ofdm tx symbol shapping 802 - ieee · pdf file5 examples of raised-cosine window matlab code...
TRANSCRIPT
OFDM TX Symbol Shaping 802.3bn
Leo Montreuil, Rich Prodan, Tom Kolze
Phoenix, January 2013
2
Recommendations
• TX window is specified as Nt samples in taper region – No need for different set of Alpha for 4K and 8K FFT. – Avoid confusion for calculation of Nt with variable Cyclic Prefix.
Alpha = Nt/Nfft, Tp = Nt/204.8e6
• Nt = {0, 32, 64, 128, 192, 256} – Tp = {0, 0.15625, 0.3125, 0.625, 0.9375, 1.25} us – Alpha = {0, 0.78125%, 1.5625%, 3.125%, 4.6875%, 6.25% } for 4K FFT – Alpha = {0, 0.390625%, 0.78125%, 1.5625%, 2.34375%, 3.125%} for 8K FFT
• A postfix of Nt samples is added, windowing is applied to cyclic prefix and postfix – Windowing is absorbed by CP. – Symbol time is independent of Window Nt. – Receiver sampling is independent of TX window. – TX window appears to RX as post-cursor multipath, affect only the following
symbol, not the previous symbol.
3
Windowing Function
4
Raised-Cosine Window
• Raised-Cosine window in frequency domain (FD):
P 𝑓 = sin 𝜋𝑓𝑇
𝜋𝑓𝑇
cos 𝜋𝛼𝑓𝑇
1 − 2𝛼𝑓𝑇 2, 0 ≤ 𝛼 ≤ 1
• Raised-Cosine window in time domain (TD):
𝑝 𝑡 =
1
𝑇, 0 ≤ 𝑡 <
𝑇 1−𝛼
21
2𝑇1 + cos
𝜋
𝛼𝑇𝑡 −
𝑇 1−𝛼
2,
𝑇 1−𝛼
2≤ 𝑡 ≤
𝑇 1+𝛼
2
0, otherwise
α = 0 is a rectangular window (no shaping)
5
Examples of Raised-Cosine Window
MATLAB code for TX window p: Nfft = 4096; % FFT size CP = 256; % Nb. samples in Cyclic Prefix Alpha = 1/32; % RX Alpha
Nt = 2*round(Nfft*Alpha/2); % Nb. samples in taper region p = 1/2*(1+cos(pi*[-Nt+1/2:Nt-1/2]/Nt)); % Raised-Cosine in TD p = [p(1:Nt), ones(1,Nfft+CP-Nt), p(Nt+1:2*Nt)]; % Add ones in middle
Taper Region weight for Alpha = 1/128 (32 points): 0.0006 0.0054 0.0150 0.0292 0.0480 0.0711 0.0984 0.1295
0.1642 0.2022 0.2429 0.2862 0.3316 0.3785 0.4266 0.4755
0.5245 0.5734 0.6215 0.6684 0.7138 0.7571 0.7978 0.8358
0.8705 0.9016 0.9289 0.9520 0.9708 0.9850 0.9946 0.9994
The taper region should not change with different CP Nt = Alpha*Nfft
6
OFDM TX Windowing, RX sampling offset unaffected by TX Windowing
Ts is independent of RC Window Alpha
TX SymbolNCPN
TX SymbolN+1CPN+1
TX SymbolN+2CPN+2
TX SymbolNCPN
TX SymbolN+1CPN+1
TX SymbolN+2CPN+2
Tg Tu
Ts
Ts
Tg Tu Tp
RX RymbolN+1RX SymbolN RX SymbolN+2
PostfixPrefix
Rect. window OFDM
RC Window OFDM
RX sampling
Overlapby Tp
7
Leakage in In-Band and Adjacent SC-QAM
8
4K FFT, Nt = 128, CP = 1.25 us, 8 MHz Spectral Exclusion, SQRT-RC 12% 5.35 MHz Filter
-5 -4 -3 -2 -1 0 1 2 3 4 5-70
-60
-50
-40
-30
-20
-10
0
10
Frequency (MHz)
Magnitude (
dB
)
Power Spectral Density
OFDM
SC-QAM
OFDM leakage in SC-QAM
Leakage = -52.04 dBc
9
4K & 8K FFT, CP = 1.25 us, 8 MHz Spectral Exclusion, SQRT-RC 12% 5.35 MHz Filter
0 20 40 60 80 100 120-55
-50
-45
-40
-35
-30
-25
Nb of Taper samples
Leakage (
dB
c)
OFDM Leakage in SC-QAM Channel vs Nb of Taper Samples
4K FFT
8K FFT
∆ = 2.5 dB
10
OFDM TX Power Spectral Density, CP = 1.25 us
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9-70
-65
-60
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
Frequency Offset from Band-Edge (MHz)
Ma
gn
itu
de
(d
B)
4K FFT, Power Spectral Density at Band-Edge
Nt = 0
Nt = 32
Nt = 64
Nt = 128
Nt = 256
11
Adjacent Channel Guard-Band, 6 MHz rectangular and SQRT-RC 12% 5.35 MHz Filter, CP = 1.25 us
0 20 40 60 80 100 120 140 160 180 200 220 240 2600
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
Nt samples in taper region
Gu
ard
Ba
nd
BW
(M
Hz)
4k FFT, OFDM Power Leakage vs Nt
-45 dBc, 5.35 MHz
-50 dBc, 5.35 MHz
-55 dBc, 5.35 MHz
-45 dBc, 6.0 MHz
-50 dBc, 6.0 MHz
-55 dBc, 6.0 MHz
12
In-Band Exclusion BW, 6 MHz rectangular and SQRT-RC 12% 5.35 MHz Filter, CP = 1.25 us
0 20 40 60 80 100 120 140 160 180 200 220 240 2606
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
12.5
13
13.5
14
Nt samples in taper region
Ex
clu
sio
n B
W (
MH
z)
4k FFT, OFDM Power Leakage vs Nt
-45 dBc, 5.35 MHz
-50 dBc, 5.35 MHz
-55 dBc, 5.35 MHz
-45 dBc, 6.0 MHz
-50 dBc, 6.0 MHz
-55 dBc, 6.0 MHz
13
In-Band Exclusion BW, 8 MHz rectangular and SQRT-RC 15% 6.952 MHz Filter, CP = 1.25 us
0 20 40 60 80 100 120 140 160 180 200 220 240 2608
8.5
9
9.5
10
10.5
11
11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
Nt samples in taper region
Ex
clu
sio
n B
W (
MH
z)
4k FFT, OFDM Power Leakage vs Nt
-45 dBc, 6.952 MHz
-50 dBc, 6.952 MHz
-55 dBc, 6.952 MHz
-45 dBc, 8.0 MHz
-50 dBc, 8.0 MHz
-55 dBc, 8.0 MHz
14
OFDM TX Power Spectral Density, CP = 1.25 us
-0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9-70
-65
-60
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
5
Frequency Offset from Band-Edge (MHz)
Ma
gn
itu
de
(d
B)
8K FFT, Power Spectral Density at Band-Edge
N
t = 0
Nt = 32
Nt = 64
Nt = 128
Nt = 256
15
Adjacent Channel Guard-Band, 6 MHz rectangular and SQRT-RC 12% 5.35 MHz Filter, CP = 1.25 us
0 20 40 60 80 100 120 140 160 180 200 220 240 2600
0.25
0.5
0.75
1
1.25
1.5
1.75
2
2.25
2.5
2.75
3
3.25
3.5
3.75
4
Nt samples in taper region
Gu
ard
Ba
nd
BW
(M
Hz)
8k FFT, OFDM Power Leakage vs Nt
-45 dBc, 5.35 MHz
-50 dBc, 5.35 MHz
-55 dBc, 5.35 MHz
-45 dBc, 6.0 MHz
-50 dBc, 6.0 MHz
-55 dBc, 6.0 MHz
16
In-Band Exclusion BW, 6 MHz rectangular and SQRT-RC 12% 5.35 MHz Filter, CP = 1.25 us
0 20 40 60 80 100 120 140 160 180 200 220 240 2606
6.5
7
7.5
8
8.5
9
9.5
10
10.5
11
11.5
12
12.5
13
13.5
14
Nt samples in taper region
Ex
clu
sio
n B
W (
MH
z)
8k FFT, OFDM Power Leakage vs Nt
-45 dBc, 5.35 MHz
-50 dBc, 5.35 MHz
-55 dBc, 5.35 MHz
-45 dBc, 6.0 MHz
-50 dBc, 6.0 MHz
-55 dBc, 6.0 MHz
17
In-Band Exclusion BW, 8 MHz rectangular and SQRT-RC 15% 6.952 MHz Filter, CP = 1.25 us
0 20 40 60 80 100 120 140 160 180 200 220 240 2608
8.5
9
9.5
10
10.5
11
11.5
12
12.5
13
13.5
14
14.5
15
15.5
16
Nt samples in taper region
Ex
clu
sio
n B
W (
MH
z)
8k FFT, OFDM Power Leakage vs Nt
-45 dBc, 6.952 MHz
-50 dBc, 6.952 MHz
-55 dBc, 6.952 MHz
-45 dBc, 8.0 MHz
-50 dBc, 8.0 MHz
-55 dBc, 8.0 MHz
Thank You