MOB Subject 7 –IEEE 802.11 standards Wifi performances

Master of Computer Science 1 - MOB Mobile Internet and Surrounding

Fladenmuller Baey - ”IEEE 802.11standards” 1/8

MOB Subject 7 –IEEE 802.11 standards

Wifi performances

1. Impact of the transmission quality

One is interested here in the impact of radio transmission errors on the performances of a

wireless network and in the relation between transmission and fragmentation quality. One takes

here the standard IEEE 802.11b as an example.

1. Let p be the binary error probability on a communication channel used by a local network

and n be the length of a physical frame in bytes. What is the error probability q on a frame?

It will be supposed that the errors on the bits are independent.

A. N. : p = 10-6

, n = 2370 bytes (maximum length of a MAC frame in conformity with the

802.11 standard (2346 bytes) + PHY header of 24 bytes).

A frame is error just if any bit has undergone a transmission error. The corresponding

probability can be written: (1 p)8n

The probability of error per frame can be written thus:

q = 1 – (1 – p)8n

= 0,018781399

2. For an error probability q per frame, determine the average number N of transmissions has

to effect to succeed the correct transmission of a frame? For the digital application, one will

take p = 10-6

.

Reminder: 1 + 2q + 3q

2

+ … + iqi-1

+ … =

(1 )

1

2

q

The probability that a frame need to be exactly i transmissions correctly transmitted can be

written: p(i) = qi – 1(1 – q)

The average number of transmissions necessary to succeed a correct transmission is written

so:

1 [1 (1 ) ]

1

1

1

(1 )

1

( ) (1 ) (1 )

2 8

1 1

n

i i

q q p

q

N ip i iq q q iq

  











        

 

1,0191

(1 )

1

8





 n

p

3. One wants to make a first coarse evaluation of the bit rate lost because of the

retransmissions on error. One thus does not take any other factor in account but the errors of

transmission. One supposes in first approximation that all bits of the physics frame are send

with the same flow.

a) For a error probability per frame q and a nominal capacity d of transmission, what is the

useful bit (goodput) and what is the lost flow at the time of the retransmissions for a

channel which is used permanently (there is always a frame to transmit i.e. is the

channel is saturated)?

A. D. : d = 11 Mbit/s and p = 10-6

.