Self-Interference Canceller for Full-Duplex Radio Relay Station Using Virtual Coupling Wave Paths

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1 Sef-Interference Canceer for Fu-Dupex Radio Reay Station Using Virtua Couping Wave Paths Kazunori Hayashi Yasuo Fujishima Megumi Kaneko Hideaki Sakai Riichi Kudo and Tomoki Murakami Graduate Schoo of Informatics, Kyoto University, Kyoto, Japan E-mai: Te/Fax: E-mai: Te/Fax: E-mai: Te/Fax: E-mai: Te/Fax: /4755 NTT Corporation, Yokosuka, Japan E-mai: E-mai: Abstract The paper considers a couping wave canceer for fu dupex radio reay station using adaptive antenna array. Taking advantage of the fact that couping waves to be canceed at the reay station consist of its own past transmitted signas, we propose a beamforming method using not ony received signas at actua antenna eements but aso virtua received signas, which are generated in the reay station with artificia channe impuse responses, that is to say, virtua couping wave paths. With the approach, the proposed method can eiminate couping waves without increasing the number of actua antenna eements even when the number of couping wave paths is arge due to high speed communications. Computer simuation resuts show that the proposed method achieves couping wave canceation with smaer number of antenna eements than that of couping wave paths. I. INTRODUCTION There has been an increasing interest in the utiization of radio reay stations for enhancing wireess communications systems. In particuar, the concept of fu dupex radio reay station using the same radio resources for the transmission and the reception has drawn much attention due to the potentia impact on the spectra efficiency. In such a reay system, a couping wave from the transmitter to the receiver of the same reay station causes serious probems, such as distortion of the signa or osciation. So far, couping wave canceation schemes using adaptive fiter have been proposed [1]-[4], however, the approach requires the gain of the ampifier at the reay station to be sma enough to guarantee the stabiity of the adaptive fiter. On the other hand, an adaptive antenna array can be used for the canceation of the couping waves as we [5][6], but a arge number of antenna eements are needed in order to obtain the necessary degree of freedom of the antenna array to cance the couping wave in high speed communications systems. In this paper, we consider the couping wave canceation scheme for fu dupex radio reay stations using adaptive antenna array. Taking advantage of the fact that the couping waves to be canceed at the reay station consist of its own past transmitted signas, we propose a beamforming method using not ony received signas at actua antenna eements but x(n) BS BS to RS path H (z) 1 H (z) M Rx. antenna array r 1 (n) r M (n) w * 1 y(n) couping wave path C (z) 1 C (z) M reay station w M * z -a G(z) g u(n) RS to MT path Tx. antenna Fig. 1. Fu dupex radio reay station using adaptive antenna array. aso virtua received signas, which are generated in the reay station with artificia FIR (Finite Impuse Response) fiters, that is to say, virtua couping wave paths. The proposed method can obtain sufficient degree of freedom to cance the couping waves by just increasing the number of FIR fiters in the reay station without increasing the number of actua antennas. Moreover, the proposed canceer can operate in a bind manner for a specia configuration. Computer simuation resuts show that the proposed approach using sufficient number of virtua couping wave paths can achieve the canceation regardess of the number of actua antennas. II. SYSTEM MODEL Consider the downink communication using fu dupex radio reay station as shown in Fig. 1, where transmit (Tx.) antennas of the base station (BS) and the reay station (RS) have singe eement, whie the receiving (Rx.) antenna of the RS is an antenna array with M eements. The transmitted signa from the BS x(n) is assumed to be white, zero mean and variance of σx. The received signa at the m-th antenna eement of the RS is given by r m (n) = h m x(n ) c m k u(n k)n m (n), (1) MT

2 where {h 0 m,,h m } and {c 0 m,,cm } are impuse responses of the channe from the BS to the m-th antenna eement and from the Tx. antenna of the RS to the m-th antenna (namey, the m-th couping wave path), respectivey. Moreover, n m (n) is the additive white noise with zero mean and variance σ n, and u(n) is the transmitted signa from the RS. In the figure, and H m (z) = h mz, () C m (z) = c k mz k, (3) are the transfer functions of the corresponding channes. Defining the received signa vector r(n) as r(n) =[r 1 (n) r M (n)] T = h x(n ) c k u(n k)n(n), (4) where h =[h 1 h M] T, c k =[c k 1 c k M ] T, n(n) =[n 1 (n) n M (n)] T, the output of the adaptive antenna array is obtained by the inner product between r(n) and beamforming vector w = [w 1 w M ] T as y(n) =w H r(n) = w H h x(n ) w H c k u(n k)w H n(n). (5) The fundamenta roe of the RS is to forward the signa from the BS to the mobie termina (MT) with the ampification. After giving the gain g by the ampifier, the transmitted signa from the RS is written as u(n) =gz a y(n), (6) where z a is a deay of a ( L) sampes artificiay introduced so as to make u(n) uncorreated with x(n) [3]. From (5), in order to eiminate the couping wave, the beamforming vector has to satisfy the condition w H c k =0, (k =0,,K 1), (7) where the number of equations is K and that of variabes {w 1,,w M } is M. This means that the number of antenna eements M has to be greater than the number of paths K for the perfect canceation of the couping wave for any reaization of the couping wave path. Therefore, with the conventiona approach, we need a arge number of antenna eements for high speed transmissions, because of the higher time resoution due to high samping rate [7]. x(n) BS to RS path H (z) 1 H M (z) Rx. antenna array reay station w 1 * w M * w^ * 1 virtua antenna array w^ * Q couping wave path C (z) 1 C (z) M C ^ 1 (z) Tx. antenna z -a G(z) C ^ Q(z) virtua couping wave path Fig.. Proposed radio reay station with virtua couping wave paths. III. PROPOSED COUPLING WAVE CANCELLER g u(n) A. Virtua Couping Wave Paths The couping waves comprise the reay station s own past transmitted signa u(n k), (k =1,,K 1), which is avaiabe if it has a memory device. This means that the reay station can generate artificia received signas of couping wave paths using u(n k) and some appropriate FIR fiters. We ca the FIR fiters as virtua couping wave paths and the output signas are processed together with the received signas at actua antenna eements. With the approach, we can increase the degree of freedom of the antenna array for couping wave canceation without adding actua antenna eements. Note that the artificia couping waves are composed ony by u(n k)s and do not incude signas from the BS or the additive noise. To be more specific, Q virtua couping wave paths of FIR fiters are empoyed in the reay station as shown in Fig.. The impuse response of the q-th FIR fiter is defined as {ĉ 0 q ĉq } and the transfer function is given by Ĉ q (z) = ĉ k q z k. (8) Denoting the received signa of the q-th virtua couping wave path as ˆr q (n), and defining the virtua received signa vector as ˆr(n) =[ˆr 1 (n) ˆr Q (n)] T, (9) the concatenated received signa vector of r(n) and ˆr(n) is given by r(n) =[r T (n) ˆr T (n)] T = h x(n ) c k u(n k)ñ(n), (10)

3 where h =[h T 0 1 Q ] T, c k =[c T k ĉt k ] T, ĉ k =[ĉ k 1 ĉ k Q] T, ñ(n) =[n T (n) 0 1 Q ] T. Defining virtua beamforming vector as ŵ =[ŵ 1 ŵ Q ] T, (11) and the concatenated beamforming vector as w =[w T ŵ T ] T, (1) the output of the adaptive antenna array is written as y(n) = Therefore, if w H h x(n ) w H c k u(n k) w H ñ(n). (13) w H c k =0, (k =0,,K 1) (14) hods, the couping waves are competey eiminated. Compared with (7), we recognize that the number of the variabes {w 1,,w M, ŵ 1, ŵ Q } of (14) is increased by the number of the virtua couping wave paths Q. This enabes us to increase the degree of freedom of the adaptive antenna array for the canceation of the couping waves. B. Impuse Responses of Virtua Couping Wave Paths We propose two practica methods to determine the impuse responses of virtua couping wave paths. If we can empoy the same number of FIR fiters as the ength of the impuse response of the couping wave paths K, the couping waves can be eiminated by setting { ĉ k β, q = k q =, (15) 0, otherwise where β is an arbitrary constant. Henceforth, we ca the approach VCC (virtua couping channe) 1. On the other hand, an aternative method (VCC) is appicabe for the case of Q<K. VCC uses reaizations of random variabes of independent and identica distribution as ξ 0 1 ξ1 ξ 0 ĉ 0 =..,, ĉ ξ =., (16) ξq 0 ξ Q where each ξs t (s = 1,,Q, t = 0,,K 1) is a reaization of a random variabe Ξ t s from a certain distribution. C. Beamforming Vector of Proposed Adaptive Array We consider the beamforming vector based on the MMSE criterion. Assuming that d is the deay time of the path with the maximum power as d = argmax h, (17) the cost function can be written as J( w) =E[ x(n d) w H r(n) ]. (18) Note that the assumption is just for the simpicity and we can aso set the weighted sum of x(n ), =0,,L 1 to be the desired signa in order to improve the SNR (Signa to Noise Ratio) at the MT. The optima MMSE beamforming vector is obtained as where w MMSE = σ xr r h d, (19) R r =E [ r(n) r H (n) ] = σx h hh σu c k c H k σnrñ, (0) [ ] IM 0 Rñ =, (1) 0 0 and ( ) denotes Moore-Penrose pseudo inverse. Here, we use pseudo inverse because R r may be singuar. D. Bind Couping Wave Canceation When M =1, the proposed method can operate in a bind manner. Here, the term bind means that the beamforming vector can be updated without any prior information such as piot signas or h d. Note that, with the configuration, ony the couping waves can be canceed using the signas from the virtua paths, whie the antenna cannot steer the beam pattern to any other signas. As a resuts, a the signas from the BS are captured in this case. By setting the weight of the actua antenna to be 1, we obtain the optimum beamforming vector as w = ( v H R 1 r k v) 1 R 1 r v, () where v = [ ] T. As for the correation matrix, we can repace R r by a sampe correation matrix obtained by using the update rue ˆR r (n) = n 1 n ˆR r (n 1) 1 n r(n) rh (n). (3) IV. NUMERICAL RESULTS Tabe I shows the numerica experiment conditions. The channes between the BS and the RS, and couping wave paths are assumed to be Rayeigh fading channe with and 13 paths, respectivey. OFDM (Orthogona Frequency Division Mutipexing) signaing with FFT (Fast Fourier Transform) size of 64 and the guard interva of 16 is used as the moduation scheme. We set the gain of the ampifier at the

4 TABLE I SYSTEM PARAMETER OF NUMERICAL EXPERIMENT BS-RS channe Rayeigh fading ( paths) Couping wave paths Rayeigh fading (13 paths) Transmission scheme OFDM Mod./Demod. scheme QPSK coherent detection FFT size 64 Guard ength 16 Gain at the RS g =10 5 The number of trias 100, 000 RS to be g =10 5 and VCC1 is used for the virtua couping wave paths. For the evauation of the couping wave canceation performance, we adopt BER (Bit Error Rate) at the output of the adaptive array of the RS, athough the RS does not have to decode the received signa in the actua operation. Figure 3 iustrates the BER versus the received SNR of the RS, where the sum of the number of actua and virtua antennas is kept to 16. From the figure, we can see that the proposed method can achieve the best performance when M =3and Q =13. This is because the proposed method with Q 13 can competey eiminate the couping waves, whie greater M is desired from a view point of the diversity effect on the signas from the BS. This aso means that the capabiity of the virtua antennas to cance the couping waves is better than that of the actua antennas. The gain given by the RS to the desired signa depends not ony on the gain of the ampifier g but aso the beamforming vector, therefore, we have evauated the overa gain defined as g w H h i j h j i. (4) Figure 4 shows the overa gain performance of the proposed method. We can see that M =3and Q =13can achieve the best gain performance again. This is because, with Q =13, a the degree of freedom of the actua antenna can be used ony for the reception of the desired signas from the BS. Finay, we have evauated the performance of the proposed method with M = 1 and bind operation. The correation matrix is obtained by (3) and the normaized SCE (squared canceing error) defined as y(n) 10 og wh h x(n ) 10 (5) wh h x(n ) is used for the performance metric. Figure 5 iustrates the SCE performance using the beamforming vector after the adaptation of 5, 000 steps. From the figure, we can see that the couping wave is amost perfecty canceed and ony the observation noise is remaining in the output of the array. V. CONCLUSIONS In this paper, we have proposed a couping wave canceer with an adaptive array for the reaization of a radio reay BER gain M=1, Q=15 M=, Q=14 M=3, Q=13 M=4, Q=1 M=5, Q=11 M=6, Q= x Fig. 3. BER performance target vaue 4 M=1, Q=15 M=, Q=14 M=3, Q=13 M=4, Q=1 M=5, Q=11 M=6, Q= Fig. 4. Gain performance station, which can simutaneousy transmit and receive signas using the same carrier frequency. The key issue about the proposed method is the introduction of the virtua couping wave paths using the reay station s past transmitted signas. Moreover, we have proposed a bind couping wave canceation scheme with an omni directiona antenna and virtua antennas. From the numerica resuts, it can be concuded that the proposed approach with sufficient number of virtua couping wave paths can efficienty eiminate the couping waves even when their number is greater than that of actua antenna eements. REFERENCES [1] K. Yamazaki, R. Hayashi, F. Ishizu, M. Miyake, Y. Takeuchi, and K. Haeiwa, A study on a oop canceer for SFN in digita terrestria broadcasting, IEICE technica report. RCS, vo. 100, no. 194, pp , Juy 000 (in Japanese).

5 SCE [db] Fig. 5. SCE performance (M =1) [] K. Imamura, H. Hamazumi, K. Shibuya, M. Sasaki, Loop interference canceation method for reay station in singe frequency networks, J. Inst. Image Information Teevision Eng., vo. 54, no. 11, pp , 000 (in Japanese). [3] H. Sakai, T. Oka, and K. Hayashi, Simpe adaptive fiter method for canceation of couping wave in OFDM signas at SFN reay station, Proc. EUSIPCO 006, Sept [4] L. Sun and A. Sano, Adaptive couping wave canceation for SFN reay station in OFDM systems, IEICE Trans. Commun., vo. J89-A, no. 10, pp , Oct. 006 (in Japanese). [5] M. Shirakabe, T. Fujii, and M. Nakagawa, Couping interference reduction system using adaptive array antenna in SFN repeater, IEICE technica report. NS, vo. 101, no. 195, pp. 37-4, Juy 001 (in Japanese). [6] B. Chun, E. -R. Jeong, J. Joung, Y. Oh, and Yong H. Lee, Pre nuing for sef interference suppression in fu dupex reays, Proc. of APSIPA ASC 009, Sapporo, Japan, Oct [7] A. Godsmith, Wireess communications, Cambridge University Press, 005.

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