Analysis of Propagation Model in Conformance with IEEE 802.16-2009-based Fixed Wireless Networks

Jaime Jarrín, Paúl Bernal, Román Lara

Abstract—This paper describes a simulator implementation of a propagation model proposed by Yong Soo Cho, which permits to estimate the losses of the wireless channel for a communication system in conformance with IEEE 802.16-2009 Fixed OFDM WirelessMAN. We used Matlab® to program the simulator, which considers the channel losses and reflect their effects on the physical layer. The system implementation considers the modulations defined in the standard, with different channel coding rates. The program permits to obtain results about channel losses, transmit power as a function of BER, transmit power as a function of Eb/No. The channel considers losses produced by the wireless medium with shadowing, and it is related to an AWGN channel described by a standard deviation obtained from the Eb/No produced by the transmit power. We compared Yon Soo Cho, SUI and Free Space models at 3.5 GHz to obtain the bit error probability. The main result showed by Yong Soo Cho model have differed related to SUI model, in the way to estimate the shadowing for that it is determined Yong Soo Cho model is valid for rural areas without changes.

Keywords – WiMAX, SUI, IEEE 802.16-2009, PHY FIXED WIRELESS MAN OFDM

I. INTRODUCTION Any standard for wireless communications technology have

mathematical models which will allow to provide the behavior of a link, to analyze transmission power, modulation used, propagation models, and others; to determine the feasibility of implementing, i.e. models are essential to define the characteristics of a link. Therefore, the main objective of this paper was to provide a simulator for IEEE 802.16-2009 physical layer [2], based on the study made by Yong Soo Cho [1].

This document are performed several studies on the IEEE 802.16-2009 standard, which is an amendment that reviews and consolidates all previous versions of standard leaving them as obsolete. It corresponds to the most stable version to date of WiMAX, which has been thoroughly studied and interpreted in [3]. This paper focuses only on the WirelessMAN FIXED OFDM PHY, on which the studies and analysis are carried out.

The propagation model proposed by Yong Soo Cho motivates the development of this work, since the mathematical model of channel losses allows for designing a wireless channel to simulate the way the noise affects each one of the symbols transmitted through it, and to know the mode of operation and importance of all stages of WiMAX that arise in IEEE 802.16-2009.

II. KEY FEATURES IEEE 802.16-2009 In order to understand the wireless channel design, it is

important to describe the main features that set the standard.

A. Modulation Schemes There are four modulation types defined in IEEE 802.16-

2009. BPSK, QPSK, 16QAM and 64QAM, in which the number of information bits (M) is equal to 1, 2, 4 and 6, respectively.

B. Code Rate The channel encoder is formed by the concatenation of a

Reed-Solomon (RS) block and a convolutional encoder (CC), which, by using the process known as punctured obtains various coding rates. In TABLE I. shows the Reed-Solomon code form, convolutional encoder rate and the resulting rate from the concatenation of two encoders, which will be used for calculations to design of wireless channel [4].

TABLE I. CODE RATES

Modulation RS Code CC rate Combined rate

BPSK (12,12,0) 1/2 1/2 QPSK (32,24,4) 2/3 1/2 QPSK (40,36,2) 5/6 3/4

16-QAM (64,48,8) 2/3 1/2 16-QAM (80,72,4) 5/6 3/4 64-QAM (108,96,6) 3/4 2/3 64-QAM (120,108,6) 5/6 3/4

C. OFDM Signal Parameters The standard defines the elements that characterize the

signal being sent through the wireless channel.

1) Primitive Parameters definitions

- BW: channel bandwidth. - Nused: Number of subcarrier used. - n: Sampling factor. This parameter is related with

the BW and Nused to determine the subcarrier spacing and the useful symbol time. G: This is the ratio of Cyclic Prefix (CP).

2) Derived Parameters definitions

- NFFT: Size of FFT, its value is 256. - Sampling frequency

Fs=floor(n x BW/8000)x8000 (1) - Subcarrier spacing Manuscript received July 18, 2012; revised January 28, 2013; accepted April

7, 2013. Date of publication June 4, 2013; date of current version December 24, 2013. J. Jarrín, C.P. Bernal and R.A. Lara are with the Department of Electrical and Electronic Engineering, Universidad de las Fuerzas Armadas, Quito-Ecuador, 171-5-231B e-mail: (see ttp://wicom.espe.edu.ec/contactos.html

∆f=Fs/NFTT (2) - Useful symbol time

Tb=1/∆f (3) - CP time

Tg=G x Tb (4) - OFDM symbol time

Tsym=Tb+Tg (5) - Sampling time

Tsam= Tb/NFTT (6)

III. PROGRAM DESIGN

A. Propagation Model The model proposed by Yong Soo Cho is based on studies

of a log-normal channel measurement with shadowing obtained by AT&T on its own WiMAX network in rural areas, since it highlights three types of terrain as shown in TABLE II.

TABLE II. TERRAIN TYPES

Type Description A

For hilly terrain with moderate-to-heavy obstacles densities.

B For intermediate paht loss conditions. Medium density of obstacles.

C For flat terrain with light obstacles densities.

Each terrain considered a different shadowing value depending on the number of obstacles present, and is necessary to calculate all the parameters described below to estimate the losses of the channel.

1) Correlation coefficient for the carrier frecuency

It allows the model is compatible with all operating frequencies.

Cf=6log10fc2000

(7)

2) Correlation coefficient for the receive antenna

It allows the prediction of shadowing corrections in the receiver; it depends on the type of terrain that is being estimated.

CRX=  -10.8log10

hRx2

for Type A y B

-20log10 hRx2

for Type C (8)

3) Terrain Factor

It describes the terrain in the mathematical model.

𝛾=a-bhtx+chtx

(9)

The parameters a, b, c depends on the type of terrain and is described in TABLE III. ; hex represents the transmitter height in meters.

TABLE III. PARAMETERS VALUES FOR A,B,C MODELS

Parameter Model Type A Type B Type C

A 4.6 4 3.6 B 0.0075 0.0065 0.005 C 12.6 17.1 20

4) Modified reference

Make a correction to the model so that it is consistent at all distances.

d0' =d010

-  cf  +  CRX10γ (10)

Finally, using (1), (2), (3), (4) and (5) can calculate the propagation loss of the wireless channel as shown in (6).

PL dB =20log10

4πdλ

                                                                 for d≤d0'

20log104πd0

'

λ+10𝛾 d

d0+Cf+CRX for d>d0

' (11)

B. Wireless Channel Design The first thing to do is link budget, which is shown in

Figure 1 is considered the gains and losses of the communication system, this is calculated as indicated in (12) and (13).

Fig. 1. Link Budget

PRxdBm=PTxdBm+GTx+GRx-L [dBm] (12)

L=Pathloss+cableLoss+ConectorLoss  [dB] (13)

where: PRx: Receive power in dBm. GTx: Transmit antenna gain. GRx: Receiving antenna gain. L: Losses. Pathloss: Losses en wireless channel in dB cableLoss: cable loss in dB. ConectorLoss: Connector loss in dB.

Knowing the reception power, the following is to calculate the signal to noise ratio (SNR)

SNRRx=PRxdB-10log(KTaB) (14)  

where: PRxdB: Reception power in dB. (dB=dBm-30)

Ta: Ambient temperature in Ecuador (approximately 18 y 25°C) in Kelvin.

K: Boltzmann constant 1,380x10-23 B: Receiver Bandwidth in Hz.

Then, with the SNR is possible to calculate the bit energy ratio as a function of power spectral density of noise (Eb/No):

EbNodB =10 log Tsym

Tsam+SNR-10log(M) (15)  

where: Tsym: OFDM symbol time Tsam: Sampling time M: Number of information bits

With this, you can finally get the standard deviation (σ) of the channel AWGN (Additive White Gaussian Noise) with shadowing that is intended to design, which will add to the information sent by the channel.

σ= 1

2rateEbNo (16)

where:

rate: code rate used.

C. Implementation of WiMAX transmitter In Figure 2, it is showed the block diagram of the WiMAX

transmitter, which is programmed in MATLAB®, as established by the IEEE standard 802.16-2009, channel coding done by concatenating the Reed-Solomon encoder and convolutional encoder.

Fig. 2. Transmitter block diagram

D. Implementation of Wireless Channel In Figure 3, the wireless channel implementation is

presented as explained in section B, this allows to generate AWGN noise to each OFDM transmitted symbol.

Cálculo de SNR

Pathloss

Receive power

stimation

SNR calculation

Adding Noise

To receiver

From transmitter

Propagation characteristics

Fig. 3. Wireless channel block diagram

E. Implementation of WiMAX receiver Similarly to the transmitter, the WiMAX receiver is

programmed in MATLAB® as shown in Figure 4, it is

considering all the parameters in the standard, using the characteristic of a minimum-distance demodulator and a channel decoder implemented with Viterbi hard decision.

Fig. 4. Receiver block diagram

F. Graphical interface Graphical interface or GUI, is programed only in GUIDE

of MATLAB® and provides a learning environment for the user and allows the following functions:

- Simulation with a string of bits preset - Simulation with an audio signal - Loss of Channel Graph based on the distance - Graphic BER vs. Eb/No - Transmitter power vs. BER graph - Transmitter power vs. Eb/No graph

IV. RESULTS

A. Simulator Figures 5 and show two GUI windows, which allow

calculating channel losses and getting the graph of BER against Eb/No. These two windows represent only one example of the simulator, each of the graphs mentioned in Section III literal F. Graphical interface, may be obtained through this form.

Fig. 5. GUI for calculte channel loss.

Fig. 6. GUI for obtain BER Vs. Eb/No graph

B. Wireless channel losses To estimate losses is used 3.5GHz frequency, transmitter

with a height of 20m and 10m for the receiver, this specs are settled down to simulate rural environments with the most critical case of obstructions using the terrain A. Figure 7 shows the loss of the wireless channel without shadowing correction which is estimated in a loss of 169.6 dB to 5 km, whereas, in Figure 8 is presented channel losses but with the shadowing correction and it is estimated a loss of 165.9 dB.

Fig. 7. Terrain A without shadowing correction

The difference of 3.7dB in both cases is due to the shadowing correction factor proposed by AT&T, which being measured on its rural WiMAX network, they notes that there are fewer propagation losses.

Fig. 8. Terrain A with shadowing correction

C. Validating of the propagation model Because the proposed propagation model is new, it is

essential to compare against other already established, in this case it is selected the model of SUI (Stanford University Interim), which is designed exclusively for WiMAX and adapted from urban areas to rural areas [5], and the free space

model, which is a generic model that only considers the channel losses unobstructed. For the simulations will test the three environments considered the same characteristics: antenna height, bandwidth, and link budget at 5 km, terrain type A and modulation 64QAM ¾.

Figure 9 shows the propagation loss between the three models of study; at 5 km the Yon Soo Cho model’s losses is equal to 165.94 dB, SUI, 171.74 dB and the free space is 117.3 dB. Between free space and Yon Soo Cho model there is a difference of 47.7 dB because the free space model does not consider all the features of the terrain, but against the SUI model, the model of Yon Soo Cho estimated 5.8 dB less.

Fig. 9. Comparison of the three propagation models

Confirming the above, in Figure 10. shows the results of sending bits across the three channels, as previously mentioned because the free space model has such low losses, its bit error probability (Pberror) is always zero, while between SUI and Yon Soo Cho model there is a difference of 0.2W. The main difference is shadowing considerations for each model, while SUI uses a value set to 8.2dB, the proposed model performs a prediction of the shadowing corrections, this is due to the difference of 5.8dB between the models, indicating that in rural environments there are fewer obstructions, then the shadowing is lower and resulting that a lower power is required to achieve an error-free transmission.

Fig. 10. Validating the model

100 101 102 103 10440

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120

140

160

180

200Modelo de Yon Soo Cho, fc=3.5GHz

Distancia[m]

Path

loss

[dB]

htx=20 [m],hrx=10[m], terreno=A

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200Modelo de Yon Soo Cho, fc=3.5GHz

Distancia[m]

Path

loss

[dB]

htx=20 [m],hrx=10[m], terreno=A

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-50

0

50

100

150

200Comparación Pérdidas de Propagacion, fc=3.5GHz, htx=20 [m],hrx=10[m], terreno=A

Distancia[m]

Path

loss

[dB]

Modelo de Yon Soo ChoEspacio LibreModelo del Sui

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

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Pberror Vs. PTx

Pber

ror b

it

PTx [W]

Modelo Yon Soo ChoModelo SUIEspacio Libre

D. Relations between the transmit power and BER In a real-life transmission, at the time of link budget

calculation, it’s goal is always looking for a power transmission which allows us to reduce the BER, that just in case you can’t increase the antenna gain; that’s why this simulator can make that estimation, in the case of these simulations is used a transmit power from 0 to 1W, 100mW step, transmitting antenna height of 20m, 10m receiving antenna, the link budget calculation at 5 km, additional losses 2.8dB, BW equal to 3.5MHz, G = 1/16.

The result of this simulation is shown in Figure 11, which is observed the behavior of the BER of all modulations with all code rates defined in the standard, this is related to the Eb/No.

But what is meant to obtain a relationship between Ptx and BER, for this it is necessary the use of Figure 12 in which indicate the relationship between transmit power and the Eb/No previously indicated in Figure 11. Then, with the result of the previous figures can be obtained TABLE IV. which is a summary of the results obtained, this allows to know the required transmit power for each of the modulations in order to obtain an error-free communication (BER = 0).

Fig. 11. BER Vs.Eb/No

TABLE IV. RELATIONSHIP BETWEEN PTX AND EB/NO

Modulation Eb/No [dB] for BER=0 Ptx [mW] BPSK 4 <100

QPSK 1/2 6 <100 QPSK 3/4 6 <100

16 QAM 1/2 8 <100 16 QAM 3/4 10 200 64 QAM 2/3 12 400 64 QAM 3/4 12 600

Fig. 12. Ptx Vs. Eb/No

V. DISCUSION After making a comparison with the model of SUI, the

propagation model proposed by Yon Soo Cho is valid, and highlights its functionality only for rural areas, which is designed initially.

If the desired use of modulation with a higher encoding rate, it requires more transmit power for an Eb/No which allows free communication errors in transmission.

This simulator provides the basic features of WiMAX, which can improve efficiency by using turbo codes instead of the channel coder implemented by concatenating Reed-Solomon, and convolutional code, this is described in the advanced part of the standard IEEE 802.16-2009, also considers implementing the Viterbi soft decision decoder.

VI. ACKNOWLEDGMENTS The authors gratefully acknowledge the contribution of

Universidad de las Fuerzas Armadas ESPE for the support in the development of this project through the Wireless Communications Research Group (WiCOM).

REFERENCES [1] Soo Cho, Yong, “MIMO-OFDM WIRELESS COMMUNICATIONS

WITH MATLAB ”, Wiley-IEEE PRESS, Noviembre 2010. [2] IEEE, “IEEE Standard for Local and metropolitan area networks.Part

16: Air Interface for Broadband Wireless Access Systems”, http://standards.ieee.org/getieee802/download/802.16-2009.pdf

[3] Barajas, Héctor, “WiMAX”, http://es.scribd.com/doc/63052555/Equipo-2-WiMax-Documento, publicado 16 de Febrero de 2011.

[4] Haykin, Simon “MODERN WIRELESS COMMUNICATIONS”, Segunda Edición, Prentice Hall, Estados Unidos de América 2005.

[5] Shahajahan, Mohammad, “Analysis of Propagation Models for WiMAX at 3.5 GHz”, http://es.scribd.com/doc/54217861/28/Stanford-University-Interim-SUI-Model.

[6] Yánez, Álex, “Diseño de una red WIMAX (IEEE 802.16e) que brinde servicios de voz y datos en el sector de Sangolquí”, Escuela Politécnica del Ejército, Sangolquí Septiembre 2008

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Pb e

rror

BER vs Eb/No G=1/16

BPSKQPSK1/2QPSK 3/416QAM 1/216QAM 3/464QAM 2/364QAM 3/4

0 0.2 0.4 0.6 0.8 1-10

-5

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25

30Ptx Vs Eb/N0 G=1/16, BW=3.5GHz

Ptx [W]

Eb/N

0 [d

B]

BPSK 1/2QPSK 1/2QPSK 3/416QAM 1/216QAM 3/464QAM 2/364QAM 3/4

[7] Galvis, Alexander “Modelos de canal inalámbricos y su aplicación al diseño de redes WiMAX”, Universidad Pontificia Bolivariana, Medellín 2006.

[8] Signal To Noise Ratio, http://www.rfcafe.com/references/electrical /snr.html .