Multi-Group Wireless Multicast Broadcast Services Using Adaptive ...

Multi-Group Wireless Multicast Broadcast Services Using Adaptive Modulation and Coding: Modeling and Analysis Yu-Cheng Liang, Ching-Chun Chou, Hung-Yu Wei Department of Electrical Engineering, National Taiwan University

Abstract—Adaptive modulation and coding (AMC) is attracting research interest in wireless multicast broadcast services (MBS). AMC increases the system throughput by utilizing possible good channel states instead of using robust modulation and coding schemes. A model for the AMC in an MBS system with multiple MBS groups is provided, and stochastic analysis using Markov chain is also applied for modeling analysis. Simulation results show extremely high correspondence to the proposed mathematical model. Keywords- adaptive modulation and coding; multicast broadcast service; multiple MBS group

I.

feedback;

INTRODUCTION

A conventional MBS scheme applies robust modulation and coding to transmit at a low data rate, which causes extra overheads. To avoid such a waste on radio bandwidth and improves system performance, adaptive Modulation and Coding (AMC) has been applied to MBS recently. For instance, the next generation WiMAX IEEE 802.16m standard considers the possibility to apply AMC for multicast and broadcast services. With AMC, modulation and coding scheme (MCS) is adjusted dynamically during MBS transmission. MCS determines the data rate of wireless transmission, and AMC provides the option to utilize MCS at a higher rate if the channel state permits. Traditional research on AMC usually deals with only single MBS group problems. However, multi-group modeling is more suitable for future wireless system. Multimedia applications would mostly serve multiple subscriber groups. Data distribution is also composed of different receiver groups. These services may simultaneously reside in one single BS. Thus it is necessary to consider multi-group MBS modeling of AMC. There are several prior works related to AMC. She et al. propose cross-layer video streaming systems utilizing feedback channels for the required channel states in AMC [1] [2]. Deb et al. propose another layered video coding combined with AMC [3]. Chi et al., on the other hand, present a rate-allocation mechanism for multicast to dynamically switch the transmission rates [4]. Chen et al. propose MCS adaptation on video multicasting by using different feedback schemes [5] [6]. The relations between feedback channel

structures and AMC are investigated. These prior works study the applications of single group AMC. The performance gain is also investigated using system level analysis. Mathematical models corresponding to the proposed system are also provided in these works. However, if we wish to expand our research field to include multimedia or data services of multiple groups, a more general system model is required. A generalized model for multi-group MBS using AMC should be developed. We propose a Markov chain model for the MBS using AMC, in which the cost of feedback channel is considered, the possible gain of AMC is investigated, and the scheduling for multiple MBS groups are studied. To conclude, AMC yields more throughput increment on multi-group scenarios compared to single-group ones. II.

SYSTEM MODEL

In the system, one base station (BS) is present in the system along with multiple mobile stations (MS). These mobile stations form several MBS groups. MBS data are transmitted from the base station to the mobile stations within distinct MBS groups. We also assume perfect channel state information at the BS. The BS schedules one MBS group for data transmission at the beginning of a frame. The selection is based on group state. MBS must be able to serve every receiver within the group. Thus the MCS should follow the receiver with the worst channel states. This most robust MCS within the MBS group is called the group state. The BS selects the MBS group with highest group state for transmission, and data are distributed to the subordinate MSs within the group for a short period. The MBS data may be sent using 1 or multiple channels for transmission. After the period, the BS will pick another MBS group for data transmission according to the group state. In this model, the MBS group selection becomes a max-min problem: Max( group state of all MBS group ) group state = Min(the channel state of MBS group users) A. Channel State and MCS transition Model We divide the level of channel quality into (C+1) level. That is, channel states are from 0 to C. Wireless channels varies

from time to time. In this case, we are investigating the group state of a specific MBS group under varying channels. Thus we need a channel-state transition matrix for each channel. The MCS for the specific channel is updated by a given period. Both MCS and channel state are varying. If the MCS and the channel state do not match, there might be low data rate on good channel or high error rate over channel in poor conditions. The error rate is determined by the channel state s and MCS setting m. Therefore, an error probability matrix is also needed, due to the possible relations between s and m. It is consisted of , , where si, mj denotes the related s and m level. Group state report Group 1

BS selects one MBS group for data transmission Group state report Group state report

TABLE I NOTATIONS AND DESCRIPTIONS Notations

DESCRIPTIONS

N ng C e

Number of groups. Number of channels (receivers) in the g-th group. The best channel quality. Error probability matrix. The probability that the ig-th channel in the g-th group jump from state x to y. Channel-state Transition matrix for the ig-th channel in the g-th group. Channel-state Transition matrix for the g-th group (1).

, , , ,

,

,

One possible combination of picking k elements from N-1 elements. See Definition 1. The state of the ig-th channel in the g-th group.

e(ctg)

The probability that the ig-th channel in the g-th group at state j at any time slot when the system enters steady state. e(ctg)≡E[error rate | sg=ctg]

, ,

BS

Group N

Group 2

The state of the g-th group. , ,

The probability that BS transmits group during one

packets to the g-th time slot. ,1 The probability that all receivers in the g-th group successfully receive packets during one time slot. Number of successful received packets for group g during one time slot The state of the ig-th channel in the g-th group at time slot d. The state of the g-th group at time slot d.

Figure 1: System model for Group Selection

Error probability

Channel states from 0 to C s1 …… sC

es 0 ,m0

Corresponding MCS level m0 m1 …… mC

esc ,m0

s0

es0 ,m1

...

es0 ,mc …

esc ,m1

…

e s c , mc

es1 ,m0 …

…

Figure 2: Channel state and MCS transition setting. The channel state s and MCS level m determines the corresponding error for the current (s, m) pair.

Figure 1 and Figure 2 illustrate the system modeling. For each MBS group, a corresponding channel state s and MCS level m are stored using a row transition matrix. In each period of data transmission, BS selects an MBS group with the highest rate for transmission. Referring to the current channel states and the MCS, we can deduce the throughput from the error probability transition matrix. The system performance could be calculated using the model mentioned above by stochastic analysis. B. Notations All the notations in our modeling are presented in Table I. Corresponding descriptions are also included. There are three parts in Table I. The parameters in the first part are used to describe the system. The parameters in the second part are used in steady state analysis. The parameters in the third part are used in transient analysis. , ,

(1) ,

Definition 1: k and g are integers. 0

1,1

,

.

,

,

The probability that the ig-th channel in the g-th group at state j at time slot d.

, , ,

, ,

, ,

, , ,

Number of successful received packets for group g at time slot d

,

, ,

if

,

where ,1

1

1,

\

,

,

The meaning of , , is one possible combinations of picking k elements from N-1 elements, 1, \ . For fixed k, there are possible ways. For example, let N=5, k=3, g=2, 4. The combination of there are 4 kinds of , , , 1 each , , are: {1,3,4},{1,3,5},{1,4,5},{3,4,5}. III.

MODEL ANALYSIS AND DISCUSSION

We can deduce the expected system throughput from the model mention in section II under both steady and transient cases. A. Steady Channel State Assume that the system will reach the steady state after a period of operation. represents the steady-state , , probability of the ig-th channel in the g-th group at state j. If the system enters the steady state, the value of , , would be fixed at any time slot.

For simplicity, we define two parameters as follows. ,

∏

∑

,

,

∏

∑

, ,

(7) (2)

,

1

(3)

,

denotes the number of channel at state sg in the g-th , we list all terms in Table II. group. To compute 1 We can derive 1 by summing these terms up.

Then we can find out that ,

,

1

(4)

1

,

,

1

,

,

1 (8)

Next, we define two functions , , , , , 1 , ∑

, , ,

∏

,

1 ,

,

, ,

, ,

1

(5)

,

,1

(6)

1

is the probability that the The meaning of , , , , picked k group states are equal to the g-th group state, and the other N-1-k group states are lower than the g-th group state. These k groups are chosen according to , , .

, , , 1

,

,

1 (9)

TABLE II AND CORRESPONDING AVG. PACKET SUCCESS RATE

,

n0 ng

∏

, ,

1

,

summation over any combination of x1,y1

ng-1

∏

, ,

,

,

,

,

1

,

1

,

·

For

1,

1,

∏

∏

, ,

,

,

,

,

1

1

,

,

For 1, but a

(10)

, , again. In this case, we define , These two notations have similar meaning as to those in Section III (A), “Steady Channel State.” The notations will simplify the process of equation derivation.

summation over any combination of xm,ym

ng-k

B. Transient with Initial Channel State Probability In this section, we turn our attention to the transient behavior. The word “transient” indicates the time transition process. It means that given the information at time slot d, the system performance at time slot d+1 could be predicted. Such scenario provides us with the insight of the channel states and MCS transition. We can derive , , from the vector and matrix inner product for each group.

1, b

,

∏

,

∏

∑

(11)

, ,

∑

, ,

1

(12)

,

, Using the same definition for , , , , and the same method, we can find out , , , . Its form is similar to the previous case.

1

represents the probability that The function , , , there are exactly k group states equal the g-th group state. 1

, , , 1 ,

,

,

1

(13)

C. Predict Throughput Based on Previous Group States In this section, we focus on throughput prediction. Now we only know every group state, , but we do not have any information about the channel state, s , , at time slot d. Besides, we have the channel-state transition matrix, channelstate probability, and error probability matrix. We will use the provided information to predict the system performance at time slot d+1. This scenario is especially useful for system design. We could predict the system performance with limited real-time information. For channel-state probability at time slot d, we use notation similar to channel-state probability in the Steady Channel State. Now, , , denotes the probability of the ig-th channel in the g-th group at state j at time slot d. ∏

∑

∏

, ,

∑ ,

,

,

,

∏

∑

,

, ∑

,

,

, ∑

,

,

,

,

(16)

denotes the number of channel at state sg in the g-th group at time slot d. , ,

, ,

(17)

To compute (17), we list all components in Table III

again. After applying weighted summation over these terms,

,

, ∏

,

and

∑

, ,

(14) ,

,

We define

∏

∑

,

,

, ∑

∏

,

∑

,

,

, ∑

,

,

(15)

1

,

,

(18)

Using the same method TABLE III COMPONENTS FOR COMPUTING (17) n0

Pr

ng

∏

, ,

,

,

1

,

∏

, ,

,

,

,

,

, 1

,

∑

,

∑

,

,

summation over any combination of xm,ym ∏

For 1,

, 1,

but

(19)

,

,

1

, ,

(20)

, ∑

, , ,

,

∏

,

,

, ,

,

,

(21)

Hence, the data throughput can be derived.

1,

, ,

1

,

,

1,

∏

, ,

1

,

,

, ,

,

For

nh-k

,

In this case we must define the function and with slight difference. This is to capture the steady-state system throughput under this scenario.

summation over any combination of x1,y1

nh-1

1

,

,

,

, ,

,

, , , 1

,

,

,

,

,

,

,

1

,

,

,

1

(22)

,

∑

,

∑

,

, ,

IV.

PERFORMANCE EVALUATION

To verify our models, simulation should be carried. We implement our simulator using MATLAB codes. There are multiple channels and MBS groups within the system. Channel state of each channel is varying all the time. MCS is

updated periodically. The BS selects the MBS group with highest group state for transmission in each transmission period. Two groups reside in the system. 106 turns (time slots) are taken in the simulation, and related performance metrics are recorded. We first evaluate the effectiveness of our problem formulation. In section II, we formed the problem as a maxmin problem. However, it is possible that the BS may use other strategy for MBS group selection. Round-Robin method is used for comparison in this case. We can see that the proposed max-min formulation has more throughput than RR one. Second, the effectiveness of the mathematical modeling is verified. Simulation results are compared with the modeling outputs. The x-axis is the initial channel state setting. We can observe that the simulation results match the modeling results perfectly under different initial channel states setting.

V.

We propose a generalized model for using AMC in multigroup MBS. Channel states and MCS variation are gracefully modeled in this paper, and the corresponding transmission error rate is integrated into this structure. Given our current simulation results, the proposed model exhibits extremely high correspondence with our simulations.

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

Figure 3: Evaluation on max-min and RR formulation

Figure 4: The simulation results and mathematical model for two MBS groups

CONCLUSIONS

James She, Xiang Yu, Fen Hou, Pin-Han Ho, and En-Hui Yang, ”A Framework of Cross-Layer Superposition Coded Multicast for Robust IPTV Services over WiMAX,” IEEE Wireless Communications and Networking Conference, 2008., pp. 3139-3144, 2008 James She, Xiang Yu, Pin-Han Ho, and En-Hui Yang, ”A cross-layer design framework for robust IPTV services over IEEE 802.16 networks,” IEEE Journal on Selected Areas in Communications, Vol. 27, pp. 235245, 2009 Supratim Deb, Sharad Jaiswal, and Kanthi Nagaraj, ”Real-Time Video Multicast in WiMAX Networks,” INFOCOM 2008. The 27th Conference on Computer Communications. IEEE, pp.1579-1587, April, 2008 Hsin-Yu Chi, Chia-Wen Lin, Yung-Chang Chen, and Chih-Ming Chen, ”Optimal rate allocation for scalable video multicast over WiMAX,” IEEE International Symposium on Circuits and Systems, pp. 1838-1841, May, 2008 Jianfeng Chen, Ning Liao, Yntao Shi, and Jun Li, ”Dynamic region based modulation for video multicasting in mobile WiMAX network,” 11th IEEE Singapore International Conference on Communication Systems, 2008., pp.1668-1673, Nov. 2008 Jianfeng Chen, Ning Liao, Yntao Shi, and Jun Li, ”Link Adaptation for Video Multicasting in Mobile WiMAX Network,” 6th IEEE Consumer Communications and Networking Conference, 2009., pp. 1-6, Jan. 2009