Multiuser Two Way Relaying Schemes in the ... - Semantic Scholar

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 10, OCTOBER 2013

Multiuser Two Way Relaying Schemes in the Future Cellular Network Duckdong Hwang, Suk-Gi Hong, and Tae-Jin Lee

Abstract—We propose a set of multiuser two-way relay beamforming schemes in the cellular network. While the previous schemes are applicable only when there exist a single base station (BS) and a single relay station (RS) with the same number of antennas, multiple BSs or multiple RSs can exist in the proposed scheme without such restriction on the numbers of antennas. The degree of freedoms (DoF) achievable are analyzed and conditions to achieve these DoF values are presented. Both the decode-andforward (DaF) protocol and amplify-and-forward (AaF) protocol are considered. It turns out that the channel alignment and the interference alignment in the multi-cell environment act the key roles in the development. We also provide an interference alignment scheme in the multi-cell environment that improves the achievable DoF values upon those of the previous schemes. The simulation results corroborate that the proposed beam-forming works as analyzed. Index Terms—Two-way relaying, cellular network, multiple antennas, multi-user, degree of freedom.

I. I NTRODUCTION

T

O respond to the ever increasing demand for wireless data traffic, cooperative relaying techniques have been introduced [1], [2]. The benefit comes from the opportunistic (or planned in the cellular network) positioning of the relays so that the receivers can find alternative paths when they are deeply faded from the transmit sides. However, the half duplex constraint of the cooperative relaying limits the applicability of the techniques to the coverage expansion of cell edge area where the signal power level is weak due to the propagation loss. Two-way relaying, where they overlap two transmissions of a bidirectional user pair into a common spectral resource with some form of physical layer network coding [3]–[5], is expected to overcome this limitation and afford the benefit of relaying over the entire cell area such that overall spectrum usage efficiency is enhanced. Multiple antenna techniques can be combined with two-way relaying and bring the benefit of multiple input multiple output (MIMO) into the relaying advantage [4] as well.

Manuscript received January 13, 2013; revised April 28 and June 27, 2013; accepted August 12, 2013. The associate editor coordinating the review of this paper and approving it for publication was G. Abreu. This research was supported by the MSIP (Ministry of Science, ICT & Future Planning), Korea, under the ITRC (Information Technology Research Center) support program supervised by the NIPA (National IT Industry Promotion Agency) (NIPA-2013-(H0301-13-1005)). D. Hwang and T.-J. Lee are with the College of Information and Communication Engineering, Sungkyunkwan University, Suwon, Korea (e-mail: [email protected], [email protected]). T.-J. Lee is the corresponding author. S.-G. Hong is with the Mobile Communications Division, Samsung Electronics, Suwon, Korea. Digital Object Identifier 10.1109/TWC.2013.090413.130008

Multiuser MIMO (Mu-MIMO) [6] is a cellular specific technique to exploit the spatial multiplexing capability of the MIMO into serving multiple users in the cell area over the same spectral resource. A code division multiple access (CDMA) based multi-user two-way relaying is considered in [7], where the spatial dimension is not utilized. As MIMO is combined with two-way relaying, Mu-MIMO can also be implemented in the two-way relay settings [5], [7]–[14] to further improve the degree of freedom (DoF) of the system. Since two users form a bidirectional traffic pair in the twoway communications, multi-pair two-way relaying [10]–[12], [14] is the frequently referred term for the Mu-MIMO twoway relaying. One of the important technical challenges in Mu-MIMO is the handling of the interference among the user signals. Since it is natural to assume that the base stations (BS) have more antennas than the mobile stations (MS), the multiuser interference is generally handled at the BS with interference suppression beam-forming. Similarly in the twoway relay setting, the relay station (RS) does the role of BS and hence the interference is handled at the relay. A measure that captures the multiplexing capability of a transmission system is DoF, which tells how many streams of data a system can multiplex into the dimensions of interest in the high SNR region. The maximum DoF of a single cell with M antennas at the base station is M , and hence M streams addressed to M different single antenna users can be multiplexed. When there are K pairs of single antenna users (2K users) in a network, the RS with 2K − 1 antennas can apply the zero-forcing principle for the interference removal and afford 2K DoF of two-way traffic in two time phases [10]– [12]. When multiple antenna users are employed, the same DoF of two-way traffic is supported by the RS with only K antennas [14] by aligning the channel vectors of pairing users. Though these schemes [10]–[12], [14] are not confined to the cellular setting, they can be deployed in cellular networks without much effort since two-way traffic is expected to be common inside a cell area as well. The Mu-MIMO two-way relaying in the cellular setting is considered in [8], [9], [15], [16], where a BS, a RS and multiple MSs are deployed according to the roles in the cellular context and the BS-MS traffics are implemented in a bidirectional two-way fashion through the RS. These schemes guarantee 2M DoF for the two-way traffic in two time phases when the numbers of antennas at the BS and RS are M each. However, the schemes in [8], [9], [15], [16] only work for the case where there are a single BS, a single RS with an equal number of antennas while cellular networks are evolving into heterogeneous networks (HetNet) [17], [18] and the network

c 2013 IEEE 1536-1276/13$31.00 

HWANG et al.: MULTIUSER TWO WAY RELAYING SCHEMES IN THE FUTURE CELLULAR NETWORK

structure will become much more complicated. Therefore, in this work, we propose generalized beam-forming schemes that are free of those limitations and thus are useful in the HetNet environment. In HetNets, there can be multiple pico/femto BSs and Relays serving small areas within the macro BS cell area. Therefore, the system models, we consider here, include the cases with multiple BSs or multiple RSs and unequal numbers of antennas. The tools that make the new schemes so much powerful are the alignment of the pairing user channels [14], [19], [20] and the interference alignment [21]–[27]. Compared to the multi-cell interference alignment result of [27], we come up with further enhanced DoF values in the multi-cell interference network. The achievable DoF values of the proposed schemes are presented as well. The paper is organized as follows. In Section II, the system model and the beam-forming schemes with different relaying protocols are presented. The proposed schemes are analyzed in Section III and Section IV. Multiple BSs case and multiple RSs case are treated in Section III and Section IV respectively. After the simulation results are presented in Section V, we conclude the paper in Section VI. Notations: The bold lower case letter represents a vector and the bold upper case letter represents a matrix. The notations AH is the hermitian transpose of matrix A. The notation Aa,b represents the element of A at the a-th row and b-th column position. AF denotes the Frobenius norm of A. The notation diag[a1 , . . . , aL ] produces a block diagonal matrix with vectors a1 , . . . , aL on its diagonal blocks. The notation A† represents the pseudo inverse of A. The matrices Ia and 0b represent the a × a identity matrix and b × b all zero matrix respectively. II. S IGNAL AND S YSTEM M ODEL A. System Model The multi-user two-way MIMO relaying in the cellular network is depicted in Fig. 1. There are BSs, RSs and MSs in the network and the direct channels from BSs to MSs do not exist. The BSs can be macro or pico/femto BS stations. Each BS has Mb antennas, each RS has Mr antennas and each MS has Mm antennas. In Fig. 1 (a), a single RS serves multiple BSs and MSs while a single BS serves multiple RSs and MSs in Fig. 1 (b). In Fig. 1 (a), the channel from the j-th BS to the RS is denoted by the Mr × Mb matrix Hj and the channel from the RS to the k-th MS is denoted by the Mm × Mr matrix Gk . In Fig. 1 (b), the channel from the BS to the j-th RS is denoted by the Mr × Mb matrix Hj and the channel from the j-th RS to the k-th MS is denoted by the Mm × Mr matrix Gk,j . The elements of these channel matrices are independent and identically distributed zero mean complex Gaussian random variables with unit variance and do not change over the entire transmission period. Also, we assume that the channels are reciprocal such that the channel matrix for the reverse direction of a link is the transpose of the original channel matrix (the channel from the RS to the j-th BS is Htj ). Fig. 1 (a) corresponds to the situation where multiple small cells with a overlapped cell area share a common RS to serve the associated MSs in their cells while Fig. 1 (b) corresponds

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Fig. 1. The multi-user two-way MIMO relay in the cellular network. (a) multiple base stations case. (b) multiple relay stations case.

to the situation where multiple RSs are available in a cell and the BS serve the associated MSs through these RSs. Note that Mb = Mr , Mm = 1 with single BS, single RS and Mb MSs is the case considered in [8], [9], [15], [16] while J = K with Mr = J is the case considered in [14]. The case, J = K and Mr = 2K − 1 with Mb = Mm = 1 is considered in [10], [11]. The BSs in Fig. 1 (a) are treated as another set of MSs in [10], [11], [14] and thus the situation in Fig. 1 (a) can be thought as a special case of [10], [11], [14]. Beyond the scope of this paper is the case where multiple cells, each with its own BS and RS, exist nearby and interfere with each other while serving their own associated MSs. The first hop (from BSs to RSs) is the MIMO interference channel where the achievable scheme only for the three user case is known [23] while only the upper bound of DoF is available [28] for general numbers of users. Therefore, it is hard to find the combinations of the interference alignment and the channel alignment that maximize the DoF in the network of this case with general numbers of BSs. We leave this problem for a future work. We leave this case as a future work. The MSs are grouped into J disjoint user sets and each set is associated with a BS (or RS in Fig. 1 (b)). Let k0 = 0 ≤ k1 ≤ . . . ≤ kJ = K, then the j-th BS (or RS in Fig. 1 (b)) and the MSs from kj−1 + 1 to kj are associated and the j-th BS in Fig. 1 (a) has a message symbol vector xj = [xj,kj−1 +1 , . . . , xj,kj ]t , where the symbol xj,k is destined to the k-th MS. In Fig. 1 (b), the BS has a vector

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 10, OCTOBER 2013

x = [x1 , . . . , xK ]t . Similarly, the k-th MS has a message symbol yk to be delivered to the associated BS in Fig. 1 (a) or to the BS in Fig. 1 (b) through the j-th RS with which the MS is associated. All the entities in the network are assumed to use the same beam-forming for the transmission and the reception of the message symbols. The k-th MS uses a Mm ×1 beam-forming vector wk for yk . The j-th BS uses a Mb × (kj − kj−1 ) beam-forming matrix Fb,j for the message symbol vector xj = [xj,kj−1 +1 , . . . , xj,kj ]t and the i-th RS uses a Mr × Mr beam-forming matrix Fr,i . The RSs can use either the amplify-and-forward (AaF) protocol or the decode-and-forward (DaF) protocols, however they are in the half-duplex mode. In the cellular convention, the traffic from the BS to MS is called the down-link transmission and the other-way is called the up-link transmission. These two traffics are transmitted with an overlapped way in two-way communications such that the spectral efficiency loss due to the multi-hop relay transmissions is recovered. Therefore, the two-way transmission is composed of two phases, where the BSs and MSs transmit the bidirectional messages in the first phase and the RSs decode these messages1 or amplify the received signals and transmit the physical layer network coded signals to the BSs and MSs in the second phase. Finally, BSs and MSs decode the message from the pairing entity after removing the self-interference caused by the message signal they have sent in the first phase.

Then, the RSs generate the modulated signal zk (the same modulation format as in xk and yk ) of the XOR coded signal and form the vector z in Fig. 1 (a) or the vectors z1 . . . , zJ in Fig. 1 (b). Finally, they transmit the beam-formed signals Ftr z in Fig. 1 (a) and Ftr,1 z1 , . . . , Ftr,J zJ in Fig. 1 (b) toward the BSs and MSs in the second phase. The signals2 received at the j-th BS in Fig. 1 (a) and at the BS in Fig. 1 (b) in the second phase are given respectively as rb,j = Htj Ftr z + nb , rb =

J 

Hti Ftr,i zi + nb,i .

(2)

i=1

Here, nb and nb,i are the additive white Gaussian noise at the RS in Fig. 1 (a) and at the i-th RS in Fig. 1 (b) respectively, whose elements have unit variance. The signals received in at the k-th MS in Fig. 1 (a) and in Fig. 1 (b) are given respectively as rk = Gk Ftr z + nk , rk =

J 

Gk,i Ftr,i zi + nk .

(3)

i=1

Here, nk is the additive white Gaussian noise at the k-th MS, whose elements have unit variance. C. AaF Relaying

B. DaF Relaying 2

2

Let Pb = KE[|xk | ] and Pm = KE[|yk | ] for all k. In the first phase, the signals received at the RS in Fig. 1 (a) and at the i-th RS in Fig. 1 (b) are given respectively as rr =

J 

Hj Fb,j xj +

j=1

rr,i = Hi Fb x +

K 

Gtk wk yk + nr ,

k=1 K 

Gtk,i wk yk + nr,i .

(1)

k=1

Here, nr and nr,i are the additive white Gaussian noise at the RS in Fig. 1 (a) and at the i-th RS in Fig. 1 (b) respectively, whose elements have unit variance. In the DaF protocol, the RS applies the K × Mr receive beam-former matrix Fr (in Fig. 1 (a)) or ki × Mr matrix Fr,i (in Fig. 1 (b)) to rr and rr,i respectively to decode all the messages y1 . . . , yK and x1 , . . . , xJ (in Fig. 1 (a)) or yi and xi (in Fig. 1 (b)), where yi is the vector composed of yk pairing with xi according to the association and k i is the number of elements in xi or yi . If they succeed in decoding the message sets, the RSs network code the message pairs according to their association. For example, the binary representations of the symbols xk and yk are XOR coded, where we assume that the binary sizes of xk and yk representations are the same and hence they are transmitted with the same modulation format. 1 In the proposed scheme, the interference from the other pairs is zero-forced and the decoding for each pair is done separately at the RS. We assume that the maximum likelihood (ML) decoding is performed to decode the two pair message signals in the first phase. Otherwise, we can break the first phase of the two-way DaF protocol into two phases for the separate transmissions from the two parties. In this case, the total two-way transmission is done in three phases.

In the AaF protocol, the RSs simply apply the beamformers to the received signals in Eq. (1) as γFr rr in Fig. 1 (a) and γ1 Fr,1 rr,1 , . . . , γJ Fr,J rr,J in Fig. 1 (b) and transmit them toward the BSs and MSs in the second phase, where γ, γ1 , . . . , γJ are scalars to constrain the RS transmit power such that Pr = E[γFr rr 2 ] and Pr,i = i Pr kK E[γi Fr,i rr,i 2 ]. The same expressions in Eqs. (2) and (3) are effective with the substitutions z and zi with γrr and γi rr,i respectively. Finally, the BS in Fig. 1 (b) and the j-th BS in Fig. 1 (a) apply the receive beam-forming matrices Ftb and Ftb,j to the signals in (2) respectively. Similarly, the k-th MS applies the receive beam-former wk to the signal in (3) respectively. D. Decoding and Degree of Freedom Suppose xk is transmitted through the j-th BS in the first phase (xk is a element in xj ) and fb,k be one of the column of Fb,j that corresponds to decoding of yk , then the decoding at the j-th BS is done in the pair-wise manner (subtracting out the self-interference from the symbol xk it already knows and t rb,j has no interferences decodes yk ). This is possible if fb,k from the symbols pertaining to other pairs (xl , yl , l = k). Similarly at the k-th MS, we need the condition that wkt rk has no interferences from the symbols pertaining to other pairs. Then, the MS also can subtract out the interference from the symbol yk it already knows and decode xk . When the DaF protocol is used, fr,k a column of Fr,i needs the t condition that fr,k rr,i has no interferences from the symbols 2 Note that the channel with the smaller gain among the two pairing entities in the DaF protocol becomes the bottleneck for the transmission of the bidirectional traffic.

HWANG et al.: MULTIUSER TWO WAY RELAYING SCHEMES IN THE FUTURE CELLULAR NETWORK

pertaining to other pairs. Then, the DaF RS decodes jointly the xk and yk with the ML decoding. Our schemes will zeroforce the interferences from the other pairs through the channel alignment [14], [20] and the interference alignment in the multi-cell network [24]–[27] so that the signals from each pair is decoded separately. We analyze the proposed system models in the sense of degree of freedom. Suppose Rk (P ) be the information rate of the k-th user and P be the system power. Then, the system DoF can be mathematically defined as 2K k=1 Rk (P ) DoF = lim . (4) P →∞ log Ps In practice, however, it is easy to count the number of streams in the system that can be multiplexed into the system and decoded without being interfered by the other streams in the system. We follow the latter approach here. III. M ULTIPLE BASE S TATIONS We consider the network model in Fig. 1 (a) in this section. Let H = [H1 , . . . , HJ ], FB = diag[Fb,1 , . . . , Fb,J ], G = [Gt1 , . . . , GtK ] and W = diag[w1 , . . . , wK ]. For the DaF protocol, the pair-wise manner decoding without the interferences from other pair signals at the RSs, at the BS and at the MSs is possible if t t • Fr HFB and Fr GW are diagonal matrices with all zero off diagonal elements. t t • For all j, Fb,j Hj Fr is a shifted diagonal matrix whose diagonal elements are shifted to the right by kj−1 + 1. t • For all k, the elements of the vector wk Gk Fr are all zero except for the k-th element position. These conditions force the inter-stream interference to be nulled out so that the pair-wide decoding principle in subsection II-D can be applied. Similarly for the AaF protocol, the pair-wise manner decoding without the interferences from other pair signals at the BSs and at the MSs is possible if t t t t • For all j, Fb,j Hj Fr HFB and Fb,j Hj Fr GW are shifted diagonal matrices whose diagonal elements are shifted to the right by kj−1 + 1. t • For all k, the elements of the vectors wk Gk Fr HFB and t wk Gk Fr GW are all zero except for the k-th element position. We need to find FB , Fr and W satisfying the conditions above. Suppose the conditions for the DaF protocol are met, then the conditions for the AaF protocol are trivially met with the same BS, MS beam-formers (FB , W) and setting the RS beam-former as Fr = Fr,DaF Ftr,DaF , where Fr,DaF is the RS beam-former found for the DaF protocol. We show in this section that the conditions for the DaF case above are achieved through the channel alignment technique in [14]. If Mb + Mm ≥ Mr + 1, the Theorem 1 of [14] states that we can find the pair of vectors wk and fb,k such that Hk fb,k = sk Gtk wk , where sk is a complex number. Suppose Hk fb,k = sk Gtk wk is satisfied for all k, then the signal vectors from two MSs in a pair occupy a single spatial dimension and forming the pseudo inverse of the effective channel matrix GW as Fr ( Fr = ([Gt1 w1 , . . . , GtK wK ]t )† ) makes the effective channel matrices HFB , GW diagonal and the vector

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wkt Gk to have zero elements except for the k-th position. Therefore, the conditions above are satisfied. Similarly, if we put Fr = ([Gt1 w1 , . . . , GtK wK ]t )† [Gt1 w1 , . . . , GtK wK ]† , then the conditions for AaF protocol are satisfied. Lemma 1 proves the achievable DoF of the proposed beamforming in this section. Lemma 1: With the channel alignment technique in [14], we can achieve up to min{Mr , JMb } DoF in the network in Fig. 1 (a) when Mb + Mm ≥ Mr + 1. Proof: Once the channels of a pair of users are aligned, we can form the pseudo inverse Fr of up to K = Mr MSBS pair channels. On the other hand, each BS can form up to Mb independent columns of the beam-former matrix Fb,j . Therefore, the maximum achievable DoF is bounded by min{Mr , JMb }. Note that the scheme in [9] is the special case of the scheme in this paper, where J = 1, Mm = 1 and Mb = Mr . With the Mr × Mr identity matrix W, the BS beam-former is given as FB = H† G with an appropriate power scaling. IV. M ULTIPLE R ELAY S TATIONS We consider the network model in Fig. 1 (b) in this section. ˜ = [Ht1 , . . . , Ht ], FR = diag[Fr,1 , . . . , Fr,J ] and G ˜i = Let H J t t [G1,i , . . . , GK,i ]. For the DaF protocol, the pair-wise manner decoding without the interferences from other pair signals at the RSs, at the BS and at the MSs is possible if t t ˜ • For all i, Fr,i Hi Fb and Fr,i G i W are shifted diagonal matrices whose diagonal elements are shifted to the right by ki−1 + 1. t˜ • Fb HF R is a diagonal matrix with all zero off diagonal elements. • For all k, the elements of the vector wkt [Gk,1 , . . . , Gk,J ]FR are all zero except for the k-th element position. For the AaF protocol, the pair-wise manner decoding without the interferences from other pair signals at the BSs and at the MSs is possible if t˜ t t t t˜ ˜t ˜t t • Fb HF R [H1 , . . . , HJ ] Fb and Fb HFR [G1 , . . . , GJ ] W are diagonal matrices with all zero off diagonal elements. • For all k, the elements of the vectors and wkt [Gk,1 , . . . , Gk,J ]FR [Ht1 , . . . , HtJ ]t Fb ˜ t1 , . . . , G ˜ t ]t W are all zero wkt [Gk,1 , . . . , Gk,J ]FR [G J except for the k-th element positions. Similarly as in Section III, the same BS, MS beam-formers FB , W satisfying the DaF conditions work for the AaF case as well while the modification for the RS beam-former is needed as FR = FR,DaF FtR,DaF , where FR,DaF is the RS beam-former found for the DaF protocol. In Section III, the relay beam-former FR suppresses the inter-pair interference while the beam-formers of the BS and MS in a pair are aligning their effective channels toward the relay. With the model in Fig.1(b), it is hard to apply the channel alignment for the multiple relays at the same time. Instead, we can make the signal vectors from MSs associated with the other (J − 1) RSs take only a limited number of spatial dimensions at the i-th RS, which turns the right hand side (RSs to MSs links) of Fig.1(b) into a set of interference-free multiuser channels (the signal dimensions taken up by MSs at each RS is less

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 10, OCTOBER 2013



min(Mb , JMr ) when Mm > (J − 1)Mr , m  − 1})}) min(Mb , max{Mr , J(min{Mr ,  JM−1

otherwise. (6)

Proof: Once the MS beam-formers wk and the RS beamformer Fr,i are determined as in the Appendix A, the network on the right hand side of Fig. 1 (b) provides the DoF up to K in Eq. (5). If Mb ≥ K, then we can form Fb such that ˜ R )† , which satisfies the conditions for Ftr,i Hi Fb Ftb = (HF t˜ and Fb HFR at the same time. Therefore, the maximum achievable DoF is bounded as in Eq. (6). V. S IMULATION R ESULTS In Fig. 2 and Fig. 3, we plot the average sum rate results of the configuration in Fig. 1 (a) for the DaF protocol RS and the AaF protocol RS. The same configurations used in the DaF protocol are used in the AaF protocol as well. The numbers of BSs (J) in the network are 2 and 3. We assume that the

50 J=2,M =3,M =4,M =2 b

r

m

J=3,Mb=4,Mr=6,Mm=3

Sum Rate (bps/Hz)

than or equal to Mr ). Suppose we can find W such that ˜ ¯ i,n W ¯ n ) = Mr − T, ∀n, 0 < T < Mr − 1, where ∀i, rank(G ˜ ¯ i,n and n is the index of an MS associated with the i-th RS; G ¯ n are matrices constructed from G ˜ i and W without Gt W n,i and wn respectively. Note that this is an equivalent condition used in the interference alignment for the multi-cell multiuser network [24], [25], [27]. Then, we can form the column of Fr,i that corresponds to the beam-forming vector for the n-th user pair as the zero-forcing vector of the interference from these Mr − T dimensions and the channel vectors (wkt Gk,i ) of the other MS associated with the i-th RS (given that Mr ≥ ki +T ). ˜ R diagonal The BS beam-former Fb is one that makes Ftb HF if Mb ≥ JMr . In [27], the authors present a DoF upper bound of the multicell interference MIMO channel, where a two step beamforming approach is used for the handling of inter-cell and intra-cell interferences, however the size of dimension toward which the other-cell interference vectors are aligned, is fixed to one. In the following Proposition 1, we modify the scheme in [27] such that the dimension size of the interference plane where other-cell interferences are aligned can be optimized to produce the best achievable DoF values. Proposition 1: The RSs to MSs network on the right hand side of Fig. 1 (b) provides the achievable DoF K up to  JMr when Mm > (J − 1)Mr , K= Mm max{Mr , J(min{Mr ,  J−1  − 1})} otherwise, (5) where · is the integer ceiling function. Proof: See the Appendix A In Appendix A, the MS beam-formers wk force the interference vectors at the RSs to be constrained to T dimensional subspace and the RS beam-formers Fr,i zero force the remaining inter-pair interference. Therefore, the conditions for ˜ i W and wt [Gk,1 , . . . , Gk,J ]FR are satisfied. We need Ftr,i G k to find fb,k the column of the BS beam-former corresponding (pairing) to the k-th MS such that the conditions for Ftr,i Hi Fb ˜ R are met. Satisfying these conditions, the achievand Ftb HF able DoF in the multiuser two-way network in Fig. 1 (b) is summarized in the Lemma 2. Lemma 2: We can achieve the DoF in the network shown in Fig. 1 (b) up to

40

J=3,M =2,M =3,M =2 b

r

m

J=3,Mb=3,Mr=5,Mm=3 30

20

10

0

0

10

20

30

40

50

60

SNR(dB) Fig. 2. The sum rate curves of the two-way multiuser cellular network in Fig. 1 (a) when the DaF protocol is used at the RSs. 45

40 J=2,M =3,M =4,M =2 b

r

m

J=3,Mb=4,Mr=6,Mm=3

35

Sum Rate (bps/Hz)

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J=3,Mb=2,Mr=3,Mm=2 30 J=3,M =3,M =5,M =3 b

r

m

25

20

15

10

5

0

0

10

20

30

40

50

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SNR(dB) Fig. 3. The sum rate curves of the two-way multiuser cellular network in Fig. 1 (a) when the AaF protocol is used at the RSs.

distances between MSs and the RS are half of those between the RS and BSs and thus the elements of the channel matrix Gk,i ) are scaled according to the path loss exponent (the path loss exponent of 3 is used in the simulation). This assumption of the distance distribution is suited for small cells (pico/femto BSs). The sum rate results of the K pairs are normalized by two so as to take the two-phase transmission of the two-way relaying into consideration. When the transmission of the twoway DaF protocol is implemented in three phases, the sum rate curves of the DaF protocol should be scaled appropriately. We set the transmission power of the RSs twelve dB down from the BS power (Pb (dB) = Pr (dB) + 12(dB)), which is near the worst case relay power assumption in the small cell environment. Assuming that power control is applied, the MS power is set to three dB down from the BS power. The SNR is defined as SN R = Pb +Pr +Pm (with unit noise power). The antenna sets are selected such that Mb + Mm ≥ Mr . Overall,

HWANG et al.: MULTIUSER TWO WAY RELAYING SCHEMES IN THE FUTURE CELLULAR NETWORK

K 

+ log2 (1 + |γwkt Gk Fr Hj fb,k |2 Pb /K)]/2,

50

r

m

J=2,M =6,M =4,M =4 b

r

m

J=4,Mb=8,Mr=3,Mm=7 40

J=4,Mb=9,Mr=4,Mm=7 J=2,M =9,M =4,M =7 b

30

r

m

J=3,M =3,M =1,M =3 b

r

m

20

0

(7)

t [log2 (1 + |γj fb,k Htj Ftr,j Gtk,j wk |2 Pm /K)

k=1

b

J=3,Mb=9,Mr=4,Mm=7

10

where j is the BS the k-th MS is associated. When DaF protocol is used, we take the minimum value of the sum rates of two hops in pairing channels (i.e. for the forward link, min{Fr,DaF Hj fb,k Pb /K,Ftr,DaF Gtk wk Pr /K}) since the minimum is the bottleneck of the bidirectional channels. In Fig. 4 and Fig. 5, we plot the average sum rate results of the configuration in Fig. 1 (b) when the DaF protocol and the AaF protocol are used at the RSs respectively. Again, the same set of network configurations are tested for both the DaF RSs and the AaF RSs. The numbers of RSs (J) used are 2, 3 and 4 and the same transmission power condition is used again. The locations of BS and MSs from the RSs also are the same as in Fig. 2 and Fig. 3. Except for the sixth case (J = 2, Mb = 9, Mr = 4, Mm = 7), the number of antennas at the BS (Mb ) is set to the number of maximum DoF available from the multi-cell interference channel on the right hand side of Fig. 1 (b). Therefore, Mb is the total DoF achievable in the network for these cases while the DoF is JMr in the sixth case. The same trend is observed from the sum rate curves of the DaF and the AaF, where the slopes of the curves exhibit that the predicted DoF values are closely followed by the proposed scheme. Overall, the sum rate is largely dependent on the DoF value while the dependence on the number of RSs (J) or the relay antenna configuration (Mr ) is also manifested. The fifth and the sixth cases with the same antenna configuration and different J values exhibit a large SNR gap because a large J lessens the user loading of the RSs and hence the loss from zero forcing is reduced. In the final case, we have enough MS antennas (Mm ≥ (J − 1)Mr ) to keep the MS beam-forming direction from interfering the other RSs and the DoF of min{Mb , JMr } achieved. Since the inter-pair interference is aligned and nulled out, the system sum rates for AaF protocol are calculated as R=

J=3,M =6,M =3,M =5

t [log2 (1 + |γfb,k Htj Ftr Gtk wk |2 Pm /K)

k=1

K 

60

+ log2 (1 + |γj wkt Gk,j Fr,j Hj fb,k |2 Pb /K)]/2, (8)

where j is the RS the k-th MS is associated. For the DaF protocol, we take the minimum value of the sum rates of two hops in pairing channels.

0

5

10

15

20

25

30

35

40

45

SNR(dB) Fig. 4. The sum rate curves of the two-way multiuser cellular network in Fig. 1 (b) when the DaF protocol is used at the RSs.

45

J=3,M =6,M =3,M =5

40

b

r

m

J=3,Mb=9,Mr=4,Mm=7

35

Sum Rate (bps/Hz)

R=

70

Sum Rate (bps/Hz)

the slopes of the curves in the DaF and AaF cases demonstrate that the predicted DoF values (min{JMb , Mr }) are achieved while the AaF protocol yields little inferior performance to the DaF protocol. With the setting we take (small RS power), the overall system behave as a relay network, where relays are much closer to the sources than the destinations. This explains why DaF cases achieve better sum rates than AaF cases. When the number of RS antennas (Mr ) is small, we can observe better sum rate results in low SNR because not much channel power is lost from the zero-forcing operation at the RS (Fr ) in the case. Since the inter-pair interference is nulled out, the system sum rates for AaF protocol are simply calculated as

5205

J=2,M =6,M =4,M =4 b

r

m

J=4,M =8,M =3,M =7

30

b

r

m

J=4,M =9,M =4,M =7 b

25

r

m

J=2,M =9,M =4,M =7 b

20

r

m

J=3,M =3,M =1,M =3 b

r

m

15

10

5

0

0

5

10

15

20

25

30

35

40

45

SNR(dB) Fig. 5. The sum rate curves of the two-way multiuser cellular network in Fig. 1 (b) when the AaF protocol is used at the RSs.

VI. C ONCLUSION A set of multiuser two-way relay beam-forming schemes in the cellular network is proposed. Based on the channel alignment [14], [20] and the interference alignment in the multi-cell network [24]–[27], the proposed schemes provides the flexibility, where the configuration of the network and antenna combinations in the network are not much constrained compared to the previous arts [8], [9], [15], [16]. The DoF performance of the proposed scheme is analyzed and the conditions to achieve these DoF values are presented. The DoF values are not dependent on whether we use the decodeand-forward protocol or the amplify-and-forward protocol. For the development in this work, we provide an interference alignment scheme in the multi-cell environment that improves the performance of the previous schemes. The simulation results confirm that the proposed schemes work as the analysis predicts.

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 12, NO. 10, OCTOBER 2013

A PPENDIX A. Proof of the Proposition 1 Suppose we only consider the network in the right hand half side of Fig. 1 (b). Then, the network is equivalent to a cellular network, where the RSs do the role of BSs with the MSs associated with Jthese RSs and the i-th RS serves Ki (≥ 1) MSs with K = i=1 Ki . Our analysis focuses on the Multiple Access Channel (MAC, from MSs to RSs), however we can achieve the same DoF with the same scheme in the Broadcast Channel (BC, from RSs to MSs) as well if we use the updown duality shown in [26]. Among the signals from the K MSs reaching the i-th RS, only Ki MS signals are associated with the i-th RS. The remaining K − Ki signals are the intercell interference for the i-th RS, which should be forced to be aligned and nulled out. We number MSs such that the first K1 MSs are associated with the first RS, the next K2 MSs are associated with the second RS and so on. The received signal for the first BS is y1 =

K1  k=1

Gtk,1 wk xk +

K 

Gtk,1 wk xk + n1 .

(9)

k=K1 +1

The Mr × 1 vector n1 is the additive complex white Gaussian noise.  ¯ 1 be the Let the columns of Mm × Jl=2 Kl matrix G interference vectors (Gtk,1 wk , for all k > K1 ) from the other cell MSs. If the condition ¯ i ) = T (T ≤ Mr ) rank(G

(10)

is satisfied for all i, then the i-th cell RS has M − T interference free dimensions. If Eq. (10) is not satisfied for some k, these MS signals generate interference to the i-th RS. Assume there are K0 such MSs in the network, which do not satisfy Eq. (10) for all the RSs in the network. Then, these K0 MS signals (not aligned) are suppressed by the inner zero forcing matrix as in [27]. Let the i-th RS beam-former is the product of the inner and the outer beam-formers as Fr,i = Fr,i,1 Fr,i,2 . The outer zero forcing ZF receiver nulls out the intra-cell interference at the i-th cell RS. We have the following signal model. ri = (Fr,i,1 Fr,i,2 )t yi ,

(11)

where the Ki × Mr outer ZF matrix Ftr,i,2 is composed of the ˇ i . Here, G ˇ i has, as top Ki rows of the pseudo inverse of G t t its columns, Fr,i,1 Gk,i wk , k = Ki−1 + 1, . . . , Ki . The association of these K0 MSs with the RSs can be arbitrary, therefore we simply let them associated with the first RS without loss of any generality. Define K1 = K0 + K1 , which is the number of MSs served by the first RS. The pre-coders wk , k = 1, . . . , K0 ˆ1 = of these MSs are arbitrary non zero vectors. Let G t t t t ˆ [G1,1 w1 , . . . , GK0 ,1 wK0 ], G2 = [G1,2 w1 , . . . , GK0 ,2 wK0 ], ˆ J = [Gt w1 , . . . , Gt ... ,G 1,J K0 ,J wK0 ]. From the Singular Value Decomposition (SVD) of these matrices, we can find the Mr ×(Mr −K0 ) inner zero forcing matrices Fr,1,1 , Fr,2,1 , . . . ˆ 1, G ˆ 2, , Fr,J,1 , whose column spaces span the null spaces of G ˆ J respectively. To decode these K0 MS signals, the ... ,G ˆ 1 to the first cell RS applies the zero forcing matrix of G

received vector y1 . To decode the remaining K1 , K2 , . . . , KJ users respectively, Ftr,i,1 is multiplied to yi at the i-th cell RS, resulting in a (Mr − K0 ) × 1 vector y ˜i . Now, we check the condition to satisfy the condition in Eq. (10) for the inner zero forced signals y ˜i at the RSs to which the MS does not belong. Let the interference plane of the RSs be P1 , P2 , . . . , PJ , where the columns of Mr × T (0 ≤ T < Mr −K0 ) matrix Pi are spanned by the column space of Fr,i,1 (i.e., there exists a matrix Ai that makes Pi = Fr,i,1 Ai ). For the k-th MS among the next K1 MSs after K0 MSs, the precoder wk should satisfy the equations in Eq. (12) at the same time. (12) Gtk,i wk = Pi ai , i = 2, . . . , J. Here ai is an complex vector of dimension T × 1. Eq. (12) is equivalently represented as ⎡ t ⎤ Gk,2 ⎢ .. ⎥ (13) ⎣ . ⎦ wk = diag[P2 , . . . , PJ ]a, t Gk,J where a = [at2 , . . . , atJ ]t . Since the elements of the channel matrices are i.i.d., the condition (J − 1)T + Mm > (J − 1)Mr is necessary [14], [20] for us to find a wk that can steer the interference matrices G2,k wk , . . . , GJ,k wk toward the predefined interference plane as in Eq. (12). If Eq. (12) is satisfied similarly for all k = K1 + 1, . . . , K toward the other RS cells to which they do not belong, then the interference vectors toward any RS are aligned to the interference plane of the RS and Eq. (10) is satisfied. There are Mr − K0 − T dimensions free of other cell interference at each RS and hence we can have K1 = K2 = K3 = Mr − K0 − T intra RS cell MSs. In system-wide, we have K = K0 + J(Mr − K0 − T ) = J(Mr − T ) − (J − 1)K0 MSs. Note that the dimension size of the interference plane Mm , 0 ≤ T < Mr − K0 T is constrained as T > Mr − J−1 and that the value K is inversely proportional to T and K0 . When Mm > (J − 1)Mr , we have enough MS antennas (Mm ) to align the interference and hence we set K0 = T = 0 and K1 = K2 = K3 = Mr , which produces the system-wide DoF of K = JMr . Otherwise, we set Mm T = Mr + 1 −  J−1 , K0 = 0 and get the system-wide Mm DoF K = J(min{Mr ,  J−1  − 1}), where each RS can serve Mr −T MS streams. Note that we get the system-wide DoF of K = Mr when we simply set T = 0, K0 = Mr . Therefore, Mm  − 1})} we can achieve K = max{Mr , J(min{Mr ,  J−1 when Mm ≤ (J − 1)Mr . The inner and the outer beamformers at the i-th RS become as follows  Fr,1,2 = IMr , Fr,i,1 = 0Mr , ∀i(> 1) when K = Mr , Fr,i,1 = IMr otherwise. (14) R EFERENCES [1] J. Laneman and G. W. Wornell, “Distributed space-time coded protocols for exploiting cooperative diversity in wireless networks,” IEEE Trans. Inf. Theory, vol. 49, no. 10, pp. 2415–2425, Oct. 2003. [2] A. Sendonaris, E. Erkip, and B. Aazhang, “User cooperation diversity— part 1: system description,” IEEE Trans. Commun., vol. 51, no. 11, pp. 1927–1938, Nov. 2003.

HWANG et al.: MULTIUSER TWO WAY RELAYING SCHEMES IN THE FUTURE CELLULAR NETWORK

[3] T. Oechtering and H. Boche, “Bidirectional regenerative half-duplex relaying using relay selection,” IEEE Trans. Wireless Commun., vol. 7, no. 5, pp. 1879–1888, May 2008. [4] R. Zhang, Y. Liang, C. Chai, and S. Cui, “Optimal beamforming for two-way multi-antenna relay channel with analogue network coding,” IEEE J. Sel. Areas Commun., vol. 27, no. 5, pp. 699–712, June 2009. [5] C. Esli and A. Wittenben, “One and two-way decode-and-forward relaying for wireless multiuser MIMO networks,” in Proc. 2008 IEEE Globecom. [6] G. Caire and S. Shamai, “On the achievable throughput of a multiantenna Gaussian broadcast channel,” IEEE Trans. Inf. Theory, vol. 49, no. 7, pp. 1691–1706, July 2003. [7] M. Chen and A. Yener, “Multi-user two-way relaying: detection and interference management strategies,” IEEE Trans. Wireless Commun., vol. 8, no. 8, pp. 4296–4305, Aug. 2009. [8] C. Esli and A. Wittenben, “Multiuser MIMO two-way relaying for cellular communications,” in Proc. 2008 IEEE PIMRC. [9] Z. Ding, I. Krikidis, J. Thompson, and K. Leung, “Physical layer network coding and precoding for the two-way relay channel in cellular systems,” IEEE Trans. Signal Process., vol. 59, no. 2, pp. 696–712, Jan. 2011. [10] Z. Ding, T. Wang, M. Peng, W. Wang, and K. Leung, “On the design of network coding for multiple two-way relaying channels,” IEEE Trans. Wireless Commun., vol. 10, no. 6, pp. 1820–1832, June 2011. [11] Z. Zhao, Z. Ding, M. Peng, W. Wang, and K. Leung, “A special case of multi-way relay channel: when beamforming is not applicable,” IEEE Trans. Wireless Commun., vol. 10, no. 7, pp. 2046–2051, July 2011. [12] J. Joung and A. H. Sayed, “Multi-user two-way amplify-and-forward relay processing and power control methods for beamforming systems,” IEEE Trans. Signal Process., vol. 58, no. 3, pp. 1833–1846, Mar. 2010. [13] Y. Jang and Y. H. Lee, “Performance analysis of user selection for multiuser two-way amplify-and-forward relay,” IEEE Commun. Lett., vol. 14, no. 11, pp. 1086–1088, Nov. 2010. [14] D. Hwang, S. Kim, and C. Park, “Channel aligned beamforming in twoway multi-pair decode-and-forward relay down-link channels,” IEEE Wireless Commun. Lett., vol. 1, no. 5, pp. 464–467, Oct. 2012. [15] S. Toh and D. Slock, “A linear beamforming scheme for multi-user MIMO AF two-phase two-way relaying,” in Proc. 2009 IEEE PIMRC. [16] H. Yang, B. Jung, and J. Chun, “Zero-forcing based two-phase relaying with multiple mobile stations,” in Proc. 2008 Asilomar Conf. [17] D. Lopez-Perez, I. Guvenc, G. Roche, M. Kountouris, T. Quek, and J. Zhang, “Enhanced intercell interference coordination challenges in heterogeneous networks,” IEEE Wireless Commun. Mag., pp. 22–30, June 2011. [18] A. Damnjanovic, J. Montojo, Y. Wei, T. Ji, T. Luo, M. Vajapeyam, T. Yoo, O. Song, and D. Malladi, “A survey on 3GPP heterogeneous network,” IEEE Wireless Commun. Mag., pp. 10–21, June 2011. [19] R. S. Ganesan, T. Weber, and A. Klein, “Interference alignment in multiuser two way relay networks,” in Proc. 2011 IEEE VTC – Spring. [20] H. Chung, N. Lee, B. Shim, and T. Oh, “On the beamforming design for MIMO mutipair two-way relay channels,” IEEE Trans. Veh. Technol., vol. 61, no. 7, pp. 3301–3306, Sept. 2012. [21] T. Gou and S. A. Jafar, “Degrees of freedom of the K user M × N MIMO interference channel,” IEEE Trans. Inf. Theory, vol. 56, no. 12, pp. 6040–6057, Dec. 2010. [22] S. A. Jafar and M. J. Fakhereddin, “Degrees of freedom for the MIMO interference channel,” IEEE Trans. Inf. Theory, vol. 53, no. 7, pp. 2637– 2642, July 2007. [23] V. R. Cadambe and S. A. Jafar, “Interference alignment and degrees of freedom of the K-user interference channel,” IEEE Trans. Inf. Theory, vol. 54, no. 8, pp. 3425–3441, Aug. 2008.

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[24] C. Suh, D. Tse, and M. Ho, “Downlink interference alignment,” in Proc. 2010 IEEE Globecom. [25] T. Kim, D. Love, B. Clerckx, and D. Hwang, “Spatial degree of freedom of the multicell MIMO multiple access channel,” in 2011 IEEE Globecom. [26] C. Suh and D. Tse, “Interference alignment for cellular networks,” in Proc. 2008 Allerton Conf. Commun., Control, Comput. [27] D. Hwang, “Interference alignment for the multi-cell multiuser interference channel,” IEEE Commun. Lett., vol. 16, no. 6, pp. 831–833, June 2012. [28] M. Razaviyayn, G. Lyubeznik, and Z. Luo, “On the degrees of freedom achievable through interference alignment in a MIMO interference channel,” IEEE Trans. Signal Process., vol. 60, no. 2, pp. 812–821, Feb. 2012. Duckdong Hwang received his B.S. and M.S. in electronics engineering from Yonsei University, Korea. He received the Ph.D. degree in electrical and computer engineering from University of Southern California, L.A., in May 2005. In 2005, he joined Digital Research Center, Samsung Advanced Institute of Technology as a research staff member. Since 2012, he has been an Research Associate Professor in the School of Information and Communication Engineering at Sungkyunkwan University, Korea. He, also, worked for Daewoo Electronics in Korea from 1993 to 1998 as an engineer. He is interested in the physical layer aspect of the next generation wireless communication systems, including multiple antenna techniques, interference alignment & management, cooperative relays and their applications in the heterogeneous small cell networks. Sukgi Hong has received the B.S. degree in information and control engineering from Kwangwoon University, Seoul, Korea in 2011 and M.S. degree in IT convergence from Sungkyunkwan University, Suwon, Korea in 2013. Since March 2013, he has been an engineer in the Mobile Communications Division, Samsung Electronics. His research interests include cognitive femtocell networks, resource allocation, and interference management.

Tae-Jin Lee received his B.S. and M.S. in electronics engineering from Yonsei University, Korea in 1989 and 1991, respectively, and the M.S.E. degree in electrical engineering and computer science from University of Michigan, Ann Arbor, in 1995. He received the Ph.D. degree in electrical and computer engineering from the University of Texas, Austin, in May 1999. In 1999, he joined Corporate R&D Center, Samsung Electronics where he was a senior engineer. Since 2001, he has been an Associate Professor in the School of Information and Communication Engineering at Sungkyunkwan University, Korea. He was a visiting professor in Pennsylvania State University from 2007 to 2008. His research interests include performance evaluation, resource allocation, Medium Access Control (MAC), physical layer processing and design of communication networks and systems, wireless LAN/PAN/MAN, ad-hoc/sensor/RFID networks, next generation wireless communication systems, and optical networks. He has been a voting member of IEEE 802.11 WLAN Working Group, and is a member of IEEE and IEICE.