4x4 TimeDomain MIMO
encoder with OFDM Scheme in WIMAX Context
Mohamed.Messaoudi^{1},
Majdi.Benzarti^{2}, Salem.Hasnaoui^{3}
AlManar University, SYSCOM
Laboratory / ENIT, Tunisia
^{1}messaoudi.jmohamed@gmail.com, ^{2}benzarti.enit@yahoo.fr, ^{3}Salem.Hasnaoui@enit.rnu.tn
Abstract The Standard Worldwide Interoperability for
Microwave Access (WiMAX) offers the opportunity to develop applications that
require more bandwidth and increased communication up to 50 km. Through
literature reviews, the coding block is done in the frequency domain of the
OFDM chain in a wireless communication system. This solution offers outstanding
performance within the meaning of binary error rate and throughput. We propose
to design a Simulink model of 4x4 OFDM transmission chain for WIMAX context and
using a coding block in the temporal domain to test system performance and
compare it to the one used in the frequency domain .We use the IEEE 802.16
standard [1] for the construction of the OFDM symbol, the generation of the
preamble and the choice of the cyclic prefix length. Our choice is situated to
test the performances of the system when the coding block is in the temporal
domain. Our simulated chain offers a slightly better performance than the chain
where the MIMO encoder is located in the frequency domain. This approach
provides the ability to expand the number of transmitting antennas without
revising all of the calculations.
KeywordsMIMO Encoder; WIMA; ODFM; BER; SNR (Eb/No);
IFFT/FFT; performance
Through studies of
literature [2], we found that the coding STBC block is located in the frequency
domain of the chain [3]. i.e. the output of the constellation is reconstructed
through block coding sequences as N such that N is the number of transmit
antennas. Each sequence contains samples and replicas join other samples in
other sequences. Each sequence is the amount of information in the OFDM symbol.
This context provides a good performance in the wireless communication system.
Our goal is to achieve an OFDM chain in the context WiMAX and the block coding
is located in the temporal part to compare it with the chain where the coding
block in the frequency domain. Then we propose to send and receive the same
OFDM symbol through four antennas.The
IEEE 802.16 standard introduces the multicarrier modulation OFDM. OFDM is
based on the simultaneous transmission of multiple orthogonal frequencies
narrow, often called OFDM subcarriers. The number of subcarriers is often
noted N frequencies that are orthogonal to each other [4]. This orthogonality
substantially eliminates interference between channels and greatly reduces
intersymbol interference (ISI) by avoiding multiple frequencies for selecting
channels. Each frequency is modulated with a possibly different digital
modulation. If the transmitted signal is attenuated over a subcarrier, we can
get to another.The frequency associated with each of these
channels is then much smaller than if the total bandwidth is occupied by a
single modulated. This is known as a single carrier. With OFDM, the
communication system provides a smaller frequency bandwidth for each channel is
equivalent to greater time periods and then better resistance multipath
propagation. To transmit each K symbol on separate frequencies, we are in a
position to add an encoder with a rate
performances of the proposed
transmission scheme are analyzed via simulations. A comparative study with the
OFDM transmission scheme where the MIMO encoder is performed behind pilot
insertion. Finally, the conclusion is drawn in section V.
2.1
Brief
description of the OFDM transceiver chain
The simulated chain consists of two
main parts: the OFDM transceiver chain and the multiantenna MIMO channel in
WIMAX context.
The simulated chain is as follows:
Figure 1 OFDMMIMO Scheme in Time Domain Case
The encoded data will be punctured to adjust the rate of
transfer in WIMAX from rate
2.2 MIMO encoder technique
a.
Transmitter
The structure of space time block
coding for this case is as follows:
Each OFDM symbol contains 256
complex samples.
The signal is converted to the time
domain by means of the inverse fast Fourier transform (IFFT) algorithm. After
that, a cyclic prefix (CP) with the aim of preventing intersymbol interference
is added and the resulting signal has a length of
At time t0: the samples s1, s2 and s3 are respectively sent
through the antenna number 1, 2 and 3. For four consecutive times, the
TimeDomain MIMO encoder finishes sending the three samples and so on until the
entire OFDM symbol. The following table describes the sending structure of
these samples:
Table 1 Distribution of samples on the antennas during the
time
Time 
Antenna
n° 

1 
2 
3 
4 

t_{0} 




t_{0}+T 




t_{0}+2T 




t_{0}+3T 




Our transmission system is modeled
by the following equation:
b.
Receiver
At the reception, we need the channel estimation to properly
detect the transmitted data. We must solve (1) at the end to extract the
samples sent
For each recipient antenna
The channel coefficients are:
Where
Then (4) is as follows:
The input data for the MIMO decoder is:
The output of the MIMO decoder
è
The duration of transmission the sequence which contains a
modulated OFDM symbol and the cyclic prefix through the Rayleigh Channel can be
equal to
3. SIMULATION
RESULTS
The OFDM signal is transmitted over
the Rayleigh channel for various values of the signal to noise
ratio (SNR). To evaluate the performance of each value of SNR, the received
signal is demodulated and the data received will be compared to the original
information. The simulation result is in the form of curves of the bit error
rate and throughput over many signals to noise ratios (SNR). In this part we
are interested in comparing the MIMOOFDM scheme in the case where the MIMO
encoder is situated in the frequency domain with the OFDMMIMO scheme where the
MIMO encoder is located in time domain (after IFFT modulation).
Table 2 Simulation Parameters [1] and [5]
Simulation Parameters 

Standard 
IEEE 802.16
(Fixed WIMAX) 
Channel
Bandwidth 
5 Mhz 
Source Coding 
Convolutif
(1/2) 
Time Domain
MIMO Encoder 
OSTBC
(4Tx4Rx) 
Cyclic Prefix
Length 
1/4 
Constellation 
BPSK, QPSK,
16QAM, 64QAM 
Useful symbol
period Tb 
44,44
(μs) 
Gard Time
Tg=Tb/G(μs) 
11,11
(μs) 
Subcarrier
spacing (KHz) 
11.2 
IFFT Length 
256 
Data
Subcarrier Used 
200 
Number of
pilot Subcarrier 
8 
Upper guard 
28 
Lower guard 
27 
NDC 
1(prefix 128) 
Maximum
Number of Antennas 
4 
Channel model 
Rayleigh 
Based on the parameters in Table 2, the MIMOOFDM
transmission scheme is simulated in MatlabSimulink software. Figure 2 presents
the variation of Bit Error Rate
Table
3 BER values vs. SNR for different MIMO systems
SNR/MIMO 





0,1 
0,1 
0,003 
0,0085 

0,1 
0,04 
0,002 
0,0002 

0,04 
0,02 
0,0002 
0,00004 

0.01 
0.005 
0.00004 
0.00002 
Figure 2. Bit Error Rate as a function of signal to noise
ratio for different antenna system
Figure 3 Bit Error Rate as a function of signal to noise
ratio for different constellation
In MIMO channel, when we increase
the number of transmission and/or reception antenna, dramatically increase the
performance. In figure 2, the bit error rate is equal to 0.1 for 2X1 MIMO
system and decreases to 0.0085 for 4x4 MIMO systems to a value of signal to
noise ratio that is equal to 4. Increasing the value of the signal to noise
ratio, we notice a significant decrease in bit error rate. For the same value
of the signal to noise ratio, we show that the value of the bit error rate for
4x4 MIMO systems is the lowest. In figure 3, we extract the bit error rate for
4x4 MIMO systems at different modulation. Performance is better for the BPSK
modulation for low values of signal to noise ratio. With a
gradual increase in the signal to noise ratio, we find that the big order
modulations would be better. Comparing with the performance of MIMOOFDM system
in the frequency domain, we derive the bit error rate is somewhat low.
3.
CONCLUSION
This
contribution introduces a Time Domain MIMO encoder where the bloc of MIMO
encoder is situated in the time domain. Our study prepares us to simulate a
MIMOOFDMMIMO scheme that encodes both in the frequency and time domains. This
solution permits designer to adjust multiple 4x4 MIMO blocks to perform higher
order MIMO systems. For example, if we want to design an OFDM chain with 16
antennas, we can insert two blocks MIMO encoder with 4 antennas. This solution
provides us the ability to expand the number of transmitting antennas without
revising all of the calculations.
[1] IEEE Computer
Society & IEEE Microwave Theory and Techniques Society, “IEEE Standard for
Local and metropolitan area networksPart 16: Air Interface for Fixed Broadband
Wireless Access Systems”, October 2004, Volume 895
[2] Hardeep Kaur,
M.L Singh “Bit Error Rate Evaluation of IEEE 802.16 (WiMAX) in OFDM System”,
February 2012, Volume 40– No.12
[3] Amalia Roca, Inc” Implementation of a WIMAX
simulator in Simulink” Vienna, February 2007, pp.69, Volume 127
[4] MarcAndré Cantin, Laurent Moss & Guy
Bois, ” WiMax 802.16: Version 5.0”,23 February 2007, Volume 18
[5] Loutfi Nuaymi, John Wiley & Sons
Inc”WIMAX: Technology for Broadband Wireless AccessPart Two: WIMAX Physical
Layer” 2007, Volume 310