Transcript of 畢業論文 - chur.chu.edu.tw
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
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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