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