Abstract—Based on the analysis of the technical principles and the system model of the MIMO and OFDM technologies, a simple MIMO-OFDM wireless communication system is constructed. The system is composed of transmitter, channel, receiver, and so on. Space-time coding is done in the transmitter, the signal is launched after OFDM modulation, and the process of the receiver is the inverse process of the transmitter. The system performance is simulated by using the software Matlab, the experiment result shows that the MIMO-OFDM wireless communication system has better performance when there are more antennas. But, with the increase of the carrier number, the system performance will reduce because of the interference between sub-carriers.
Keywords - MIMO; OFDM; Matlab; space time coding; wireless communication
I. INTRODUCTION
Looking backward the development process of the wireless communication, the first generation of mobile communication system can only provide voice service. The second generation digital mobile communication system has better performance, but the bandwidth is restricted[1].The 3G system can enhance the data rate and cover the global earth, but with the continuous development of data, images, video, and other multimedia applications, the available data rate will be quickly saturate.
The demand on the bandwidth of the communication system is higher and higher. In view of the shortage of bandwidth spectrum nowadays, in order to transmit data with high speed and high capacity, the wireless communication should have very high spectrum efficiency and the capacity of overcoming the channel fading in the environment of multi-path channel. It is very difficult to match these requests for the traditional modulation technique, but the MIMO-OFDM system combining the OFDM and MIMO technologies can meet the requirements.
Based on studying MIMO and OFDM, a simple MIMO-OFDM system is constructed, and its performance is simulated.
II. BASIC THEORIES
With the rapid development of wireless data and multimedia applications, the demand on transmission rate and QoS assurance of wireless communication system is
correspondingly rising, the OFDM and MIMO technologies are gaining more and more attention[2].
A. MIMO Technology MIMO which is short for Multiple Input Multiple
Output uses multiple antennas at the same time in the transmitter and receiver of the communication system, and it can increase the transmission rates by using the random fading and multi-path propagation. Its key technology is space-time signal processing, that is, it processes the signal by using several time domain and space domain. The MIMO technology is a very effective method of increasing the capacity of the channel and system[3].
We suppose that the number of the transmitting antennas is MT, transmitted signal is sj(t),j=1,…,MT, the number of the receiving antennas is MR, received signal is yi(t),i=1,…,MR, then the relation between the transmitted signal and received signal is written as:
Ri
M
jjjii Mitntsthty
T
,...,1,0),()()()(1
,
Where, hi,j(t) denotes the channel impulse response between the transmitting antenna of number j and the receiving antenna of number i. The channel of the MIMO system can be expressed by a matrix:
)()()(
)()()()()()(
(
,2,1,
,22,21,2
,12,11,1
ththth
thththththth
tH
TRRR
T
T
MMMM
M
M
The receiver with multi-antenna can separate and decode the data stream by using advanced space-time coding, and get the best processing method. In particular, because the N sub-streams are sent to the channel at the same time and each transmitted signal occupies the same frequency band, the bandwidth is not increased. If the channels are independent, the MIMO system can create a number of parallel space channels. It is sure to increase the data rate by using these channels to transmit information independently.
For a MIMO system with N transmitting antennas and M receiving antennas, it is assumed that the channel is independent Rayleigh fading channel and N, M are very large, then the channel capacity C is
2009 International Conference on Information Technology and Computer Science
2min( , ) log ( / 2)C M N BWhere, B is the signal bandwidth, is the average signal-to-noise of the transmitter, min(M, N) is the smaller of M and N. The above formula shows that the maximum capacity of the system will increase linearly with the raise of the minimal number of antennas when the power and bandwidth are fixed. MIMO technology can improve immensely the capacity of wireless communication system and the channel reliability, as well as reduce the error rate
The structure of the MIMO system is as figure 1.
Figure 1. MIMO system structure
B. OFDM OFDM which is short for Orthogonal Frequency
Division Modulation is a multi-carrier modulation technology. Firstly, it converts the high-speed serial data stream to low-speed parallel string which can be transmitted in N sub-channels. Then, the technology modulates them by N sub-carriers which are orthogonal with each other. Lastly, the N modulated singles are sent together. The destination receives them with relevant sub-carrier, and restores the original high-speed data by parallel/serial conversion[4].
Suppose that T is the width of the OFDM symbols, Nis the number of sub-channels, fc is the carrier frequency of sub-carrier of number 0, di (i=0,1,…,N-1) is the data symbol allocated to each sub-channel,
otherwiseTt
tretc,0
2,1
Then, the OFDM symbols can be expressed easily, and the equivalent complex baseband notation is
1
0exp 2
2
0
N
i s si
s s
s s
T is t d retc t t j t tT
t t t T
s t t t t t tFor the system with larger N, the equivalent complex
baseband signal can be achieved with inverse discrete Fourier transform method. We make ts=0 and ignore the rectangular function, and the sample rate is T/N, so that
1
0
2exp 0 1N
k ii
iks s kT N d j k NN
It can be seen that sk can be equivalent to IDFT operations of di. Simply, in order to restore the original symbol di, the receiver carries out the inverse transform.
According to the above analysis, we can see that the modulation and demodulation of the system can be
replaced by IDFT/DFT. By the N-point IDFT operation, the frequency domain symbol di is transformed to time domain symbol sk. After radio frequency carrier modulation, the symbol is sent to wireless channel.. Each of output data skof IDFT is the superposition of all sub-carrier signal.
The system structure is as figure 2. The Insertion of the protection interval can eliminate the inter-symbol interference. Usually, the protection interval should be larger than the largest multi-path delay length, so, the code interferences can be prevented from.
Figure 2. OFDM system structure
III. DESIGN OF MIMO-OFDM SYSTEM
A. Combination of MIMO and OFDM OFDM inherits the characteristics of multi-carrier
parallel modulation and corresponding growth of symbol from the traditional MCM. It is very easy to achieve accurate symbol synchronization with the help of the guard interval or cyclic prefix, the sub-symbol interference of the dada transmission in the wireless channel with serious multi-path delay can be overcome effectively. Moreover, OFDM has another advantage that it has unique frequency domain block modulation and frequency domain channel equalization technology, and it can reduce the estimated calculation amount and the complexity of hardware design and enhance the utilization of the spectrum greatly.
With the original transmission bandwidth and power consumption, the MIMO technology can make full use of the multi-path channel between the transmitter and receiver, and transmit parallel multi-channel data independently or partly independently, which greatly enhances the spectrum usage efficiency of wireless transmission.
MIMO system can use the multi-path component of the transmission to a certain extent, that is to say, MIMO can resist multi-path fading, but for frequency selective deep fading, the MIMO system remains powerless. The nowadays solution method of frequency selective fading of the MIMO system is to use a balanced technology in general, another method is to use OFDM which is the core technology of the next-generation mobile communications. The new technology requires extremely high frequency spectrum utilization, but the function to improve the spectrum utilization is limited by OFDM. Exploring space
( )s kˆ( )s k
DestinationSpace- time
coding
Space-time
decodingSource
558557557557557557557557557557557555555
resources based on OFDM, that is, MIMO-OFDM, can provide a higher data rate.
B. MIMO-OFDM system model The MIMO-OFDM wireless communication system is
based on packet only for the analog antenna number is 1×2, 2×2, 2×3, and 2×4, and it can support 64, 128, 256 and 512 point FFT transform, the number must be greater than 10 and less than FFT point number, modulation may be BPSK or QPSK, convolution code rate is 1/2, 2/3 or 3/4, channel type is Rician or Rayleigh, and we suppose the sub-channels are independent[5]. We assume that the estimate of the receiver is ideal and the number of packets can not be set too small. The system model is as figure 3.
Figure 3. MIMO-OFDM system structure
1) Transmitter model Suppose that the original signal is a sequence of 0,1
and the average is 0.5, the packet length is decided by the size of the FFT that the number of packets is made by simulation input.
We send the packet which is transmitted in different signal to noise ratio and simulate the simulation system performance under different signal to noise ratio. The convolution encoding of the original data can greatly enhance the coding gain and decrease the complexity. The system provides 3 coding rate: 1/2, 2/3 and 3/4. In order to simulate different carrier number and FFT point, the system uses a zero-filling technology which can prevent the inter-carrier interference of the OFDM system. The original is modulated after the signal processing, the system can select BPSK or QPSK. According to the given antenna number, the system implements the transmission Diversity of MIMO, that is, the signals are assigned to each of the antennas averagely, and then OFDM or IFFT is carried on, and cyclic prefix added to each signal of antenna is used as protection interval. In this simulation, we assume that the maximum delay is 200ns, protection interval is 800ns, bandwidth is 20MHz,. 2) Channel model
For the signal of the each channel with multi-path propagation, the fading and delay are changed randomly. Then, the received signal after the multi-path propagation is the composition of all channels’ signals with different fading and delay[6].
Suppose that the transmitted wave is tA 0cos , the received signal after n paths propagation can be written as:
01
( ) ( ) cos[ ( )]n
i ii
R t t t t
where: )(ti is the amplitude of the received signal of channel i; )()( 0 tt ii , and )(ti is the transmission delay of channel i which is different with different time;
A large number of observation shows that the change of )(ti and )(ti with the change of time is very slow compared with the cycle of launching carrier frequency, that is, )(ti and )(ti are slow-changed random process.Suppose that:
n
iiic ttX
1
cos)()( , n
iiis ttX
1
sin)()(
Then, the received signal can be expressed as: 0 0
0
( ) ( )cos ( )sin
( )cos[ ( )]c sR t X t t X t t
V t t twhere, V(t) is envelopment of synthesis wave R(t), and
)(t is the phase.
2 2( ) ( ) ( )( )( ) arctan( )
c s
s
c
V t X t X tX t
tX t
)(ti and )(ti are changed very slowly, so, )(tX c ,)(tX s and V(t), )(t are changed slowly. Then, R(t) can
be seen as a narrow-band process, and the received signal envelopment V(t) is subjected to rayleigh distribution.
)(2)(2
xuexxfx
Where, is the average power of the received signal, and )(xu is unit step function.
0001
)(xx
xu
When there is line-of-sight transmission between transmitter and receiver, the received signal envelope does not obey the Rayleigh distribution but Ricean distribution. The latter is often defined by the Ricean coefficient K which is the power ratio of channel average weight to scattering weight. Then the probability density function of the Ricean distribution is as follows:
)()1(2)1(2)( 0
)1( 2
xKKxIeKxfK
K
Where I0 is the first class zero-order modified Bessel function which is defined as
2
0
cos0 2
1)( dexI x
When there are no direct transmission path, K=0, I0(0)=1. Rice probability density function is degraded to Rayleigh probability density function 3) Receiver model
559558558558558558558558558558558556556
The signal reaches the receiver through channel. The processing of the receiver happens to be the reverse process of the transmitter.
Firstly, the receiver removes the cyclic prefix of the signal, and then carries through FFT transform and gets the signal before OFDM. As the zero-filling is implemented before, then, the receiver should get rid of them to convert it to coherent signal. In the simulation, we assume that the receiver knows about channels, that is to say, the receiver has perfect estimate of the channels, then the Zero-Forcing can be done.
According to the channel impulse response, the receiver demodulates the corresponding BPSK or QPS and restores the original information, and the total process is completed.
IV. SYSTEM IMPLEMENTATION
The MIMO-OFDM wireless communication system is implementation by the software Matlab. In order to get better simulation results, we assume that the number of packets is 1000, since there are no direct light channel in the actual mobile communications, we select Rayleigh channel as the channel and BPSK model, and the convolution coding rate is 1/2.
Figure 4 shows the system performance that the point number of FFT is 64,16, the number of antennas is 1×2,2×2,2×3 and 2×4. In general, the system performance is better as the antenna number increases. The system performance with 2×4 antennas excels that with 2×2 antennas.
Figure 4. System performance with different antenna numbers
Figure 5 shows the system performance with 2×2 antenna and 16,32,64,128 carriers. The system performance decreases with the increase of the carrier number, especially, the increase is very obvious when the antenna number is from 16 to 32, but the system performance is similar when the antenna number is 32, 64 or 128.
Figure 5. System performance with different carrier number
V. CONCLUSION
Based on summing up the work of our predecessors, we brings forward a simple MIMO-OFDM wireless communication system. The system structure is very simple and it is simulated by matlab. The experiment results show that the system has good performance when there are more antennas especially the number of the receiver antennas is greater than that of the transmitter antennas and the other conditions are the same. But, the increase of the carrier number can decrease the system performance because of the interference between each sub-carrier.
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[4] A. Naguib, N. Seshadri, and A. R. Calderband. “Increasing data rate over wireless channels”, IEEE Signal Processing Mag. vol. 9,. pp.76-92, May 2000.
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