Receiver-Oriented Subcarrier Decomposition Broadcast Scheduling

Algorithm for Wireless Mesh Networks

Jong-Hong Park and Jong-Moon Chung

School of Electrical and Electronic Engineering

Yonsei University

{jhwannabe, jmc}@yonsei.ac.kr

Abstract

Effective broadcast scheduling algorithms (BSAs)

are needed to schedule in a time-division multiple-

access (TDMA) frame for the orthogonal frequency

division multiple access (OFDMA) based wireless

mesh networks. In this paper, we propose a new

broadcast scheduling algorithm for subcarrier

decomposition based wireless mesh networks designed

from the MAC layer point of view.

Keywords: OFDMA, broadcast scheduling algorithm,

wireless mesh network, channel utilization.

1. Introduction

OFDMA is one of the promising access techniques

to support high speed wireless communication systems.

There are many BSAs which are developed based on

the broadcast scheduling problem (BSP) formulations

for single channel ad-hoc networks. However, there is

no formulation considering multiple subcarrier access

schemes for OFDMA wireless mesh networks.

In this paper, we present a Receiver-oriented

Subcarrier Decomposition (RSD) broadcast scheduling

algorithm for OFDMA wireless mesh networks.

2. Receiver-oriented Subcarrier

Decomposition BSP Formulation

In case of a broadcast scheduling algorithm for an

OFDMA wireless mesh network, each frame is formed

by a fixed number of time slots. A network consisting

of N nodes can be described by a graph G=(V, E),

where vertices in V={1, 2,…, N} are nodes capable of

transmitting and receiving signals in the network, and

E refers to the set of undirected link between nodes in

the network. We assume that nodes i and j are in E if

distance from i to j is smaller than D, which means that

these nodes are in each other’s simultaneous

transmission range for the OFDMA network.

The topology of an OFDMA network can be

described by an N×N symmetric binary matrix C, the

connectivity matrix. The matrix, C={cij} (i,j=1,…,N),

can be defined by

otherwise,0

and ),( if,1 jiEjicij

(1)

Each frame consists of M time slots and each node

should be scheduled to transmit at least one time slot.

To express a transmission schedule, we use a M×N

binary matrix S={smi}, where

otherwise,0

frame ain slot th at the transmits if,1 mismi (2)

To express a receiver schedule, we use a M×N

binary matrix R={rmi}. A receiver schedule also has M

time slots and each node must be scheduled to receive

at least one time slot, which can be described as

follows.

otherwise,0

frame ain slot th at the receives if,1 mirmi

(3)

The whole network channel utilization is given by,

M

m

N

i

miCH

sNMN

1 1

11 (4)

where NCH denotes the number of sub-channels.

Then, the RSD broadcast scheduling problem

formulation can be described as follows.

(a) Minimize the frame length M.

(b) Maximize the channel utilization

Subject to: 11

M

m

mir (5)

2 mjmiij rrc (6)

1 mjkjmiik rcrc (7)

where i,j,k =1,…,N, i ≠ j ≠ k, m =1,…,M.

Table 1: RSD Algorithm Description

The first constraint means that each node should

receive at least once in a frame. Constraint (6) implies

that every two stations, which are one-hop apart, must

be scheduled to receive in different time slots.

Constraint (7) implies that every two stations, which

are two-hop apart, must be scheduled to receive in

different time slots.

Table 1 describes the proposed RSD broadcast

scheduling problem formulation for wireless mesh

networks. Once receiving nodes are scheduled in

successive frames by the algorithm without collisions,

each receiving node’s one-hop neighboring nodes can

obtain transmission opportunity and transmit according

to scheduling table.

3. Performance Evaluation

The performance of the receiver-oriented subcarrier

decomposition (RSD) BSP formulation for wireless

mesh networks is compared to the performance of

single channel networks [3]. The nodes are randomly

distributed in an area of 100 km2. The simultaneous

available range, D, is assumed to be 1.75 km.

1 1.5 2 2.5 3 3.5 4 4.5 50

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Node Density

Ave

rag

e C

ha

nn

el U

tiliza

tio

n

RSD-2

RSD-3

SVC[3]

Figure 1: Average Channel Utilization

Figure 1 shows the average channel utilization

varying the number of nodes in the network. RSD-2

and RSD-3 represent the proposed algorithm with two

and three sub-channels, respectively. Based on Figure

1, results show that the RSD broadcast scheduling

algorithm can provides performance improvement in

channel utilization.

4. Conclusion

In this paper, we proposed a new BSP formulation

based on receiver-oriented subcarrier decomposition

for wireless mesh networks, where the nodes are

capable of transmitting simultaneously by

characteristics of OFDMA and depending on local

situations. The result shows that the proposed

algorithm is effective in OFDMA scheduling

transmissions for mesh networks, in terms of the

channel utilization.

Acknowledgement This research was supported by the Information

Technology Research Center (ITRC) support program

(NIPA-2013-H0301-13-1002) supervised by the National IT

Industry Promotion Agency (NIPA) of the Ministry of

Science, ICT & Future Planning (MSIP), Republic of Korea.

References [1] A. Ephremides and T. V. Truong, “Scheduling Broadcast

in Multihop Radio Networks,” IEEE Trans. Commun., vol.

38, no. 6, pp. 456-460, June 1990.

[2] G. Wang and N. Ansari, “Optimal Broadcast Scheduling

in Packet Radio Networks using Mean Field Annealing,”

IEEE J. Sel. Areas. Commun., vol. 15, no. 2, pp. 250-260,

Feb. 1997.

[3] J. Yeo, H. Lee, and S. Kim, “An Efficient Broadcast

Scheduling Algorithm for TDMA Ad-hoc Networks,”

Comput. Oper. Res., no. 29, pp. 1793-1806, 2002.

Functions CH Set of sub-channels. NEIGHBOR(i) Set of nodes that are one-hop apart from

node i CHECK(m,i,CH) Boolean function for checking that the

mth slot can be assigned as a receiving node to the ith node using one of the sub-channels CH. Among the stations in NEIGHBOR(i), if no one has the mth slot for transmitting or receiving using one of the sub-channels CH, then CHECK(m,i) returns 1, otherwise returns 0.

Phase 1 Step 0: Ordering the nodes by decreasing the order of the

number of one-hop and two-hop neighbors. Step 1: m=1, i=1 Step 2: If (CHECK(m,i,CH)=1), then rmi=1 and smj=1 for ∀j

of NEIGHBOR(j) and go to Step 3. Else go to Step 4. Step 3: If (i=N) then STOP. Else then m=1, i=i+1 and go to Step 2. Step 4: m=m+1 and go to Step 2. Phase 2 Step 0: Ordering the nodes by decreasing the order of the

number of one-hop and two-hop neighbors. Step 1: m=1, i=1 Step 2: If (CHECK(m,i,CH)=1), then rmi=1 and smj=1 for ∀j

of NEIGHBOR(j). Step 3: If (m=M and i=N) then STOP Else if (m=M and i<N) then m=1, i=i+1 and go to

Step 2. Else then m=m+1 and go to Step 2.