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OFDM Transceiver using HDL

By: Paul Pethsomvong & Zachary Asal

Advisors: Dr. Yufeng Lu & Dr. In Soo Ahn

Department of Electrical and Computer Engineering, Bradley University, Peoria IL 61625

5/14/2014

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Abstract

Orthogonal Frequency Division Multiplexing (OFDM) has been widely used in digital

communication systems such as digital video broadcasting, IEEE-802.11a, g, n, ac, and 4G

cellular technologies. OFDM-based digital communication systems are resilient to

multipath fading in wireless environments and have low inter-symbol interference. The

project aims to design and verify a complete OFDM transceiver system on Field

programmable gate arrays (FPGA) using hardware description language. Simulink

simulation has been completed for the OFDM system. For the implementation, IFFT and

FFT data streaming core from Xilinx are used in the project. The OFDM transceiver system

with a 16-quadrature amplitude modulation (QAM) has been successfully implemented on

Xilinx FPGA boards.

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Acknowledgments

First and foremost, we would like to thank our advisors, Dr. Yufeng Lu and Dr. In Soo Ahn.

The project could not be possible without their valuable advice and guidance during the

course of the project. We would also like to thank Bradley University ECE Department for

providing us with a good environment and laboratory facilities to complete this project.

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Table of Contents

I. Introduction ........................................................................................................................................ 5

II. OFDM Background ........................................................................................................................... 5

III. OFDM Transceiver Methods ........................................................................................................ 7

IV. Simulation Results and Analysis ............................................................................................. 11

V. Implementation Results ............................................................................................................... 13

VI. Conclusion ....................................................................................................................................... 17

VII. References ..................................................................................................................................... 18

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List of Figures

Figure 1: Complex Envelope…………………….…………………………………………………………………6

Figure 2: OFDM System Block Diagram…………………………………………………………….………..8

Figure 3: 16-QAM Constellation………………………………………………………………….….…………..9

Figure 4: Simulink Model…………………………………………………………………………….….….……..11

Figure 5: Input and Output from Transceiver………………………………………………….…..……12 Figure 6: Error Percentage Difference………………………………………………......................…….12

Figure 7: Timing for Continuous Streaming Data………………………………...…………………..13

FigAure 8: 16-QAM Constellation (Transmitter)…………………………………………….………..14

Figure 9: 16-QAM Constellation (Receiver)…………………………………………………….….…….15

Figure 10: Itransmitted and Ireceived………………………………………………………………..……..……….16

Figure 11: Qtransmitted and Qreceived……………………………………………………………………..….….17

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I. Introduction

The purpose of this project is to implement a complete OFDM system using field

programmable gate arrays (FPGA) and very high speed integrated circuit hardware

description language (VHDL). With the use of FPGAs the OFDM system is reconfigurable for

future expansion. The project aims to create a system that is reusable by future students in

the Bradley University Electrical Engineering program.

Due to its reconfigurability and high through-put performance, FPGAs are widely used in

embedded applications such as automotive, communication, industrial automation, motor

control, and medical imaging [1]. This project uses a modified QPSK system by Anthony

Gaught, Alexander Norton, and Christopher Brady for the QAM modulation [2].

II. OFDM Background

Orthogonal Frequency Division Multiplexing

OFDM has been widely used in a variety of digital communications such as digital video

broadcasting, IEEE-802.11a, g,n, ac, and 4G cellular technologies. Digital communication

systems using OFDM are resilient to multipath fading in wireless environments and have

low inter-symbol interference. The project aims to design and verify a complete Orthogonal

Frequency Division Multiplexing (OFDM) transceiver system on Field programmable gate

arrays (FPGA) using VHDL. Simulink simulation has been completed for the OFDM system.

For the implementation, IFFT and FFT data streaming core from Xilinx are used in the

project. Inverse Fast Fourier transform (IFFT) and Fast Fourier Transform (FFT) are

critical operations in OFDM. The IFFT translates the data embedded in frequency domain to

time domain. The FFT operation in the receiver translates the received time domain signal

to frequency domain for data recovery. There are many high through-put and computation-

efficient algorithms used in the implementation of IFFT and FFT.

OFDM Signal

An orthogonal frequency division multiplexing (OFDM) signal is made of closely spaced

modulated carriers, called sub-carriers. These sub-carriers can be modulated by different

modulation methods like QPSK or QAM. Typically when carrier modulation occurs, the

resulting sidebands of the modulation process are spread apart and, occupy in a wide

spectral band. Because of the wide spectral occupancy and many carriers, the overall signal

can survive in the presence of fading due to mulipaths in wireless communication

environments. When carriers in some sub-bands experience severe attenuation, the data

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can be reassigned to other carriers. Hence, the OFDM is inherently robust to multipath

fading.

OFDM is a technique for transmitting data in parallel by using a large number of

modulated carriers with sufficient frequency spacing so that the carriers are orthogonal

[4]. OFDM signal is constructed in the baseband and requires baseband signal processing.

The complex envelope for the OFDM signal is g(t). The variables in Equation 2 are

described as follows: Ac is the carrier amplitude, 𝜔𝑛 is the element of the N-element parallel

data vector w = [𝜔0, 𝜔1, … , 𝜔𝑁−1], and the orthogonal carriers are 𝜑𝑛(𝑡) as seen below in

Equation 2.

𝑔(𝑡) = 𝐴𝐶 ∑ 𝜔𝑛𝜑𝑛(𝑡), 𝑤ℎ𝑒𝑟𝑒 0 < 𝑡 < 𝑇𝑁−1𝑛=0 (1)

𝜑𝑛(𝑡) = 𝑒𝑗2𝜋𝑓𝑛𝑡 𝑤ℎ𝑒𝑟𝑒 𝑓𝑛 =1

𝑇(𝑛 −

𝑁−1

2) (2)

The duration of the data symbol on each carrier is T seconds, which insures the carriers are

spaced 1/T Hz apart. This separation assures that the carriers are orthogonal, since 𝜑𝑛(𝑡)

satisfies the orthogonality condition seen in Equation 1 [4].

𝜑𝑛(𝑡) and 𝜑 ∗𝑚(t) are said to be orthogonal with respect to each other over the interval

a<t<b if they satisfy the condition in Equation 3 described below.

∫ 𝜑𝑛(𝑡)𝜑𝑚∗ (𝑡)𝑑𝑡 = 0, 𝑤ℎ𝑒𝑟𝑒 𝑛 ≠ 𝑚

𝑏

𝑎 (3)

Figure 1: Complex Envelope

As the modulated signal passes through the channel, the signal is distorted by the channel

imperfections and noise in the channel. The result is a band pass signal-plus-noise

waveform that arrives at the receiver input, r(t) shown in Figure 1. The information sent is

recovered through the receiver and �̌� denotes the corrupted version of the input

information m [4].

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Advantages and Disadvantages of OFDM

The primary advantage of OFDM is that the signal can survive better in severe channel

conditions over single-carrier schemes. OFDM can be aided further by simpler channel

equalizations than those of the single carrier modulation systems. Several slowly-

modulated wideband signals can survive better than one rapidly-modulated narrowband

signal. The simplification of channel equalization results in a low symbol rate allowing the

guard interval between symbols affordable. Simplification also eliminates interference,

makes time-spreading manageable, and “facilitates the design of single-frequency networks

where several adjacent transmitters send the same signal simultaneously at the same

frequency [5].

Another advantage of OFDM is its resilience to multipath. Multipath is the effect of multiple

reflected signals arriving at the receiver with different phases, resulting in interference and

frequency-selective fading. OFDM overcomes this by utilizing slower symbol rates for each

subcarrier and wide bandwidth by combining subcarrier bands. Since multipath is a major

degradation of signal integrity in the mobile wireless setting, OFDM is preferred in making

signals more survivable [6].

OFDM is also resistant to time dispersion. OFDM is resistant because the low symbol rate

allows fading to be slow enough for a channel to be considered constant during one OFDM

symbol interval. This low symbol rate is a result of cyclic prefix, which is one of OFDM’s

crucial attributes that allows OFDM to reduce interference and simplify the channel

equalization in a demodulator [6]. The cyclic prefix is used to trim and align data. It

mitigates delay spread. The cyclic prefix also extends the symbol period by copying the end

of the symbols and placing it before the symbols begin.

III. OFDM Transceiver Methods

Transmitter

The subcarriers are modulated in baseband independently using quadrature amplitude

modulation (QAM). The baseband modulated data are IFFTed to obtain the baseband time

domain OFDM signal. The cyclic prefix is used as a guard interval in order to reduce the

intersymbol interference. Parallel-to-serial conversion is performed and passband

modulation is performed to move the spectrum to the transmisstion spectrum band for

transmission.

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Receiver

The transmitted signal described above will be received with sever attenuation. Serial-to-

parallel conversion is required to manipulate data through the system. To obtain the

original signal the cyclic prefix must be removed and then the FFT must be performed. A

basic block diagram of an OFDM transceiver system is shown in Figure 2.

Figure 2: OFDM System Block Diagram

Parallel-to-serial/ Serial-to-parallel

It is necessary to convert a serial bit stream into several parallel bit streams to be divided

among the individual carriers. Once the bit stream has been divided among the individual

subcarriers, each subcarrier is modulated as if it was an individual channel before all

channels are combined back together and transmitted as a whole. The receiver performs

the reverse process to divide the incoming signal into appropriate sub-carriers and then

demodulating these individually before reconstructing the original bit stream [6]. In order

to complete FFT/IFFT, the data must be placed in parallel .

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IFFT/FFT

The IFFT/FFT process is the most important block in the OFDM communication system. IFFT gives OFDM its orthogonality. The IFFT transforms the amplitude and phase of each component into a time domain signal. It converts a specified number of complex data points into the same number of points in time domain. Similarly, FFT at the receiver side performs the reverse task i.e. conversion from time domain back to frequency domain [6]. In this project, the IFFT and FFT are implemented using the Xilinx core generator.

Add/remove cyclic Prefix

In order to preserve the sub-carrier orthogonality and the independence of subsequent OFDM symbols, a cyclic guard interval is introduced. The guard period is determined by the duration of the channel impulse response and specified in terms of the fraction of the number of samples that make up an OFDM symbol. Thus, the OFDM symbol is extended by copying the tail and gluing it to the front. Addition of cyclic prefix results in circular convolution between the transmitted signal and the channel impulse response. Frequency domain equivalent of circular convolution is simply the multiplication of a transmitted signal’s frequency response and channel frequency response. The received signal is only a scaled version of transmitted signal in frequency domain, therefore eliminating distortions caused by severe channel conditions, mainly multipath fading [6]. Modulator/Demodulator For modulation, a 16-QAM was used. Four in-phase (I) values and four quadratuare (Q) values are used. Each QAM symbol carries four bit information. There are sixteen states which results from 24. With a 16-QAM sixteen noticeable points are visible from the I and Q data. A constellation for the QAM is shown in Figure 3.

Figure 3: 16-QAM constellation

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Project Outline The project was divided into two stages. The first stage was to construct and simulate an

OFDM transceiver system using Simulink. The Simulink model is shown in Figure 4 was

created and tested to verify that the system is designed correctly and function properly

before coding HDL.

In the second stage, after verifying the results of the Simulink model, HDL was used to describe the transceiver. The transceiver code was implemented on an FPGA board. The specifications for the design are listed in Table 1.

Specification Chosen Value

FPGA System Clock 100 MHz

Carrier Frequency 25 MHz

Symbol Rate 12.5 Msps

Data Rate 50 Mbps

FFT Size 32

Symbol Time 8 * 10-8 sec

Modulation Scheme 16-QAM

Table 1: Specifications

Specification calculations

• FPGA System Clock = 100 MHz

• Symbol Rate Rs = 12.5 Msps

• Data rate Rb= Rs · N = 50 Mbps

• Bits per symbol N = 4

• Symbol time = 1/ Rs

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IV. Simulation Results and Analysis

A Simulink model of the OFDM system below was tested first without the QAM modulation

scheme. The goal was to implement the block diagram described in Figure 2 into Simulink.

Figure 4: Simulink model of the OFDM system block diagram in Figure 2

In the Simulink model, the input used was an 8 bit sound file with a sampling rate of 44.1

kHz and a frame size of 2048 bits. The frame size was chosen because it was the same

frame size as used by the 802.11a standard. The transpose blocks were used as serial-to-

parallel and paralleltoserial blocks. To add the cyclic prefix a sub matrix block was used to

concatenate the first five symbols of the data entered. A comparator was used to compare

results of the output to the input. In this model, y(t) = x(t)*h(t), where * means convolution,

so the output y(t) is equal to the convolution of the transmitted signal x(t) and the channel

impulse response h(t). A channel length of three is chosen in this model and a cyclic prefix

of five. In this model a 2048 bit sixteen sample was IFFTed using the radix-2 IFFT/FFT.

The parameters chosen were based on a scaled down version of the 802.11a specifications.

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Figure 5: Input and Output from Transceiver A sound file was sent through the Simulink model in order to test the accuracy of the

system. To show this comparision, the input and output was placed on top of each other.

The sound was observed before and after it went through the implemented OFDM system

in order to test the accuracy of the system. There were no noticeable differences between

the two sounds however the waves were similar as seen in Figure 5. The percentage

difference between input and output over time is shown in Figure 6.

Figure 6: Error Percentage Difference Time(sec) – X axis

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The error as seen in Figure 6 varies between a -1.5% and 8.5%. The difference between

input and output and was calculated using Equation 4. The error remained below +/- 2%

except for four instances where error spiked. The results seemed to show that the system

worked properly.

% 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑠𝑖𝑔𝑛𝑎𝑙−𝑅𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑠𝑖𝑔𝑛𝑎𝑙

|𝑇𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑 𝑆𝑖𝑔𝑛𝑎𝑙| (4)

V. Implementation Results After satisfactory results in stage 1, the system was implemented using VHDL and FPGAs.

An initial attempt was made to code all the blocks of the OFDM system from scratch. To

account for time constraints and the fact that majority of people in the engineering industry

recycle or modifies code, the decision was made to modify an old senior project QPSK

system. The QPSK system was modified to a 16-QAM which was used for modulation. For

the FFT/IFFT the Xilinx core generator was used. The core generator allows the user to

input parameters desired and outputs code. Results were obtained from the oscilloscope.

A 32-bit streaming FFT/IFFT core was used for the FFT/IFFT core. This means that the

signal to start processing is always high so, other than the start-up time, there are no

pauses in the processing. Forward or inverse FFT is controlled fwd_inv signal. For the

fwd_inv signal “1” means inverse and “0” means forward.

Figure 7: Timing for continuous Streaming data

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The FFT data was unable to be shown because there were not any 32-bit DACs available.

The PMOD DA2 which was used in this system was only able to output 12-bits at a time and

the FFT used output 32-bit signals.

Next, the 16-QAM system is discussed, how verification of the system was accomplished is

explained, and the results of that verification are presented. In Figure 8 the 16-QAM plot for

the transmitter side of the system with the sixteen points as marked in red. Initially the

QAM system was not as smooth. When modification of the previous code began, the

random symbol generator was not working so the clock divider was removed in the symbol

generator to resolve the issue. While this fixed the issue, it made the system run too fast

and made the output constellation fuzzy. To fix this issue the clock divider from the original

system was rewritten so that it held each symbol for eight clock cycles.

Two methods were used to verify the function of our 16-QAM system. To begin with, the

QAM constellation was examined. Afterwards, the I and Q waveforms were examined. The

result was a very clean looking 16-QAM constellation. The only issue that occurred

involved the spacing of the points. From comparing the results to Figure 3, it can be seen

that the middle four points were a little farther from the origin than expected. This was

most likely due to an issue already present in the QPSK system modified from a previous

senior project. The most likely cause of this is a timing issue or a data conversion issue due

to phase ambiguity of the receiver phase locking. Such phase ambiguity is resolved by

transmitting a pre-amble or differential encoding of the data at the transmitter. The points

should be appearing at (-3000,-1000,1000,3000) on each axis. In the end the cause of the

spacing issue was unable to be determined.

Figure 8: 16-QAM Constellation (Transmitter)

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Figure 9 shows the receiver side 18-QAM constellation. While there is still distortion left

from the channel, there are very clear groupings around each of the 16 points. The spacing

issue seen in the transmitter constellation is still present in the receiver side constellation.

Figure 9: 16-QAM Constellation (Receiver)

The 16-QAM transmitter and receiver were compared to the 16-QAM constellation seen in

Figure 3. The four groupings in each quadrant are seen in both the transmitter and

receiver. The reason that the sixteen points are not isolated is because in Figures 8 and 9

are a snapshot of the data running was taken. The snapshot was taken while running in real

time in order to show the jumps between points. It is seen that the points jump to other

points as denoted by red dots.

The next step in the verification process is to examine the transmitted and received I and Q

values. Figure 10 shows the transmitted I values in orange and the received I values in blue.

The transmitted values, which correspond to the very clean-looking constellation, appear

as expected in Figure 10. The waveform looks similar to the received waveform in blue.

You can see the four different values for I (-3000,-1000,1000,3000) in the transmitter

waveform like those visible in the received waveform.

The waveforms are not exactly the same even though they are similar. As mentioned above,

this is likely due to a 90 degree phase rotation present at the receiver which has not been

corrected. To improve the similitude of the waveforms, phase correction would need to be

done in the receiver of the QAM system.

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Figure 10: Itransmitted and Ireceived

Figure 11 shows the transmitted Q values in orange and the received Q values in blue. The

transmitted values, which correspond to the very clean-looking constellation, appear as

expected in Figure 11. The waveform looks similar to the received waveform in blue. You

can see the four different values for I (-3000,-1000,1000,3000) in the transmitter

waveform like those visible in the received waveform.

Figure 11: Qtransmitted and Qreceived

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Originally, there were issues with the transmitted I and Q values. The waveforms were vary

jagged and the four different symbols for each were not visible. Upon examination of the

previous senior project report, it was found that there were no figures or data to show that

the I and Q values for the previous senior project were correct. It was concluded that the

resultin problem was already present in the QPSK project when before it was modified. To

fix this issue, the system was slowed down to 1/4th of the overall speed it was running at

previously. It was deteremined this was the most likely the problem because the FPGA

board used had a 100 MHz clock while the QPSK senior project used a 50 MHz. Since the

system was running at twice the speed, the internal clock speed was cut by half. This

improved the waveform but it still was not satisfactorily clear so the speed was cut in half

again.

VI. Conclusion

In this project a complete OFDM transceiver was simulated and tested using VHDL. Design

was verified by first building and testing a Simulink model before implementation. The

finalized HDL code was successfully implemented on a Digilent Genesys FPGA board based

on the Virtex 5 by Xilinx. Part of the HDL code was reconfigured from a previous senior

project of a QPSK system for the 16-QAM system used in the current project.

In conclusion, verification of the system was unable to be completed. The initial I and Q

waveform issues on the transmitter side were fixed. This was done by slowing the whole

system down. Although the waveforms are similar they are not the same, the most likely

cause is a 90 degree phase rotation that is not being corrected. However, a complete and

functioning OFDM system was built. In the future, performance evaluation is much needed

and more OFDM carriers can be added to make a system closer to the 802.11a standard.

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VII. References

[1] Alan C. Brooks, Stephen J. Hoelzer, “Design and Simulation of Orthogonal Frequency

Division Multiplexing (OFDM) Signaling”, 15 May 2001

[2] Anthony Gaught, Alexander Norton, and Christopher Brady, “FPGA-based 16 QAM

communication system”, May 2013

[3] Langton, Charan, “Orthogonal Frequency Division Multiplex (OFDM) Tutorial” 2002

[4] Leon Couch, “Digital and analog communication systems”, 8th ed., Boston: Pearson,

2013

[5] Li, Zhi Young, “OFDM transceiver design with FPGA and Demo on DE2-70 board” 07

September 2008

[6] Shahbaz Abbasi and Shazer Baig, “Hardware Implementation of OFDM Transmitter

and Receiver using FPGA

[7] Xilinx Logicore generator IP Fast Fourier Transform, San Jose, CA 2011