This document summarizes a simulation of an IEEE 802.16-2004 OFDM physical layer model in MATLAB. The model includes key parameters like modulation type, bandwidth, SNR, delays, and more. By changing these parameters, their effects on performance metrics like BER are observed. Key findings include higher SNR and larger bandwidth resulting in better performance with more widely spaced constellation points and lower BER. Larger cyclic prefix also improves performance by reducing inter-symbol interference. The document concludes the model is viable for analyzing important WiMAX parameters and their impacts.

1. 
Abstract—This paper describes an end to end base band model
of the physical layer of a WiMAX (Worldwide Interoperability
for Microwave access) system in a simulated environment
(MATLAB), which follows the IEEE® standard 802.16-2004. It
models the OFDM- based physical layer which is known as the
Wireless MAN (the 802.16 family of standards) in IEEE. By
changing different parameters in the model results and variations
are observed. The model parameters changed or observed by the
variations in the result are the rate id (identification), channel
bandwidth, cyclic prefix, SNR (Signal to Noise Ratio), discrete
path delays, BER (bit error ratio) and the Amplifier Non
Linearity.
Index Terms— 802.16-2004, OFDMA WIMAX Wireless
Internet.
I. INTRODUCTION
The IEEE 802.16-2004 models the OFDM-based physical
layer supporting all mandatory coding and modulation
options.It also shows Space-Time Block Coding (STBC), an
optional transmit diversity scheme allocated for use on the
downlink. It shows the implementation of digital pre-
distortion, a process for extending the linear range of a
nonlinear amplifier. The standard specifies the air interface of
fixed broadband wireless access (BWA) systems supporting
multimedia services[r]. OFDM (Orthogonal Frequency
Division Multiplexing) is developed to support high data rate
and can handle multi carrier signals. In mobile WiMAX FFT
size can varies between 128 and 2048 and to keep the
subcarrier spacing at 10.94 KHz, the FFT size should be
adjusted which is helpful to minimize Doppler spreads.Since
there are different channel bandwidth like, 1.25, 5, 10 and 20
MHz etc. FFT sizes are 128, 512, 1024 and 2048 respectively.
For OFDMA-PHY, the suitable symbol time is 91.4 μs and the
symbol duration is 102.9 μs and number of symbols in 5 ms
Frame is 48.0 [9].
Abbreviation definition:
1. OFDM: Orthogonal frequency Distribution
Multiplexing
2. SNR: Signal to noise Ratio
3. WiMAX: Worldwide Interoperability for Microwave
access
4. Hz: Hertz (Kilo or Mega)
5. FFT: Fast Fourier Transform
6. FEC: Forward Error Correction
7. NumGuardBand: Number of Guard Bands
8. Rate ID: Rate Identification
9. The ISI(inter symbol Interference)
10. QAM-: Quadrature Amplitude Modulation
11. CP: Cyclic prefix
12. dB: decibel
13. BPSK: Binary Phase shifting key
14. MIMO: multipath output channel
15. AWGN: Additive white Gaussian noise
16. OFDM-PHY/OFDM-PHYLINK: OFDM based
Physical Layer
17. NSC/fs: Basic symbol length
18. NG/S: length of the cyclic prefix
19. T: Length of OFDM symbol
20. NU: Number of Subcarriers
21. GUI: Guide
II. SIMULATION OF IEEE 802.16-2004 OFDM PHY LINK,
INCLUDING SPACE-TIME BLOCK CODING
The simulation was run from the model which displayed
five different windows. By double clicking on the model
parameters block on the model, it shows the channel band
width at 3.5MHz, the cyclic prefix factor (G) at 1/8, low SNR
(Signal to Noise ratio) thresholds for rate control (dB) at
values [4 10 12 19 22 28]. It was also observed from the
model that the amplifier non-linearity has been set to
‘disabled’.
A. Run the simulation model
The simulation results after running the model shows
following:
Fig 1 WMAN 802. 16-2004 OFDM PHY with STBC.
The communication system model of the WiMAX model
has the transmitter, channel and receiver which are typical in
telecommunications. From Fig 1 it was observed that the
transmitter blocks are the FEC (Forward Error Correction) and
modulator bank along with the OFDM modulator pilot. The
channels of the model are the MIMO (multipath output
Wireless Broadband Internet
Akinola Leo B. Dasilva 08196366, University of Hertfordshire, School of Engineering and
Technology.

2. channel) and the AWGN (Additive white Gaussian noise)
channel shown in Fig1. The receiver of the systemas shown in
Fig 1 also are the OFDM demodulator and demodulator block
along with the FEC bank.
What is carried out in the system is a generation of random
bit data that models a downlink burst consisting of an integer
number of OFDM symbols which is sent for forward error
correction (FEC). Modulation is then carried out using one of
the BPSK, QPSK, 16-QAM or 64-QAM. After modulation the
OFDM signal is transmitted among several subcarriers to the
channels and finally the reverse of the transmission mediumis
implemented in the receiver (from modulation to
demodulation) [6].
B. OFDM Subcarriers
The total amount of OFDM subcarriers used in the model is
256.
Fig 2 FEC & ModulatorBank Subsystem
By double clicking the FEC and Modulator bank block the
channel block model is observed to get the total amount of
data subcarriers. The function block labelled R which is
highlighted in Fig 2 outputs the number of data subcarriers
and the number of FDM symbols respectively. The total
number of data subcarriers as shown by the output of the
highlighted function block is 192.
Fig 3 PILOT Block Subsystem
The pilot block was double clicked to display its channel
block in Fig 3. The total number of pilot subcarriers is 8. From
Fig 3 it is observed that the total input of the input packing
block (highlighted in the diagram) is 8 which is being sent to
the sample block.
Fig 4 Demodulator and FEC Bank block Subsystem
Part of the OFDM Demodulator property is the number of left
and right guard subcarriers which is shown in the model
parameter of the OFDM Demodulator block subsystemas
NumGuardBand carriers. The multiport switches (one
highlighted in Fig 4) show the number of left and right guard
band subcarriers. The left guard band has a total of 28
subcarriers (from 7 to 1). In particular, the multiport switch
highlighted shows the value of the right guard band. From Fig
4 it is observed that a bias value of -1 is sent to the BPSK
which makes the right guard band a total of 27 subcarriers.
With all these observations the totalsubcarriers add up to 256.
C. The Rate ID Parameter
The rate ID is defined by WiMAX standard. In Fig 2 which
is the FEC and Modulator Bank Subsystem, it is observed that
different rate ID are assigned to the 7 modulation blocks. The
Rate ID simply shows the modulation technique used by the
model.
Fig 5 RateID showing the rate ID value as 0.
The rate ID with value 0 is the BPSK modulation technique.

3. Table1. Showing Sets of Seven Rates for OFDM-PHY.
D. Comment(s) on Transmitted and Received Spectrum and
Constellation Diagram.
After running the simulation, the results are given below:
Fig 6 Constellation diagram of the received signal
After running the model, the constellation appears to be
scattered which shows that there is noise in the system.
Fig 7 Spectrum Plot of the Transmitted Signal
The spectrum plot in Fig7 shows 2 transmitted signals out
of phase.
Fig 8 Spectrum plot of the Signal at the channel Output
From the constellation diagram it is observed that there is
noise in the system because of the separation of the
constellation spots, which indicate distortion in the system.
The spectrum plot of the transmitted signal shows the two
transmitted signals. The spectrum plot of the Signal at the
channel output shows clearly the waveform of a BPSK
modulation due to the phase reversal also known as phase
shift.
E. Changing Bandwidth and observation ofPerformance
1. Changing the bandwidth from 3.5MHz to 1.5MHz
Fig 9 WMAN 802. 16-2004 OFDM PHY with STBC at
1.5MHz Bandwidth.
2. Changing the bandwidth from 1.5MHz to 4.5 MHz
Fig 10 WMAN 802. 16-2004 OFDM PHY with STBC at
4.5MHz Bandwidth.
When the Bandwidth parameter changes,the amount of
subcarriers shown on the transmitted diagram change. From
the two diagrams it is observed in the Spectrum plot of the
transmitted signal at 1.5MHz compared to the same plot at
4.5MHz the subcarriers are less. The SNR value also
changes.At 4.5MHz the SNR value is -0.1737 while the
SNR value at 1.5MHz is 0.8333. It can be concluded from
these values that there is less noise at the smaller bandwidth
which has the higher SNR value. The constellation diagram
also shows that the constellation points are more widely
spread in the 4.5MHz bandwidth.
F. Changing cyclic prefix for observation of performance
In wireless transmission the transmitted signals might be
distort by the effect of echo signals due to presence of
multipath delay. The ISI(inter symbol Interference) is totally
eliminated by the design when the CP (cyclic prefix) length G
is greater than multipath delay. After double clicking the
model parameters block, the cyclic prefix was changed.The

4. two different values which gave different outputs were 1/32G
and ¼G:
Fig 11 WMAN 802. 16-2004 OFDM PHY with STBC at ¼G .
Fig 12 WMAN 802. 16-2004 OFDM PHY with STBC at
1/32G.
At 1/32G the SNR is 0.8383 and the BER is 0.1915 while at
1/4G the SNR of the systemis 0.4493 while the BER is
0.1897. It is observed from these values that when the cyclic
prefix is reduced there is less noise in the system because of
the higher SNR value. With higher SNR value also implies a
lower BER of the system.
G. Changing SNR for observation of performance
The signal to noise ratio is a ratio that consists of the
amplitude of the signal,the amplitude of the noise. The SNR
block in the Channel subsystem showsthe SNR based on
received signal power.[5]
The SNR value was changed initially to 30dB, which shows
the constellation, points closer that when they were at 1dB
initially.
Fig 13 SNR at 30db
FIG 14 SNR at 20dB
SNR(dB) SNR Est. BER(G) RATE ID
30 21.64 0 4
25 19.92 0 4
20 17.24 0 3
15 13.33 0.0003776 3
14 12.6 0.006169 3
13 10.64 3.553e-05 2
Table 2 Showing values at different SNR (dB)
The constellation diagram of the SNR (dB) is spread,which
decreases the separation between the adjacent states . The
change of the rate ID means the change of the modulation
technique. The subcarriers reduce or increase when a different
modulation technique is used.
H. Fixed SNR
Keeping the SNR of the systemfixed at 15dB, the delay from
[0 0.4 0.9] to [1 0.8 1.8]. The SNR changed from 13.33 to
12.82 while the BER changed from 0.0003776 to 0.001114.
Changing the delay increased the amount of noise in the
systemslightly. Distortion is observed from the constellations

5. points on the signal.
Fig15. SNR at 15dB and delay path at [1 0.8 1.8]
Multipath fading of the channel is done by tapped delay line
matrix. This type of fading is modelled as a tapped delay line
with 3 taps with non-uniform delays [29]. The gain associated
with each tap is characterized by a distribution (Rician with a
K-fact>0, or Rayleigh with K-fact =0) and the maximum
Doppler frequency [8].
The modulation depends on the amount of data to be
transmitted over the channel. If the amount of data increases
the modulation technique will follow suit by using the rate id
to signify which modulation technique to use.Therefore, the
modulation technique is dependent on the rate ID.
I. Non-linearity in the Model.
After the introduction of non-linearity in the model from the
model parameters GUI, the rate ID is 1, the Est. SNR(dB) is
6.71 and the BER is zero. The signal distortion is at the
received signal. The amplitude output and phase difference
has changed,
Fig16 Output of the Non-linearity Ideal Model.
The transmitted signals have a no constant power envelop.
This means that any non- linearity in the transmitter will cause
in-band noise and adjacent channel interference; the distance
of the WiMAX broadband Internet will be reduced [1].
J. Plot SNR Versus BER
Theoretical values were inserted in the simulation to find out
Bit Error Rate against Signal-to- Noise Ratio for all different
bandwidths.
BW(MhZ) CPs BER Est
SNR
Errors SNR
3.5 1/4 0.2709 -1.0657 31219 1
3.5 1/32 0.2669 -0.4301 37226 1
10 ¼ 0.2648 -1.824 87761 1
10 1/32 0.2688 -2.809 107925 1
3.5 ¼ 0.00678 0.6697 781 4
3.5 1/32 0.006819 1.552 961 4
10 ¼ 0.0072 0.4749 2386 4
10 1/32 0.007071 -0.7297 2839 4
Table 3 Showing values from simulation
From the table it can be observed that as the Est SNR
decreases from the top to bottom, so does the BER increase
also from the top to the bottom.
k. Calculation of Data rate
The length T of OFDM symbol is the basic symbol length
added to the length of the cyclic prefix which is represented as
T= NSC/fs +NG/S. each symbol contains NU subcarriers that
carry Mbit of information each. Hence the bit rate R is
(excluding FEC): R =NU*M/T =NU*M*fs/(NSC+NG). The
data rate depends on the bandwidth, level of signal used and
the channel[3].
III. CONCLUSION
This paper described analyses of the WiMAX model,
simulations and real time subsystems have shown the viability
of this approach. Important parameters like SNR, the
estimated SNR, the delay, bandwidth, rate ID and the cyclic
prefix were observed to see how they affect the signal
generated by the 802.16-2004 OFDM PHYLINK, WITH
SPACE TIME . The rate ID determines what modulation
technique will be used. WiMAX has freedom to select QAM
and QPSK as its modulation techniques depending on the
situation. WiMAX adjusts its modulation scheme based on
signal to Noise Ratio (SNR). To maintain SNR, WiMAX used
different modulation schemes such as; for SNR = 22dB, the
modulation is 64QAM, for SNR=22dB, the modulation is
16QAM and for SNR=9dB, modulation is QPSK etc [7].
To maintain the frequency orthogonality and reduce the delay
due to multipath propagation,cyclic prefix is added in the
OFDM signals. In wireless communication the data are
transmitting through the wireless channel with respective
bandwidth to achieve higher data rate and maintain quality
service.
Bit error rate is one parameter used to access the systemthat
can transmit digital signal from one end to the other end. If
transmitter and receiver’s medium are good at a particular
time and signal to noise ratio (SNR) is high then Bit error is
very low.
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