ECE 734

Final Project ReportProf. Yu-Hen Hu

Methods of modulation and demodulation in OFDM system: implement and analysis for BER

performance, hardware performance, and hardware complexity

by

Hsin-Yu Chen

AbstractThe structure and algorithm of IDFT DFT, the conventional method used in

modulation/demodulation process in OFDM system, has matured today. Researchers

have developed new transforms in an effort to replace this traditional structure, such

as DHT-based structure (Discrete Hartley Transform) and DWT-based (Discrete

Wavelet Transform) structure. In this project, all three structures will be implemented

in MATLAB to acquire their BER (Bit Error Rate) performances, and the results will

be compared and analyzed along with other two aspects, hardware performance and

hardware complexity to gain a complete view of their advantages and disadvantages.

IntroductionIn OFDM system, IDFT DFT hardware in the transceiver is conventionally

designed jointly to carry out IDFT and DFT functions for transmission and receiving

processes, respectively. To date, the development of IDFT DFT structure and

algorithm used in the modulation/demodulation process has reached its maturity. In

the last few decades, researchers have proposed several alternative transforms to

replace IDFT DFT, such as DHT (Discrete Hartley Transform) IDHT (Inverse

Discrete Hartley Transform) and DWT (Discrete Wavelet Transform) IDWT (Inverse

Discrete Wavelet Transform). Past research has individually compared one of the

many transforms to the DFT-based structure on one or two of the performance aspects,

such as BER performance, hardware performance, or hardware complexity. For

example, the DHT-based structure in research [1] generates similar BER performance

and lower complexity. A DWT-based structure in research [2] shows better BER

performance under certain conditions. A lot of effort [3] [4] [5] was put into

implementing the hardware to lower the complexity or increase the operating speed.

Motivation and GoalAs indicated in the background research review, researchers in the field of

OFDM system have compared DHT-based and DWT-based structure to DFT-based

structure on either the BER performance or the hardware performance and complexity.

However, I have not found research that offers an exhaustive comparison among all

three structures with their respective BER performance, hardware performance, and

hardware complexity. I believe by running a synthesized analysis with all three

structures on all the aspects will give us more complete information and will provide a

useful direction for future research to invest their research time and money.

DFT-based OFDMAn Orthogonal Frequency Division Multiplexing (OFDM) system is a

multi-carrier system which utilizes a parallel processing technique allowing the

simultaneous transmission of data on many closely spaced, orthogonal sub

Inverse Discrete Fourier transform (IDFT) and Discrete Fourier transform (DFT) in a

conventional OFDM system are used to multiplex the signals together and decode the

signal at the receiver respectively.

x = √ ∑ XThe system adds cyclic prefixes (CP) before transmitting the signal. The purpose

of this is to increase the delay spread of the channel so that it becomes longer than the

channel impulse response. The purpose of this is to

interference (ISI). However, the CP has the disadvantage of reducing the spectral

containment of the channels.

DHT-based OFDM For the current DFT-based OFDM

compute a long-length IDFT, and the demodulator needs to compute a long

DFT. For such computations, a great number of complex multiplications are required.

Clearly, the complexity of a D

corresponding modulator and

transforms. The N-point IDFT is defined as:

x = √ ∑ X H , n=0, 1 ,…,N

d OFDMAn Orthogonal Frequency Division Multiplexing (OFDM) system is a

carrier system which utilizes a parallel processing technique allowing the

simultaneous transmission of data on many closely spaced, orthogonal sub-carriers.

rier transform (IDFT) and Discrete Fourier transform (DFT) in a

conventional OFDM system are used to multiplex the signals together and decode the

signal at the receiver respectively. The N-point IDFT is defined as:

W , n=0 ,1 ,…,N-1, where W = e π/

The system adds cyclic prefixes (CP) before transmitting the signal. The purpose

of this is to increase the delay spread of the channel so that it becomes longer than the

channel impulse response. The purpose of this is to minimize inter-symbol

interference (ISI). However, the CP has the disadvantage of reducing the spectral

Here is the diagram of DFT-based OFDM:

based OFDMbased OFDM-based transceivers, the modulator needs to

length IDFT, and the demodulator needs to compute a long-length

DFT. For such computations, a great number of complex multiplications are required.

Clearly, the complexity of a DFT -based OFDM would be reduced if the

ng modulator and demodulator could be replaced by discrete Hartley

point IDFT is defined as:

, n=0, 1 ,…,N-1, where H = sin 2πk/N + cos 2

carrier system which utilizes a parallel processing technique allowing the

carriers.

rier transform (IDFT) and Discrete Fourier transform (DFT) in a

conventional OFDM system are used to multiplex the signals together and decode the

The system adds cyclic prefixes (CP) before transmitting the signal. The purpose

of this is to increase the delay spread of the channel so that it becomes longer than the

interference (ISI). However, the CP has the disadvantage of reducing the spectral

tor needs to

length

DFT. For such computations, a great number of complex multiplications are required.

discrete Hartley

2πk/N

The DHT involves only real

the DFT, there have been a number of fast algorithms and hardware architectures

available for the DHT computation. It is shown that the proposed DHT

achieves the same transmission performance as the DFT

less computational complexity.

DWT-based OFDM In DFT-based OFDM, a CP is added to eliminate ISI. But this can decrease

bandwidth efficiency greatly. Discrete

alternative platforms for replacing ID

spectral containment of the channels is better since it do

DWT-based OFDM an advantage of bandwidth efficiency. The N

defined as:

φ(t) = 1, 0 ≤ t

Here is a diagram of DWT-based OFDM:

The DHT involves only real-valued arithmetic and has an identical inverse. Like

the DFT, there have been a number of fast algorithms and hardware architectures

available for the DHT computation. It is shown that the proposed DHT-based OFDM

achieves the same transmission performance as the DFT-based OFDM, but requires

l complexity. Here is the diagram of DHT-based OFDM:

based OFDMbased OFDM, a CP is added to eliminate ISI. But this can decrease

bandwidth efficiency greatly. Discrete Wavelet transforms have been considered as

placing IDFT and DFT. By using the transform, the

spectral containment of the channels is better since it does not use CP which gives

based OFDM an advantage of bandwidth efficiency. The N-point IDFT is

≤ , (−1, 1/2 ≤ t ≤ 1) , x = ∑ C φ(t − nT)

based OFDM:

valued arithmetic and has an identical inverse. Like

the DFT, there have been a number of fast algorithms and hardware architectures

based OFDM

based OFDM, but requires

based OFDM, a CP is added to eliminate ISI. But this can decrease

Wavelet transforms have been considered as

FT. By using the transform, the

es not use CP which gives

point IDFT is

Simulation

Stage 1

Using MATLAB to create an OFDM system (without channel effect, CP and noise)

and then run simulation with a random input. The results, as shown below, indicate

that both DHT-based and DWT-based OFDM generates the same output as IDFT/DFT.

Therefore, it is safe to say that IDFT/DFT can be replaced by either IDHT/DHT or

IDWT/DWT.

A. Input data:

0 10 20 30 40 50 60 700

0.5

1

1.5

2

2.5

3

Data

Am

plitu

de

Input

B. DHT-based OFDM output data:

C. DWT-based OFDM output data:

0 10 20 30 40 50 60 700

0.5

1

1.5

2

2.5

3Output

0 10 20 30 40 50 60 700

0.5

1

1.5

2

2.5

3Output

Stage 2

I added the AWGN channel into the OFDM system and calculated the BER for each

system. The results showed that DWT out performed both DFT and DHT system

while the later two produced very similar BER performance.

Table 1: SIMULATION PARAMETERS

Number of DWT point 2048

Number of DHT point 2048

Number of DFT point 2048

Modulation BPSK

Channel AWGN

0 5 10 15 20 2510

-5

10-4

10-3

10-2

10-1

Eb/No, dB

Bit E

rror

Rate

Bit error probability curve for BPSK modulation

simulationDWT

simulationDFTsimulationDHT

Conclusion In BER performance simulation, different orthogonal based OFDM systems

(DFT-based OFDM, DWT-based OFDM, and DHT-based OFDM systems) were

compared over AWGN channel. DWT-based OFDM system performs much better

than DHT-based OFDM and DFT-based OFDM systems on AWGN channel. The

BER performance of DHT-based OFDM is almost the same as that of DHT-based

OFDM system over AWGN channel.

In hardware comparison, research has suggested that DHT-based OFDM has the

potential to lower the hardware complexity compare to DFT-based OFDM because it

has an identical inverse and real-valued arithmetic [2][10]. However, it is still too

early to determine its efficiency without more fully developed hardware architecture

and algorithm.

DWT-based OFDM was only recently introduced to be applied in OFDM system

but it holds a even better potential to produce low hardware complexity because it

doesn’t need a CP. With its strong BER performance shown in this study, it is worth

starting/continuing the development of its hardware architecture and algorithm.

References

1. C. L. Wang and C. H. Chang, “A novel DHT-based FFT IFFT Processor for

ADSL transceivers,” in Proc. 1999 IEEE Int. Symp. Circuits Syst., Orlando, FL,

May 30 - June 2, 1999, pp. 51-55

2. K. Abdullah and Z. M. Hussain, “Studies on DWT-OFDM and FFT-OFDM

Systems”, SMIEEE, 2009

3. Y. Jung, H. Yoon, and J. Kim, “New efficient FFT algorithm and pipeline

implementation results for OFDM/DMT applications,” Consumer Electronics,

IEEE Trans., vol. 49, no. 1, pp. 14 - 20, Feb. 2003

4. D. F. Chiper and V. Munteanu, “A new design approach to VLSI parallel

implementation of discrete Hartley transform”, Volume 1, 17-20 June 1996

Page(s):207 - 212 vol.1 Digital Object Identifier 10.1109/ ISIE. 1996.548420

5. Lung-Hee Suk, Dae-Won Kim, Taek-Won Kwon, Suk-Kun Hyung, Jun-rim Choi,

“A 8192 complex point FFT/IFFT for COFDM modulation scheme in DVB-T

system,” Proceedings of IEEE International SOC Conference 2003, pp. 131-134,

Sept. 2003.

6. Lihong Jia, Yonghong Ciao, Jouni Isoaho, Hannu Tenhunen, “A new

VLSI-oriented FFT algorithm and implementation,” Proceedings of ASIC 1998,

pp. 337-341, Sept. 1998.

7. R. N. Bracewell, “The fast Hartley transform,” Proc. IEEE, vol. 72, pp.

1010-1018, Aug. 1984.

8. H. S. Hou, “The fast Hartley transform algorithm,” IEEE Trans. Comput., vol.

C-36, pp. 147-156, Feb. 1987.

9. C. -L. Wang, C. -T. Ho, and Y. -T. Chang, “A novel systolic design for fast

computation of the discrete Hartley transform,” in Proc. IEEE Thirtieth Asilomar

ConJ Signals, Systems & Computers, pp. 1067- 107 I , Nov. 1996.

10. C. -L. Wang and C. -H Chang, “A novel DHT-based FFWIFFT processor for

ADSL transceivers,” in 1999 IEEE