the video layer as m < m . Therefore, layer is either transmitted with modulation m ≥ m or not transmitted. (g,)

≤

(g,−1)

χm 0,

,

if m ≥ m , ∀ g, > 1 otherwise

(6)

We now state the power-aware scalable video multicast problem. We are given an OFDMA frame of S · C tiles and

Power-Aware Scalable Video Multicast

In this section, we show the N P -hardness of the poweraware scalable video multicast problem and propose a 2approximation algorithm which always derives a feasible resource allocation such that the energy consumption for reception is no more than twice that of any feasible allocation. 3.1

≤ 1, ∀ g,

m=1

χm

3.

Problem Hardness

Before our solution to the target problem, we first show its N P hardness by a reduction from the partition problem, which is known to be N P -complete [10]. T HEOREM 1. The power-aware scalable video multicast problem is N P -hard. P ROOF. The input to the partition problem is a set of n integers, A = {a1 , a2 , ..., an }. The output is Y ES if and only if A can be partitioned into two subsets Z and A \ Z that have the same sum, 1 i.e., ∑ai ∈Z ai = ∑ai ∈Z / ai = 2 ∑ai ∈A ai . Given an instance A of the partition problem, we show how to construct, in polynomial time, an instance S, C, M, G, g g Lg , Nm , γm , λ(g,) , Rm of our problem such that A can evenly be partitioned if and only if there exists a resource allocation with energy consumption no more than n. The construction procedure is as follows: The available symbols and subchannels are respectively set as S = 2 and C = 12 ∑ai ∈A ai . There is only one modulation (i.e., M = 1). Let us consider n groups (i.e.,

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g

G = n), each of which consists of one single user (i.e., Nm = 1, ∀ m = 1, 1 ≤ g ≤ n). Every group g requests a video encoded into one layer (i.e., Lg = 1, ∀ 1 ≤ g ≤ n) of a data rate ag (i.e., λ(g,) = ag , ∀ = 1, 1 ≤ g ≤ n), and the data rate provided by a single tile with the modulation is set as γm = 1, ∀ m = 1. Thus, (g,) the layer of group g needs ag tiles to carry (i.e., tm = ag , ∀ m = 1, = 1, 1 ≤ g ≤ n). The data rate requirement of the user in g group g is set as Rm = ag , ∀ m = 1, 1 ≤ g ≤ n. To complete the proof, we shall show that two evenly partitioned subsets can be used to derive a resource allocation with energy consumption no more than n, and vice versa. Since each subset corresponds to a symbol, and each integer corresponds to the layer of a group, the assignment of integer ag into a subset implies that the layer of the corresponding group g occupies ag tiles in the corresponding symbol. Because every layer is carried in either symbol, every user needs to receive exactly one symbol. Thus, the total energy consumption is n. On the other hand, if the total energy consumption is no more than n, then no user can receive two symbols. It implies that every layer is carried in only one symbol, and the subset can evenly be partitioned by assigning the corresponding integer into the corresponding subset. The existence of a polynomial-time algorithm for the partition problem implies the same for our problem. We conclude that the power-aware scalable video multicast problem is N P -hard. 3.2 3.2.1

A 2-Approximation Algorithm Algorithm Description

In this section, we propose a two-stage greedy algorithm and prove that the greedy strategy leads to a 2-approximation algorithm for the power-aware scalable video multicast problem. Stage 1 of the algorithm determines which video layers of each group ought to be transmitted and with which modulations, provided the data rate requirements of all the users are satisfied. In Stage 2, appropriate tiles are then allocated to the video layers determined in Stage 1, so as to minimize the total energy consumption for reception. Algorithm 1 Input: S, C, M, G, Lg , Nm , γm , λ(g,) , Rm (g,) Output: χ(m,s,c) g

g

(g,)

χm ← 0, ∀ g, m, for all 1 ≤ g ≤ G do g mˆ ← min{m | ∀ Nm = 0} ←1 for all mˆ ≤ m ≤ M do g g while τm < Rm do (g,) 7: χm ← 1 8: ← +1 1: 2: 3: 4: 5: 6:

the (mˆ + 1)-modulation users, and so on (Line 5). Note that, in g g ≤ Rmˆ for any i > 0, then (mˆ + i)-modulation this way, if Rm+i ˆ g users can be satisfied with τmˆ , and no video layer is selected to transmit with modulation mˆ + i by our algorithm. 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23:

(g,)

χm,s,c ← 0, ∀ g, m, , s, c φ←0 for all 1 ≤ g ≤ G do for all 1 ≤ m ≤ M do (g,) for all with χm = 1 do (g,) tm ← λ(g,) /γm (g,) if φ + tm > S ×C then return no feasible solution else (g,) for all 1 ≤ i ≤ tm do φ ← φ+1 s ← Cφ c ← φ − (s − 1) ×C (g,) χ(m,s,c) ← 1 (g,)

return χ(m,s,c) , ∀ g, m, , s, c

In Stage 2, as shown in Lines 9-23, we start to allocate tiles to the video layers selected in Stage 1. An indicator function (g,) χ(m,s,c) is used to indicate if layer of group g selected to transmit with modulation m is carried in the tile indexed by symbol s and subchannel c, and is initialized as 0, ∀ g, m, , s, c (Line 9). A variable φ initialized as 0 is used to count the current number of allocated tiles (Line 10). If layer of group g is selected to (g,) transmit with modulation m (Lines 11-13), then it requires tm tiles to carry (Line 14). If the to-be-allocated tiles are more than the available, then we return no feasible solution (Lines 15-16), else we allocate appropriate tiles to the video layer (Lines 1722). In order to minimize the energy consumption for reception, the data of a layer should be carried in as few symbols as possi(g,) ble. Therefore, we simply allocate tm continuous tiles (starting from the first empty tile of the current symbol) to the layer, and the counterparts of the indicator function are set as 1 accordingly. Note that if a symbol is fully occupied, then the tiles required for the rest of the layer are allocated from the next symbol. At the end of the algorithm, we return the indicator function (g,) χ(m,s,c) (Line 23). 3.2.2

Properties

For the rest of this section, we shall analyze the time complexity of Algorithm 1 and prove that it is a 2-approximation algorithm for the power-aware scalable video multicast problem.

In Stage 1, as shown in Lines 1-8 of Algorithm 1, an indica(g,) tor function χm is employed to indicate if layer of group g is selected to transmit with modulation m, and is initialized as 0, ∀ g, m, (Line 1). For each group g, we find the highest modulation mˆ that can be received by any user in the group (Line 3) and start layer selection from the base layer (Line 4). For the m-modulation ˆ users, we incrementally select video layers to transmit with modulation mˆ until the data rate requirement of the users is satisfied (Lines 6-8). We then select video layers from the remainder to transmit with modulation mˆ + 1 to satisfy

ˆ L EMMA 1. The time complexity of Algorithm 1 is O(GM LSC), where Lˆ = max Lg . ∀g

(g,)

P ROOF. Each index combination of the indicator function χm is initialized as 0 and updated to 1 only once (if it happens). The time complexity of Stage 1 is obviously dominated by the ˆ With a similar time required for the initialization, i.e., O(GM L). argument, Stage 2 appears to spend most of its time initializing (g,) the indicator function χm,s,c . Therefore, the time complexity of ˆ Stage 2 is O(GM LSC), and the time complexity of the algorithm is dominated by the running time of Stage 2.

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L EMMA 2. Stage 1 of Algorithm 1 derives the minimum number of tiles required by any user, provided the requirements of all the users are satisfied. P ROOF. We prove this lemma by contradiction. Suppose that ∗(g,) that can satisfy there exists another indicator function χm some user with fewer tiles, say an m-modulation user of group g, provided all the other users are satisfied. It implies that, there must be a layer of group g which is transmitted with (g,) modulation m ≤ m in χm , and this layer is either transmitted ∗(g,) with a modulation higher than m or not transmitted in χm (otherwise, it is impossible to use fewer tiles for the user). Now, let us consider any m -modulation user of group g (such a user must exist; otherwise the layer will not be transmitted with m (g,) ∗(g,) in χm ). In either case of χm , the m -modulation user cannot receive the layer (and any other higher layer) because of the dependence constraint defined in Equation 6. Consequently, the ∗g g user will receive a data rate τm that is no more than τm − λ(g,) , (g,) g where τm is the data rate the user can receive in χm . Since ∗(g,) g ∗g g χm can also satisfy the user, we have τm − λ(g,) ≥ τm ≥ Rm . It is a contradiction because Line 6 of Algorithm 1 ensures that g g g g if τm ≥ Rm , then τm − λ(g,) < Rm . T HEOREM 2. Algorithm 1 is a 2-approximation algorithm for the power-aware scalable video multicast problem. P ROOF. We prove this theorem by showing that a user always (g,) receives at most one more symbol in χ(m,s,c) than it receives in any optimal solution. Without loss of generality, let us consider any user in the network system, say an m-modulation user of group g. The number of tiles (derived by Stage 1) to carry the (g,) (g,) g Lg · ti . video layers needed by the user is ρm = ∑m i=1 ∑=1 χi g In Stage 2, we simply allocate continuous ρm tiles for these g layers. Let βm denote the number of symbols with which these tiles are associated (i.e., the user needs to receive), and let k ≤ C be the remaining tiles in the current symbol (when we start to allocate the first tile for these layers). Then, we have g 1, if 1 ≤ ρm ≤ k, g βgm= ρ Ck + mC−k , otherwise.

4.

Performance Evaluation

4.1

Simulation Setups

This section developed a simulation model by C++ programs to verify the proposed algorithm, denoted as 2-APP, in comparison with two algorithms. The first one is a brute-force algorithm, denoted as OPT, which derived optimal solutions. The other is a conventional approach revised based on that in [9], denoted as CONV, which did not consider power saving. It first ran the stage 1 of our algorithm to select video layers and their corresponding modulations. Then it randomly allocated resources to the layers with uniform distribution. We conducted extensive simulations with parameters set based on the IEEE 802.16m system description document3 for a 10MHz spectrum in 3.5 GHz range [5]. The number of available symbols were set as 50, and that of available subchannels varied from 5 to 15. We considered one base station with a number of groups varied from 1 to 20. Each group consisted of 10 to 20 users. Each user randomly placed with uniform distribution in the coverage area of the base station with distance between 350 to 1000 meters [11] and required a data rate. We assume that users with better channel conditions always required higher data rates. Each group randomly selected a video sequence from 5 standard video test sequences: Akiyo, Foreman, Mobile, Mother-and-daughter, and Stefan all at CIF resolution, all of which can be downloaded at [14]. Each video sequence was encoded with the SVC extension [3] of H.264/MPEG4-AVC, where the maximum number of layers was set as 10. Each layer can possibly be transmitted with one of the six types of modulations listed in the IEEE 802.16e standard [4]. The signal-tonoise (SNR) range recommended for each modulation is listed in Table 2 [11, 12], where the SNR value of each user was to reflect the highest modulation the user can receive, namely an m-modulation user with m = 1, 2, ..., or 6. The path loss model was assumed as PL(dB) = 35.2 + 35 log10 (d), where d was in units of meters [11]. The noise figure and antenna gain were set as 5 dB and 17 dB [11]. The results were derived as an average value over 100 independent simulations. Table 2. Modulation-coding schemes with SNR ranges

(8)

m 1 2 3 4 5 6

∗g

On the other hand, let βm denote the number of symbols that the user needs to receive in an optimal solution. We have proved g in Lemma 2 that ρm is the minimum number of tiles required by g this user, provided all the user are satisfied. ρm tiles must be g associated with at least ρCm symbols, in the sense that β∗g m ≥

g ρm ≥ 1. C

(9)

By comparing (8) with (9), we reach a conclusion that g ρm ≤ 1 + β∗g ≤ 1+ m. C

βgm

(10)

Now we compute the total energy consumption of all users (g,) for reception in the solution χ(m,s,c) derived by Algorithm 1. G

M

∑∑

Nmg ×

g=1 m=1

≤

G

S

∑

s=1 M

C m Lg (g,)

i=1 =1 c=1

χ(i,s,c) G

G

=

M

∑ ∑ Nmg × βgm

g=1 m=1

g=1 m=1

(11)

Coding rate 1/2 3/4 1/2 3/4 1/2 3/4

γm (kbps) 4.8 7.2 9.6 14.4 19.2 21.6

SNR range (dB) [3.7164, 5.9474) [5.9474, 9.6598) [9.6598, 12.361) [12.361, 16.6996) [16.6996, 17.9629) [17.9629, +∞)

Simulation Results

Figure 2 shows the impacts of the number of groups on energy consumption (measured by the number of received symbols). As expected, the number of received symbols increases as the number of groups increases. It is because more groups result in more multicast service requests. The results shows that, on the average, 2-APP consumes 1.39 times energy than OPT, and CONV consumes 4.42 times than 2-APP, when there are 12 available subchannels in a symbol. As can be seen in the figure, the capability of 2-APP in terms of energy efficiency is even 3 In

g=1 m=1 M

g ∗g ∑ ∑ Nmg × (1 + β∗g m ) ≤ 2 × ∑ ∑ Nm × βm

4.2

Modulation QPSK QPSK QAM16 QAM16 QAM64 QAM64

IEEE 802.16m superframe structure consisted of four 5ms frames, there are about 120 downlink symbols and 21 subchannels, both of which depend on parameters set in the physical layer [5]. In practical systems, besides multicast services, downlink resources are shared by other applications [11] such as FTP, HTTP, etc.

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x 10

9 8 7 6

CONV, 5 Subchannels CONV, 12 Subchannels 2−APP, 5 Subchannels 2−APP, 12 Subchannels OPT, 5 Subchannels OPT, 12 Subchannels

5 4 3 2 1 0 1

5

10

15

Number of multicast groups

20

4

8

x 10

7

CONV, 8 Groups CONV, 16 Groups 2−APP, 8 Groups 2−APP, 16 Groups OPT, 8 Groups OPT, 16 Groups

6 5 4 3 2 1 0 5

10

15

Data rate received Number of symbols (kbps) received per second

4

10

Number of symbols received per second

Number of symbols received per second


Number of available subchannels

4

1

x 10

CONV 2−APP OPT

20 groups, 10 subchannels

0.5

0

1

2

3

4

5

6

(a) m−modulation users 4

4 3

x 10

CONV 2−APP OPT

20 groups, 10 subchannels

2 1 0

1

2

3

4

5

6

(b) m−modulation users

Figure 2. Impacts of number of multicast Figure 3. Impacts of number of available Figure 4. Impacts of channel conditions groups on energy consumption subchannels on energy consumption on symbols and data rates received at users more significant as the network size increases, compared to the conventional approach. Figure 3 shows the impacts of the number of available subchannels on energy consumption. As we can see, the number of received symbols decreases as the number of subchannels increases, when 2-APP or OPT is adopted as the algorithm for resource allocation. The reason for the phenomenon is that a symbol of more subchannels can provide more data rates and the two algorithms attempt to minimize the number of symbols any user needs to receive. Contrarily, the number of available subchannels has no significant impact on the performance of CONV, because it allocates radio resource without the consideration of energy consumption but with uniform distribution. The results show that OPT is 1.34 times more energy efficient than 2-APP, and 2-APP is 4 times than CONV, when there are 8 multicat groups. We observed that the capability of 2-APP is more prominent when there are more possibilities of resource allocation. Figure 4 shows the impacts of channel conditions on the symbols and data rates received at users. As can be seen in Figure 4(b), users with better channel conditions require higher data rates in our simulation setting, so m-modulation users need to receive more symbols and consume more energy than m modulation users if m > m , as shown in Figure 4(a). The results show that OPT outperforms 2-APP in terms of energy efficiency by 1.39 times, and 2-APP outperforms CONV by 3.9 times, when there are 20 groups and 10 subchannels. It is worth noticing that the capability of 2-APP is more prominent when users are with better channel conditions and require higher video quality, as shown in Figure 4(a).

5.

Conclusion

This paper studies the resource allocation problem for scalable video multicast with adaptive modulation and coding in 4G wireless systems. The objective is to minimize the total energy consumption of all mobile devices for reception, provided the video quality required by all the users are satisfied. We first show the N P -hardness of target problem. Then we propose a two-stage greedy algorithm that is proved to be of an approximation ratio of 2. The simulation results show that the proposed algorithm is very effective in the reduction of energy consumption, compared with a conventional approach, and can efficiently obtain a feasible solution, compared to an optimal algorithm with brute-force search. Its capability is even more prominent when networks are of larger scale or users demand higher video quality.

Acknowledgement The authors would like to thank CyberLink Education Foundation. This work was partially supported by the Excellent Research Projects of National Taiwan University through grant 99R80304 and by the National Science Council through grants 98-2219-E-002-021 and 99-2628-E-002-00, which the authors gratefully acknowledge.

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