FRAME LENGTH DESIGN FOR MULTIBAND-OFDM ULTRA

WIDEBAND NETWORKS

Liaoyuan Zeng, Eduardo Cano, Michael Barry and Sean McGrath

Wireless Access Research Centre, University of Limerick, Limerick, Ireland

Keywords:

Ultra Wideband, Prioritized Contention Access, Saturation Throughput, Frame Length, Bit Error Rate, Multi-

band Orthogonal Frequency Division Multiplexing, Rayleigh Fading.

Abstract:

A new design of the optimal MAC frame payload length for maximizing the saturation throughput of the

Prioritized Contention Access (PCA) of the WiMedia Ultra Wideband (UWB) standard in Rayleigh fading

channel is presented in this paper. In the WiMedia standard, the Multiband Orthogonal Frequency Division

Multiplexing (MB-OFDM) is used as the basic physical scheme. The proposed design is based on the through-

put analysis carried out by extending an original Enhanced Distributed Contention Access (EDCA) model for

802.11e into the MB-OFDM UWB protocol. The extended model considers the effects of the bit error rate, the

transmission opportunity limits, and the uniqueness of WiMedia MAC timing structure. The station through-

put is sensitive to the frame payload length, and the optimal frame payload length increases exponentially

when the value of the signal-to-noise ratio is higher. The optimal payload length is independent of the number

of the active stations, data rate, and the priority of the Access Categories (ACs). Therefore, a station can

dynamically adapt the length of the transmitted frame in the MAC layer according to the current SNR level so

as to maximize its saturation throughput in the MB-OFDM UWB network.

1 INTRODUCTION

Ultra wideband (UWB) technology is an emerging

candidate for short-range wireless communications

and precise location systems (Win and Scholtz, 1988).

The Federal Communication Commission (FCC) de-

ﬁnes UWB signal as a wireless transmission in the un-

licensed 3.1-10.6 GHz band that possesses a -10 dB

bandwidth greater than 20% of its centre frequency

or one exceeding 500 MHz (Federal Communications

Commission, 2002). In recent years, extensive re-

search work in both academia and industry has been

focused on the design and implementation of UWB

systems due to its ability to provide very high data

rate with low power and low cost for Personal Com-

puting (PC), Consumer Electronics (CE), and mo-

bile applications in a short-range. In 2002, the IEEE

802.15.3a Task Group was initially formed planning

to standardize the speciﬁcations of an UWB Physi-

cal layer (PHY) for the high-speed Wireless Personal

Area Networks (WPAN). One of the two leading PHY

speciﬁcations is Multiband Orthogonal Frequency Di-

vision Multiplexing (MB-OFDM) UWB, supported

by WiMedia Alliance (WiMedia Alliance, 2008) who

later standardized its own Medium Access Control

(MAC) speciﬁcation based on MB-OFDM UWB (Ba-

tra et al., 2003).

The WiMedia MAC protocol (ECMA Interna-

tional, 2005) is implemented in a distributed man-

ner, implying that no central coordinator is used for

network management. The beacon frame is trans-

mitted by every station for synchronization, network

topology control, and channel access coordination.

This distributed architecture brings high reliability

and better mobility than the centralized networks.

Other advantages include the ease of system design,

performance evaluation, and simulation (Vishnevsky

et al., 2008). This MAC-PHY speciﬁcation was then

adopted by ECMA (ECMA International, 2005) as

a standard for short-range wireless communications,

and has already received intensive support from the

global industry.

In the WiMedia MAC protocol, two fundamental

medium access mechanisms are deﬁned, one is the

contention based Prioritized Channel Access (PCA),

and the other one is the reservation based Distributed

Reservation Protocol (DRP). PCA is designed for

network scalability and is very similar to the En-

113

Zeng L., Cano E., Barry M. and McGrath S. (2008).

FRAME LENGTH DESIGN FOR MULTIBAND-OFDM ULTRA WIDEBAND NETWORKS.

In Proceedings of the International Conference on Wireless Information Networks and Systems, pages 113-120

DOI: 10.5220/0002024501130120

Copyright

c

SciTePress

hanced Distributed Channel Access (EDCA) mech-

anism used in the IEEE 802.11e systems (IEEE Std.

802.11e, 2003). In PCA, four priorities are assigned

to four types of applications called Access Categories

(ACs, i.e. backgroud, best effort, video, and voice).

Higher prioritized AC has higher probability to ac-

cess the channel due to shorter backoff period. Ev-

ery AC has a pre-deﬁned transmission period, known

as Transmission Opportunity (TXOP). DRP is used

mainly for isochronous trafﬁc, by which network sta-

tions are allowed to arbitrarily reserve a period of time

for exclusive data transmission.

In comparison with other MACs, the WiMedia

MAC has not received a lot of attention in the litera-

ture. In (Zang et al., 2005), the theoretical maximum

throughput of the WiMedia MAC is evaluated for a

error-free wireless channel. In (Wong et al., 2007),

a three dimensional discrete-time Markov chain was

used to analyze the saturation throughput of the PCA

schemes by employing simpliﬁed DRP rules and ﬁxed

Bit Error Rate (BER). The effects of the TXOP limi-

tation and the backoff counter freezing were not con-

sidered in the paper. A packet aggregation and re-

transmission MAC scheme for the error-prone high-

data-rate UWB Ad Hoc networks was proposed in (Lu

et al., 2007). The control procedure of the proposed

MAC scheme is based on the IEEE 802.11 (IEEE Std.

802.11, 1999) model.

This paper focuses on the design of the optimal

MAC frame payload length (frame length) for max-

imizing the saturation throughput of the WiMedia

PCA scheme over the Rayleigh fading channel. A

large frame length tends to result in high Packet Er-

ror Rate (PER), and a small one usually leads to

high transmission overhead for the system. Both of

these situations will decrease the saturation through-

put. Therefore, there is an optimal frame length value

for the system to achieve the maximum throughput.

The frame length adaptive function can be imple-

mented in the MAC layer.

The proposed design is based on the saturation

throughput analysis. Since the PCA is very similar

to the extensively studied EDCA mechanism (Xiao,

2005)(Deng and Chang, 1999)(Mangold et al., 2002),

the throughput analysis is carried out by extending

the EDCA model proposed in (Kong et al., 2004) for

IEEE 802.11e into the UWB region. In (Kong et al.,

2004), an analytical model of the EDCA scheme us-

ing a three-dimensional discrete time Markov chain

was developed. This model accurately reﬂects the pri-

oritized backoff procedures by considering the back-

off deferring due to other station’s transmission, and

different length of the backoff procedure, as well as

the contention between different ACs within a station.

Figure 1: The format of PCLP.

This original model is extended by taking into account

a BER model based on the Rayleigh fading channel,

TXOP limitations, and the uniqueness of WiMedia

MAC timing structure. The new model is more ac-

curate for accomplishing the WiMedia MAC protocol

speciﬁcations.

The paper is organized as follows. In section 2 Wi-

Media PHY and MAC protocol is reviewed. In sec-

tion 3 the PCA’s saturation throughput performance

is analyzed following the introduction to the extended

analytical model, and the optimal frame length design

is provided . The numerical results analysis is carried

out in section 4. Concluding remarks are given in Sec-

tion 5.

2 WIMEDIA MAC AND PHY

PROTOCOL OVERVIEW

This section provides a review of the WiMedia PHY

and MAC speciﬁcations, and speciﬁcally focuses on

the introduction of the WiMedia PCA schemes.

2.1 WiMedia MB-OFDM PHY

In the WiMedia PHY protocol, the UWB bandwidth

is divided into fourteen sub-bands, each with 528

MHz. The OFDM symbols are allocated to each sub-

bands for transmission. In each of the sub-band, a to-

tal number of 122 sub-carriers are used for data trans-

mission.

Data packets coming from the MAC layer to the

PHY are converged into Physical Layer Convergence

Protocol (PLCP) frame. The frame consists of a

PLCP preamble, a PLCP header and a frame payload,

as depicted in Figure 1. The preamble and header

serve as aids in the demodulation, decoding, and de-

livery of the frame payload at the receiver. It is as-

sumed in this manuscript that no bit error will oc-

cur within the PLCP preamble and header since they

are transmitted at the lowest data rate (39.4 Mbps) in

small sizes. MAC frame payload is formatted into

PLCP frame payload which can be transmitted at the

data rate from 53.3 to 480 Mbps.

Before a transmission, the PLCP header and pay-

load are ﬁrst coded using punctured convolutional

code. Next, the data stream is interleaved and then

mapped using either Quadrature Phase Shift Keying

WINSYS 2008 - International Conference on Wireless Information Networks and Systems

114

Figure 2: WiMedia MAC superframe structure.

(QPSK) (data rate≤200 Mbps) or Dual-Carrier Mod-

ulation (DCM) (data rate>200 Mbps). Subsequently,

each mapped symbol is modulated into a OFDM

symbol by the OFDM modulator using Inverse Fast

Fourier Transform (IFFT). Finally, the OFDM sym-

bols are mapped onto the corresponding sub-carriers

according to the time-frequency code and transmitted

into the UWB wireless channel.

Rayleigh fading is used in the analysis to model

the UWB channel fading (Lai et al., 2007). Thus, the

average BER of the transmitted data can be expressed

as

P

BER

= 1/2[1 −

p

γ/(1 + γ)], (1)

where γ is the average SNR per bit.

Since the convolutional coding process enables

the receiver to correct several bit errors of the data

stream transmitted over the fading channel, the value

of the PER can be calculated as (Taub and Schilling,

1986)

p

0

e

=

L

c

∑

i=n+1

L

c

n + 1

P

(n+1)

BER

(1 − P

BER

)

(L

c

−n−1)

, (2)

where L

c

is the length of the convolutional coded pay-

load, and n is the maximum number of bit that can be

corrected by the convolutional coding.

For simplicity, the value of the PER is approxi-

mated as

p

e

= 1 − (1 − P

BER

)

8L

, (3)

where L is the length of the payload in bytes. It can be

observed that p

e

≥ p

0

e

when the payload size is large.

So, p

e

represents an upper bound expression for the

PER.

2.2 WiMedia MAC

The basic time division of the WiMedia MAC is su-

perframe. It contains a variable length beacon period

and a data transmission period. A superframe com-

prises 256 Medium Access Slots (MASs) of 256 µs

each. The structure of a superframe is shown in Fig-

ure 2.

Every superframe starts with a beacon period

(BP) during which the beacon frames are mandatorily

transmitted by each station to provide timing refer-

ence, carry control information, and broadcast chan-

nel reservation information for the entire superframe.

A BP consists of up to 96 beacon slots (BSs), each

lasts 85 µs and could only be exclusively occupied by

one station during a superframe. The ﬁrst two BSs

at the start of a BP are called signaling BS, while the

following slots including 8 extension BSs are used for

stations to join the existing communication group. It

is assumed in this paper that each BP is always com-

pact, which means there is no empty BSs existing ex-

cept for the ﬁxed-length signaling and the extension

BSs. Thus, the length of a BP only depends on the

number of the active stations within a communication

group.

The PCA schemes provide prioritized backoff pro-

cedure to different ACs. Basically, before starting a

data transmission, a station must sense the channel as

idle for a period called Arbitrary Inter-frame Space

(AIFS), plus an additional backoff period. The length

of the AIFS is smaller in higher prioritized ACs.

After sensing the channel as idle for the duration

of AIFS, the station starts the backoff period. The

duration of a backoff period is speciﬁed by a backoff

counter which will decrease by one when the channel

is still sensed as idle during that backoff slot. Only

when the backoff counter reaches zero, can the sta-

tion initiate the transmission. The value of the back-

off counter is uniformly sampled from the interval

[0, CW[AC]], where CW[AC] is the Contention Win-

dow (CW) size of the AC and is randomly selected

from [CWmin, CWmax]. Its initial value is set to

CWmin. Generally, the value of CWmin, CWmax,

and the difference between them are lower in higher

prioritized ACs. The value of CW[AC] will be set

to min(CWmax[AC], 2CW[AC]+1) in order to reduce

the frame collision probability if the pervious transac-

tion for the this AC was not ﬁnished or failed.

If the channel is sensed as busy during either the

AIFS or backoff period, the station will defer from

sensing the channel for a period of time called Net-

work Allocation Vector (NAV). This parameter indi-

cates the duration of the ongoing transmission. When

the deferring ends, the paused backoff procedure will

be resumed after the channel being sensed as idle for

another AIFS.

Each station has the data packets of each AC

buffered in its own queue, as shown in Figure 3. Each

AC is recognized as a virtual station and contends for

medium access by applying the PCA rules. If a col-

lision occurs among different ACs within a station,

known as virtual collision, the higher priority AC will

be granted medium access by a virtual collision han-

dler.

Once a station accesses the channel, it has a du-

ration of TXOP for one or more frame transmissions

or retransmissions without backoff. The maximum

FRAME LENGTH DESIGN FOR MULTIBAND-OFDM ULTRA WIDEBAND NETWORKS

115

Figure 3: ACs queues and virtual collision.

Figure 4: RTS/CTS exchange, successful transmission, re-

transmission and collision time.

number of frames that can be successfully transmit-

ted during a TXOP is denoted by N

T XOP

. It is as-

sumed in this paper that Request-to-Send/Clear-to-

Send (RTS/CTS) scheme is used. Thus, before a

frame transmission, an RTS frame and a CTS frame

are exchanged between the communication pairs.

When the RTS/CTS frame processing is successfully

completed, the frame transmission will start. A suc-

cessful frame transmission is conﬁrmed when the

sender successfully receives an immediate acknowl-

edgement (Imm-ACK) from the target receiver within

an expected period. Otherwise, the sender must re-

transmit the previous frame as long as the remaining

time in the TXOP is adequate for the new transmis-

sion. Figure 4 shows the transmission mechanisms.

The length of a TXOP is further restricted by the

start of the next BP (also the end of a superframe) or

the next DRP reservation. No PCA transmission may

delay or foreshorten BP or DRP reservation.

The DRP scheme provides a collision-free chan-

nel access. The scheme allows the stations to arbitrar-

ily reserve a number of MASs within the data trans-

mission period for exclusive communication. For

simplicity, it is assumed that only PCA scheme is im-

plemented, and the DRP scheme is not implemented.

3 THROUGHPUT ANALYSIS AND

FRAME LENGTH

OPTIMIZATION

The saturation throughput is a fundamental perfor-

mance indicator deﬁned as the stable throughput limit

reached by the system as the offered load increases

(Bianchi, 2000). The analysis considers a ﬁxed num-

ber of stations, denoted by M. Each of the station has

multiple ACs and every AC is assumed to always have

packets for transmission. A station will transmit as

many packets as it can including retransmissions dur-

ing its TXOP. The analysis ignores the signal propa-

gation delay because propagation delays are small (in

nano-second) in a short-range UWB network.

3.1 Analytical Model

To extend the model presented in (Kong et al., 2004)

for the WiMedia PCA scheme, new assumptions and

new transition probabilities will be introduced to the

three-dimensional Markov chain. Initially, as stated

in section 2, the limitation of a TXOP is further re-

stricted by the next BP. For simplicity, it is assumed

that any ongoing TXOP will be ﬁnished before the

end of a superframe, and that collision information

will be inferred to the transmitter before the end of

the current superframe. A collision is conﬁrmed by

the transmitter if the expected ACK from the target re-

ceiver is not received within the expected period. The

duration of inferring this collision equals to that of a

successful transmission, as shown in Figure 4. The

probability that a station is activated within the PCA

period is calculated to statistically ensure that every

TXOP starts and ends within the PCA period. This

probability is denoted as P

PCA

, and given in (Wong

et al., 2007) as

P

PCA

= N

PCA

/N

SF

(4)

N

PCA

= N

SF

− N

BP

(5)

N

BP

= d(M + N

BSig+BExt

)T

BS

/T

MAS

e, M ≤ M

MAX

,

(6)

where N

PCA

, N

SF

, and N

BP

are the number of MASs

occupied by a PCA period, a superframe, and a BP,

respectively. The parameters T

BS

and T

MAS

are the

duration of a beacon slot and MAS duration in µs,

respectively. The parameter N

BSig+BExt

is the length

of the signaling and extension BS in total, and M

MAX

is the maximum number of stations allowed in a BP.

There is still probability that the next BP will arrive

between two adjacent TXOPs, or during the backoff

period.

The channel busy probability p

b

in the Markov

chain of (Kong et al., 2004) caused by the transmis-

sion of any station in a considered slot time is ex-

tended to p

b

+ P

BP

, since the WiMedia MAC also de-

ﬁnes the channel as busy during the BP. The previous

backoff process will resume subsequently.

The new stationary probability for an AC

i

to at-

tempt to access the channel within the PCA period in

a randomly chosen time slot is expressed as

τ

i

= [(1 − p

i

m+1

)/(1 − p

i

)]b

0,0,0

,

(7)

WINSYS 2008 - International Conference on Wireless Information Networks and Systems

116

where m is the maximum number of the backoff stage,

and b

0,0,0

is the probability for a station to be in the

original state. The expression of b

0,0,0

given in (Kong

et al., 2004) is extended as

b

0,0,0

= [

1 + N(p

b

+ P

BP

)

(p

b

+ P

BP

)

1 − (1 − (p

b

+ P

BP

))

A

i

+1

(1 − (p

b

+ P

BP

))

A

i

+1

+ dT

si

e(1 − p

i

m+1

) + (1 + dT

c

ep

i

)

1 − p

i

m+1

1 − p

i

+

1 + N(p

b

+ P

BP

)

2(1 − (p

b

+ P

BP

))

A

i

m

∑

j=0

W

j

p

i

j

]

−1

.

(8)

In (8), p

i

is the collision probabilities of the AC

i

,

and p

b

is the channel busy probability. The value of

W

j

is CW size depends on the backoff stage j and sat-

isﬁes W

j+1

= 2W

j

+ 1. In addition, the parameters T

si

and T

c

are the length of AC

i

’s TXOP and the collision

time which is the period elapsed before a station con-

ﬁrms a collision, respectively. A

i

is the duration of

each AC

i

’s AIFS.

Furthermore, the value of N in (8) is the expected

frozen time calculated using the value of the NAV

and the length of the BP. Since the value of the NAV

equals to the corresponding TXOP the expression of

N can be expressed as

N =

3

∑

i=0

p

si

T XOP

i

+ P

BP

N

BP

, (9)

where p

si

(16) is the probability that an AC

i

’s frame

can be transmitted successfully. Note that all the time-

related values are expressed with the same unit: back-

off slot σ.

The probability that a station attempts to access

the channel in any given time slot can be found us-

ing equation (7). It is equal to the probability that the

station has any type of AC’s data buffered for trans-

mission and is expressed as

τ = 1 −

3

∏

i=0

(1 − τ

i

) . (10)

Then, the collision probability of the AC

i

can be

written as

p

i

= 1 − (1 − τ)

M−1

∏

i

0

>i

(1 − τ

i

0

), (11)

where i

0

> i means that AC

0

i

has higher priority than

AC

i

. Equation (11) considers that a collision will oc-

cur if at least one of the other stations transmits or the

higher prioritized AC

i

in the station is transmitted at

the same time.

The probability that the channel is occupied by a

given AC

i

is the probability that the data is transmitted

or collide, and is given by

υ

i

= [dT

si

e(1 − p

i

m+1

) +dT

c

e

1 − p

i

m+1

1 − p

i

]b

0,0,0

. (12)

Thus, the probability that the channel is occupied

by a given station is

υ = 1 −

3

∏

i=0

(1 − υ

i

) . (13)

Furthermore, the probability that a channel is

busy, p

b

, which is also the probability that there is at

least one station transmitted or collide on the channel

can be expressed as

p

b

= 1 − (1 − υ)

M

. (14)

The successful access probability of the AC

i

within a time slot is the probability that the backoff

counter for this AC reaches zero at any backoff stage.

This probability is illustrated as

p

ti

= [dT

si

e(1 − p

i

m+1

)]b

0,0,0

. (15)

Finally, the probability that the AC

i

’s frame can be

transmitted successfully is the probability that there is

no other higher priority ACs in the same station and

only one station is transmitting. This probability is

given as

p

si

=

M p

ti

(1 − υ)

M−1

∏

i

0

>i

(1 − υ

i

0

)

1 − (1 − υ)

M

. (16)

Equations (7)–(16) form a set of nonlinear equa-

tions, which means that it can be solved by means of

numerical methods.

3.2 Throughput

The normalized system throughput, S

i

, is deﬁned as

the fraction of time in which the channel is used

to successfully transmit the payload bits, and is ex-

pressed as

S

i

= [p

si

p

b

P

PCA

N

T XOP

(1 − p

e

)L/R]·

{[(1 − p

b

) + P

BP

]σ + p

si

p

b

P

PCA

T

si

+ p

b

P

PCA

(1 −

3

∑

j=0

p

s j

)T

c

}

−1

.

(17)

In (17), the factor p

si

p

b

P

PCA

N

T XOP

(1 − p

e

)L/R is

the mean amount of time needed for the payload in-

formation to be successfully transmitted in the PCA

period, and R is the ﬁxed data rate.

Furthermore, the term [(1 − p

b

) + P

BP

]σ is the

expected number of the idle time slots due to ei-

ther non-transmission or BP’s occupation. The term

FRAME LENGTH DESIGN FOR MULTIBAND-OFDM ULTRA WIDEBAND NETWORKS

117

(1 −

∑

3

j=0

p

s j

)T

c

denotes the mean collision time for

the AC, and the value of the T

c

can be calculated using

T

c

= T

RT S

+ 2T

SIFS

+ T

CT S

Timeout

, (18)

where T

SIFS

is the duration of the Small Inter-frame

Space (SIFS), and T

RT S

is the time for the transmis-

sion of an RTS frame. T

RT S

is denoted as

T

RT S

= T

Preamble

+ T

Header

, (19)

where the value of T

Preamble

and T

Header

are the dura-

tion of the PLCP preamble and header, respectively.

In (18), the value of T

CT S

Timeout

equals to the suc-

cessful transmission time of a CTS which further

equals to the value of T

RT S

. The reason is that the size

of the RTS and the CTS frames are the same. Thus,

the value of T

c

equals to the duration for a successful

RTS/CTS frame exchange, denoted as T

s

.

The value of the N

T XOP

is calculated by

N

T XOP

i

= b

T

T XOP

i

− T

G

− T

s

T

PPDU

+ 2T

SIFS

+ T

ACK

c, (20)

where T

G

is the guard time, and T

PPDU

is the transmis-

sion time for the PLCP Protocol Data Unit (PPDU),

expressed as

T

PPDU

= T

Preamble

+ T

Header

+ T

SY M

N

Frame

. (21)

In (21), the value of T

SY M

is the OFDM symbol

interval, and N

Frame

is the number of OFDM symbols

of the PLCP payload. The calculation of these param-

eters is speciﬁed in the WiMedia standard.

Finally, by substituting (18)–(21) into (17), the

normalized throughput for an AC can be obtained.

3.3 Frame Length Optimization Design

The optimal frame length L in bits can be obtained

by solving the equation dS

i

/dL = 0 which can be ex-

pressed as

dS

i

dL

=

(1 − P

BER

)

L

+ L(1 − P

BER

)

L

log(1 − P

BER

)

G + HL

−

LH(1 − P

BER

)

L

(G + HL)

2

= 0 .

(22)

In (22), the parameter G is denoted as

G = A × D, (23)

where the factor A and D are expressed respectively

as

A = [(1 − p

b

) + P

BP

]σ + p

si

p

b

P

PCA

T

si

+

p

b

P

PCA

(1 −

3

∑

j=0

p

s j

)T

c

,

(24)

D = T

Preamble

+ T

Header

+ 2T

SIFS

+ T

ACK

+

6d(L

FCS

+ L

Tail

)T

SY M

/N

IBP6S

e .

(25)

Furthermore, the factor H in (22) is denoted as

H = A × E, (26)

where the term E is expressed as

E = 6dT

SY M

/N

IBP6S

e . (27)

Finally, the optimal length, L

opt

, can be calculated

from (22) as

L

opt

= {Glog(1 − P

BER

)+

[G

2

log

2

(1 − P

BER

)

2

− 4HGlog(1 − P

BER

)]

1/2

}·

[−2log(1 − P

BER

)H]

−1

.

(28)

It can be observed that the value of the optimal

frame length strongly depends on the value of the

BER which is decided by the value of the SNR. Equa-

tion (28) also shows that the value of the optimal

frame length is independent of the transmit data rate.

4 NUMERICAL RESULTS

The saturation throughput performance of the ACs

is initially investigated as a function of the frame

length. Subsequently, the variation of the optimal

frame length value against the value of the SNR is

analyzed. The used data rate is set to 200 Mbps, and

the number of the active stations is set to 10. It is

assumed that each station has all types of the ACs ac-

tivated (AC

0

to AC

3

). AC

3

has the highest priority.

The parameters used to obtain numerical results are

summarized in Table 1.

Both Figure 5 and Figure 6 illustrate that the satu-

ration throughput is sensitive to the frame length and

reaches the maximum at certain frame length value.

For example, when the SNR value is set to 24.0 dB

which corresponds to the BER value of 1.0e-3, the

saturation throughput of all the ACs reaches their cor-

responding maximum value when the frame length in-

creases to a value slightly more than 110 bytes. It can

be seen that the AC

2

has the highest maximum satura-

tion throughput value instead of the AC

3

. The reason

is that the AC

2

presents the longest TXOP duration

(1024 µs) which is much longer than that of the AC

3

(256 µs). The throughput value gradually decreases to

nearly zero when the frame length increases to more

than 500 bytes due to the large value of the PER.

It is also noticeable that the value of the optimal

frame length corresponding to the maximum satu-

ration throughput becomes larger when the SNR is

higher. For example, when the SNR is set to 14.0

WINSYS 2008 - International Conference on Wireless Information Networks and Systems

118

Table 1: Calculation and Simulation Parameters.

Parameter Value Parameter Value

M 10 N

IBP6S

375

T

Header

5.08µs T

Preamble

9.375µs

T

SY M

312.5ns T

G

12µs

T

SIFS

10µs σ 9µs

T

MAS

256µs T

BS

85µs

N

BSig+BExt

10 N

SF

256

AIFSN

AC

0

7 AIFSN

AC

1

4

AIFSN

AC

2

2 AIFSN

AC

3

1

TXOP

AC

0

512µs TXOP

AC

1

512µs

TXOP

AC

2

1024µs TXOP

AC

3

256µs

CW

AC

0

[15,1023] CW

AC

1

[15,1023]

CW

AC

2

[7,511] CW

AC

3

[3,255]

dB, the optimal frame length value of AC

2

is approx-

imately 12 bytes which is smaller than 110 bytes ob-

tained when the SNR is 24.0 dB. The reason is that

higher SNR values lead to lower BER values, and this

results in a lower PER value according to equations

(1) and (3).

Furthermore, the results show that the optimal

frame length value is not affected by the change of

the priority of the AC. For instance, when the SNR

value is set to 14.0 dB, all of the ACs have almost the

same optimal frame length value of approximately 12

bytes. This observation is clearly illustrated in Fig-

ure 7. It can be seen that the values of the optimal

frame length of all the ACs increase exponentially as

the SNR value is higher. The variation proﬁles are al-

most the same for all of the ACs under different SNR

conditions.

Finally, Figure 8 illustrates the effect of the num-

ber of the active stations on the size of the optimal

frame length. It can be seen that the value of the opti-

mal frame length of AC

2

is always stable for any num-

ber of the active stations from two to thirty. Thus, it

means that the optimal value of the frame length can

be treated as independent of the number of the active

stations, the data rate, and the priority of the AC in the

WiMedia standard. Therefore, a station can dynami-

cally adapt the size of the transmitted frame length in

the MAC layer according to the current SNR level so

as to maximize its saturation throughput in the MB-

OFDM UWB network.

5 CONCLUSIONS

A new design of the optimal frame length for max-

imizing the saturation throughput of the WiMedia

PCA scheme over Rayleigh fading channel is pro-

posed. Initially, the analytical model of (Kong et al.,

0 5 10 15 20 25 30 35 40 45 50

0

0.5

1

1.5

2

2.5

3

3.5

x 10

−3

Length of the Payload

Saturation Throughput

AC0,SNR=14.0dB

AC1,SNR=14.0dB

AC2,SNR=14.0dB

AC3,SNR=14.0dB

Figure 5: Saturation throughput of the ACs against the

frame length (SNR=14.0dB).

0 50 100 150 200 250 300 350 400 450 500

0

0.005

0.01

0.015

0.02

0.025

0.03

Length of the Payload

Saturation Throughput

AC0,SNR=24.0dB

AC1,SNR=24.0dB

AC2,SNR=24.0dB

AC3,SNR=24.0dB

Figure 6: Saturation throughput of the ACs against the

frame length (SNR=24.0dB).

0 5 10 15 20 25

0

20

40

60

80

100

120

Average SNR (dB) per bit

Optimized Frame Length

AC0

AC1

AC2

AC3

Figure 7: The optimal frame length varies with respect to

the SNR.

2004) originally for EDCF scheme is extended into

the MB-OFDM UWB region for the throughput anal-

ysis. Subsequently, the proposed optimal frame

length design is carried out based on the extended

model. The new model inherits the advantages of the

original model and more importantly, the new model

takes into account the effect of TXOP limits and the

FRAME LENGTH DESIGN FOR MULTIBAND-OFDM ULTRA WIDEBAND NETWORKS

119

0 5 10 15 20 25 30

0

20

40

60

80

100

120

Number of the Active Stations

Optimized Frame Length

AC2,SNR=24.0dB

AC2,SNR=14.0dB

AC2,SNR=4.0dB

Figure 8: The optimal frame length varies with respect to

the number of active stations.

effect of the Rayleigh fading channel on the BER

value.

The results obtained in the simulation show that

the value of the throughput is sensitive to the frame

length and reaches the maximum at certain frame

length value. The optimal frame length increases ex-

ponentially when the value of SNR is higher and can

be treated as independent of the number of the active

stations, the data rate, and the priority of the AC in

the WiMedia standard. A station can then dynami-

cally adapt the transmitted frame length value in the

MAC layer according to the current value of the used

SNR so as to maximize its saturation throughput in

the MB-OFDM UWB network.

REFERENCES

Batra, A., Balakrishnan, J., and Dabak, A. (2003). “TI phys-

ical layer proposal for IEEE 802.15 task group 3a,”

IEEE P802.15-03/142r2-TG3a.

Bianchi, G. (2000). Performance analysis of the IEEE

802.11 distributed coordination function. IEEE J. Se-

lect. Areas. Commun., 18(3):535–547.

Deng, D.-J. and Chang, R.-S. (1999). A priority scheme

for IEEE 802.11 DCF access method. IEICE Trans.

Commun., E82-B(1):96–102.

ECMA International (2005). ECMA 368: High Rate Ultra

Wideband Phy and Mac Standard, Geneva: ECMA

International.

Federal Communications Commission (2002). “Revision of

part 15 of the commissions rules regarding ultra wide-

band transmission systems,” First Report and Order,

ET Docket 98-153, Washington, D.C.: Federal Com-

munications Commission.

IEEE Std. 802.11 (1999). Wireless LAN Medium Access

Control (MAC) and Physical Layer (PHY) Speciﬁca-

tions, IEEE Std. 802.11, 1999 Edition.

IEEE Std. 802.11e (2003). Wireless medium access

control (MAC) and physical layer (PHY) speciﬁca-

tions: Medium access control (MAC) enhancements

for quality of service (QoS), IEEE Std. 802.11e/Draft

5.0.

Kong, Z., Tsang, D. H. K., Bensaou, B., and Gao, D. (2004).

Performance analysis of IEEE 802.11e contention-

based channel access. IEEE J. Sel. Areas Commun.,

22(10):2095–2106.

Lai, H., Siriwongpairat, W., and Liu, K. (2007). Perfor-

mance analysis of multiband OFDM UWB systems

with imperfect synchronization and intersymbol inter-

ference. IEEE Journal of Selected Topics in Signal

Processing, 1(3):521–534.

Lu, K., Wu, D., Qian, Y., Fang, Y., and Qiu, R. C. (2007).

Performance of an Aggregation-Based MAC Protocol

for High-Data-Rate Ultrawideband Ad Hoc Networks.

IEEE Trans. on Vehicular Tech., 56(1):312–321.

Mangold, S., Choi, S., May, P., Klein, O., and Hiertz,

G. (2002). IEEE 802.11e wireless LAN for Quality

of Service, Proceedings European Wireless, Florence,

25-28 Feb., 2002, 32-39.

Taub, H. and Schilling, D. L. (1986). Principles of Commu-

nication Systems. McGraw-Hill, 2nd ed. New York p.

575-578.

Vishnevsky, V. M., Lyakhov, A. I., Safonov, A. A., Mo,

S. S., and Gelman, A. D. (2008). Study of Beaconing

in Multihop Wireless PAN with Distributed Control.

IEEE Trans. on Mobile Computing, 7(1):113–126.

WiMedia Alliance (2008). [Online], available:

www.wimedia.org/ [accessed 27 Mar. 2008].

Win, M. Z. and Scholtz, R. A. (1988). Impulse radio: How

it works. IEEE Communications Letters, 2(2):36–38.

Wong, D., Chin, F., Shajan, M., and Chew, Y. (2007). Sat-

urated Throughput of PCA with Hard DRPs in the

Presence of Bit Error for WiMedia MAC, Proceedings

Global Telecommunications Conference, Washington,

D.C., 26-30 Nov., 2007, 614-619.

Xiao, Y. (2005). Performance analysis of priority schemes

for IEEE 802.11 and IEEE 802.11e wireless LANs.

IEEE Trans. Commun., 4(4):1506–1515.

Zang, Y., Hiertz, G. R., Habetha, J., Otal, B., Sirin, H.,

and Reumerman, H.-J. (2005). Towards high speed

wireless personal area network - efﬁciency analysis of

MBOA MAC, Proceedings of the International Work-

shop on Wireless Ad-Hoc Networks, London, 23-26

May 2005, 10-20.

WINSYS 2008 - International Conference on Wireless Information Networks and Systems

120