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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.

Multi-user MIMO Relay System with Self-interference Cancellation Lingfan Weng and Ross D. Murch Department of Electrical and Computer Engineering Hong Kong University of Science and Technology Clear Water Bay, Hong Kong Email: {lingfan, eermurch}@ust.hk

Abstract— Next generation wireless communication systems need to support data rates much greater than 3G systems. This will require more efficient utilization of the radio resource. Relay and MIMO (Multiple Input Multiple Output) techniques can significantly enhance system power efficiency, extend system coverage and are considered promising candidates for next generation wireless communication systems. In this paper, we propose a multi-user MIMO relay protocol which utilizes self-information to subtract the interference in two-way communication systems. It is shown that the proposed protocol achieves more than 30% capacity gain compared to previously proposed multi-user MIMO relay protocols in various system scenarios. An adaptive relay power allocation algorithm is also discussed to further increase the system power efficiency.

I. I NTRODUCTION New network infrastructure needs to be developed for next generation wireless communication systems. One key reason [1] is that significantly higher data rates impose serious power implications. This is because the per symbol energy decreases linearly with increasing data rate given a fixed transmit power. Relay based multi-hop wireless networks turns out to be an economically justifiable solution and have attracted research and industry interest recently. A disadvantage of relays, however, is that if they operate in half-duplex mode, i.e., they cannot transmit and receive at the same time, part of the radio resource needs to be allocated for the transmission between the relays and the mobiles, which considerably reduces the system throughput. This is one of the major obstacles that hinder the development of relay based wireless multi-hop networks [1]. Various methods have been discussed to overcome the difficulty. In [2], channels from neighboring cells are reused, while in [3] unlicensed spectrum is utilized for the relay to mobile link. Another method is to consider two-way communications where both the basestation and the mobile intend to transmit data to each other. In this situation, the self-information can be utilized to subtract the interference in the receivers [4]- [6] so as to significantly increase the system capacity and thus compensate the radio resource loss (which is called self-interference cancellation method onwards). This idea was actually first considered by Shannon [4] and it was extended to the relay networks recently in [5], [6]. This work is supported by Hong Kong RGC grant HKUST 6164/04E

MIMO (Multiple Input Multiple Output) has also been regarded as one of the key techniques to realize gigabit data rates in next generation wireless communication systems [7]. However, more antennas are likely to be installed at the basestations and the relays rather than the mobiles. To fully exploit the system capacity, multiple users should be served simultaneously by a relay [7]. This motivates developing multi-user MIMO relay systems, which differ from MIMO relay systems discussed in [8]- [10], where a relay only communicates with a single user. A prior work on multi-user MIMO relay systems can be found in [11] where an amplify and forward relay protocol has been proposed, in which the relay does not decode the received signals from the source but simply processes them with matrix multiplications. In this paper, we consider two-way multi-user MIMO communication systems and propose a relay protocol which utilizes the self-interference cancellation method. We assume decode and forward protocol instead of amplify and forward protocol considering that analog repeaters will increase the noise level which might limit their performance in certain scenarios [1]. The capacity of our protocol is analyzed and shown to achieve at least 30% gain compared with other multiuser MIMO relay protocols. An optimal relay power control problem is also solved by uplink and downlink duality [12] to further enhance the system power efficiency. What is more, by simulations, we also briefly discuss the situations where the relays cannot increase the system capacity. The paper is organized as follows: the system model is described in Section II; Section III introduces our multi-user MIMO relay protocol and discusses its capacity; In Section IV, an adaptive relay power control algorithm is developed; Section V shows the numerical results which justify the significant performance gain of our protocol under various system scenarios and the conclusion is given in Section VI. II. S YSTEM M ODEL The model of our multi-user MIMO relay system is illustrated in Fig.1. There is one basestation, one relay and two mobile users in the system. The basestation and the relay are equipped with two antennas while the mobile users each has only one antenna. The system is assumed to operate in TDD (Time Division Duplex) mode. Two data streams s1 and s2 are transmitted by the basestation to user 1 and user 2,

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 g11

s1 , s2

G =γ

 g 21

 h11    h12 

h1 = γ u 

g12  g 22 

x1 User 1

Basestation

Relay

x2  h21   h22 

h2 = γ u 

d Fig. 1.

User 2

du

System model

while user 1 and user 2 are also simultaneously transmitting data streams x1 and x2 to the basestation. All data streams are transmitted through the relay and there is no direct link between the basestation and the users. We also assume that two users are close to each other so that they can always successfully decode the data transmitted from the other user and the distances from both users to the relay are the same, which are denoted as du . Furthermore the distance between basestation and the relay is denoted as d. Let h1 = γu [h11 , h12 ]T be the channel between the first user and the relay, h2 = γu [h21 , h22 ]T be the channel between g11 g12 the second user and the relay, and G = γ be g21 g22 the channel between the basestation and the relay. Here, the superscript T denotes the matrix transpose. γ and γu are the square roots of the path loss from the basestation to the relay and the path loss from two users to the relay. The path loss exponent is set to be four, i.e., γ 2 ∝ 1/d4 and γu2 ∝ 1/d4u . The elements {hij , gij ; i = 1, 2; j = 1, 2} are assumed to be independent zero mean complex Gaussian random variables with unit variance. We further assume the channels are quasistatic, i.e., they are constant during one TDD frame but change independently between different frames and the channel state information is perfectly known at the transmitter. One feature of two-way communication is the ability to utilize the self-information to cancel out interference so as to increase system capacity, which can be briefly explained as follows [4]- [6]: Assume a single basestation and a single user transmitting to each other through the relay. The relay will first receive data streams from both the basestation and the user. Then the relay will simply superimpose these two data streams and broadcast. At the basestation, due to the fact that it has information of the data stream that the relay is transmitting to the user, the basestation can cancel out the corresponding interference introduced by that data stream. Thus the relay to basestation channel is interference-free and significant capacity gain can be obtained. Of course, the relay to user link can be processed in the same way.

III. M ULTI - USER MIMO R ELAY P ROTOCOLS In this section, we will discuss various multi-user MIMO relay protocols including: the simplest decode and forward protocol (original protocol), the relay waterfilling amplify and forward protocol (relay waterfilling AF protocol) [11] and the proposed multi-user MIMO relay protocol with selfinterference cancellation (two-way relay protocol). The capacity of the two-way relay protocol will also be discussed. A. Protocols description 1) Original protocol: A TDD frame is equally divided into four time slots, which are allocated for the transmissions from basestation to relay, from relay to two users, from two users to relay, and from relay to basestation in turn. The waterfilling algorithm is applied to the channels between the basestation and the relay, dirty paper coding [13] is applied to the relay to users channel and successive interference cancellation is applied to the users to relay channel, all of which are capacity achieving approaches [7]. 2) Relay waterfilling AF protocol [11]: A TDD frame is equally divided into four time slots. In the first time slot, the basestation transmits two data streams s1 and s2 with equal power on two eigenchannels of G. The relay does not decode received data steams but linearly processes them by multiplying a 2-by-2 matrix. Then in the second time slot the relay will transmit the processed signals to two users simultaneously. In the third and fourth time slots, x1 and x2 are processed similarly. Based on the channel state information, the relay will optimize the system capacity by adjusting the matrix coefficients and the user priorities. Please refer to [11] for detail of the algorithms. 3) Two-way relay protocol: A TDD frame is equally divided into three time slots. In the first time slot, the basestation transmits s1 to the relay with power PB = E[sH 1 s1 ]. At the same time, user 1 also transmits x1 to the relay with power Pu = E[xH 1 x1 ]. Here the superscript H denotes the Hermitian transpose and E{.} is the expectation operator. User 2 listens to the transmission of user 1 and will use the decoded information to cancel out the interference in the third time slot. As a result, the received 960


signal at the relay in the first time slot can be expressed as: (1) yR

= γGs1 + γu h1 x1 +

(1) nR

(1) nR

where is the receiver noise. In the second time slot, the basestation transmits s2 to the relay with power PB = E[sH 2 s2 ]. At the same time, user 2 also transmits x2 to the relay with power Pu = E[xH 2 x2 ]. User 1 listens to the transmission of user 2 and will use the decoded information to cancel out the interference in the third time slot. As a result, the received signal at the relay in the second time slot can be expressed as: (2)

(2)

yR = γGs2 + γu h2 x2 + nR (2)

where nR is also the receiver noise. In the third time slot, the relay transmits to basestations and users simultaneously by simply superimposing two data steams. As a result the transmitted signal is: b = bx + bs where bx is the data transmitted to the basestation and bs s is that to the users, with power Prx = E[bH x bx ] and Pr = H E[bs bs ] respectively. As the basestation has knowledge of bs , it can perform self-interference cancellation and the signal received can be expressed as: yB = γGH bx + nB . Similarly, the signals received at two users after interference cancellation are y1 = γu hH 1 bs + n1 ; y2 = γu hH 2 bs + n2 . In the above equations, nB , n1 , and n2 are all noises at the receivers. B. Capacity of two-way relay protocol For the first time slot, successive interference cancellation, which is the capacity-achieving approach for a multiple access channel, is performed at the relay. Depending on the decoding order, the capacity of user 1 to relay channel is given by: Pu 2 1 (1) H Cx = log det I + 2 γu h1 h1 3 σ or Cx(1) =

H PB 2 det(I + Pσu2 γu2 h1 hH 1 1 + 2σ 2 γ GG ) log H PB 2 3 det(I + 2σ ) 2 γ GG

where σ 2 is the noise variance. The corresponding capacity of the basestation to relay channel is: Cs(1) =

H PB 2 det(I + Pσu2 γu2 h1 hH 1 1 + 2σ 2 γ GG ) log 3 det(I + Pσu2 γu2 h1 hH 1 )

or Cs(1) =

PB 1 log det I + 2 γ 2 GGH . 3 2σ

We can select the decoding order which yields larger sum capacity C, which will be given at the end of this subsection.

For the second time slot, the capacity of the user 2 to (2) relay channel Cx and the capacity of the basestation to relay (2) channel Cs can be obtained similarly, which will not be addressed here. For the third time slot, the relay to basestation channel is just a 2-by-2 MIMO channel, whose capacity is achieved by the waterfilling algorithm [7], which is: 2 1 Px 2 2 log 1 + ri γ λ Cx(3) = i 3 i=1 σ2 x where λi is the i-th eigenvalue of G and Pri is the power allocated to the i-th eigenchannel of G. The relay to users channel is just a 2 × 1 · · · 2 MIMO broadcast channel [13], [12], whose capacity is achieved by dirty-paper coding, which is:  

Cs(3) =

2  1  log 1 + 3 i=1 

 s 2 H Pri γu |hi vi |2   i−1  s H 2 2 2 σ + Prj γu |hj vj | j=1

where the beamforming vector vi is determined by MMSE criterion [12]. To sum up, the system sum capacity in a TDD frame is thus given by:

C = min Cx(1) + Cx(2) , Cx(3) + min Cs(1) + Cs(2) , Cs(3) . IV. A DAPTIVE R ELAY P OWER C ONTROL In the third time slot, we can further increase the system capacity by adaptively allocating relay power to the two channels, the relay to basestation channel and the relay to users channel. The optimization problem can be written as:

(1) (2) (3) + C , C max min C x x x x ,P x ,P s ,P s Pr1 r2 r1 r2

(1) (2) (3) + min Cs + Cs , Cs ; (1) s.t.

x x s s Pr1 + Pr2 + Pr1 + Pr2 ≤ Pr ,

which appears difficult to solve directly. However, by uplink and downlink duality [12], we can formulate (1) into a convex optimization problem. The idea is: the uplink and the downlink achieve the same maximum sum capacity with the same sum (3) power, which means the part Cs in (1) can be replaced by a x x and Pr2 . dual uplink part without affecting the results of Pr1 So the optimization problem (1) can be reformulated as: s s qr1 qr2 2 H 2 H max log det I + γ h h + γ h h 1 1 2 2 x ,P x ,q s ,q s Pr1 σ2 u σ2 u r2 r1 r2 2 Px 2 2 + log 1 + ri γ λi ; (2) σ2 i=1 2 Px 2 2 s.t. log 1 + ri γ λ ≤ Cx(1) + Cx(2) ;(3) i 2 σ i=1 s s qr1 qr2 2 H 2 H log det I + 2 γu h1 h1 + 2 γu h2 h2 σ σ ≤ Cs(1) + Cs(2) ; (4)

x x s s Pr1 + Pr2 + qr1 + qr2 ≤ Pr

(5) 961


s s where qr1 and qr2 are the power allocated to user 1 and user 2 in the dual uplink channels s qs qr2 2 H and log det I + σr12 γu2 h1 hH + γ h h are the 1 σ2 u 2 2 s s and qr2 corresponding uplink capacity. Although qr1 x x are not the same as Pr1 and Pr2 , they can play the role of x x x and Pr2 in solving the optimization problem and Pr1 and Pr1 x can be obtained by uplink and downlink duality after we Pr2 s s get qr1 and qr2 . We have obtained a standard convex optimization problem (2). However, the exact analytical solutions are still too complex to be written. Instead, in the following, an algorithm is developed to approach the optimal solution numerically: Step 1: Solve the convex optimization problem (2) with only the power constraint (5). Step 2: Check if the solutions satisfy the constraint (3). If x x and Pr2 by solving the following problem: not, then get Pr1 x x + Pr2 min Pr1 2 x Pri 2 2 log 1 + 2 γ λi = Cx(1) + Cx(2) . σ i=1

s.t.

s s Then, if qr1 and qr2 has been fixed by the previous step, go to x x and Pr2 and solve (2) again with Step 4. Otherwise, fix Pr1 only power constraint (5). Step 3: Check if the solutions satisfy the constraint (4). If s s and qr2 by solving the following problem: not, then get qr1

min

x x + qr2 qr1

s qs 2 qr2 H s.t. log det I + r1 γ h h + γ 2 h2 hH 1 u 1 2 σ2 σ2 u

= Cs(1) +Cs(2) .

x x and Pr2 have been fixed by the previous step, go Then, if Pr1 s s and qr2 and solve (2) again with to Step 4. Otherwise, fix qr1 only power constraint (5). Go back to Step 2. s s s s s s + Pr2 = qr1 + qr2 , calculate Pr1 and Pr2 Step 4: With Pr1 by the uplink and downlink duality.

V. S IMULATION R ESULTS AND D ISCUSSIONS In this section, simulations are performed to demonstrate the capacity gain of the two-way relay protocol over the original protocol and the relay waterfilling AF protocol in various system scenarios. We also show the capacity of the protocol in which no relay is used and briefly discuss when the relay can increase the system capacity and when it can not. In every scenario, the basestation, the relay and the users are assumed to be aligned. The distance between the basestation and the users, d + du , is always the same, although the ratio between d and du will be changed. The power of the users is also kept as a constant for all the scenarios, while the power of the basestation and the relay can be either equal to or four times that of the users. Finally, the capacity curves are generated by averaging over more than 100,000 channel realizations. As can be observed from Fig.2 to Fig.5, the two-way relay protocol achieves at least 30% capacity gain over the original relay protocol and the relay waterfilling protocol in all the scenarios. The power control algorithm is more effective in the scenarios where the capacity of the relay to users channel

is much higher than the capacity of the relay to basestation channel because it can adaptively allocate the power based on the channel conditions in these cases. However, it can also be observed that, the no relay protocol capacity curve has larger slope at high SNRs than two-way relay protocols and is even superior to all the relay protocols in Fig.5 where d1 = 5×d2 and PB = Pr = 4×Pu . To explain this, let us define the degree of freedom of the channel to be the dimension of the received signal [7]. The no relay protocol achieves highest degree of freedom among all the protocols because it does not allocate radio resource to the transmission between the relay and the users. And the role that the relay is playing is actually to trade some degree of freedom of the channel for system power enhancement. As is known, the capacity increases logarithmically with power. So the relay will not be helpful in systems where increasing power can not increase capacity, which we can observe in high SNR regions from Fig.2 to Fig.5. In fact, the reason that the two-way relay protocol can surpass other relay protocols is also because it creates more degrees of freedom by performing self-interference cancellation. The results suggest us to install relays in systems which are power-limited, i.e., increasing system power can significantly increase the system capacity. Another reason that the no relay protocol can be superior to all the relay protocols in Fig.5 is that the relay is much nearer to the users than the basestation and the overall system capacity is restricted by the relay to basestation channel. So, the results also suggest us to select the relay approach, if the relay is in the middle of the basestation and the users. VI. C ONCLUSION Capacity loss due to the radio resource occupied by the relay transmission is one of the important properties that hinder the development of relay assisted wireless networks. In this paper, we propose a two-way relay protocol by applying self-interference cancellation method into a multi-user MIMO system. The capacity of the two-way relay protocol is analyzed and compared to other multi-user MIMO relay protocols by simulation. It can be observed that the two-way relay protocol can achieve more than 30% capacity gain than the previously proposed protocols. An adaptive power allocation algorithm is also developed to further enhance the capacity gain. What is more, we also discuss the conditions for a relay to be helpful from the degree of freedom of the channel and the power efficiency tradeoff point of view. However, it is worth mentioning that this two-way relay protocol requires the users to listen to each other’s transmission first, which would limit its application into situations where more than two users are simultaneously communicating to the basestation through the relay. R EFERENCES [1] R. Pabst et al., “Relay-based deployment concepts for wireless and mobile broadband cellular radio,” IEEE Communication Magazine, vol. 42, pp. 80-89, Sep. 2004. [2] V. Sreng, H. Yanikomeroglu, and D. D. Falconer, “Relayer Selection Strategies in Cellular Networks with Peer-to-Peer Relaying,” Proceedings of IEEE VTC Fall’03, Orlando, FL, Oct. 2003.

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14 Two−way relay protocol Two−way relay protocol with power allocation Original relay protocol Relay waterfilling AF protocol No relay

12 Two−way relay protocol Two−way relay protocol with power control Original relay protocol Relay waterfilling AF protocol No relay

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d = du and PB = Pr = Pu .



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Fig. 3.

d = 5×du and PB = Pr = Pu .



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[3] H. Wu, C. Qiao, S. De, and O. Tonguz, “Integrated Cellular and Ad Hoc Relaying Systems: iCAR,” IEEE Journal on Selected Areas in Communications, vol. 19, pp. 2105-2115, Oct. 2001. [4] C. E. Shannon, ”Two-way communication channels,” Proceedings of 4th Berkeley Symp. Math. Stat. and Prob., vol. 1, pp. 611-644. 1961. Reprinted in Key Papers in the Development of Information Theory, New York: IEEE Press, 1974, pp. 339-372. [5] B. Rankov and A. Wittneben, “Spectral Efficient Protocols for Nonregenerative Half-duplex Relaying,” Proceedings of Allerton Conference on Communication, Control, and Computing, Monticello, IL, Sep. 2005. [6] W. Chen, K. B. Letaief and Z. Cao, “A cross layer method for interference cancellation and network coding in wireless networks,” Proceedings of IEEE ICC’06, Istanbule, Turkey, Jun. 2006. [7] D. Tse and P. Viswanath, “Fundamentals of Wireless Communication,” Cambridge University Press, 2005. [8] B. Wang, J. Zhang, and A. Host-Madsen, “On the capacity of MIMO relay channels,” IEEE Transactions on Information Theory, vol. 51, pp. 29-43, Jan. 2005. [9] O. Munoz, J. Vidal, and A. Agustin, “Non-regenerative MIMO relaying with channel state information,” Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA, Mar. 2005. [10] H. Bolcskei, R. U. Nabar, O. Oyman, and A. J. Paulraj, “Capacity scaling laws in MIMO relay networks,” IEEE Transactions on Wireless Communications, vol. 5, pp. 1433-1444, Jun. 2006. [11] T. Tang, C. B. Chae, R. W. Heath. Jr., “On Achievable Sum Rates of A Multiuser MIMO Relay Channel,” Proceedings of IEEE ISIT’06, Seattle, WA, Jul. 2006. [12] P. Viswanath and D. N. C. Tse, “Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality,” IEEE Transactions on Information Theory, vol. 49, pp. 1912-1921, Aug. 2003. [13] G. Caire and S. Shamai, “On the achievable throughput of a multiantenna Gaussian broadcast channel,” IEEE Transactions on Information Theory, vol. 49, pp. 1691-1706, Jul. 2003.

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