tension project, IEEE 802.11a, started in September 1997.

It added an OFDM(Orthogonal Frequency Division Mul-

tiplexing) PHY that supports up to 54 Mb/s data rate.

Since IEEE 802.11 a operates in the 5 GHz band, com-

munication with plain IEEE 802.11 devices is impossible.

This lack of interoperability led to the formation of IEEE

802.11 g, which introduced the benefits of OFDM to the

2.4 GHz band. As IEEE 802.11 g’s extended rate PHY

provides DSSS-compatible signaling, an easy migration

from IEEE 802.11 to IEEE 802.11 g devices became

possible. While IEEE 802.11b uses only DSSS technol-

ogy, IEEE 802.11g uses DSSS, OFDM, or both at the 2.4

GHz ISM band to provide high data rates of up to 54

Mb/s. combined use of both DSSS and OFDM is

achieved through the provision of four different physical

layers. These layers coexist during a frame exchange, so

the sender and receiver have the option to select and use

one of the four layers as long as they both support it. The

four different physical layers defined in the IEEE 82.11g

standard are ERP-DSSS/CCK, ERP-OFDM, ERP-DSSS/

PBCC and DSSS-OFDM. From the above four physical

layers, the first two are mandatory and the other two are

optional [1].

As the first project whose targeted data rate is meas-

ured on top of the MAC layer, IEEE 802.11n provides

user experiences comparable to the well known Fast

Ethernet (IEEE 802.3u). Far beyond the minimum re-

quirements that were derived from its wired paragon’s

maximum data rate of 100 Mb/s, IEEE 802.11n delivers

up to 600 Mb/s. Its most prominent feature is MIMO

(Multiple-Input Multiple-Output) capability. A flexible

MIMO concept allows for arrays of up to four antennas

that enable spatial multiplexing or beam forming. Its

most debated innovation is the usage of optional 40 MHz

channels. Although this feature was already being used

as a proprietary extension to IEEE 802.11a and IEEE

802.11g chipsets, it caused an extensive discussion on

neighbor friendly behavior. Especially for the 2.4 GHz

band, concerns were raised that 40 MHz operation would

severely affect the performance of existing IEEE 802.11,

Bluetooth (IEEE 802.15.1), ZigBee(IEEE 802.15.4), and

other devices. The development of a compromise, which

disallows 40 MHz canalizations for devices that cannot

detect 20 MHz-only devices, prevented ratification of

IEEE 802.11n until September 2009. As a consequence

of 20/40 MHz operation and various antenna configura-

tions, IEEE 802.11n defines a total of 76 different MCSs.

Figure 1 provides an overview of the IEEE 802.11 PHY

amendments and their dependencies [2].

Copyright © 2013 SciRes. CN

H. C. LEE

12

A key element to the IEEE 802.11 success is its simple

MAC operation based on the DCF protocol. This scheme

has proven to be robust and adaptive to varying condi-

tions, able to cover most needs sufficiently well. Follow-

ing the trends visible from the wired Ethernet, IEEE

802.11’s success is mainly based on over provisioning of

its capacity. The available data rate was sufficient to

cover the original best effort applications, so complex

resource scheduling and management algorithms were

unnecessary. However, this may change in the future.

Because of the growing popularity of IEEE 802.11,

Wireless LANs are expected to reach their capacity lim-

its. Moreover, applications like voice and video stream-

ing pose different demands for quality of service. There-

fore, traffic differentiation and network management

might become inevitable. Figure 2 shows IEEE 802.11

MAC layer amendments

3. FER Analysis

3.1. FER of Fixed Wireless Channel

In IEEE 802.11a/g wireless LAN, fixed wireless channel

isassumed to be Rayleigh fading channel. The probability

of bit error is upper bound by

Figure 1. The IEEE 802.11 PHY layer amendments and

their dependenc ie s[2].

Figure 2. The IEEE 802.11 MAC layer amendments[2].

1

free

b

dd

PB

k

dd

P (1)

where

f

ree

d

B is the free distance of the convolutional

code, d is the total number of information bit ones on

all weight d paths, d is the probability of selecting a

weight d output sequence as the transmitted code se-

quence, and k is the number of information bits per clock

cycle. Because the weight structure is generally accepted

that the first five terms in equation (1) dominate, equa-

tion (1) can be rewritten as

P

4

1free

free

d

b

dd

PB

k

dd

P (2)

The probability of selecting the incorrect path when d

is odd.

1

2

1

ddi

i

dd

i

d

Pp

i

p

(3)

where p is the probability of channel bit error. The prob-

ability of selecting the incorrect path when d is even.

2

2

1

2

1

11

22

dd

di d

i

dd

i

d

d

Ppp p

d

i

p

(4)

To achieve data rates of 54 Mbps for wireless access,

the IEEE 802.11 a standard utilizes MQAM (6q

,

64M

) with convolutional coding at rate r = 3/4. We

obtain the approximate channel bit error probability for

the sub-channel for MQAM with a square constella-

tion as

th

i

3

3211

2

3

2

3211

2

1

41

3211

221 1

1

21

311

11

bi

ibI

i

i

bi

bI

i

i

qr

dqr M

id

bI

I

qr

dqr M

bI

I

e

M

pqr M

qc M

e

M

qr M

cq M

(5)

where 22.6 0.1c

is empirically obtained and d = 1

for HDD. i

is the ratio of direct-to-diffuse signal

power on the sub-channel.

th

i

has 0 in a pure

Rayleigh fading channel and ranges from 0 to 10 in a

composite Rayleigh/Ricean fading channel. bi

is the

ratio of received average energy per bit-to-noise power

spectral density on the sub-channel. The overall

p is

the average of the probability of bit error on each of the

N OFDM sub-channels [5, 6].

th

i

Copyright © 2013 SciRes. CN

H. C. LEE 13

1

1N

i

i

p

N

p (6)

Note that for either no channel fading or for all sub-

channels experiencing the same fading (that is, i

and for all

i

bb ), then i.

i

pp/N

bbo

is

the ratio of received average energy per bit-to-noise

power spectral density ,

E

is the ratio of direct-to-dif-

fuse signal power. Now, using equation (6) in equation (3)

or (4) and taking the result into equation (2), we obtain

the performance of 64 QAM with HDD over Ricean

fading channels. For basic access mechanism, a data

packet including the PHY header and the MAC header

needs retransmission if any one bit of them is corrupted.

We define a variable which is the probability that a

backoff occurs in a station due to bit errors in packets.

We further assume that bit errors randomly appear in the

packets. So frame error rate is represented by (7).

P

c

1(1 )

p

reamble ACKLPHYMACPL

hh

PP

cb

(7)

CSMA/CA is also used as the MAC scheme in IEEE

802.11n wireless LAN, and it has basic and RTS/CTS

access scheme. Although there is a successful RTS/CTS

transmission in the time slot, a frame has to be retrans-

mitted when there is a bit error in a payload. For conven-

ience, we define a variable which is the probability

that a backoff occurs in a station due to bit errors in

packets. We further assume that bit errors randomly ap-

pear in the packets and A-MSDU scheme is used. So

frame error rate is represented by (8).

P

e

1(1 )

L

P

e q (8)

where L is the aggregated MAC frame’s size. For a con-

volutional code with a coding rate kc/nc, the bit error rate,

denoted as q, can be approximated by

1

2

1()1( is odd)

free free

free

ddi

free i

bb free

d

ci

d

qqqd

i

k

(9)

()1

1

1

2

122

()(1)

22

( is even)

free free

free bb

cfree

free free

free

bb

free

c

free

ddi

di

qq

i

qkd

i

dd

dqq

d

k

d

where dfree is the maximum free distance of the convolu-

tional code and qb is the probability of a bit error for the

M-QAM[5].

2( 1)

s

b

M

q

qM

(10)

qs is the SER(Symbol Error Rate) under the Rician fading

channel.

2

min 2

2

min

()

(|| ||)

8

()

()

1

44 8

2

min

1

()

()

18

dH

d

K

sK

qe

d

K

(11)

K is the Rician factor may be interpreted as the average

SNR at the receive antenna in a SISO fading link. dmin is

the minimum distance of separation of the underlying

scalar constellation. H is MR MT channel transfer func-

tion and 2

|| ||

H

is the squared Frobenius norm of the

channel [6, 7].

3.2. FER of Mobile Wireless Channel

Mobile wireless channel is assumed to be flat fading

Rayleigh channel with Jake spectrum. The channel is in

fading states or inter-fading states by evaluating a certain

threshold value of received signal power level. If and

only if the whole frame is in inter-fading state, there is

the successful frame transmission. If any part of frame is

in fading duration, the frame is received in error. In the

fading channel fading margin is considered and defined

as ρ = Rreq/Rrms, Where Rreq is the required received

power level and Rrms is the mean received power. Gener-

ally, the fading duration and inter-fading duration can be

taken to be exponentially distributed for ρ<-10dB. With

the above assumptions, let be the frame duration,

then the frame error rate is given by (12).

Tpi

1(

f

i

Ti

FERP tTpi

Ti T

)

(12)

where, is inter-fading duration and

it

f

t is fading du-

ration. is the mean value of the random variable

and

Ti it

f

T is the mean value of the random variable

f

t.

is the probability that inter-fading duration

lasts longer than . Since exponential distribution is

()Pti Tpi

Tpi

assumed for ,

it()exp(iTpi

Pt TpiTi

)

. For Rayleigh fading

channel, the average fading duration is given by (13).

exp()1

2

Ti fd

(13)

iTTf

is 1

f

N, where

f

N is the level crossing rate,

which is given by 2exp( )fd

. is the maxi- df

mum Doppler frequency and evaluated as

.

is the

mobile speed and

is wavelength. Frame error rate

can be expressed by (14).

1 exp(2)d

F

ERf Tpi

(14)

Copyright © 2013 SciRes. CN

H. C. LEE

14

Equation (14) shows that frame error rate is deter-

mined by fading margin, maximum Doppler frequency

and frame duration. Since fading margin and maximum

Doppler frequency are hard to dynamically control, the

only controllable parameter is frame duration to get re-

quired frame error rate. For the RTS/CTS access mode,

the frame duration

p

iTis

H

RTS CTSDATA ACK

TTTT T

.

H

T is preamble transmission time + PLCP header trans-

mission time + MAC header transmission time.

D

ATAT

ACKT is

MSDU transmission time and is ACK frame

transmission time.

R

TS is RTS frame transmission time

and is CTS frame transmission time[6,7].

T

CTS

T

4. Numerical Results of FER over the Fading

Channel

4.1. FER Results with Fixed Stations

In the Figure 3, Pc(P, b

, K) shows FER(Frame Error

Rate) due to b

, the ratio of received average energy per

bit- to-noise power spectral density[6,7]. K means Rician

factor and P means payload size. And as expected, the

FER performance improves with K and the smaller pay-

load size is, the better performance is.

In the Figure 4, qs(ρ,K) shows SER(Symbol Error

Rate) and Pe(K,ρ,ns,P) shows FER(Frame Error Rate)

[6,7]. K means Rician factor and as expected, the FER

performance improves with K and the smaller subframe’

payload size is, the better performance is.

(a) IEEE 802.11a OFDM

(b) IEEE 802.11g ERP-OFDM

(c) 802.11g DSSS-OFDM

Figure 3. Frame error rate of IEEE 802.11a/g fixed LAN

over Rayleigh fading channel.

(a) SER

(b) FER

Figure 4. SER and FER of IEEE 802.11n fixed LAN over

Rician fading channel.

4.2. FER Results with Mobile Stations

In the Figures 5(a)-(c), the symbol fer (,

, P) shows

frame error rate of IEEE 802.11a/g. In the Figure 5(d),

the symbol fer (ns, ,

, P) shows frame error rate of

IEEE 802.11n with the horizontal parameter of sub-

frame’ payload size. In the Figure 5(e), the symbol fer (,

ns,

, P) shows frame error rate of IEEE 802.11n using

the number of subframes as the horizontal parameter. It

is generally identified that the higher mobile speed is, the

C

opyright © 2013 SciRes. CN

H. C. LEE

Copyright © 2013 SciRes. CN

15

higher FER is. In case of payload size, the same result

mentioned above is also acquired.

(e) IEEE 802.11n OFDM (58.5 Mbps, number of subframe)

Figure 5. Frame error rate of IEEE 802.11a/g/n mobile LAN.

5. Remarks

(a) IEEE 802.11a OFDM (54 Mbps)

This paper explored the FER performance of MAC layer

in the IEEE 802.11a/g/n wireless LAN under the er-

ror-prone channel. The fixed wireless channel was as-

sumed to be Rayleigh fading channel and the mobile

wireless channel was assumed to be flat fading Rayleigh

channel with Jake spectrum. The MAC protocol that they

are based upon is the same and employs a CSMA/CA

protocol with binary exponential back-off. IEEE 802.11

DCF is the de facto MAC protocol for wireless LAN

because of its simplicity and robustness.

REFERENCES

(b) IEEE 802.11g ERP-OFDM (54 Mbps)

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