Michael Grigoropoulos, MSc Networks and Data Communications COURSEWORK, Kingston University The purpose of this assignment is to analyze and simulate the physical layer of the 802.11a standard and compare the different modulation and coding schemes it can use. A theoretical approach of the protocol will be presented and also a practical simulation using Matlab and Simulink.

1. FACULTY OF ENGINEERING
DEPARTMENTS OF ELECTRONICS AND AUTOMATION
TECHNOLOGICAL EDUCATIONAL INSTITUTE OF PIRAEUS
MSc IN NETWORKING AND DATA COMMUNICATIONS
COURSEWORK
MODULE:
CI715: Wireless Communications and Networks
ID: K1465156
Module Coordinator:
Dr. Stylianos Savvaidis & Dr. Myridakis Nikolaos
Date of Module:
3/1/2015
Name of Student:
Grigoropoulos Michael
Kingston University London

2. FACULTY OF ENGINEERING
DEPARTMENTS OF ELECTRONICS AND AUTOMATION
TECHNOLOGICAL EDUCATIONAL INSTITUTE OF PIRAEUS
Subject: IEEE 802.11a Physical Layer Simulation
Submission Date: 3/1/2015
Grade (%): ________________________________________________
% Grade reduction because of submission delay: _____
(5% Grade reduction per every day of Cwk delay).
Final Grade (%): ________________________________________
Kingston University London

3. IEEE 802.11a Physical Layer Simulation – MSc Networks & Data Communications - Kingston University London 3
Abstract - With the rapid development of the Internet, wireless
technologies are widely spread in order to fulfill people’s need to
communicate without the use of cables. As a result the 802.11
standard (also known as Wi-Fi) was released in 1997 by the
“Institute of Electrical and Electronics Engineers” – IEEE which
allowed devices to connect with each other using a band of
frequencies clustered around 2,4GHz, with data rates up to 1
Mbps. In 1999 the 802.11a expansion was released to provide
transmission rates up to 54 Mbps around the 5GHz frequency
band using an OFDM based physical layer and error correction
code.
The purpose of this assignment is to analyze and simulate the
physical layer of the 802.11a standard and compare the different
modulation and coding schemes it can use. A theoretical
approach of the protocol will be presented and also a practical
simulation using Matlab and Simulink.
Keywords: Physical Layer, 802.11a, simulation, OFDM
I. INTRODUCTION
In 1997 the “Institute of Electrical and Electronics
Engineers” – IEEE released the 802.11 standard, also known
as Wi-Fi. This standard allowed devices to connect with each
other using a band of frequencies clustered around 2,4GHz,
with data rates up to 1 Mbps. Early generations of 802.11
technology did not provide sufficient throughput and capacity
to allow bigger networks, such as office networks, to go
completely wireless. The IEEE tried successfully to solve this
problem and in 1999 802.11a expansion was released [1].
The IEEE 802.11a expansion provides transmission rates up
to 54 Mbps. It uses the same core protocol as the original
standard but it operates in 5 GHz band using a 52 subcarrier
orthogonal frequency-division multiplexing (OFDM). The
data rate, can be reduced to 48, 36, 24, 18, 12, 9 and 6 Mbit/s
by changing the modulation and coding rate of the model [2].
Using the 5 GHz band gives the advantage of having less
conflict issues that can cause frequent dropped connections
and degradation of service. The major disadvantage of
802.11a is the fact that due to the higher carrier frequency and
the smaller wave length used, the effective overall range of the
signal is reduced as it is easily absorbed by walls and solid
objects.
II. BACKGROUND
A. OFDM Parameters
An alternative approach to designing spectrally efficient
telecommunication systems with the presence of channel
distortion, is to divide equally the available bandwidth to a
number of subchannels.
Fig. 1 Bandwidth division
K=W/Δf subchannels are created and different symbols of
information can be transmitted simultaneously through these
K channels. This way data is transmitted with Frequency
Division Multiplexing (FDM).
For each subchannel, a carrier is used:
Xk(t)=sin(2πfkt) , k=0,1,…,K-1
fk is the central frequency for each channel. Choosing a
symbol rate 1/T for each subchannel to be equal with the
distance Δf between sequential subcarriers, the subcarriers are
orthogonal to the signaling space T, independently of their
relevant phases.
2π t
This way data is transmitted with Orthogonal Frequency
Division Multiplexing (OFDM) [3].
IEEE 802.11a Physical Layer Simulation
Michael Grigoropoulos, MSc Networks and Data Communications, Kinston University

4. IEEE 802.11a Physical Layer Simulation – MSc Networks & Data Communications - Kingston University London 4
In 802.11a the radio frequency LAN system is initially
aimed for the 5.15–5.25, 5.25–5.35 and 5.725–5.825 GHz
unlicensed national information structure (U-NII) bands. The
OFDM system uses 52 (48 data + 4 pilot sub) subcarriers that
are modulated using binary or quadrature phase shift keying
(BPSK/QPSK), 16-quadrature amplitude modulation (QAM),
or 64-QAM. Forward error correction coding (convolutional
coding) is used with a coding rate of 1/2, 2/3, or ¾ [2].
Table 1.Rate-dependent parameters
Table 2.Timing related parameters
The mathematical conventions in the signal descriptions are
described on page 10 of the IEEE Std 802.11a-1999(R2003)
(Supplement to IEEE Std 802.11-1999).
B. IFFT / FFT
The calculation of the Discrete Fourier Transform
(DFT/IDFT) is done effectively with the use of the Fast
Fourier Transform (FFT/IFFT) algorithm both in
modulation and in demodulation with period (TFFT): 3.2μs
(1/Δf) [2].
Fig 2.Inputs and outputs of the IDFT
After performing an IFFT, the output is cyclically extended
to the desired length.
C. Cyclic Prefix
Each OFDM Symbol can contain both useful bits and
overhead. The energy contained in the useful bits is
represented by the bit energy. The bit energy is spread over N
bits(N is the FFT size). Additional Ncp bits are added on top
of the useful data as a cyclic prefix. The cyclic prefix forms
the overhead. In an entire OFDM symbol, the symbol energy
is spread across N+Ncp bits [2].
Fig. 3.Symbol energy spread
The relationship that describes the above is given as:
D. Normalization factor
The OFDM subcarriers, are modulated by using BPSK,
QPSK, 16QAM or 64QAM modulation schemes. The choice
of the modulation depends on the desired rate and the SNR of
the channel. The output values of the modulator are inserted in
a normalizer which multiplies the input by a normalization
factor KMOD. The normalization KMOD, depends on the base
modulation mode [2].

5. IEEE 802.11a Physical Layer Simulation – MSc Networks & Data Communications - Kingston University London 5
Table 3.Modulation-dependent normalization KMOD
For the reverse process a denormalizer is used.
E. Encoding
All data are encoded by a convolutional encoder of coding
rate depended of the desired data rate. Coding rate R=1/2 , 2/3
or 3/4 can be used for this purpose. The convolutional encoder
uses industry standard generator polynomials, g0=1338 and
g1=1718, of rate 1/2. Poly2trellis function is used to encode
the data [2][4].
Fig. 4.Convolutional encoder 1/2
The convolutional encoder introduces redundancy into the
transmitted bit stream.
Fig. 5.Convolutional encoder 1/2
To achieve coding rate 2/3 and 3/4, a puncture (mask)
block is added after the 1/2 convolutional encoder. An output
vector is created by the puncture block by removing selected
elements of the input vector and preserving others. This way,
the encoding is transformed to 2/3 or 3/4 in each case. Before
the decoding procedure, zeros are inserted among the elements
of the input vector to the places where the puncture block
removed elements. For this procedure, an Insert Zero block is
used. Before the Insert Zero block a Bipolar Converter is used
to convert the unipolar signal into a bipolar signal.
For the decoding procedure, a Viterbi Decoder is used with
the same polynomials g0 and g1 in a poly2trellis function. The
Viterbi Decoder block decodes input symbols to produce
binary output symbols. This block can process several
symbols at a time for faster performance [5].
Fig. 6.Structure of the Viterbi decoder
Fig 7.Example of Viterbi trellis diagram
F. Data Interleaving
After the encoding, data bits are inserted in a matrix
interleaver and the output rows are interleaved by a block
interleaver. The matrix interleaver interleaves the input
vector by inserting the elements into a matrix with 16 columns
and K rows (K depends on the modulation. For example, for
BPSK modulation 3 rows are used to produce a matrix of 48
bits). The block interleaver uses two steps of permutation.
The first ensures that adjacent coded bits are mapped onto
nonadjacent subcarriers and the second that adjacent coded
bits are mapped alternately onto less and more significant bits
of the constellation and, thereby, long runs of low reliability
(LSB) bits are avoided [4].
Fist permutation:
i=(NCBPS/16)(kmod16)+floor(k/16) k ,1,…, CBPS – 1
The function floor (.) denotes the largest integer not
exceeding the parameter.
Second permutation:
j = × loor / CBPS– loor 16× / CBPS))mod s
,1,… CBPS – 1
The value of s is determined by the number of coded bits
per subcarrier, NBPSC, according to:
s = max(NBPSC/2,1)
The block deinterleaver, which performs the inverse
relation, is also defined by two permutations [4].
G. Channel
To model the channel, a single AWGN channel is used.
The AWGN Channel block, adds white Gaussian noise to the

6. IEEE 802.11a Physical Layer Simulation – MSc Networks & Data Communications - Kingston University London 6
input signal. From the properties option of that block, the
Signal to Noise ratio (dB) of the simulation we can adjusted.
H. Modulation Schemes
BPSK – Binary Phase Shift Keying
Fig 8. BPSK constellation bit encoding
For BPSK, b0 determines the I value:
Table 4.BPSK Encoding table
QPSK – Quadrature Phase Shift Keying
Fig. 9.QPSK block diagram
Fig. 10.QPSK constellation bit encoding
For QPSK, b0 determines the I value and b1 determines the
Q value:
Table 5.QPSK Encoding table
QAM – Quadrature amplitude modulation
In QAM mode, the constellation points are arranged in a
square grid. Each point has equal horizontal and vertical space
between the other constellation point. It is possible to transmit
more bits per symbol by moving to higher order constellation.
Fig. 12.16-QAM constellation bit encoding
Fig. 13.16-QAM constellation bit encoding
For 16-QAM, b0b1 determines the I value and b2b3
determines the Q value:
Table 6.64-QAM Encoding table

7. IEEE 802.11a Physical Layer Simulation – MSc Networks & Data Communications - Kingston University London 7
For 64-QAM, b0b1b2 determines the I value and b3b4b5
determines the Q value:
Table 7.64-QAM Encoding table
III. SIMULATION OF 802.11a
Simulink and Matlab provide all necessary means for
modeling and simulating many types of systems. Simulink
provides an updated library that contains ready to use blocks
(e.g. BPSK Modulator) in order to simulate any
telecommunication system. It uses a graphical interface that
makes the construction of block diagrams very easy and that is
the reason that this software was selected for the simulation.
A. BPSK mode with 1/2 coding rate (6 Mbps):
The Bernouli Binary Block generates a random binary
number which is the input of the Convolutional Encoder.
The output of the encoder, is inserted in the Matrix
Interleaver and then in the General Block Interleaver. After
being Interleaved, data is inserted in the BPSK Modulator
and then the output is multiplied by the normalization factor
KMOD. In BPSK Modulation KMOD=1 (Table 3).
Fig. 14. Normalize Block
The signal is now normalized and the next step is to be
trasmitted. An OFDM Transmitter completes this procedure.
The parameters used for the OFDM transmitter are all
included in the IEEE’s 802.11a standard (table 1, table 2). The
multiport selector block is used, to divide the signal to 48
ports which represent the 48 subcarriers that OFDM uses
devides into 6 groups (1:5, 6:18, 19:24, 25:30, 31:43 and
44:48) [2]. For the creation of a contignus output signal, a
Matrix Concatenation block is used with 11 input vectors. The
output of the Unipolar to bipolar converter splits in 4 branches
that end up as input to the Matrix Concatenation block. This 4
inputs simulate the 4 pilot subcarriers.
Fig. 15.OFDM Transmitter
The AWGN Channel block, is used to add white Gaussian
noise to the input signal before the distorted signal is received
by the OFDM receiver. The OFDM receiver implementation
is an inverse version of all OFDM transmitter functions.
Fig. 16.BPSK with 1/2 coding rate Simulink model

8. IEEE 802.11a Physical Layer Simulation – MSc Networks & Data Communications - Kingston University London 8
Fig. 16.OFDM Receiver
From that point, all the following blocks do the inverse
procedure of their respective ones (e.g matrix deinterleaver
follows the inverse procedure of matrix interleaver). Data
eventually end up in an Error Rate Calculator. The Error
Rate Calculator compares the data produced by the Bernouli
Binary with the output of the Viterbi Decoder (after
transmission and reception) and calculates the Bit Error Rate.
One Discrete-Time Scatter Plot Scope, which presents
graphically the signal to be transmitted, is placed after the
Normalize Block.
Fig. 17.Scatter Plot /Transmitted Signal (BPSK – ½)
To present graphically the signal received, one more
Discrete-Time Scatter Plot Scope is used before the
Denormalize Block.
Fig. 18. Scatter Plot /Received Signal (BPSK – ½)
To present graphically the signal transmitted by the OFDM
transmitter with the distortion caused to it by the white
Gaussian noise, a spectrum scope is placed after the AWGN
Channel block.
Fig. 19.Spectrum Scope (BPSK)
B. BPSK mode with 3/4 coding rate (9 Mbps):
The block diagram remains the same and only a puncture
block is added after the Convolutional Encoder, to give the 3/4
coding rate and also an Insert Zero Block after the Unipolar to
Bipolar converter.
Fig. 20.Puncture Block
Fig. 21.Insert Zero Block
C. QPSK mode with 1/2 coding rate (12 Mbps):
The block diagram remains almost the same. The BPSK
Modulator is replaced by a QPSK Modulator with phase offset
Pi/4 rad. The number of coded bits per OFDM symbol NCBPS
is now 96 (Table 1) and all the rest blocks are configured
accordingly.
Figure 22 and Figure 23 presents the scatter plot of the
transmitted and received signal for QPSK modulation with 1/2
coding rate, during the simulation.
Fig. 22.Scatter Plot /Transmitted Signal (QPSK – ½)

9. IEEE 802.11a Physical Layer Simulation – MSc Networks & Data Communications - Kingston University London 9
Fig. 23. Scatter Plot /Received Signal (QPSK – ½)
Fig. 24.Spectrum Scope (QPSK)
D. QPSK mode with 3/4 coding rate (18 Mbps):
The block diagram remains the same and only a Puncture
block is added after the Convolutional Encoder, to give the 3/4
coding rate and also an Insert Zero Block after the Unipolar to
Bipolar converter (Figures 20 and 21).
E. 16-QAM mode with 1/2 coding rate (24 Mbps):
The block diagram remains almost the same. The BPSK
Modulator is replaced by a Rectangular QAM Modulator
Baseband. In the properties of the QAM Modulator M-ary
Number must be 16 for 16QAM Modulation. The number of
coded bits per OFDM symbol NCBPS is now 192 (Table 1) and
all the rest blocks are configured accordingly.
Fig. 25.Scatter Plot /Transmitted Signal (16QAM – ½)
Fig. 26.Scatter Plot /Received Signal (16-QAM – ½)
Fig. 27.Spectrum Scope (16QAM)
F. 16-QAM mode with 3/2 coding rate (36 Mbps):
The block diagram remains again the same and only a
Puncture block is added after the Convolutional Encoder, to
give the 3/4 coding rate and also an Insert Zero Block after the
Unipolar to Bipolar converter (Figures 20 and 21).
G. 64-QAM mode with 2/3 coding rate (48 Mbps):
The block diagram remains almost the same. The BPSK
Modulator is replaced by a Rectangular QAM Modulator
Baseband. In the properties of the QAM Modulator M-ary
Number must be 64 for 64QAM Modulation. The number of
coded bits per OFDM symbol NCBPS is now 288 (Table 1) and
all the rest blocks are configured accordingly.
A Puncture block is added after the Convolutional Encoder,
to give the 2/3 coding rate and also an Insert Zero Block after
the Unipolar to Bipolar converter (Figures 28 and 21).
Fig. 28.Puncture Block

10. IEEE 802.11a Physical Layer Simulation – MSc Networks & Data Communications - Kingston University London 10
Fig. 29.Scatter Plot /Transmitted Signal (64QAM – 2/3)
Fig. 30.Scatter Plot /Received Signal (64QAM– 2/3)
Fig. 31.Spectrum Scope (64QAM)
H. 64-QAM mode with 3/4 coding rate (48 Mbps):
The block diagram remains exactly the same. Puncture’s
block properties are changed for 3/4 coding rate.
IV. RESULTS & DISCUSSION
Fig. 32 BER/SNR for different modulation and coding
Figure 32 illustrates the relationship between Bit Error Rate
and Signal to Noise Ratio (dB). The vertical axis illustrates the
BER while the horizontal one illustrates the SNR in dB.
Several measurments where taken for each modulation and
coding rate using the simulink project described above. From
the combined plots it is easily concluded that as the
transmission quality gets better (SNR Increaces), the Bit Error
Rate gets smaller which practicaly means that less data will be
corrupted during the transmission and reception process.
Comparing each modulation with the others for each SNR
value, it is concluded that as we move to a higher order
constellation (higher data rate) the BER is increased. In real
conditions this means that as the channel interference or/and
the distance between the transmitter and the receiver increases,
a lower order constellation should be used with a higher
coding rate to avoid conjunction, loss of data and dropped
connections.
It is possible to run the simulation for specific distance by
calculating the SNR for this distance:
1
λ C/ ,
C=3*108
≈ ,9 -> Attenuation*
N0=-174dBm/Hz (AWGN) -> Noise Spectral density
W=Bandwidth
D= Distance
dref=1
*The ideal free space path loss is n=2. Table 8 shows n values
for different environments at 5.85 GHz with outdoor
transmitters at height of 5.5 meters. An average value to use
for inside a house is 4.7 [6].

11. IEEE 802.11a Physical Layer Simulation – MSc Networks & Data Communications - Kingston University London 11
Table 8.Attenuation values for different environments
After having calculated the SNR value which corresponds
to the equivalent desired distance between the transmitter and
the receiver, it can be placed on Figure 32 to find which is the
best modulation and coding scheme to use for this distance.
In the transmitter’s plot (Figures 17, 22, 25 and 29), the
transmitted constellation, which corresponds to the selected
modulation method, can be seen. If each of this plots is
compared to the signal that is received by the OFDM Receiver
(Figures 18, 23, 26 and 30), it can be easily seen that the white
noise effects on it have distorted the signal and errors have
occurred. As the SNR value decreases the distortion becomes
more intense and eventually data is lost.
To understand the effect of a low SNR in the reception, a
comparison between two scatter plots, for two simulations
(one with 5 dB and one with 25 dB SNR) of the received
signal for 16-QAM modulation with ½ coding rate, can be
examined.
Fig. 33.Received 16-QAM signal with different SNR comparison
On the left plot, the signal does not look at all like a 16QAM.
The signal is distorted, symbols start to overlap each other and
the bit error rate is about 0,5. On the left plot however, the
signal’s reception is quite clear. The constellation resembles
the 16QAM constellation to a great extent. The Bit Error Rate
for this value of SNR is less than 10-4
(Figure 32). The same
procedure can be repeated to compare the received BPSK
signal with SNR=5 dB to a received 16QAM signal with the
same SNR value (Figure 34).
Fig. 34.Received BPSK signal (plot on the left) compared with received
16QAM signal (plot on the right) for 5 dB SNR
The BPSK signal for this SNR value is distorted but not to
an extent that this distortion will impact the connection’s
performance. On the contrary, the 16QAM signal is heavily
distorted and it does not look like a 16QAM constellation any
more. For the BPSK modulation BER is about 10-3
, while for
the 16QAM signal, BER is less than 10-1
(Figure 32).
In real conditions, when the SINR, the available transmitter
power margin, the sensitivity of the receiver etc values
change, adaptive modulation and coding is used to achieve a
better signal quality and a better BER. Adaptive modulation
systems, exhibit better performance (especially over fading
channels with multipath propagation) by exploiting channel
knowledge at the receiver and changing the modulation and
coding rate when it is needed, to achieve a more stable
connection [7].

12. IEEE 802.11a Physical Layer Simulation – MSc Networks & Data Communications - Kingston University London 12
REFERENCES
[1] OFFICIAL IEEE 802.11 WORKING GROUP PROJECT TIMELINES -
2014-11-11 [Online] Available:
http://grouper.ieee.org/groups/802/11/Reports/802.11_Timelines.htm
[2] IEEE-SA Standards Board, IEEE Std 802.11a-1999(R2003),
Supplement to IEEE Std 802.11-1999
[3] John G. Proakis and Masoud Salehi, “COMMUNICATION SYSTEMS
ENGINEERING” 2nd Ed. , Upper Saddle River, New Jersey 07458
August 3, 2001
[4] IEEE Standards Association, "Part 11: Wireless LAN Medium Access
Control (MAC) and Physical Layer (PHY) Specifications", IEEE Std
802.11™-2012, 29 March 2012
[5] Lin Costello, “Error Control Coding” Second edition, Pearson- Prentice
Hall, 2004
[6] Greg Durgin, Student Member, IEEE, Theodore S. Rappaport, Fellow,
IEEE, and Hao Xu, Student Member, IEEE , “Measurements and
Models for Radio Path Loss and Penetration Loss In and Around Homes
and Trees at 5.85 GHz”, IEEE TRANSACTIONS ON
COMMUNICATIONS, VOL. 46, NO. 11, NOVEMBER 1998
[7] Ming jia, Jianglei Ma, Peiying Zhu, Dong-Sheng Yu and Wen Tong,
"ADAPTIVE MODULATION AND CODING", United States Patent
Jia et al., Nortel Networks Limited, 2002