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Interference Cancellation with Self-interference. Constraint for Cognitive OFDM System. Daiming Qu1, Zhiqiang Wang1, Tao Jiang1, Mahmoud Daneshmand2.
Sidelobe Suppression Using Extended Active Interference Cancellation with Self-interference Constraint for Cognitive OFDM System Daiming Qu1, Zhiqiang Wang1, Tao Jiang1, Mahmoud Daneshmand2 1

Dept. of Electronics and Info. Engineering, Huazhong Univ. of Science and Tech., Wuhan, China 2 AT&T Labs Research, Florham Park, New Jersey, USA

Abstract—To improve the spectrum utilization, more and more attention was paid to OFDM based opportunistic spectrum access (OSA) systems in recent years. In this paper, to enable coexistence between a secondary user and a primary user, a novel method called EAIC was proposed for spectral sculpting of OFDM signal effectively. In EAIC, however, the cancellation signals cause self-interferences to OFDM data tones so that the symbol-error-rate (SER) performance was degraded especially in high order modulation such as 64 QAM. In this paper, a new method called EAIC with self-interference constraint (EAIC-IC) is proposed, in which we analyze the interferences caused by cancellation signals, and then formulate an optimization problem to minimize both the total sidelobe power and the selfinterferences. Simulation results show that the EAIC-IC method can provide a perfect tradeoff between spectrum notch depth and SER performance via adjusting the value of the constraint parameter.

carrier (CC) [8] [9] schemes were proposed to create deeper notches, which actively transmit cancellation signals on these tones and edge tones to cancel the sidelobe of OFDM signal. However, the sidelobe suppression of AIC and CC schemes are not deep enough and sensitive to the cyclic prefix (CP) size. Proper combination of CC and windowing was presented in [10], however, windowing the OFDM signal results in considerable reduction of system throughput.

Keywords-OFDM; out-of-band radiation; sidelobe suppression; oppotunistic spectrum access; cognitive radio

I.

INTRODUCTION

Cognitive radio and dynamic spectrum access have been proposed and obtained more and more attention [1][2] in recent years for the growing needs of improving spectrum utilization. One scheme called opportunistic spectrum access (OSA) allows secondary user to identify and exploit local and instantaneous spectrum white space where the primary user is not present. OFDM is an attractive candidate signal structure for OSA systems [3] ~ [5], because of its capability of transmitting over noncontiguous frequency bands. The coexistence between a secondary user in an OFDM based OSA system and a primary user is illustrated in Figure 1. In OFDM based OSA systems, to enable coexistence with primary user, the constituent tones/subcarriers are turned off at the primary user’s band, creating spectrum notch to limit interference [6] perceived by primary user. Schemes that create deeper spectrum notch in target spectrum band are needed for OFDM based OSA systems. To mitigate the interferences for deeper spectrum notch, [6] adopted guard bands and time domain raised cosine window. Active interference cancellation (AIC) [7] and cancellation This work was supported in part by the National Natural Science Foundation of China (No. 60702039), the International S&T Cooperation Program of China (No. 2008DFA12100), and the National High Technology Development 863 Program of China under Grant 2009AA011803.

Figure 1. OFDM based OSA secondary user coexist with primary user

Several other methods were also proposed to suppress the sidelobe effectively in recent years; however, they have their own disadvantages. Subcarrier weighting [11] [12] can not be applied to quadratic amplitude modulation (QAM) since subcarrier weights are changed block by block. Additive signal [13] method adds a complex-valued sequence to the original signal and degrades the system error performance remarkably. Adaptive symbol transition [14] method adding blocks between OFDM symbols results in lower system throughput. Constellation expansion [15] method transmits symbols from a higher order constellation set and chooses the sequence which results in the lowest-possible sidelobe power level; however, constellation expansion was not suitable for high-order modulation. In [16], we proposed Extended AIC scheme (EAIC) that extends the AIC scheme both in the time domain and in the frequency domain. The EAIC method creates very deep spectral notches of about 80 dB. Shortcoming of this method is that the EAIC tones cause self-interferences to data tones and result in system SNR degradation. In this paper, we propose a new method EAIC-IC to suppress the sidelobe of OFDM signals. In EAIC-IC scheme,

we analyze the self-interferences of cancellation signals, and formulated an optimization problem to minimize the total sidelobe power and the self-interferences. The optimization can provide a tradeoff between spectrum notch depth and selfinterference power. Simulation results show that EAIC-IC method can provide a spectrum notch depth of about 73 dB when QPSK modulation was adopted and 32 dB when 64QAM modulation was adopted, respectively, with SER loss less than 0.1 dB. For giving the SER requirements of certain specific OFDM systems, the optimal sidelobe suppression can be obtained through adjusting interference constraint parameter The rest of this paper is organized as follows. The system model based on EAIC method is presented in section II. Section III derives the self-interference to data tones caused by cancellation signals and formulates the optimization problems with self-interference constraint. Simulation results are provided in Section IV. We summarize and conclude this paper in Section V.

For

P/S

S/P

IFFT

ĂĂ

ĂĂ

k 0

j 2S kn ) N

n

0,1, , N  1

(1)

In OFDM based OSA systems, when EAIC method is applied, not only the constituent tones/subcarriers are turned off at the primary user’s channel for creating spectrum notches to limit interference perceived by primary users, but also cancellation signals c(n) of length P is added to d(n) to create spectrum notches deeper, where P is an even number and equal to or larger than N  N cp . Then the transmitted signal for one OFDM symbol is described as c ( n)  d e ( n)

,

1 N

c ( n)

j 2S ki n ) N

l

¦ C (i) exp( i 1

n 0,1,, P  1

(4)

where C (i ) is the weight of EAIC tone i. The matrix representation of the cancellation signals is c

(6)

AC

>C(1)

C(2)  C(l ) @

T

>c(0)

c(1)  c( P  1)@

T

The sidelobe power in the target spectrum band is measured by the sum of the sidelobe power at sample points ^ f1 , , f m ` , which is given by

For OFDM systems with cyclic prefix (CP), the length of d(n) should be longer to include samples of CP which has a N cp length.

t ( n)

cp

and the element of the matrix A at n-th row and i-th column is 1/ N exp( j 2S ki n / N ) .

ĂĂ

ĂĂ

N 1

P  N  N / 2

a

The cancellation signals c(n) is given by

c

In this section, EAIC method is introduced briefly. The system model of EAIC method is depicted in Figure 2. In OFDM systems, one N-subcarrier OFDM signal in the discrete time domain is

¦ D(k ) exp(

N  N cp ,

length

c is the vector form of cancellation signals

Figure 2. System model of EAIC method

1 N

of

b a  N  N cp , where a denotes the number of zeros inserted before d(0).

C

d ( n)

d(n)

(3)

where C is the vector form of EAIC tones

SYSTEM MODEL AND EAIC METHOD

II.

d e ( n)

0 d n d a 1 ­ 0 ° ®d (n  a) a d n d b  1 ° 0 b d n d P 1 ¯

n 0,1,, P  1

(2)

where d e (n) consists of d(n) and equal number of zeros before and after d(n).

Ed ( j )

P 1

¦ d (n) exp(

 j 2S nf j

e

n 0

fs

)

j

1, , m

(7)

The matrix representation is Ed

(8)

Ft d e

where d e is the vector form of OFDM data signals with zeros in both head and tail. de

ª¬0 d (0) d (1)  d ( N  N cp  1) 0 º¼

T

E d is the sidelobe power at all sample points

Ed

> Ed (1)

Ed (2)  Ed (m)@

T

and the element of Ft at j-th row and n-th column is exp( j 2S nf j / f s ) . Similarly, cancellation signals power at frequency f j is given by Ec ( j )

P 1

 j 2S nf j

n 0

fs

¦ c(n) exp(

The matrix representation is

)

j

1, , m

(9)

Ec

Ft c

(10)

Ft AC

where Ec is the cancellation signals power at all sample points,

Ec

> Ec (1)

Ec (2)  Ec (m)@ . T

To minimize the total power of transmitted signals with EAIC at the target band, the cancellation signals power Ec should cancel the sidelobe power E d effectively by choosing an appropriate C, that is, the following optimization problem has to be solved min Ed  Ec

2

(11)

C

EAIC has a better sidelobe suppression performance [16]; however, the interferences to data tones brought serious SNR degradation, and when CP is considered, the SNR will become worse, the interferences can not be ignored, and some interferences to data tones constraint should be considered, which will be discussed in next section. III.

EAIC WITH SELF-INTERFERENCE CONSTRAINT

It is obvious that EAIC introduces these interferences from two aspects. First, in the frequency domain, EAIC tones with frequency ki 'f and ki  are non-orthogonal with the tones with frequency ki 'f and ki  , so the former tones will cause interferences to data tones. Second, in the time domain, the time duration of all EAIC tones were P which is longer than the duration of one OFDM signal, so the head and tail of the current cancellation signals c(n) will be added to the OFDM symbols ahead and behind, respectively. If the duration of the head or tail of the current cancellation signals c (n ) added to the OFDM symbols ahead or behind does not occupy a whole Fast Fourier Transform (FFT) window of OFDM symbols, it means that the data suddenly dropped to zero before FFT module, which is illustrated in Figure 3, and this will introduce abundant frequency components and result in interferences to data tones.

A. Interference to former, current and latter OFDM symbols Former OFDM symbol

Current OFDM symbol

CP

CP

DATA

DATA

Latter OFDM symbol CP

DATA

+ 0

CANCELLATION SIGNAL

0

which were illustrated in Figure 3. We analyze the interferences to the three symbols, respectively. The part of cancellation signals added to the former symbol is denoted by c f (n) , and the vector form of c f (n) is given by

cf

(12)

AfC

where the rows of A f are equal to the first a rows of A in (6). We should insert some zeros before c f (n) to generate a vector of an appropriate length for N-order FFT, which is depicted in Figure 2, and then the vector form of the interferences to the former symbol is given by (13)

I f = FA fz C

where F is FFT matrix with some all zeros rows for no considering the target band tones which is turned off. A fz is T

from ª¬0 A f º¼ without the first N cp rows for the reason that CP should be removed before FFT module. The part of cancellation signals added to the current symbol is denoted by cc (n) , and the vector form of cc (n) is given by

cc

(14)

AcC

where the rows of A c are equal to the rows from a+1 to a  N  N cp of A in (6). So the vector form of the interferences to the current symbol is given by

I c = Fcc = FA cz C

(15)

where A cz is from A c without the first N cp rows for the same reason about CP. The part of cancellation signals added to the latter symbol is denoted by cl (n) , and the vector form of cl (n) is given by

cl

(16)

Al C

where the rows of Al are equal to the last a rows of A in (6). Similar to the former symbol, we should insert some zeros after cl (n) to generate a vector of an appropriate length for Norder FFT. Hence, the vector form of the interferences to the latter symbol is given by (17)

I l = FAlz C Figure 3. Interference to OFDM data caused by EAIC cancellation cignals

To simplify the analysis of interferences to data tones I, we assume that the length of cancellation signals P is no larger than three OFDM symbols, i.e., 3 N  N cp , which means that cancellation signals only impact three OFDM data symbols, including the current one, the former one and the latter one,

where Alz is from > A l same reason about CP.

0@ without the first N cp rows for the T

B. Interference constraint The whole interferences to one OFDM data symbol is given by I

2

If

2

 Ic

2

 Il

2

(18)

min Ed  Ec

2

C

 PI

2

(19)

By choosing appropriate C, the above objective function can be minimized to be the least square solution of the following linear equations [17] ª¬Ec

PI f

PIc

P I l º¼

T

> E d

0 0 0@   T

Using (8), (10), (13), (15), and (17), (20) can be rewritten as ª¬Ft A P FA fz

P FA cz

T

P FA lz º¼ C

> Ft d e

0 0 0@  T

while an about 32 dB spectrum notch depth can be created, about 13 dB better than AIC method in the same situation. 10 0 Normalized Power Spectrum Density (dB)

A new parameter P is introduced, which is a nonnegative real number that can provide a tradeoff between spectrum notch depth and interference power to data tones. The optimization problem in (11) can be rewritten as

-10

turning off

-20 -30

AIC

-40 EAIC mu=3

-50

EAIC mu=1

-60 EAIC mu=0.1

-70 -80

EAIC mu=0

-90

The linear square solution to the above linear equations is given by

80

85

90 frequency (x Ƹf )

95

100



ª Ft A º ª Ft d e º « P FA » « 0 » fz » »   C=« u« « P FA cz » « 0 » « » « » ¬ P FA lz ¼ ¬ 0 ¼

Figure 4. Spectrum of OFDM signal based on EAIC-IC with different constraint parameters, AIC, and nine tones turning off 0

10



where [ ] is known as Moore-Penrose generalized inverse.

SIMULATIONS

In this section, the performances of EAIC-IC are illustrated via simulations. For all the following simulations, a 128subcarrier OFDM system with CP of length 32 is considered. These parameters are selected according to [18]. The length of cancellation signals P is selected to be 256. In order to get power spectrum density of the transmitted signals, 10000 OFDM symbols were simulated and Welch method with Blackman window was adopted. The target spectrum band is from 84'f to 90'f , where 'f is the frequency interval between subcarriers. The sampling points from 84'f to 90'f , spaced 0.25 'f , are applied, and EAIC tones with frequencies from 83'f to 91'f , spaced 0.5'f , are applied. The normalized power spectrum density and symbol error ratio (SER) of OFDM signal with 64QAM modulation based on EAIC-IC are shown in Figure 4 and Figure 5, respectively. When the constraint parameter P is selected to be 0, it means that there is not any constraint to the interferences to data tones caused by EAIC tones, and hence, the weight of EAIC tones C was selected to cancel the sidelobe extremely, creating a notch depth about 73 dB, 54 dB better than AIC method in the same situation; meanwhile, strong interferences to data tones were introduced to OFDM data tones, about 0.77 dB signal-to-noise ratio (SNR) loss in SER 10-3. When the constraint parameter P increases, the spectrum notching performance degrades, and SER loss decreases. When P is selected to be 3, there is nearly no interferences to data tones caused by cancellation signals,

10

Symbol Error Ratio (SER)

IV.

mu=0 mu=0.1 mu=0.3 mu=1 mu=3 turning off

-1

-2

10

-3

10

-4

10

-5

10

-6

10

10

11

12

13 14 15 16 17 Signal-to-Noise Ratio (SNR) in bit (dB)

18

19

20

Figure 5. SER of OFDM signal based on EAIC-IC with different constraint parameters; 64QAM modulation

In fact, the parameter P can provide a tradeoff between spectrum notching performance and SNR degradation, which is illustrated in Figure 6. Deeper notch depth can be obtained with larger SNR loss. In practice, an appropriate value of P should be selected to satisfy the different SER requirements of specific OFDM systems, e.g., when a spectrum notch depth about 50 dB is needed, the OFDM system based on EAIC-IC has SNR loss 0.1 dB and 0.25 dB in SER 10-2 and 10-3, respectively, and when a spectrum notch depth about 60 dB is needed, the OFDM system based on EAIC-IC has SNR loss 0.2 dB and 0.5 dB in SER 10-2 and 10-3, respectively. When QPSK modulation was adopted, OFDM symbols have the same spectrum notching performance with that when 64QAM modulation was adopted, and the SER performances are much better than that when 64QAM modulation was adopted. Even though P is selected to be 0, there is nearly no

interferences to data tones, which is shown in Figure 7. Simulation results show that OFDM symbols based on EAICIC with QPSK modulation can obtain a spectrum notch depth about 73 dB nearly without any interference to data tones, i.e., in OFDM system based on EAIC method, the interference constraint is no needed when QPSK modulation is adopted.

introduced, which can provide a tradeoff between spectrum notching performance and SNR degradation. For giving the SER requirements of specific OFDM systems, the most sidelobe suppression can be obtained through adjusting interference constraint parameter. REFERENCES

75

[1]

Target Band Notch Depth (dB)

70 65

[2]

60 55

[3]

50

[4]

45 40

30

[5]

@ SER 0.001 @ SER 0.01

35

0

0.2

0.4 0.6 0.8 Signal-to-Noise Ratio (SNR) Loss (dB)

1

Figure 6. Spectrum notch versus SNR loss with different constraint; 64QAM modulation

[7]

[8]

0

10

EAIC mu=0 turning off

-1

[9]

10

Symbol Error Ratio (SER)

[6]

-2

10

[10]

-3

10

[11] -4

10

[12]

-5

10

[13]

-6

10

0

1

2

3 4 5 6 7 Signal-to-Noise Ratio (SNR) in bit (dB)

8

9

10

Figure 7. SER of OFDM signal based on EAIC-IC with P =0; QPSK modulation

V.

[14]

[15]

CONCLUSION

In this paper, we analyze the interferences to data tones caused by cancellation signals and proposed a new method EAIC-IC to constrain these interferences. Simulation results show that EAIC-IC method can provide a spectrum notch depth of about 73 dB when QPSK modulation was adopted and 32 dB when 64QAM modulation was adopted, respectively, with SER loss less than 0.1 dB. The constraint parameter P was

[16]

[17] [18]

I. J. Mitola, “Cognitive radio for flexible mobile multimedia communications,” in Proc. IEEE Mobile Multimedia Conference, Nov. 1999, pp. 3–10. S. Haykin, “Cognitive radio: Brain-empowered wireless communications,” IEEE J. Select. Areas Commun., vol. 23, no. 2, pp. 201–220, Feb. 2005. T. Weiss and F. Jondral, “Spectrum pooling: An innovative strategy for enhancement of spectrum efficiency,” IEEE Commun. Mag., vol. 42, pp. 8–14, Mar. 2004. U. Berthold and F.K. Jondral, “Guidelines for designing OFDM overlay systems,” in Proc. 1st IEEE Symp. New Frontiers Dynamic Spectrum Access Networks, Nov. 2005, pp. 626-629. H. Tang, “Some physical layer issues of wide-band cognitive radio systems,” in Proc. 1st IEEE Symposium New Frontiers Dynamic Spectrum Access Networks, Nov. 2005, pp. 151-159. T. Weiss, J. Hillenbrand, A. Krohn, and F. K. Jondral, “Mutual interference in OFDM-based spectrum pooling systems,” in Proc. IEEE Vehicular Technology Conference, vol. 4, May 2004, pp. 1873–1877. H. Yamaguchi, “Active interference cancellation technique for MBOFDM cognitive radio,” in Proc. IEEE European Microwave Conference, vol. 2, Oct. 2004, pp. 1105–1108. S. Brandes, I. Cosovic, and M. Schnell, “Sidelobe Suppression in OFDM Systems by Insertion of Cancellation Carriers,” in Proc. IEEE Vehicular Technology Conference, Vol. 1, Sept., 2005, pp. 152 – 156. S. Brandes, I. Cosovic, and M. Schnell, “Reduction of Out-of-Band Radiation in OFDM Systems by Insertion of Cancellation Carriers,” IEEE Communications Letters. vol. 10, no. 6. June 2006. S. Brandes, I. Cosovic, and M. Schnell, “Reduction of out-of-band radiation in OFDM based overlay systems,” in Proc. 1st IEEE Symposium New Frontiers Dynamic Spectrum Access Networks, Nov. 2005, pp. 662 – 665. I. Cosovic, S. Brandes, and M. Schnell, “Subcarrier Weighting: A Method for Sidelobe Suppression in OFDM Systems,” IEEE Communications Letters. vol. 10. no. 6. June 2006. I. Cosovic, S. Brandes, and M. Schnell, “A Technique for Sidelobe Suppression in OFDM Systems,” in Proc. IEEE Global Telecommunications Conference, vol. 1, 28 Nov.-2 Dec. 2005. I. Cosovic, and T. Mazzoni, “Sidelobe Suppression in OFDM Spectrum Sharing Systems Via Additive Singal Method,” in Proc. IEEE Vehicular Technology Conference, April 2007, pp. 2692-2696. H.A. Mahmoud, H. Arslan, “Sidelobe Suppression in OFDM-Based Spectrum Sharing Systems Using Adaptive Symbol Transition,” IEEE Communications Letters, Vol. 12, no. 2, pp. 133-135, Feb. 2008. S. gadarai, R. Rajbanshi, A.M. Wyglinski, G.J. Minden, “Sidelobe Suppression for OFDM-Based Cognitive Radios Using Constellation Expansion,” in Proc. IEEE wireless Communications and Networking Conference, 31 March -3 April 2008, pp. 888 - 893. Z. Q. Wang, D. M. Qu, T. Jiang, “Spectral Sculpting for OFDM Based Opportunistic Spectrum Access by Extended Active Interference Cancellation,” Global Telecommunications Conference, 2008. IEEE GLOBECOM 2008. Nov. 30 2008-Dec. 4 2008 Page(s):1 – 5. W. Gander, “Least Squares with a Quadratic Constraint,” Number. Math.36, 291-307 (1981). IEEE P802.15-03/268r3, “Multi-band OFDM Physical Layer Proposal for IEEE 802.15 Tast Group3a”, April 2004.