dual-windowed ofdm for cognitive radios · dusan matic also studied the system design aspects of...
TRANSCRIPT
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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.
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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.
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Examples of Two Design
I Overlay Design
Frequency
Pow
er D
ensi
ty
Pri
ma
ry U
ser
3
Pri
mary
Use
r 2
Pri
ma
ry U
ser
1
CR
Band
1
CR
Band
2
CR
Band
3
I Underlay Design
Noise Floor
UWB Pri
ma
ry U
ser
3
Frequency
Po
wer
D
ensi
ty
Pri
ma
ry U
ser
2
Pri
ma
ry U
ser
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,”
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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
−50
−40
−30
−20
−10
0
Normalized Frequency
Pow
er (
dB)
Rectangular (no) window
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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.
55 60 65 70 75 80 85 90
−50
−40
−30
−20
−10
0
Normalized Frequency
PS
D
Rectangular (no) windowDolph−Chebyshev window, (α=2.5)
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Result of Windowed OFDM
40 50 60 70 80 90 100 110 120
−30
−20
−10
0
Normalized Frequency
PS
D
Rectangular (no) windowDolph−Chebyshev window (α=2.5)
Figure: Spectrum of OFDM signal, with and without windowing
0 2 4 6 8 10 12 14 16 18 2010
−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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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.
55 60 65 70 75 80 85 90
−50
−40
−30
−20
−10
0
Normalized Frequency
Pow
er (
dB)
Rectangular (no) window
Figure: Single subcarrier without further processing
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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)
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Example
30 40 50 60 70 80 90 100−40
−30
−20
−10
0
Normalized Frequency
PSD
(a)
30 40 50 60 70 80 90 100−40
−30
−20
−10
0
Normalized Frequency
PSD
(b)
30 40 50 60 70 80 90 100−40
−30
−20
−10
0
Normalized Frequency
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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.
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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.
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Depth Contour
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
5
10
15
20
25
30
35
40
α
m
s = 0.05
s = 0.10
s = 0.15s = 0.20s = 0.25
Figure: Contour lines for Dnotch = 30dB
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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.
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Parameter Selection
1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
5
10
15
20
25
30
35
40
0.05 0.05 0.05
0.1
0.1
0.10.1
0.15
0.15
0.15
0.15
0.2
0.2
0.2
0.25
0.25
0.3
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
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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.
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Regular Performance
0 2 4 6 8 10 12 14 16 18 2010
−6
10−5
10−4
10−3
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Regular Performance
0 2 4 6 8 10 12 14 16 18 2010
−6
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Effect of PA
0 2 4 6 8 10 12 14 16 18 2012
14
16
18
20
22
24
26
28
30
k
d mea
n (dB
)
DWOFDM PA −30dB
0 0.5 1 1.5 2 2.510
12
14
16
18
20
22
k
snr
BPSK16QAM16QAM no PABPSK no PA
Figure: PA k-depth curve for Dnotch = 30dB and PA k-snr curve forDnotch = 30dB
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Effect of PA
0 5 10 15 20 25 3010
15
20
25
30
35
40
45
50
k
Dno
tch
DWOFDM −50dB
0 0.5 1 1.5 2 2.5 3 3.512
13
14
15
16
17
18
19
20
21
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Effect of DAC
0 2 4 6 8 10 12 145
10
15
20
25
30
level
Dno
tch
DWOFDM DAC −30dB
3 4 5 6 711
12
13
14
15
16
17
18
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
Effect of DAC
3 4 6 8 10 12 145
10
15
20
25
30
35
40
45
50
level
Dno
tch
DWOFDM DAC −50dB
4 5 6 712
14
16
18
20
22
24
26
level
snr
BPSK16QAMBPSK no DAC16QAM no DAC
Figure: DAC level-depth curve for Dnotch = 50dB and DAC level-snrcurve for Dnotch = 50dB
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
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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.
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios
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`
Di Wang, Tianqi Wang, and Alireza Seyedi Dual-Windowed OFDM for Cognitive Radios