Dual-Windowed OFDM for Cognitive Radios · Dusan Matic also studied the system design aspects of OFDM at mm-wavelengths. Exercise Consider two subcarrier signals, modulated with rectangular

Dual-Windowed OFDM for Cognitive Radios

Di Wang, Tianqi Wang, and Alireza Seyedi

March 24, 2010

Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios

1. Background and Introduction

2. System Description

3. Optimal Parameter Design

4. Simulation Results

5. Conclusion and Future Work


Background

Recent studies show that most of the assigned frequency spectrumis severely underutilized.

One major reason is that the primary users, who is licensed to usecertain spectrum band, are not busy all the time. When no primaryuser is transmitting over this bandwidth, then this part ofspectrum is idle.


Cognitive Radio

I Cognitive radios promise to address this problem by beingaware of their environment and adjust their behavioraccordingly.

I They try to identify unused spectrum segments and use themwithout harmful interference to the primary users.


Examples of Two Design

I Overlay Design

Frequency

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Pri

mary

Use

r 2

Pri

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1

CR

Band

1

CR

Band

2

CR

Band

3

I Underlay Design

Noise Floor

UWB Pri

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ser

3

Frequency

Po

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D

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1

Chakravarthy, V.D.; Wu, Z.; Shaw A.; Temple, M.A.; Kannan, R.; Garber, F.; , ”A general

overlay/underlay analytic expression representing cognitive radio waveform,”


OFDM

Orthogonal Frequency Division Multiplexing (OFDM) isparticularly attractive for underlay cognitive radios due to itsinherent capabilities in frequency domain processing.

www.WirelessCommunication.NL

Chapter: Analog and Digital Transmission Section: Multi-Carrier Modulation

Orthogonal Frequency Division MultiplexingOrthogonal Frequency Division Multiplexing (OFDM) is special form of multi-carrier modulation, patented in1970. It is particularly suited for transmission over a dispersive channel. (See further discussion of MCM overwireless channel.)

In a multipath channel, most conventional modulation techniques are sensitive to intersymbol interference unlessthe channel symbol rate is small compared to the delay spread of the channel. OFDM is significantly less sensitiveto intersymbol interference, because a special set of signals is used to build the composite transmitted signal. Thebasic idea is that each bit occupies a frequency-time window which ensures little or no distortion of thewaveform. In practice, it means that bits are transmitted in parallel over a number of frequency-nonselectivechannels. Applications of OFDM are found in

Digital Audio Broadcasting (DAB) andDigital Video Broadcasting over the terrestrial network: Digital Terrestrial Television Broadcasting(DTTB). In the DTTB OFDM transmission standard, about 2,000 to 8,000 subcarriers are used.UMTS. The UMTS Forum is selecting an appropriate radio solution for the third generation mobilestandard, as a successor to GSM. OFDM is one of the five competing proposals.Wireless LANs. OFDM is used in HIPERLAN Phase II, which supports 20 Mbit/s in propagationenvironments with delay spreads up to 1 second.

Figure: Signal spectrum of an OFDM signal, which consists of the spectra of many bits, in parallel. Rectangular pulses in timedomain produce sinc-functions in frequency domain.

Above: signal spectrum as transmitted.Below: as received in over a dispersive, time-invariant channel.

The effect of multipath scattering on OFDM differs from what happens to other forms of modulation.A qualitative description and mathematical description of OFDM is presented by Dusan Matic. Jean-Paul Linnartz reviews the effects of a Doppler spread and the associated rapid channel variations.Dusan Matic also studied the system design aspects of OFDM at mm-wavelengths.

Exercise

Consider two subcarrier signals, modulated with rectangular pulse shape of duration T. For which frequencyoffsets are the signals orthogonal? What is the effect of a mild channel dispersion on the orthogonality of thesignals? Are the signals still orthogonal if the channel is changing rapidly?

3/20/2010 Orthogonal Frequency Division Multipl…

wirelesscommunication.nl/…/ofdm.htm 1/3


Problem Description

If the necessary sub-carriers are simply turned off, without anyfurther processing, primary users still experience interference due tothe side-lobes of other sub-carriers.

55 60 65 70 75 80 85 90

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0

Normalized Frequency

Pow

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dB)

Rectangular (no) window


Windowed OFDM

One method with comparatively lower computational complexity isWindowed OFDM (WOFDM).

I In a WOFDM system, a window is used to shape the spectrumof the sub-carriers such that the side-lobes are suppressed.

I However, the window also widens the main-lobe of thesub-carrier spectrum, which causes Inter-Carrier Interference(ICI).

I Different windows can provide a trade-off between thesuppression of the side-lobes and the widening of themain-lobe.

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PS

D

Rectangular (no) windowDolph−Chebyshev window, (α=2.5)


Result of Windowed OFDM

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−30

−20

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0


PS

D

Rectangular (no) windowDolph−Chebyshev window (α=2.5)

Figure: Spectrum of OFDM signal, with and without windowing

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−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N

0

BE

R

OFDM, Dnotch

= 10dB

WOFDM, Dolph−Cheb. (α = 3.4), LMMSE, Dnotch

= 50dB

Figure: Performance loss of WOFDM


Idea of Dual-Windowed OFDM

We observe that the side-lobes of a sub-carrier generally fall withincreasing distance from the main-lobe. Therefore, thecontribution of a sub-carrier located farther away from the notchto the residual power in the notch is not significant. Thus, it is notnecessary that these sub-carriers are shaped dramatically.

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Figure: Single subcarrier without further processing








System Overview

Encoder/Interleaver/Modulator

Mapping/Notching

IFFT Window 1

Window 2

ChannelFFT/EQ

Decoder/Deinterleaver/Demodulator

IFFT

Sensing and Control

Input Output

+SplitterS/P ZPP/S

remove ZPS/P

P/S

xf,1

xf,2

xf x zfy

Figure: Dual-Windowed OFDM (DWOFDM) System Block Diagram


Transmitter

In contrast to the WOFDM system, the DWOFDM system usestwo different windows to shape the signal on different sub-carriers.After mapping data to sub-carriers, the symbol column vector, xf ,is split into two vectors, xf ,1 and xf ,2, such that xf = xf ,1 + xf ,2and xf ,1 = P1xf , and xf ,2 = P2xf , where

P1 = diag([

Lstart−m−1︷︸︸︷1, ..., 1 , 0, ..., 0,

N−Lend−m︷︸︸︷1, ..., 1 ]), (1)

and

P2 = diag([0, ..., 0,

Lend−Lstart+2m+1︷︸︸︷1, ..., 1 , 0, ..., 0]). (2)

The resulting sequences are then added to form the OFDMsymbol, x, i.e.

x = (W1,tF†P1 + W2,tF

†P2)xf . (3)


Example

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PSD

(a)

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PSD

(b)

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PSD

(c)

Figure: (a) Spectrum of subcarriers far away the notch and with a lightwindow (b) Spectrum of subcarriers near the notch and with a strongwindow (c) Overall spectrum


Effect of PA and DAC

In a real OFDM system, before symbols are transmitted to channel,we need Power Amplifier (PA) and Digital and Analog Converter(DAC). The distortion from PA and DAC can be significant.


Formula of PA and DAC

I PA:

y = x/√

(1 + (x/k)2)

I DAC: Here we apply symmetric DAC to quantize thesecontinues signals into discrete form. level is the number ofquantization levels, which will be 2m, where m is number ofbits which will be quantized as one symbol. We also definegap as the distance between two levels.

y = gap ∗ round [(x − 1

2gap)/gap] +

1

2gap

when lowerbound � x � upperbound , wherelowerbound = −(2level−1 − 1/2) ∗ gap andupperbound = (2level−1 − 1/2) ∗ gap


Receiver

yf = FHtx + Fn

= FHt(W1,tF†P1 + W2,tF

†P2)xf + Fn

= (FHtW1,tF†P1 + FHtW2,tF

†P2)xf + Fn.

Since W1,t and W2,t are diagonal, W1,tF† = F†W1, and

W2,tF† = F†W2, where W1, and W2 are circulant matrices, and

their first row is equal to the DFTs of w1 and w2, respectively.Also, since Ht is circulant, H = FHtF

†, where H is diagonal.Consequently

yf = (FHtF†W1P1 + FHtF

†W2P2)xf + Fn

= H(W1P1 + W2P2)︸︷︷︸A

xf + v,

where we let v = Fn.Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios

Receiver

Now yf is equalized byzf = Gyf ,

where G is the equalizer matrix and is equal to

I Conventional Equalizer G = H†

I LMMSE Equalizer G = RxxA†(ARxxA

† + Rvv )−1








Parameters

In this paper, we use a Tukey window with parameter s for w1, anda Dolph-Chbyshev window with parameter α for w2. Given thissetting, parameters α, s, and m must be designed such that agiven notch depth requirement is satisfied, and at the same time,the amount of generated ICI is minimized.


Depth Contour

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α

m

s = 0.05

s = 0.10

s = 0.15s = 0.20s = 0.25

Figure: Contour lines for Dnotch = 30dB


ICI Calculation

PI ,k = E

N∑n=1,n 6=k

Wknxn,f

2= E

[N∑

n=1

|Wkn|2

+N∑

n=1n 6=k

N∑m=1m 6=k

WknWkmxn,f xm,f

. (4)

PI ,k =N∑

n=1,n 6=kn/∈{Lstart ,...,Lend}

|Wkn|2.


Parameter Selection

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0.25

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α

m

0.067

0.0670.067

Notch Depth Contour Line, Dnotch

=30dB, s=0.1

ICI Contour LinesOptimal Parameter Design Point (s=0.1, m=9, α=2.2)

Figure: Optimal parameter design








Simulation Environment

I Encoded using an industry standard rate 1/3 convolutionalcode with constraint length of K = 7 and generatorpolynomials g0 = 1338, g1 = 1668, and g2 = 1718.

I Random interleaver

I BPSK and 16QAM

I At the receiver a soft-decision Viterbi algorithm is used todecode

I The OFDM system has N = 128 sub-carriers.

I A multipath Rayleigh fading channel with an exponentialpower-delay profile.

I The RMS delay spread is equal to 7.5 symbol durations.

I Assumed that the zero-padding between OFDM symbols issufficiently long, and consequently no ISI exists.

I Assumed that the receiver has perfect knowledge of thechannel.


Regular Performance

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10−5

10−4

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10−2

10−1

100

Eb/N

0

BE

R

OFDM, Dnotch

=10dB

WOFDM, Tukey (s = 0.1), LMMSE, Dnotch

=11.5dB

WOFDM, Dolph−Cheb. (α = 2.4), LMMSE, Dnotch

=30dB

WOFDM, Dolph−Cheb. (α = 2.4), no LMMSE, Dnotch

= 30dB

DWOFDM, Tukey & Dolph−Cheb., LMMSE, Dnotch

= 30dB

DWOFDM, Tukey & Dolph−Cheb., no LMMSE, Dnotch

= 30dB

Figure: BER Performance comparison for Dnotch = 30dB


Regular Performance

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10−5

10−4

10−3

10−2

10−1

100

Eb/N

0

BE

R

OFDM, Dnotch

=−10dB

WOFDM, Tukey (s=0.3),LMMSE, Dnotch

=−13.5dB

WOFDM,Dolph−Cheb. (α = 3.4) , LMMSE, Dnotch

=50dB

WOFDM,Dolph−Cheb. (α = 3.4) , no LMMSE, Dnotch

=50dB

DWOFDM, Tukey & Dolph−Cheb., LMMSE, Dnotch

= 50dB

DWOFDM, Tukey & Dolph−Cheb., no LMMSE, Dnotch

= 50dB

Figure: BER Performance comparison for Dnotch = 50dB


Effect of PA

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k

d mea

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DWOFDM PA −30dB

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k

snr

BPSK16QAM16QAM no PABPSK no PA

Figure: PA k-depth curve for Dnotch = 30dB and PA k-snr curve forDnotch = 30dB


Effect of PA

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k

Dno

tch

DWOFDM −50dB

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22

k

snr

16QAM −50dB16QAM no PABPSK −50dBBPSK no PA

Figure: PA k-depth curve for Dnotch = 50dB and PA k-snr curve forDnotch = 50dB


Effect of DAC

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level

Dno

tch

DWOFDM DAC −30dB

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12

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19

level

SN

R

DAC −30dB

BPSK DWOFDM16QAM DWOFDMBPSK DWOFDM no DAC16QAM DWOFDM no DAC

Figure: DAC level-depth curve for Dnotch = 30dB and DAC level-snrcurve for Dnotch = 30dB


Effect of DAC

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45

50

level

Dno

tch

DWOFDM DAC −50dB

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14

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20

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26

level

snr

BPSK16QAMBPSK no DAC16QAM no DAC

Figure: DAC level-depth curve for Dnotch = 50dB and DAC level-snrcurve for Dnotch = 50dB








Conclusion

I Similar to the WOFDM system, our method can createnotches with sufficient depth to avoid interference to theprimary users.

I It can obtain significantly better performance, and hasconsiderably less complexity.

I PA and DAC need to be set properly to prevent spectrumfilling and performance loss.


Future Work

I Compare the performance of other methods, like AIC andsub-carriers weighting, under PA and DAC

I Window design

Any other idea?

a a`


Documents

Dual-Windowed OFDM for Cognitive Radios · Dusan Matic also studied the system design aspects of OFDM at mm-wavelengths. Exercise Consider two subcarrier signals, modulated with rectangular