Coordination and Antenna Domain Formation in Cloud-RAN systems

Transcription

1 Coordination and ntenna Domain Formation in Coud-RN systems Hadi Ghauch, Muhammad Mahboob Ur Rahman, Sahar Imtiaz, James Gross, Schoo of Eectrica Engineering and the CCESS Linnaeus Center, Roya Institute of Technoogy (KTH arxiv: v [cs.it] 28 Jun 206 bstract We study here the probem of ntenna Domain Formation (DF in coud RN systems, whereby mutipe remote radio-heads (RRHs are each to be assigned to a set of antenna domains (Ds, such that the tota interference between the Ds is minimized. We formuate the corresponding optimization probem, by introducing the concept of interference couping coefficients among pairs of radio-heads. We then propose a ow-overhead agorithm that aows the probem to be soved in a distributed fashion, among the aggregation nodes (Ns, and estabish basic convergence resuts. Moreover, we aso propose a simpe reaxation to the probem, thus enabing us to characterize its maximum performance. We foow a ayered coordination structure: after the Ds are formed, radio-heads are custered to perform coordinated beamforming using the we nown Weighted-MMSE agorithm. Finay, our simuations show that using the proposed DF mechanism woud significanty increase the sum-rate of the system (with respect to random assignment of radio-heads. Index Terms 5G, Coud RN, radio head assignment, antenna domain formation, interference couping, boc coordination descent I. INTRODUCTION The Coud-Radio ccess Networ (C-RN is identified as one of the promising architectures to address the chaenges of 5G systems, namey, the requirement for high spectra efficiency within a particuary dense depoyment (both users and access nodes []. C-RN systems are characterized as a centraized soution for interference coordination: remote radio-heads (RRH act as access nodes, and their baseband processing capabiities vary from fu digita signa processing capabiity (i.e., base stations, to dumb antennas with no baseband capabiities (such as distributed MIMO systems. Such radio-heads are connected via high-capacity (possiby wireess ins to so-caed aggregation nodes (Ns, each essentiay acting as a arge processing unit. Thus, such architectures are natura candidates for interference coordination. In dense depoyments, coordination among base stations was identified as the ey to achieving high spectra efficiency: indeed the ideas of Coordinated Muti-point (CoMP [2], [3] and Interference ignment (I [4], [5] were centra to achieve higher spectra efficiency. However, when appied to conventiona ceuar systems, such techniques have the stringent requirement that they need to be distributed, i.e., to ony use oca CSI at each node: the overhead associated with such techniques has been identified as a (potentiay imiting factor of the sum-rate gains brought about by techniques such as I [6], [7], [8] and [9]. This essentiay puts hard imits on the effectiveness of the atter techniques. However, this imitation is ifted in the C-RN architecture, since Ns can be assumed to have perfect CSI of a arge area, and can perform coordination in a centraized manner. Earier reated wor has been reported in [0] where the authors investigate the beamforming design probem (for sum-rate maximization, in the context of ceuar systems with imited bachau capacity. In [], the authors study the probem of dynamic custering in dense depoyments (for joint transmission, by characterizing the statistics of the instantaneous signa-to-interferenceand-noise ratio (SINR, via toos from stochastic geometry. In our earier paper [2], we investigated radio-head coordination (namey coordinated beamforming, in a typica Coud RN setup, with a arge number of radio-heads and users, served by one N. In this wor, however, we oo higher into the coordination hierarchy, by investigating the so-caed ntenna Domain Formation (DF probem: given a set of radio-heads (each serving a set of users, and a set of Ns, what is the best assignment of radio-heads to Ns, such that the tota interference eaage between the Ds, is minimized. Studying the atter setup is the main contribution and novety of this paper. In that sense, we formuate the DF probem as integer programming probem, and devise an iterative agorithm for soving it. We aso reax the atter probem to obtain a ower bound on the maximum performance of our agorithm. Moreover, we investigate the effect of using a ayered coordination structure, whereby further coordination mechanism (coordinated beamforming are put in pace. We underine the that fact that this wor is currenty being extended to a journa form[3]. In the foowing, we use bod upper-case etters to denote matrices, bod ower-case to denote vectors, and caigraphic etters to denote sets. Furthermore, for a given matrix, [] i:j denotes the matrix formed by taing coumns i to j, of, 2 F its Frobenius norm, its determinant, T its transpose, and its conjugate transpose. [] i,j = a i,j denotes eement (i, j in a matrix, and [a] i eement i in a vector a. Whie I n denotes the n n identity matrix, n denotes the n vector of ones, B N denotes space of N-dimensiona binary vectors, and Π S [x] is the Eucidean projection of a vector x, into some (possiby non-convex set S.

2 H, H 2, c,2 c 2, H,2 H 2,2 U U 2 RRH RRH 2 Fig. : Toy Exampe II. SYSTEM MODEL D N Given a arge area of interest, i.e. a spatia area of a certain size, with N of RRHs and Ns, we wish to address the issue of DF, i.e. which radio heads shoud be assigned to which N. In other words, given a set R of radio heads in an area, the probem is to assign them to a set of Ds (where each D is controed by one N, such that tota interference couping between the Ds is minima. Let denote a set of Ns (where, and R the set of radio-heads where N = R. We assume that radio head i R is equipped with M i antennas, and serving users which are singe-antenna receivers (we assume singe antenna users for simpicity of exposition, though this can be extended to muti-antenna receivers. Let U i be the set of users served by radio head i R. Then, H i,j C Uj Mi denotes the channe from the antennas of radio head i R, to the users served by radio head j R, i.e. U j, and W i C Mi Ui be the precoder that RRH i empoys to serve its users U i. sma toy exampe is iustrated in Fig.. This wor essentiay addresses the interference between Ds, as this type of interference imits significanty the performance of the entire system. It is cear that for any form of operation within the Ds, as we as for any type of interference mitigation technique appied between the Ds, there are more suitabe and ess suitabe D choices for the radio heads. We assume that the oad has been pre-aocated among a Ns, impying that the th N wi have a oad of γ 0. specia case of this is when the oad is equay distributed across a Ns, i.e., γ is the same among a the Ns. Furthermore, each RRH is to be assigned to one N ony. Moreover, it is assumed that each N has perfect CSI of the users to which it is associated. Hence, the main idea in order to form Ds is to reduce the interference couping between the different Ds. Denote by α i,j R + the interference eaage between radio head i R and radio head j R, and note that this denotes the eaage in the direction of j, i.e. α i,j is a measure that represents the interference caused by RRH i on terminas associated to RRH j, if i and j are assigned to be in different Ds. Due to asymmetric channe gains and termina associations, notice in particuar that α i,j α j,i. Thus, we define a couping coefficient c i,j as the interference couping coefficient between RRH i and RRH j. The atter can be then viewed as the cost of having both radio heads in the same D. Thus, one intuitive choice for the atter is to seect c i,j as the tota interference eaage between the two radio heads, i.e., c i,j = α i,j + α j,i = H i,j W j 2 F + H j,i W i 2 F ( However, incorporating the precoders into the couping coefficients maes the overa system quite chaenging since the couping coefficients have to be updated quite frequenty. Thus, we formay define the atter quantity as, { Hi,j 2 F c i,j = + H j,i 2 F, i j (2 0, i = j Let Ψ be the matrix formed by gathering a those coefficients, i.e. [Ψ] i,j = c i,j, (i, j R 2, where Ψ R+ N N is such that Ψ = Ψ T. Furthermore, denote by x i, {0, } the binary decision variabe if RRH i is assigned to D (or not, and denote by x {0, } N the assignment vector of N. We formuate the DF probem as the foowing integer programming probem: min f({x i,j } = ( N N j i c i,jx i, x j, (P = s. t. N i= β i,x i, = γ, = x i,, i R i= x i, {0, }, (i, R Note that one can rewrite the above probem in terms of {x } as foows, min f({x } = = xt Ψx (P 2 s. t. = x N β T x = γ, x B N, where the above inequaity hods eement-wise. In the above, = x N is the assignment constraint forcing that each RRH is assigned to at most one D. Moreover, denoting by β R N + the set of oading factors for D (such that T β =,, β T x = γ is the oading constraint for the th D (i.e. the oad profie for D. Using this equivaent form, it becomes evident that f indeed is not jointy convex in a the variabes, due to the couping among x and x. However, this does revea an inherent bi-inear structure of f (taen separatey in each variabe, f is inear that we expoit for the optimization. Intuitivey, f modes the sum-tota couping that exists between the individua Ds.

3 . Boc Coordinate Descent III. PROPOSED LGORITHM The couping among the variabes in f(x,..., x, maes (P 2 a perfect candidate for a Boc-Coordinate Descent (BCD approach (aso nown as the Gauss-Siede method. In a nutshe, BCD wors iterativey, by fixing a variabes but one boc, i.e. fix (x,..., x, x +,..., x, and optimize for x, iterativey. Let n denote the iteration number, i.e., x (n denotes the vaue of x at the nth iteration. t the nth iteration, given that (x (n, x(n + are fixed, x is optimized accordingy. {x (n+ } = argmin f(x (n+,..., x (n+, x, x (n +, x = argmin f(x, z (n, (3 x where z (n = (x (n+,..., x (n+, x(n + denotes the boc of fixed variabes in the above BCD iteration. Stated differenty, in the above, x (n+ indicates that boc x (for instance has been aready updated, whie boc x + hasn t. Thus, as seen from (3, BCD generates a sequence of iterations {x (n } that converge to a imit point (this wi be formaized ater in this section. Moreover, we note that f(x, z (n (which denotes the function f(x, when the variabes in boc z (n are fixed, can be rewritten as, ( f(x, z (n = xt Ψ x (n+ + x (n x T r (n where r (n Ψ = ( = x (n+ + =+ =+ x (n is referred to as the residua of D, at the nth iteration. Moreover, we ceary see that f(x, z (n is inear, impying that when a but one boc are fixed, f is inear. This indeed shows that (P 2 is equivaent to a series of probems that are soved iterativey, and boc-by-boc. Now that we have described the BCD framewor, we focus on the soution of the optimization probem in (3, within each BCD iteration. With that in mind, the update for x, i.e. x (n+ in (3, is, argmin f(x x (n+, z (n = x (5 s. t. β T x = γ, x ω (n, x B N (4 where ω (n is the vector of residua assignments dependent on the the assignments of a other Ds. ( ω (n N x (n+ + x (n (6 = =+ The above probem is nown as a mixed integer inear program, and is NP-hard due to its inherent combinatoria nature. However, there exists many poynomia-time approximation agorithms that, for a practica purposes, sove it gobay (such efficient sovers are found in MTLB and CVX. It becomes cear at this stage that BCD transforms (P 2 into a series of parae subprobems, where each can be soved in a distributed way, i.e. ocay at each N. B. gorithm Description The use of BCD for soving (P 2 goes hand in hand with maing the probem naturay decouped: when {x } are fixed, the cost function decoupes in x can thus be soved separatey by D, without any oss in optimaity. In that sense, the optima update for x at D, depends on the assignments at a the other Ds, that have to be shared. Given assignments from other Ds, (x (n+,..., x (n+, x(n +, D forms the residua r (n, and can proceed to sove its optimization probem ocay, and update x (n+. The process is formaized in gorithm. gorithm DF via BCD Input: Ψ, N, for n = 0,,, L do // procedure at each N obtain (x (n+,..., x (n+, x(n + at D compute residua r (n, using (4 compute residua assignment ω, using (6 compute x (n+ as soution to (5 end for Output: {x (L,..., x (L } C. Convergence Let {x (n } be the sequence iterates produced by the BCD in (3, and {x } im n {x (n }. The monotonic nature of the BCD iterations is estabished beow. Lemma (Monotonicity. With each update x (n x (n +, f is non-increasing. Moreover, the sequence of function iterates {f(x (n } n converges to a imit point f({x }. Proof: Refer to ppendix though the above resut estabishes the convergence of the proposed BCD method, it ony estabishes convergence to a imit. Remar. though the updates generated by the BCD iteration are shown to converge monotonicay to a imit point, it cannot be estabished that the atter corresponds to a stationary point of f, namey due to - the presence of the binary constraint, that prevents the use of advanced BCD convergence resuts such as [4] - the couping in the assignment constraint, i.e. x x N, cannot be handed by standard BCD convergence resuts. D. Performance bounds Here we attempt to shed ight on the maximum performance that gorithm can deiver. This is achieved by reaxing the origina probem in (P 2. One of the most we nown reaxations for probems such as (P 2 is done by reaxing the

4 binary constraint on x. In this case however, we note that the oading constraint, β T x = γ, does not mae much sense: a quic oo at this case reveas that the oading constraint maes some probems infeasibe (this is expected since it is ony effective when x is binary. We thus concude that a sensibe reaxation has to invove both the binary constraint, and the oading constraint. The resuting probem becomes, min f({w } = = wt Ψw (P 3 s. t. = w N, w [0, ] N, where {w }, the optimization variabes are no onger binary. The fact that the optima soution of (P 3 is a ower bound on the origina probem (P 2, foows immediatey from the reaxation arguments. Despite its simpe form, gobay soving the above probem is not straightforward, namey due to couping among the variabes, {w }, and that f is not convex in {w } (since Ψ is not positive-definite. However, we reca that the same BCD procedure that was used to sove (P 2, can be appied to the reaxed probem. Thus, the sequence of iterates generated by the BCD is given by, w (n+ = where f(w, z (n f(w, z (n = wt Ψ ω (n argmin f(w, z (n w (7 s. t. w ω (n, w [0, ] N and ω(n are given as foows, ( w (n+ + w (n = N = ( = w (n+ + =+ =+ w (n w T r (n Let {w (n } be the sequence iterates produced by the BCD in (7, and {w } im n {w (n }. Then, by appying BCD to reaxed probem (P 3, yieds the desired ower bound on (P 2. Moreover, the resuting soution to (P 3, {w } is such that f({x } f({w }. We reca at this stage (8 that {w } doesn t necessariy correspond to an assignment variabe. Thus, a natura question is whether one can obtain an estimate of the soution to (P 2, {ˆx }, from the soution of the reaxed probem {w }. The reation between ˆx and w can be formaized as foows, ˆx = Π D [w ], where D = {w w B N, β T w = γ } (9 Stated differenty, ˆx is the Eucidean projection of w, on the non-convex set D. However, a coser oo at the atter reveas that the projection in this case, does not aways yied a unique point ˆx. Consequenty, athough the soution of the reaxed probem, w, cannot be used as a basis for assignment, we indeed use it as a ower bound on the cost function vaue that gorithm yieds. E. System-eve Operation We use gorithm to perform the assignment of RRHs to Ds. Then, there are additiona coordination mechanisms depoyed within each D: cooperation within the atter is done via custers of cooperating RRHs, that in turn are formed based on geographica distance (using agorithms such as the K-means. Moreover, a the radio heads in the atter custer perform coordinated beamforming (CB (using the we nown Weighted MMSE (WMMSE [5], to iterativey optimize their precoders. The steps in this coordination hierarchy are detaied in the tabe beow. System eve operation: - ssign users to RRHs based on highest channe energy - Compute couping coefficients matrix Ψ - Run DF agorithm to obtain RRH-to-D assignment for each D do - Custer RRH into C custers using -means (optiona - Run WMMSE (within each custer to optimize precoders end for The resut of combining the atter two coordination mechanisms is a hierarchica cooperation mode: at the highest eve, RRHs are assigned into Ds (using gorithm, then, RRHs are grouped to form coordination custers (where each is performing coordinated beamforming. The resting networ structure is iustrated in Fig. 2. Next, we mathematicay formaized the operation and performance of the system. Sum-rate performance: We assume for simpicity that each RRH is serving J users, and that the size of each custer, C m (, is the same. Moreover, et C denote the number of custers within each D. Let C m ( denote the mth custer ( m C in N ( : then C m ( R is the set of cooperating radio heads within the th D (Fig 2. For shorthand notation, we denote by i, the ith user ( i J, served by RRH ( K. Then, h (,m i,j is the (MISO channe from RRH j, to user i, in C m (. Simiary, we define v (,m i at the transmit precoder, used to serve user i, in C m (. Letting P t denote the transmit power of a radio-heads, the SINR of user i, in C m (, is given by (0. Thus, treating interference as noise at the users, the achievabe sum-rate of the system is as foows, R Σ = C J K og 2 ( + SINR (,m i ( m= i= = Under this setup we advocate, each user is subject to residua interference from users within its coordination custer, interference emanating from users in other custers (but sti within the same D, as we as interference coming from a users present in other Ds. 2 Practica spects: The matrix of couping coefficients Ψ shoud avaiabe at a the Ns, prior to the start of the agorithm: the atter can be popuated sequentiay, by having each D estimate a channes (both to its served users, and to users from other Ds via training, in an orthogona manner. Due to the fact that the assignment variabes are binary, one ony needs a ow-rate contro in between a the Ns. In the

5 D D 2 C ( C (2 C (2 2 C ( 2 Fig. 2: System-eve Operation SINR (,m i = (p,q (i, P t (h (,m p q,i P t (h (,m i,i v (,m i 2 i 2 + P t (h (r,s v (,m (r,s (,m(p,q p q,i v (r,s p q 2 + (σ (,m i 2 (0 case where = 2, due to the biinear structure of f, ony one iteration of gorithm is required for convergence: this is quite beneficia since it eeps the communication overhead to a minima eve. Moreover, one can initiaize the agorithm with severa feasibe soutions, and pic the best optima soution among them.. Simuation Setup IV. NUMERICL RESULTS Both radio heads and users are dropped uniformy within the area of interest (their positions are ept fixed throughout the simuation, where no mobiity is considered. Then, for each simuation run, channes are generated randomy: a channes are compex i.i.d, assumed to be sowy boc fading. We first investigate a system where N = 6 radio heads are depoyed, each equipped with M = 4 transmit antennas and serving J = 2 singe-antenna users (for a tota of K = 32 users. The RRHs are to be assigned to one of two Ns (i.e., = 2. In our simuations we assume that within each D, radio heads form one custer (i.e. C =, thereby forming goba coordination (GC custer within each D. Then, WMMSE is empoyed to iterativey optimize the precoders within each custer. Moreover, we assume that the oading factors are identica, whereby the RRH oad is spit equay among the two Ds, i.e. β =, and γ = N/,. For the assignment of radio heads to Ns, we benchmar our proposed scheme, gorithm, against a randomized assignment where radio heads are randomy assigned to each of the Ns. Despite the fact that the atter is not a good choice, it is however intended to be used as a ower bound on the performance of our agorithm (the atter assignment sti taes into account the equa-oading constraint, and the fact that each RRH is assigned to one D ony. Moreover, for this particuar (reativey sma case, we are abe to find the gobay optima soution to the DF probem, via exhaustive search of (P. We aso investigate two (extreme specia cases of DF, - DF based on instantaneous CSI is the case detaied in (2 where matrix of couping coefficients Ψ is based on instantaneous CSI: in this case, Ψ is updated every time the channe changes, and consequenty, the Ds have to be recomputed at every channe reaization - DF based on statistica CSI, where the couping coefficients are given by, { H i,j 2 F c i,j = + H j,i 2 F, i j (2 0, i = j where, anaogousy to H i,j, we define H i,j C Uj Mi as the matrix of pathoss factors from the antennas of radio head i R, to the users of radio head j R. Unie the instantaneous CSI case, here Ψ is computed at the beginning of the simuation, the DF performed, and remains static throughout the simuation run (since users are static. B. Resuts The sum-rate performance (refer to ( that resuts from the above setup is shown in Fig 3, where we compare the performance of our agorithm, against both the random assignment and the optima exhaustive search. Instantaneous CSI is assumed for a schemes. We can ceary see a significant performance gap between the performance of our scheme, and that of the benchmar. Moreover, ooing at the performance of the exhasutive search, reveas that there are rather arge gains from finding the gobay optima soution to the DF probem. We next investigate the extent to which repacing Instantaneous CSI with ong-term Statistica CSI, degrades the sumrate performance of the system in question (we foow the exact same setup used for the instantaneous CSI case. s shown in Fig 4, we see the same trends discussed just above.

6 verage sum rate (bits/s/hz Proposed DF Random ssignment Exhaustive Search Power aocation per RRH (dbm Fig. 3: verage sum-rate performance using instantaneous CSI M = 4, N = 6, K = 32, C =, J = 2 verage sum rate (bits/s/hz Proposed DF Random ssignment Exhaustive Search Power aocation per RRH (dbm Fig. 4: verage sum-rate performance using statistica CSI M = 4, N = 6, K = 32, C =, J = 2 Fig. 5: verage eaage vaue (M = 4, N = 6, K = 32, C =, J = 2 More importanty, as far as our agorithm is concerned, the degradation observed by going from instantaneous to statistica CSI, is extremey negigibe. This can be expoited to massivey reduce the overhead and compexity of the system (detaied in next subsection. Foowing the same setup as above, we shed ight on the behavior of the proposed DF agorithm, as a function of the SNR. In Fig 5 we show the average vaue of f that is achieved by gorithm, as we as the ower bound discussed in III-D. Though our agorithm greaty outperforms the benchmar, it is reativey far from the ower-bound (derived from the reaxed probem (P 3: however, we reiterate the fact that soutions such as the atter, do not correspond to feasibe soutions for the DF probem (thus are potentiay not achievabe within our setup. C. Discussions The numerica resuts a point to a good performance brought about by the appication of our proposed method (both in terms of achievabe sum-rates for the system, and tota interference eaage between the Ds. Moreover, as shown in gorithm, the communication overhead requirement among the Ns is quite negigibe since it consists of binary vectors ony. With that in mind, the overhead woud consist of obtaining a the CSI needed to compute Ψ, and propagate it to a the Ns (as often as needed. Though this might seem too high, our simuations aso ceary indicated that for reativey static settings, DF based on pathoss (i.e., ocationbased has virtuay the same performance as the one based on instantaneous CSI. V. CONCLUSION ND FUTURE WORK In this wor we taced the probem of DF in C-RN systems by formuating it as an integer programming probem. We empoy the we-nown BCD framewor for soving the probem and devising an iterative agorithm for that purpose. We shed ight on the convergence of the agorithm, as we as its maxima performance via simpe reaxations. Our simuations revea that this approach promises to deiver good sum-rate performance, in typica C-RN depoyments. s mentioned earier, we started to investigate more anaytica aspects of the DF probem, namey, better reaxation techniques (e.g. Lagrange Reaxation, decomposition techniques (e.g. Dantzig-Wofe Decomposition, and dua probem anaysis. The atter wi provide us with insights into fundamenta ower bounds for the DF probem. In addition, we extended the probem formuation used here, to incude both the channe and precoder effect, rather than just the channe energy (as seen in (. the above issues are investigated in great detai, in our subsequent wor [3]. We aso wish to investigate more practica scenarios, namey the so-caed hybrid CSI case, consisting of a mix between instantaneous and statistica CSI. VI. CKNOWLEDGMENT The authors gratefuy acnowedge the funding and support of their counterparts at Huawei, Finand.

7 . Proof of Lemma PPENDIX {f(x (n f 0 Note that the foowing is a direct consequence of (5 f({x (n } f(x(n+, z (n f(x(n+ 2, z (n 2... f(x (n+, z (n f({x(n+ } where the ast equaity foows from the fact that f(x (n+, z (n corresponds to the case where a variabes (x,..., x, are updated. It foows that the sequence } n converges monotonicay to a imit point REFERENCES [] M. D6.2, Initia report on horizonta topics, first resuts and 5G system concept, March 204. [2] D. Gesbert, S. Hany, H. Huang, S. Shamai Shitz, O. Simeone, and W. Yu, Muti-ce MIMO cooperative networs: new oo at interference, Seected reas in Communications, IEEE Journa on, vo. 28, no. 9, pp , 200. [3] E. Bjornson, N. Jaden, M. Bengtsson, and B. Ottersten, Optimaity properties, distributed strategies, and measurement-based evauation of coordinated mutice ofdma transmission, Signa Processing, IEEE Transactions on, vo. 59, pp , Dec 20. [4] V. Cadambe and S. Jafar, Interference aignment and degrees of freedom of the K -user interference channe, Information Theory, IEEE Transactions on, vo. 54, no. 8, pp , [5] M. Maddah-i,. Motahari, and. Khandani, Communication over MIMO X channes: Interference aignment, decomposition, and performance anaysis, IEEE Transactions on Information Theory, vo. 54, pp , ug [6] O. E yach,. Lozano, and R. Heath, On the overhead of interference aignment: Training, feedbac, and cooperation, Wireess Communications, IEEE Transactions on, vo., no., pp , 202. [7] O. E yach,. Lozano, and R. Heath, Optimizing training and feedbac for MIMO interference aignment, in Signas, Systems and Computers (SILOMR, 20 Conference Record of the Forty Fifth siomar Conference on, pp , 20. [8] S. Peters and R. Heath, User partitioning for ess overhead in MIMO interference channes, IEEE Transactions on Wireess Communications, vo., pp , Feb [9]. Lozano, R. Heath, and J. ndrews, Fundamenta imits of cooperation, Information Theory, IEEE Transactions on, vo. 59, pp , Sept 203. [0] B. Dai and W. Yu, Sparse beamforming design for networ mimo system with per-base-station bachau constraints, in Signa Processing dvances in Wireess Communications (SPWC, 204 IEEE 5th Internationa Worshop on, pp , June 204. [] N. Lee, R. Heath, D. Moraes-Jimenez, and. Lozano, Base station cooperation with dynamic custering in super-dense coud-rn, in Gobecom Worshops (GC Wshps, 203 IEEE, pp , Dec 203. [2] M. Rahman, H. Ghauch, S. Imtiaz, and J. Gross, RRH custering and transmit precoding for interference-imited 5G CRN downin, preprint avaiabe at [3] H. Ghauch, M. Rahman, S. Imtiaz, and J. Gross, ntenna domain formation: Performance imits and practica agorithms, manuscript in preparation, 206. [4] P. Tseng, Convergence of a boc coordinate descent method for nondifferentiabe minimization, Journa of Optimization Theory and ppications, vo. 09, no. 3, pp , 200. [5] Q. Shi, M. Razaviyayn, Z.-Q. Luo, and C. He, n iterativey weighted MMSE approach to distributed sum-utiity maximization for a MIMO interfering broadcast channe, IEEE Transactions on Signa Processing, vo. 59, no. 9, pp , 20.