Microsoft Word - .doc(Guard

(Four-path input)
Orthogonal Frequency Division Multiplixing (OFDM) modulation makes use of
a longer symbol duration with a guard interval to reduce frequency selective fading
and inter symbol interference (ISI). Multipath transmission results in frequency
selective fading. In OFDM, subchannel signals with narrow frequency bandwidth will
suffer amplitude attenuation only; therefore, much simpler frequency equalizers are
enough to compensate the amplitude distortion, which greatly reduces the receiver
complexity. In OFDM, the transmitter needs to calculate the IFFT of the input signal
to generate the baseband (complex-valued) signals; and the receiver needs to calculate
the FFT. If the IDFT/DFT is calculated directly, it will waste the computation
resources; thus, the application of the IFFT/FFT is necessary. One of the key
techniques in the OFDM system is the IFFT/FFT. The purpose of this thesis is to
design an efficient OFDM IFFT/FFT processor for the system. The calculation speed,
number of multipliers, gate count, write, read and latency are taken into account in
design. The pipeline structure used in this design involves the real-time process of the
four-path input and cascade-delay-commutator. To get the optimum realization of the
factor ( N 1 ) in the IFFT calculation , we propose to use the adaptive shift dividing
concept.
3


…

………………………................................15
2.4 Split-Radix FFT (SRFFT) …….………………..……20
.…….……………………...………….22
3.3.1…..…………………………………………26
1-2.OFDM------------------------------------11
1-3.-------------------------------------13
1-4.-------------------------------------------13
2-2 (a)(b)(bit reversal)-------------------------17
2-5 (a)SRFFT (b) radix-4 FFT
--------------------------------------------------------------------------------20
2-6Split-radix-------------------------------20
3-1 ----------------------------------------------------22
4-2 -------------------------------------------------33
4-3 -------------------------------------------------34
4-4 -------------------------------------------------34
4-5 -------------------------------35
4-6 -------------------------------------------------35
4-7 -------------------------------------------------36
4-8 -----------------------------------------36
4-9 --------------------------------------37
4-25 64 SRFFT(for 4-24)------------44
OFDM
IEEE 802.11a (High Performance LAN type 2,HIPERLAN/2) (Mobile Multimedia Access Communication,MMAC)
(Wireless Broadband Mutlimedia communications,WBMMC)[1]
1.1 OFDM

N

b b

11

(crosstalk)


OFDM
12
))(()( 1
0 ,∑∑
)2exp(1)( tfj T
0f

1971 Weinstein Ebert IDFT
DFT(Discrete Fourier Transform) OFDM IDFT DFT
Ts N N Tt s=Δ 0f =0
fΔ sT
1 <1.2>
IDFT S(t) S(n) OFDM
IDFT DFT 1.3 OFDM ISI ICI
( 1-3)[5]

N {X(n)}
∑ −
=
NN −2
k N

)(1 nf )(2 nf 2 x(n)
(decimation-in-time,DIT) N DFT
∑ −
=
)()( 21 kFWkF k N+= , 1,...,1,0 −= Nk
)(1 kF )(2 kF )(1 mf )(2 mf N/2 DFT )(1 kF )(2 kF
)()2/( 11 kFNkF =+ )()2/( 22 kFNkF =+
k N
)()()( 21 kFWkFkX k N+= , 12,...,1,0 −= Nk 2.1
)()()2( 21 kFWkFNkX k N−=+ , 12,...,1,0 −= Nk 2.2
)(1 kF 2)2/(N )(2 kF
2/N )(2 kFW k N )(kX
2/2/2/)2/(2 22 NNNN +=+ 2N 2/2/2 NN +
N/4 DFT N/2 DFT )(1 kF
)(2 kF
)}12({)}2({)( 12/11 ++= nfFWnfFkF k N , 14,...1,0 −= Nk 14,...1,0 −= Nn
)}12({)}2({) 4
)}12({)}2({)( 22/22 ++= nfFWnfFkF k N , 14,...1,0 −= Nk 14,...1,0 −= Nn
)}12({)}2({) 4
NN 2log)2/(
NN 2log
bWaA r N+=
bWaB r N−=
1)( 2 −NLog
17
)7(),3(),5(),1(),6(),2(),4(),0( xxxxxxxx 2-2
(shuffling)
∑∑ −
=
−
=
)2( kX )12( +kX
Nv 2log= N/2 2-3 DIF FFT NN 2log)2/( NN 2log DIT
baA +=
2.3 Radix-4 FFT
2 4
4 )34(),24(),14(),4( +++ nxnxnxnx 14/,...1,0 −= Nn
∑ =
,...,1,0 −= Nq
N/4 DFT ),( qlF N DFT

0 NW
q NW
12 8
N
∑∑∑∑∑ −
=
−
=
−
=
−
=
−
=
NW )1(2/ −= kkN N jW )(4/3 =

N/4 DFT
∑ −
=
20
4/,...,1,0 Nk =
N/4 DFT
Nv 4log= radix-4 ]}1)[(log4 3{ 4 −NN
)log4 3( 4 NN
N=16radix-23264 radix-4 12 radix-2 96
radix-2radix-2
radix-4
radix-2

Duhamel Hollmann[6][7]
radix-2 radix-4 m2
radix-2 2.1 radix-4 2.42.6
2-5 SRFFT radix-4
radix-4 SRFFT radix-4
radix-2 SRFFT
radix-2 SRFFT radix-4
n NW
2-6 Split-radix
SRFFT n
21
22
BPSKQPSK16-QAM 64-QAM

-1 -1BPSK
1 1

FFT
3-2 FFT
IEEE 802.11a 64 (IFFT) 3-3 64 4 (pilot)
48 12
matlab 64-point IFFT/FFT
3-3 0
27 36 0 802.11a
3-3 IFFT
64 SRFFT 6 SRFFT radix-2
2n IFFT/FFT

IFFTFFT stage1~5 2-6
stage6 2-3 IFFT S1~6
IFFT 1/N
EVM
EVM(error vector magnitude)EVM
3-5


4-4
EVM IFFT/FFT

:
64QAM16QAMQPSK BPSK

MSEEVM(%)EVM(db)

1/N
3-4 [S1 S2 S3 S4 S5 S6]
IFFT/FFT
[S1 S2 S3 S4 S5 S6]

28
1 S1=1/64 S2=1 S3=1 S4=1 S5=1 S6=1
3-8 1 EVM
1 BPSK EVM -40dB
-30dB BPSK


29
2 S1=1/2 S2=1/2 S3=1/2 S4=1/2 S5=1/2 S6=1/2
3-9 2 EVM
3 S1=1/4 S2=1 S3=1/4 S4=1 S5=1/4 S6=1
3-10 3 EVM

30
2 EVM -17db 1 -31db

S1 SRFFT radix-4

[S1 S2 S3 S4 S5 S6]
S1 1/4
4 S1=1/4 S2=1 S3=1/2 S4=1/2 S5=1/2 S6=1/2
3-11 4 EVM
3 EVM -44dB spec 4 EVM -46dB
3 1 4 2 4 4

SRFFT radix-4 radix-2
1/2 1/4
stage
stage ( 3-12)

31
2 radix-2 2 radix-4 2

3-10 3-11 3-13 2
13 13
10 3 EVM(dB)-44.1595dB 4
EVM(dB)-46.9109dB 4 spec -45dB
5 EVM -49.1815dB 2

3.3.4 10
20 8 12
3-14 9
32
10 13
spec 13 EVM -49.1815dB spec 13
3-14 5 EVM
33
[8]~[11]

4(CE)3 (DCS)

4-2
8−Z
8−Z
()
34
8 8
13 8 24
13

4-5
n 1 2 4 8


[16 8 12
10]
ROM
4-9
sign bit

A B A
14*10
14 C
sign bit
13


4-11
4-12 EvenOdd stage
4x 6
co m
m ut
at or
sw itc
h bZ −
4-1112 ))()(( cbaZ −−− a
b=2ac=3a a Even Stage(1) a=4 clock Odd Stage(1) a=2 clock Even Stage(2) a=1 clock
4x64x2

( 4-18)
1−Z 1−Z 1−Z 1−Z 1−Z 2−Z
1−Z
2:1
2
N
N 2
4-23 2
in2[N-1:0]
in1[N-1:0]
2−Z
1−Z
1−Z 1−Z 1−Z 1−Z 1−Z
1,4O
2,4O
3,4O
4,4O
5,4O
6,4O
1,5I
2,5I
3,5I
4,5I
5,5I
44
45
QuartusII compilation APEX20KE~(EP20K1500EBC652-1X)
( 4-264-27) 12801 Logic Element(LE) 6139 Embeded System Block(ESB) 26.81MHz
4-26 IFFT
4-27 FFT
gate count QuartusII
12 gate count 4 gate count
178168 gate count
4-28 IFFT

standard
(real-time) IC IC MasterBlaster Communication Cable ByteBlasterMV Download Cable Quartus IC
IC FPGA ELA(Embedded Logic Analyzer)
SignalTap Altera LE ESB Channel()
LE ESB
4-29 IFFT
4-1 IFFT
IFFT
4-30 FFT
4-3 FFT
FFT

(Pipeline)
Veriolg
26MHz OFDM
128 256 … CE Delay Commutator

50

[1] Anibal Luis Intini “Orthogonal Frequency Division Multiplexing for Wireless Networks”Lecture of University Of Calfifornia Santa Barbara.
[2].Chang R.W.”Synthesis of Band Limited Orthogonal Signals for Multichannel Data Transmission”, Bell Syst. Tech. J., Vol. 45, pp. 1775-1796, Dec. 1996.
[3]. Salzberg, B. R.,”Performance of an efficient parallel data transmission system”,IEEE Trans. Comm., Vol. COM- 15, pp. 805
[4]. Mosier, R. R., and Clabaugh, R.G.,”A Bandwidth Efficient Binary Transmission System”, IEEE Trans., Vol. 76, pp. 723 - 728, Jan. 1958.
[5]. Dr. Jean Armstrong,” OFDM – Orthogonal Frequency Division Multiplexing” Lecture of Department of Electronic Engineering, La Trobe University
[6]. P. Duhamel, “Implementation of split-radix FFT algorithms for complex, real, and real-symmetric data,” IEEE Trans. Acoust., Speech, Signal Processing vol. ASSP-34, pp. 285–295, Apr. 1986.
[7]. P. Duhamel and H. Hollmann, “Split-radix FFT algorithm,” Electron.Lett., vol. 20, no. 1, pp. 14–16, Jan. 1984.
[8]. Shousheng He and Torkelson M. “A new approach to pipeline FFT processor, Parallel Processing Symposium”, 1996., Proceedings of IPPS '96, The 10th International , 1996 Page(s): 766 -770
[9]. Lihong Jia and Yonghong Gao and Tenhunen H. “A pipelined shared-memory architecture for FFT processors, ” Circuits and Systems, 2000. 42nd Midwest Symposium on , Volume: 2 , 2000 Page(s): 804 -807 vol. 2
[10]. Ben Gold and Theodore Bially, ”Parallelism in Fast Fourier Transform Hardware, ” IEEE Transactions on Audio and Electroacustics, VOL. AU-21, NO. 1, February 1973
[11]. Guoan Bi Mieee and Yan Qiu Chen ” An improved fast Fourier transform algorithm, ” Information, Communications and Signal Processing, 1997. ICICS., Proceedings of 1997 International Conference on , Volume: 3 , 1997 Page(s): 1308 -1310 vol.3