MIMO OFDM using USRP

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MIMO-OFDM system implementation using GNU Radio and USRP Arjun Balakrishnan (B100303EC), Arjun P (B100155EC), Dhanush Joseph (B100701EC) Jaivendra Singh (B100874EC), Jom Joji George (B100736EC) Project Guide : Dr. A.V Babu, Associate Professor, Dept. of ECE

Abstract—In all communication systems present today, high data rate with low latency at the minimum cost is a constant demand of any user. But this requires many changes in the hardware organization. Multiple transmit and receiver antennas featuring capability for multiple input and output also called MIMO systems are a recent development that has revolutionized the communication industry by its high spectral efficiency as well as its robustness against fading and interference. Combining MIMO with orthogonal frequency division multiplexing (OFDM), it is possible to signicantly reduce receiver complexity as OFDM greatly simplies equalization at the receiver. The aim of the project is to implement a MIMO-OFDM system using GNU radio and USRP.

I.

I NTRODUCTION

OFDM is one the most pervasive modulation technique that has found it’s way in protocols such as IEEE 802.11, 4G LTE, etc and forms the backbone of major communication systems present today. Along with OFDM the other technology that has made the high speed next generation systems possible is Multiple-Input Multiple-Output (MIMO). MIMO helps to achieve high throughput and channel capacity with the aid of additional diversity gain. The combined effect of robustness of the OFDM along with the high throughput of MIMO has laid the foundation of high data rate wireless communication networks commonly known as MIMO- OFDM systems. Not only are these systems capable of providing high data rate services at low latency but also with better spectral efficiency even under severe fading environments. The hardware implementation of the MIMO-OFDM system is complex and to overcome this challenge we have used the Software Defined Radio. Initially, developed with the purpose of emulating many radios at the same time, SDR today has evolved into a indispensable tool for research in the fields of wireless and mobile communication providing a highly flexible and cost effective way for researchers to experiment. A SDR emulates real world hardware and allows the user flexibity in setting the parameters governing a system without any limitations. The components that are typically implemented in hardware like the mixers, filters, amplifiers, modulators/demodulators, detectors, etc. are instead implemented by means of software. [3] In our project we will use the open source GNU radio project as the SDR platform. GNU radio is one of the most advanced and extensively used environment available to develop SDR based application. It uses a combination of C++ and Python

to optimize DSP performance while providing an easy-to-use application programming interface. [4] To implement the MIMO-OFDM system in a real time environment we will use Universal software Peripheral Radio (USRP) hardware. The USRP is designed to allow general purpose computers to function as high bandwidth software radios. It basically serves as a digital baseband and IF section of a radio communication system. II. L ITERATURE S URVEY The key factor for successful communication is to transmit and receive the exact information signal. This is made possible with the help of various modulation techniques. Even today, we use not only the traditional ways of modulation like analog modulation but also advanced methods like Wi-Fi and 3G. Each kind of communication has its own importance with respect to complexity, efficiency, accessibility and demand. With the migration from third generation (3G) to fourth generation (4G) and expanding wireless standards, there is always a demand for newer and more reliable techniques. There has been an increase in the research being done done in the field of MIMO-OFDM systems. Some of the researches and projects that we came across are mentioned below. [15] M Viberg et al did a simualation of the MIMO system in Simulink and Embedded Matlab and tested the impact of various components like antennas on Bit Error Rate(BER).[16] Hemanth Sampath et al conducted a series of field tests to establish the performance of the MIMO communication systems. The incresed capacity and reliability are evident from the test results. [1] Yong Soo Cho et al studied the implementation of MIMO system using Matlab. [2] Similar work was crried out by Jiang Xuehua et al [14] Bloessl et al came up with the first prototype of a GNU Radio based OFDM receiver for IEEE 802.11a/g/p networks. [13] Marwanto et al conducted an experimental study of OFDM Implementation using GNU Radio and USRP-SDR wherein they seek to implement an OFDM radio signal transmitter and receiver with various modulation schemes on GNU radio using a USRP kit. A comparison is done between communication using OFDM with BPSK modulation and that using QPSK modulation. [3] Marcos Majo et al came up with a design and implementation of an OFDM-based communication system for the GNU platform. The objective in this project was to have a working prototype system for wireless communications using OFDM in its physical layer and reliable data transmission provided by an error correction mechanism.

III.

M OTIVATION

While studying about the present day high data rate technologies such as 4G, WiFi, etc some of the factors which caught our attention were the constant need to expand the bandwidth in such systems inorder to accomodate the growing number of users and provide support for bandwith intensive applications like audio and video transmission and the huge cost involved in implementing these systems. This motivated us to try study and implement a system which would encompass all the properties of a high speed system and at the same time be cost-effective and highly flexible. Thus, we took the task of implementing such a MIMO-OFDM system using the seminal concept of software defined radio or more specifically the platform of GNU Radio with USRP. IV.

To overcome this challenge there exists another highly innovative technique of Othogonal Frequency division multiplexing. A. Basics of MIMO Multiple-input and multiple-output, or MIMO is the use of multiple antennas at both the transmitter and receiver to improve communication performance. MIMO technology has attracted attention in wireless communications, because it offers significant increases in data throughput and link range without additional bandwidth or increased transmit power. It achieves this goal by spreading the same total transmit power over the antennas to achieve an array gain that improves the spectral efficiency (more bits per second per hertz of bandwidth) and/or to achieve a diversity gain that improves the link reliability (reduced fading).

A NALYSIS OF MIMO-OFDM

In order to resolve the problems of capacity and high data rate in the challenging radio environment, a novel idea to use the Multiple Element Array (MEA) at both ends of the wireless communication systems was implemented. These wireless systems were referred to as , Multiple-Input Multiple-Output (MIMO) systems having multiple transmit and multiple receiver antennas. Orthogonal frequency division multiplexing provides several advantages over the traditional FDM approach to communications channels. More specifically, OFDM systems allow for greater spectral efficiency reduced inter-symbol interference (ISI), and resilience to multi-path distortion. MIMO uses precoding, spatial and diversity multiplexing to achieve reliable and high data rate communication. Precoding refers to all spatial processing that occurs at the transmitter. In (single-stream) beamforming, the same signal is emitted from each of the transmit antennas with appropriate phase and gain weighting such that the signal power is maximized at the receiver input. The benefits of beamforming are to increase the received signal gain, by making signals emitted from different antennas add up constructively, and to reduce the multipath fading effect. In spatial multiplexing, a high rate signal is split into multiple lower rate streams and each stream is transmitted from a different transmit antenna in the same frequency channel. If these signals arrive at the receiver antenna array with sufficiently different spatial signatures and the receiver has accurate channel state information, it can separate these streams into (almost) parallel channels. Spatial multiplexing is a very powerful technique for increasing channel capacity at higher signal-to-noise ratios (SNR). Diversity multiplexing techniques are used when there is no channel knowledge at the transmitter. In diversity methods, a single stream (unlike multiple streams in spatial multiplexing) is transmitted, but the signal is coded using techniques called space-time coding. The signal is emitted from each of the transmit antennas with full or near orthogonal coding. Diversity coding exploits the independent fading in the multiple antenna links to enhance signal diversity. Because there is no channel knowledge, there is no beamforming or array gain from diversity coding. But, MIMO systems face lack of robustness and are vulnerable to inter symbol interference (ISI).

Fig. 1 :

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The MIMO system model

Figure 1 shows the MIMO system model i.e. the relation between transmitted and received data streams as the channel matrix H. MIMO Systems can provide two types of gain : 1) Spatial Multiplexing Gain - Maximize transmission rate (optimistic approach) 2) Diversity Gain - Minimize Pe (conservative approach) Spatial Multiplexing : Spatial multiplexing is a transmission technique in MIMO wireless communication to transmit independent and separately encoded data signals, so-called streams, from each of the multiple transmit antennas. Therefore, the space dimension is reused or multiplexed. If the transmitter is equipped with Nt antennas and the receiver has Nr antennas, the maximum spatial multiplexing order (the number of streams) is, Ns = min(Nt , Nr )

if a linear receiver is used. This means that a maximum of Ns streams can be transmitted in parallel, ideally leading to an Ns increase of the spectral efficiency. MIMO spatial

multiplexing achieves this by utilising the multiple paths and effectively using them as additional ”channels” to carry data. Diversity : Each pair of transmit-receive antennas provides a signal path from transmitter to receiver. By sending the SAME information through different paths, multiple independently-faded replicas of the data symbol can be obtained at the receiver end. Hence, more reliable reception is achieved. A diversity gain d implies that in the high SNR region, Pe decays at a rate of 1/SN Rd as opposed to 1/SNR for a SISO system. The maximal diversity gain dmax is the total number of independent signal paths that exist between the transmitter and receiver.

./multiplecarrier.PNG Fig. 2 :

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The different sub-carriers

The working of an OFDM system is similar to that of a muliti-carrier system where the available spectrum is divided into many small bands and the data to be send is divided into parallel data streams and transmitted on a seperate band which has sinc(πf T ) spectra for sub-carriers. The signal to be transmitted can be expressed as shown below: s(t) = cos(2πfc t + θ) s(t) = cos(2πfc t)cos(θ) − sin(2πfc t)sin(θ).....eqn(1) let cos(θ) = a and sin(θ) = b. which gives

For an (MR , MT ) system, the total number of signal paths is MR MT .

s(t) = Re{(a + jb) exp(j2πfc t)} s(t) = Re{d exp(j2πfc )}.....eqn(2) where d = a + jb is the complex modulated signals, N is the number of sub-carriers and s(t) = Re{u(t)} The OFDM signals are obtained by the addition of the N sub-carriers. This is shown in figure 3.

1 ≤ d ≤ dmax = MR MT The higher the diversity gain, the lower the Pe .

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sb (t) = Re{ B. Basics of OFDM Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies. A large number of closely spaced orthogonal sub-carrier signals are used to carry data on several parallel data streams or channels. Each sub-carrier is modulated with a conventional modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low symbol rate, maintaining total data rates similar to conventional single-carrier modulation schemes in the same bandwidth. [12] In the older systems using techniques like Frequency Division Multiple Access(FDMA), the total available bandwidth is divided into N non-overlapping sub-channels and multiplexed. Overlapping is prevented by keeping guard bands between the sub-carriers. Even though it is an effective system as it prevents Inter Channel Interference(ICI), use of guard bands between each of the sub-carriers leads to wastage of bandwidth. To overcome this the sub-carriers are replaced with N overlapping sub-carriers which are orthogonal and separated by T1 . The sub-carriers have been modulated using Phase Shift Keying(PSK) or Quadrature Amplitude Modulation(QAM). The amplitude spectrum of the signal is equal to sinc(πf T ) , which is zero for all frequencies f that are an integer multiple of 1/T, where T is the time period. This effect is shown in figure 2 which shows the overlapping sinc spectra of individual subcarriers. At the maximum of each subcarrier spectrum, all other subcarrier spectra are zero. Because an OFDM receiver calculates the spectrum values at those points that correspond to the maxima of individual subcarrier, it can demodulate each subcarrier free from any interference from the other subcarriers.

N −1 X

dn exp(j2πnfc t)}.

n=0

./subcarriers.PNG Fig. 3 :

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The OFDM signal

Considering the discrete case, IDFT is performed on the complex data sequence dn and we obtain: N −1 X

s(m) = Re{

n=0

dn exp(

N −1 X 2πn m)} = Re{ dn exp(2πfn tm )} N n=0

n where fn = and tm = mT amd m = 0, 1, 2....N − 1. NT The reduction of the symbol rate by N times, results in a proportional reduction of the relative multi-path delay spread. To completely eliminate even the very small ISI that results, a guard time is introduced for each OFDM symbol, as illustrated in figure 4. The guard time must be chosen to be larger than the expected delay spread, such that multi-path components from one symbol cannot interfere with the next symbol. It the guard time is left empty, this may lead to inter-carrier interference (ICI), since the carriers are no longer orthogonal to each other. To avoid such a cross talk between sub-carriers, the OFDM symbol is cyclically extended in the guard time. This ensures that the delayed replicas of the OFDM symbols always have an integer number of cycles within the FFT interval as long as the multi-path delay spread is less than the guard time. To minimize the SNR loss due to the guard-time, the symbol duration must be set much larger than the guard time. But an increase in the symbol time implies a corresponding increase in the number of sub-carriers and thus an increase in the system

complexity. A practical design choice for the symbol time is to be at least five times the guard time, which leads to an SNR loss that is reasonable.[10] ./isi.PNG Fig. 4 :

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Inter Symbol Interference

Summary of advantages of OFDM : 1) High spectral efficiency as compared to other double sideband modulation schemes, spread spectrum, etc 2) Can easily adapt to severe channel conditions without complex time-domain equalization. 3) Robust against co-channel interference, intersymbol interference (ISI) and fading caused by multipath propagation. [12]

C. GNU Radio SDR was devised with the sole objective of reducing the dependence of a communication system on hardware to minimum and emulating these dedicated signal processing devices in software. This translation into software would make all the processing possible on an all-purpose commodity PC. This not only makes SDR a cost effective technique but also a solution which obviates the restrictions in the form of suitable hardware availability. Moreover, SDR allows users to set the system properties according to their needs thus providing very high flexibility. GNU Radio: In our project we shall use GNU Radio, a powerful open source tool to develop SDR applications.GNU Radio is primarily developed using the GNU/Linux operating system, but, Mac OS and Windows are also supported. GNU radio comprises of two types of modules first the ones that take care of the signal processing needed in the system and second are the parts of GNU radio that interconnect these signal processing modules and let us configure them according to our needs. In GNU Radio, a radio system is represented as a directed signal flow graph where graph vertices are known as signal processing blocks and edges indicate a connection between the two blocks. Data flows in one direction from a signal source to one or more signal sinks. This construction of software radio is similar to development of hardware radios, but with an additional restriction that the signal flow in a flow graph cannot form a feedback cycle, so implementation of any feedback mechanisms must be contained within one signal processing block. The signal processing modules are programmed in C++ and are usually in the form signal filters, equalizers, FFT modules, etc. Whereas, the connecting modules are programmed in Python.Using a high level language like Python allows users to quickly create different applications by constructing a signal flow graph simply by making connections between smaller building blocks. GNU Tools 1) GRC GRC is a graphical tool which provides a user interface that lets us create signal flow graphs and activates its source code. This graphical interface, by means of

graphical blocks, allows us to set the input parameters which are taken by the source code of each block in order to generate a signal flow.There are mainly four kinds of blocks: • Source blocks: Their main functionality is to generate an output signal by means of some input parameters. For this reason, these blocks have no input signal. There are many types of sources, depending on the number of output ports, data type, vector lengths, etc. • Sink blocks: In this case, there is no output signal. Sink blocks receive an input signal with a specific data type and length, and, using certain input parameters, the input signal is stored in a vector, file or sent to a binded TCP1or UDP2 socket. • Operation blocks: These blocks use a configurable number of input signals with configurable data types, to produce a certain number of output signals with specific data types, using the input parameters to perform a certain operation on the samples at the input. These operations can be modulations or demodulations, coding operations, filters, synchronizations, type or stream conversions, etc. • Visualization blocks: These blocks can be classified as a type of sink block which generates a graphical output from the input signals. In this group of blocks, we can mention scopes to provide a time domain representation, FFT sink for a frequency domain screening, constellation plots, etc. 2) C++ Signal processing blocks process streams of data from their input port to their output port. The input and output ports of a signal process block are variable. So a block can have multiple outputs and multiple inputs. The signal processing blocks are written in C++. 3) Python About Python,it is a script language is used to connect the signal processing blocks together. In Python the necessary signal sources, sinks and processing blocks are selected and configured with the correct parameters. GNU Radio modules are able to operate with infinite streams of data of a certain type. Figure 5 shows the system diagram of a MIMO-OFDM system. To test the MIMO-OFDM system in real time environment additional hardware is required for transmiting and receiving signals known as the Universal Software Radio Peripheral (USRP). The USRP is a device designed by Ettus Research with the objective of converting between the digital baseband signal that is processed in the host computer and the analog intermediate frequency (IF) signal when necessary. The USRP has been specifically developed for SDR and it is highly compatible and commonly used with the GNU Radio software suite to create complex softwaredefined radio systems. The USRP hardware driver (UHD) is the device driver provided, which supports Linux, MacOS, and Windows platforms. Several frameworks including GNU Radio, LabVIEW, MATLAB and Simulink use UHD. The USRP has an architecture in which a motherboard provides the following subsystems: clock generation and synchronization, FPGA, ADCs,DACs, host processor interface,

Fig. 5 : MIMO - OFDM System Diagram

and power regulation. These are the basic components that are required for baseband processing of signals. A modular front-end, called a daughterboard, is used for analog operations such as up/down-conversion, filtering, and other signal conditioning.This modularity permits it to serve applications that operate between DC and 6 GHz. Figure 6 illustrates the basic block diagram of USRP.

USRP/USRP 2 system. Basically what it does is to perform high bandwidth math, and to reduce the data rates to something you can squirt over USB2.0 /GE ON USRP/USRP 2 respectively •

Daughter boards On the mother board there are two slots . One of these slots is for TX and the other is for RX . Each daughter board slot has access to ADC/DAC . The daughter boards are used to hold the RF receiver interface or tuner and the RF transmitter.

In stock configuration the FPGA performs several DSP operations, which ultimately provide translation from real signals in the analog domain to lower-rate, complex, baseband signals in the digital domain. In most use-cases, these complex samples are transferred to/from applications running on a host processor, which perform DSP operations. The code for the FPGA is open-source and can be modified to allow high-speed, lowlatency operations to occur in the FPGA.

Fig. 6 : USRP Block Diagram Some important parts inside USRP are as • • •

ADC Section There are 4 high-speed 12-bit ADC converters. The sampling rate is 64M samples per second. In principle, it could digitize a band as wide as 32MHz. DAC Section At the transmitting path, there are also 4 high-speed 14-bit DA converters. The DAC clock frequency is 128 MS/s, so Nyquist frequency is 64MHz. FPGA Understanding what goes on the USRP/USRP 2 FPGA is the most important part for the GNU Radio users. All the ADCs and DACs are connected to the FPGA. This piece of FPGA plays a key role in the

V.

C URRENT S TATUS

We started with exploring the tools and functions related to GNU Radio. But since, GNU Radio is a very complex software it requires a good grasp on it’s basic structure and understanding of programming languages like python and C++ to design various signal modules. With our current level of understanding we were able to implement a basic OFDM modulator and analyse the frequency response for the same.

A. Observations

Fig.Theoretical Frequency response

Fig.Increased Noise floor

We observed that the simulated frequency response obtained was similar to theoretical response of an OFDM system.

Fig.Decreased Overtones

Fig.Observed frequency response Some other observations made were:

1) The system has bandwidth of 15kHz and a noise floor of -50dB. 2) GNU Radio allows one to vary Noise voltage and the multiplication constant while observing the response. 3) When the noise voltage was increased the peak of frequncy response remained constant whereas the amplitude of sidelobes(noise floor) increased. This as can be inferred will result in lossy communication where the demodulator would not be able to function properly due to excessive noise. 4) When the overtones defined for OFDM modulator was decreased from 200 to 50 the bandwidth reduced.

B. Channel Estimation Channel Estimation is the process of characterizing the effect of the physical medium on the input sequence. Even with a limited knowledge of the wireless channel properties, a receiver can gain insight into the data sent over by the transmitter. The main goal of Channel Estimation is to measure the effects of the channel on known or partially known set of transmissions. Orthogonal Frequency division multiplexing (OFDM) Systems are especially suited for channel estimation. The sub carriers are closely spaced. While the system is generally used in high speed applications that are capable of computing channel estimates with minimum delay. Training Based Channel Estimation Channel is estimated based on the training sequence which is known to both transmitter and receiver. The receiver can utilize the known training bits and the corresponding received samples for estimating the Channel. • Least Squares(LS)

Fig.OFDM Modulator in GNU Radio

•

Minimum Mean Squares(MMSE) Least Squares

The Least Squares Error (LSE) estimation method can be used to estimate the system by minimizing the squared error between estimation and detection In matrix form, it can be written as y = Xh So the error e can be defined as e = y” − y Where y is the expected output. The squared error (S) can be defined as S = |e|2 S = (y” − y)2 S = (y” − y)(y” − y)t

Where superscript t stands for complex transpose of a matrix. S = (y” − Xh)(y” − Xh)t

This equation can be minimized by taking its derivative w.r.t hand equating it equal to zero. The final equation we get is: h = (X t X)−1 X t y which can be written as h = (X −1 y) This equation can be implemented on SISO as well as MIMO systems. Problem in implementing MIMO When inputs are transmitted from Tx antennas, they are affected by the channel. Each Rx antenna is receiving signals from each Tx antenna. Now the received signal at Rx antenna is not a product of single channel response and single input signal but it is combination of signals from each Tx antenna multiplied with their respective channel responses. Solution • To overcome this problem matrix properties were exploited. • Instead of using one pilot, two pilots were used. • The use of two pilots were to make the matrices square and the number of equations must be equal to the number of unknown variables. • Then equating the equations channel response for each channel is calculated. • Use of multiple pilots is a drawback in multiple antenna system.

lsmim1.jpg Fig.Theoretical Channel Scatterplot(LS MIMO) lsmimes.jpg Fig.Estimated Channel Scatterplot(LS MIMO) lsf.jpg Fig.Frequency Response and Normalised Frequency Response(LS MIMO)

Problem in implementing MIMO When inputs are transmitted from Tx antennas, they are affected by the channel. Each Rx antenna is receiving signals from each Tx antenna. Now the received signal at Rx antenna is not a product of single channel response and single input signal but it is combination of signals from each Tx antenna multiplied with their respective channel responses. Received signal is combination of all the transmitted signals following their own paths. In MMSE matrix properties cannot be utilized as was the case in LS. The algorithm does not include simple matrix operations

Minimum Mean Squares The MMSE estimator minimizes the mean-square error. If X is transmitted over a channel h such that y = Xh Error Error is given as

Solution • First we train our receiver for all channels • The pilot is transmitted from each transmitter separately • At a time all the inputs except for one Tx are zero. • Using the MMSE technique and set of equations, channel response will be calculated for each channel. mmsea.jpg

e = y” − y Fig.Theoretical Channel Scatterplot(MMSE MIMO) where y is the expected output Mean square error=mean (y” − y)2 =

E = (y” − y)2

mmsees.jpg Fig.Theoretical Channel Scatterplot(MMSE MIMO) snrmmse.jpg Fig.SNR Vs BER for OFDM system with MMSE based Receivers

where E is operator for expected value VI.

W ORK S CHEDULE

Concept of expected value and correlation can be used to derive the equations for finding the channel response. Rgg = auto covariance matrix of g RY Y = auto covariance matrix of Y RgY = auto covariance matrix of g and Y The estimated channel Hmmse can be found out by the equation

SemesterVII 1) Literature survey 2) Implementation of OFDM in Matlab 3) Understanding the functioning of GNU radio and learning programming specific to it. 4) Implementing OFDM system in GNU radio

Hmmse = F ∗ (RgY ∗ RY−1Y ∗ Y )

SemesterVIII 5) Using USRP to perform real time implementation of OFDM system in GNU radio. 6) Implementing MIMO-OFDM system in Matlab. 7) Implementing MIMO-OFDM system in GNU radio. 8) Analysis 9) Conclusion

where F is a noise matrix. RgY = Rgg ∗ F 0 ∗ X 0

RY Y = X∗F 0 ∗Rgg ∗F 0 ∗X 0 +varianceof noise∗Identitymatrix

R EFERENCES [1]

The equation can be used for both SISO as well as MIMO systems.

Yong Soo Cho, Jaekwon Kim, Won Young Yang, Chung-Gu Kang, MIMO-OFDM Wireless Communication with MATLAB, Singapore, John Wiley Sons (Asia), , 2010. [2] Jiang Xuehua, Chen Peijiang, Study and Implementation of MIMOOFDM System Based on Matlab, International Conference on Information Technology and Computer Sciences, pp. 554-557, 2009.

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[16]

Marcos Majo, Design and Implementation of an OFDM-based Communication System for the GNU Radio Platform, Master Thesis, Institut Fur Kommunikationsnetze Und Rechnersysteme, Germany, 2009. Lee K. Patton, A GNU Radio Based Software-Defined Radio, Master Thesis, Wright State University, United States of America, 2007. Proakis, J. G., Salehi, M. (2007). Fundamentals of communica- tion systems. Pearson Prentice Hall, India. GNU Radio. http://gnuradio.org/redmine/wiki/gnuradio Ettus Research LLC, ed. USRP2: The Next Generation of Software Radio Systems. Mountain View, CA, USA. Josh Knows. http://www.joshknows.com/ Presentation on Multiple Input Multiple Output Systems, www.cse.buffalo.edu Vijaya Chandran Ramasami, Orthogonal Frequency Divison Multiplexing http://www.magnadesignnet.com en.wikipedia.org/wiki/Orthogonal frequency-division multiplexing Marwanto, Arief and Sarijari, Experimental study of OFDM implementation utilizing GNU radio and USRP-SDR, 2009 Bastian Bloessl, Michele Segata, Christoph Sommer and Falko Dressler, An IEEE 802.11a/g/p OFDM Receiver for GNU Radio M. Viberg, Chalmers University of Technology, M. Bilal, Barcelona University (Chalmers M.Sc.),Simulation of MIMO Antenna Systems in Simulink and Embedded Matlab Hemanth Sampath, Shilpa Talwar, Jose Tellado, and Vinko Erceg, Iospan Wireless Inc A Fourth-Generation MIMO-OFDM Broadband Wireless System: Design, Performance, and Field Trial Results