Implementation of MIMO-OFDM with Equalization for Frequency Selective Channels
Abstract— : With increasing number of users, large data being generated and limited bandwidth available for systems, efficient multiplexing techniques are needed that use the available bandwidth efficiently. Also due to big data applications, the data rate requirement has also increased form kbps to almost Gbps. To address the issues of high bandwidth and data rate requirement, yet limited bandwidth availability, MIMO based networks are becoming very popular for wireless networks. In this present work, Space time block coding (STBC) is used for MIMO systems to implement massive MIMO practically. The multiplexing technique used is Orthogonal Frequency Division Multiplexing (as used by wireless LANs, WANs etc.) for better spectral efficiency.
Zero Forcing equalization is used to revert the negative effects of the channel. The performance is evaluated in terms of Bit Error Rate (BER) and it has been shown that the proposed technique achieves lesser BER compared to previously existing techniques.
Keywords—Internet of Things (IoT), Multiple Input Multiple Output (MIMO), Space Time Block Coding (STBC), fading, Bit Error Rate (BER)
I. INTRODUCTION
Internet of Things (IoT) is an ecosystem of connected physical objects that are accessible through the internet Presently, both fixed Wireless Networks and Mobile Ad-hoc Networks are facing the following challenges:
increasing number of users
increased bandwidth requirement for multimedia applications
overall limited bandwidth availability.
Hence Multiple Input-Multiple Output (MIMO) and Massive MIMO based networks are being used to face the challenge especially in IoT applications. MIMO systems enhance the channel capacity even at same bandwidth. OFDM increases the spectral efficiency and is widely used in LANs and WANs.
.Fig.1 Physical representation of IoT To combat the effect of frequency selective fading, multiple input multiple output is generally combined with orthogonal frequency- division multiplexing system, which transforms the frequency-selective fading channels into parallel flat fading sub channels, as long as the cyclic prefix inserted at the beginning of each orthogonal frequency-division multiplexing symbol is longer than or equal to the channel length. The signals on each subcarrier can be easily detected by a one-tap frequency domain equalizer. In cases where a short cyclic prefix (CP) is inserted for growing bandwidth efficiency, before because of some unforeseen channel behavior scheme, the effect of Pranjali Singh Tiwari
M.Tech Scholar (EC) JNCT, Rewa
Prof. Sushil Chaturvedi Asst. Professor (EC)
JNCT, Rewa
frequency-selective fading cannot be completely eliminated, and inter carrier interference and inter symbol interference will be introduced. The signals on each subcarrier can be easily detected by a one-tap time domain equalizer. Equalization techniques are thus important in multiple input multiple output-orthogonal frequency-division multiplexing access systems
These multiple input multiple output wireless technique, combined with orthogonal frequency- division multiplexing, in have allowed for the easy transmission of symbols in time, or frequency and space. Now different coding systems have been developed [2]. The example is the Alamouti Space Time Block code which could extract spatial and temporal diversity. And many other codes have also been proposed which have been able to achieve some or all of the available diversity in the channel at various transmission rates.
The space time block coding (STBC) is a technique used in wireless communications system to transmit multiple copies (data) of a data stream across a number of antennas and to exploit the various received versions of the data to improve the reliability of data-transfer system.
The fact that the transmitted signal must traverse a possibly difficult environment through scattering, reflection, refraction and so on and may then be additional corrupted by thermal noise in the receiver means that some of the received copies of the data will be 'better' than others technique. This redundancy results in a higher chance of being able to use one or extra of the received copies to correctly decode the received data. In fact, space combines all the copies of the received signal in an optimal way to extract as much information from every of them as possible.
There are two main types of space-time codes, namely space-time block codes and space-time trellis codes. Space-time block codes operate on a block of input symbols, in producing a matrix output whose columns characterize time and rows represent antennas system [4]. It is contrast to single-antenna block codes for the AWGN
channel communication, and space-time block codes (STBC) do not generally provide coding gain, and unless concatenated with an outer code.
These code symbols are generated by the space- time encoder in such a way that coding gains, as well as high spectral efficiency are achieved.
Their main feature is the provision of full diversity by very simple decoding scheme. The Space-time coding finds its application in cellular communications system well as in wireless local area networks.
II. BASICS OF EQUALIZATION UNDER FREQUENCY SELECTIVE CHANNELS
The concept of equalization is fundamentally very important to mitigate the effects of noise and distortions induced by a channel. The equalizer tries to mitigate the effects of the wireless channels that cause distortions at the receiver. It can be seen that the equalizer acts just prior to the receiver after sensing what the channel has done to a signal. . In mobile radio channels always changes and multipath causes time dispersion of the digital information is known as inter-symbol-interference, it makes too difficult to detect the actual information at the receiver. Moreover it cannot be rectified even by increasing the signal power at the transmitting end. Therefore such errors are called irreversible errors. The only way out is to reverse the detrimental effects using equalizers so as to improve the reliability of communication through wireless and broadcast modes.
Let the channel have an impulse response h(t).
Since any practical system can sense the channel in the discrete time domain, therefore the channel impulse response can be re-considered as h(n).
Let the channel in the frequency domain be H(z).
Then the output of the channel is:
𝒚 𝒏 = 𝒙 𝒏 ∗ 𝒉(𝒏) (1) 𝒀 𝒛 = 𝑿 𝒛 . 𝑯(𝒛) (2) Where, * stands for convolution
x(n) is the input to the channel y(n) is the output of the channel
The aim at design of an equalizer is the design of a system with a transfer function
𝑬 𝒛 = 𝟏
𝑯(𝒛) (3) There are several ways in which the system with the transfer function E(z) can be practically implemented.
Fig.2 Use of Equalizer in Data Network The different techniques result in different equalizer structures. Different equalizer structures can be Linear Equalizers, MLSE Equalizers, Zero Forcing Equalizers, Adaptive Equalizers, and Decision Feedback Equalizers etc.
III. MIMO SYSTEMS
In multiple-input multiple-output (MIMO) communications, the system is equipped with multiple antennas at both the transmitter and the receiver technique. The multiple antenna scheme gives a more reliable performance through array gain, diversity and spatial multiplexing. These concepts are briefly discussed below.
The growing demand of multimedia services and the progress of Internet related contents lead to increasing interest to high speed communications network. The requirement for flexibility and wide bandwidth imposes the use of efficient transmission systems that would fit to the characteristics of wideband channels especially in wireless environment where the channel is very challenging process. In wireless environment the signal is propagating since the transmitter to the receiver along number of different paths, collectively referred as multipath communication.
While propagating the signal power drops of due to the following effects: a path loss, macroscopic fading and microscopic fading. The fading of the signal can be mitigated by different diversity
methods. To obtain diversity, in signal is transmitted through multiple independent fading paths in time, frequency or space and combined constructively at the receiver.
Fig.3 Block Diagram of a generic MIMO system
𝑹𝒙𝒙 = 𝑬{𝑿𝑿𝑯} (4)
Orthogonal frequency division multiplexer transforms the frequency-selective fading channels into parallel flat fading sub channels, as long as the cyclic prefix inserted at the beginning of each orthogonal frequency division multiplexer(OFDM) symbol is longer than or equivalent to the channel length.
IV. SPACE TIME BLOCK CODING (STBC) STBC stands for space time block coding.
It is the process of re-arranging data bits/
data packets in the form of a matrix in which:
Number of Columns = No. of MIMO transmitters
No. of Rows = No. of time slots needed to transmit the entire data
The STBC technique is used to practically implement massive MIMO systems practically.
V. OFDM
Orthogonal Frequency Davison Multiplexing is one of the major factors for high data rates and spectral efficiency. The comparative spectra of FDM and OFDM are shown in figure below.
Fig.4 Spectrum of FDM and OFDM The mathematical condition for the orthogonality of two signals is given by:
𝒙𝟏 𝒕 . 𝒙𝟐 𝒕 𝒅𝒕 = 𝟎𝟎𝑻 (5) Here,
x1(t) is the first signal x2(t) is the second signal T is the time period
For, N signals, the condition becomes:
𝒙𝟏 𝒕 . 𝒙𝟐 𝒕 𝒙𝟑 𝒕 … … . 𝒙𝒏(𝒕)𝒅𝒕 = 𝟎𝟎𝑻 (6)
The graphical equivalent is the coincidence of the crests of one signal with the nulls of the other.
VI. PROPOSED METHODOLOGY Step-1:-
Generate random binary data for a MIMO system.
Step-2:-
Generate orthogonal signals for OFDM.
OFDM utilizes the spectrum efficiently.
Step-3:-
Apply Space Time Block Coding (STBC). It is a technique in which we re-arrange the data in the form of a matrix with the number of columns equal to the number of transmitters and number
of rows equal to the number of time slots needed to transmit the entire bit stream i.e.
C=i, where C = no. of columns and I is number of Transmitters
R=t, where R= no. of rows and t is number of time slots
This step is often referred to as MIMO encoding.
Step-4:-
Design different channel models i.e.
1) AWGN 2) Nakagami 3) Rayleigh 4) Rician Step-5:-
Obtain the signal after passing through channel by multiplying the frequency domain signal and channel frequency response i.e.
Y(f)=X(f).H(f) Where,
Y(f) is signal after passing through channel H(f) is channel frequency response
X(f) is the frequency domain signal before passing through channel.
Step-6:-
Design and apply equalization. The equalizer used in this work is the zero forcing equalizer.
The equalizer response should be the inverse of the channel i.e.
E=1/H.
The zero forcing equalizer tries to force the mean square error (mse) of the channel estimation to zero.
Step-7:-
Apply MIMO decoding.
Step-8:-
Compute the bit error rate (BER) and Spectral efficiency of the system.
BER = (No. of error bits at receiver)/(Total number of transmitted bits)
Spectral efficiency is the data rate obtained per Hertz of bandwidth i.e. in bits/s/Hz
VII. SIMULATION RESULTS
The BER performance and spectral efficiency for different fading channels is shown below. The evaluation parameters are:
1) BER
2) Spectral efficiency.
The results have been compiled for four different channels.
The simulations are carried out on MATLAB (Matrix Laboratory) due to the availability of in built mathematical functions and tools to support wireless communications and models. The BER and spectral efficiency analysis ensues.
Fig: 5 Performance of OFDM over AWGN channel
Fig: 6 Performance of MIMO-OFDM over AWGN channel
Fig: 7 Spectral Efficiency of MIMO-OFDM over AWGN channel
Fig: 8 Performance of OFDM over Nakagami channel
Fig: 9 Performance of MIMO-OFDM over Nakagami channel
Fig: 10 Spectral Efficiency of MIMO-OFDM over Nakagami channel
Fig: 11. Performance of OFDM over Rayleigh channel
Fig: 12 Performance of MIMO-OFDM over Rayleigh channel
Fig: 13 Spectral Efficiency of MIMO-OFDM over Rayleigh channel
Fig: 14 Performance of OFDM over Rician channel
Fig: 15 Performance of MIMO-OFDM over Rician channel
Fig: 16 Spectral-Efficiency of MIMO-OFDM over Rician channel
CONCLUSION -: It can be seen from the previous slide that the BER obtained in previous work is between 10-3 and 10-4 at an SNR of 15dB In the proposed work, a BER of almost 10-5 is obtained at an SNR of 10dB Hence it can be seen that for lesser SNR needed, the proposed system achieves lesser BER compared to previous work. Moreover, the proposed system analyzes and tests the BER performance for 4 different channel models i.e. AWGN, Nakagami, Rayleigh and Rician while the previous work considers only an AWGN channel.
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