Control-Data Separation across Edge and Cloud for Uplink Communications in C-RAN

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1 1 Control-Data Separation across Ege an Clou for Uplink Communications in C-RAN Jinkyu Kang, Osvalo Simeone, Joonhyuk Kang an Shlomo Shamai (Shitz) School of Engineering an Applie Sciences, Harvar University, Cambrige, MA, USA Department of Electrical Engineering, KAIST, Daejeon, South Korea CWCSPR, NJIT, Newark, NJ, USA Department of Electrical Engineering, Technion, Haifa, Israel Abstract Fronthaul limitations in terms of capacity an latency motivate the growing interest in the wireless inustry for the stuy of alternative functional splits between clou an ege noes in Clou Raio Access Network (C-RAN). This work contributes to this line of work by investigating the optimal functional split of control an ata plane functionalities at the ege noes an at the Remote Clou Center (RCC) as a function of the fronthaul latency. The moel uner stuy consists of a twouser time-varying uplink channel in which the RCC has global but elaye channel state information (CSI) ue to fronthaul latency, while ege noes have local but timely CSI. Aopting the aaptive sum-rate as the performance criterion, functional splits whereby the control functionality of rate selection an the ecoing of the ata-plane frames are carrie out at either the ege noes or at the RCC are compare, emonstrating the potential avantages of implementing control functions at the ege. Inex Terms Clou-Raio Access Network (C-RAN), fronthaul, control ata separation, Fog networking. I. INTRODUCTION The evolution of the Clou Raio Access Network (C- RAN) architecture, as trace from its origin to more recent stuies [1], points to a shift from fully centralize baseban processing an control to a more balance functional split between clou an ege. In particular, while the basic C-RAN system prescribes the implementation of all functions, excluing possibly analog-to-igital an igital-to-analog conversion, at a clou processor, more recent proposals enable a flexible number of functionalities to be carrie out at the ege noes. This shift is ictate by the realization that a fully centralize C-RAN system entails significant, an possibly prohibitive, requirements on the fronthaul connections between ege noes an clou, see, e.g., [2], [3] an references therein. The emarcation line between the functionalities to be implemente at the clou an at the ege is typically rawn to inclue a given number of physical-layer functions at the ege noes, such as synchronization, FFT/IFFT an resource emapping [2]. In contrast, reference [4] proposes the application of the ata-control separation architecture [5] as a guiing principle for the separation of functionalities between ege an clou with the aim of aressing fronthaul latency limitations. The work of O. Simeone has been partly supporte by the U.S. NSF uner grant CCF The work of S. Shamai has been supporte by the European Union s Horizon 2020 Research An Innovation Programme, grant agreement no UE 1 UE 2 S I 1 (t) S RRS 1 I 2 (t) RRS 2 wireless fronthaul Fig. 1. Uplink of the consiere C-RAN system. RCC In particular, following [6], [7], it is argue therein that the implementation of HARQ control functionalities at the ege can be an enabler for the reuction of transmission latency even in the presence of significant elays on the fronthaul links. In this work, we stuy the optimal functional split of control an ata plane functionalities at the ege noes an clou for uplink communication. We specifically focus on the following functionalities: (i) the control plane functionality of the ata rate selection, an (ii) the ata plane functionality of ata ecoing. We aim at assessing the impact of fronthaul latency on the relative performance of ifferent splits, whereby rate selection an ata ecoing may be performe separately at either clou or ege. The moel uner stuy consists of a twouser time-varying uplink channel in which the RCC has global but elaye CSI ue to fronthaul latency, while the ege noes have local but timely CSI. Aopting the aaptive sum-rate as the performance criterion (see, e.g., [8]), ifferent functional splits base on the control-ata separation architecture are compare through analysis an numerical results. The rest of the paper is organize as follows. We escribe the system moel an performance metric in Sec. II. We analyze ifferent control-ata functional splits between RCC an RRSs in Sec. III for a Markov channel moel with an arbitrary number of states. In Sec. IV, numerical results are presente. Concluing remarks are summarize in Sec. V. II. SYSTEM MODEL AND PERFORMANCE METRIC We consier the uplink of a C-RAN illustrate in Fig. 1, which consists of K access points, referre to as remote raio systems (RRSs), a remote clou center (RCC), an K active user equipments (UEs). Note that we use the nomenclature of [1] to emphasize that the RRSs may be enowe with more processing capabilities than a stanar RRH in a C-RAN

2 2 system. We focus here on the scenario with K =2in orer to simplify the arguments, but the analysis can be generalize to larger systems [9]. Each UE i is assigne to a RRS, which is ientifie as RRS i. System Moel: With the aim of highlighting the impact of interference on the optimal functional split between RRSs an RCC, we moel the uplink channels as illustrate in Fig. 1. The signal to noise ratio (SNR) between an UE i an RRS i is enote as S, an is assume to be constant over T transmission intervals, while the SNR between an UE j an the RRS i = j is enote as I i (t), an is assume to vary across the time inex t =1, 2,...,T, which runs over the transmission intervals. Note that the assumption of a constant SNR between UE i an RRS i can be in practice justifie in the presence of power control at the UE. The more general scenario with time-varying irect channels is stuie in [9]. Furthermore, we assume an ergoic phase faing channel with each transmission interval (see, e.g., [10]), so that the channel matrix between the UEs an the RRSs at any channel use k of the transmission interval t =1, 2,...,T can be written as [ Se jθ 11(t,k) H(t, k) = I2 (t)e jθ21(t,k) I1 (t)e jθ12(t,k) Se jθ 22(t,k) ], (1) where the phases θ ij (t, k) are uniformly istribute in the interval [0, 2π], mutually inepenent, an vary in an ergoic manner over the channel use inex k within each transmission interval t. Note that an ergoic phase faing moel may be appropriate on wireless channels where its phase may vary rapily over all possible states ue to small scale mobility an the phase information θ ji (t, k) is available at the receiver [10], [11]. Each RRS i is connecte to the RCC via a fronthaul link with a elay of transmission intervals. As an example, fronthaul transport latency is reporte to be aroun 0.25 ms in [12] for single-hop fronthaul links an can amount to multiple millisecons in the presence of multihop fronthauling, while fronthaul-relate processing at the RCC can take fractions to a few millisecons [13]. As a result, for transmission intervals of, say ms, can be as large as 3 5. Due to the fronthaul elay, the RCC has global but elaye CSI, namely I i (t ) for i {1, 2}. In contrast, each RRS i at time t has local but instantaneous CSI about the cross-channel I i (t). This information can be obtaine, e.g., by means of uplink training in a Time Division Duplex system. For tractability, we assume at first that the SNR I i (t) on the cross-channel between UE j an RRS i with i = j is in two states, namely I L an I H with I H I L. Moreover, the time-varying interference state is governe by the Markov Chain in Fig. 2, with transition probabilities p = Pr[I i (t+1) = I H I i (t) =I L ] an q = Pr[I i (t +1)=I L I i (t) =I H ].The channels I i (t) for i =1, 2 are mutually inepenent. Base on the efinitions above, the probability that the interference state y changes the state x for x, y {I L,I H } after transmission intervals can be written as Pr [I i (t) =x I i (t ) =y] =β x y (), (2) 1-p L p q H 1-q Fig. 2. Markov moel for the cross-channel processes I 1 (t) an I 2 (t). where the probability β x y () is obtaine as the (x, y) entry of the matrix T, with [ ] 1 p p T = (3) q 1 q being the transition matrix of the Markov chain in Fig. 2. Moreover, the stationary probabilities for the low an high states are obtaine as π L = q p + q an π H = p p + q, (4) respectively. A memory parameter μ can be also efine as μ 1 p q an is the secon eigenvalue of the transition matrix T. Accoringly, μ =1represents a static interference process an μ =0represents an i.i.. interference process. The memory parameter μ can be relate to the coherence time of the channel (see Sec. IV). A more general Markovian moel for the cross-channels, as well as for the irect channels, is stuie in [9]. RCC-RRS Functional Splits: Our focus is on the optimization of the functional split between RCC an RRSs, that is, between clou an ege. Specifically, we consier three ifferent control-ata functional splits, as escribe below; (i) Decentralize control-ecentralize ata (DC-DD) functional split amounts to the most conventional cellular implementation in which control an ata plane functionalities are carrie out at the RRSs, that is, at the ege; (ii) Centralize controlcentralize ata (CC-CD) functional split correspons to the stanar C-RAN implementation in which the RCC carries out both control an ata processing; (iii) Decentralize controlcentralize ata (DC-CD) functional split is this hybri implementation in which each RRS iniviually performs ecentralize control an the RCC instea performs centralize joint ata ecoing. Performance Metric: To compare ifferent functional splits, we will use the performance metric of the aaptive sum-rate (with no power control) use in [8] an references therein. This is efine as the average sum-rate that can be achieve while guaranteeing no outage in each transmission slot, where the average is taken here with respect to the steay-state istribution (4) of the ranom channel gains {I 1 (t),i 2 (t)}. To be more precise, in each transmission interval, transmission rates R 1 for user 1 an R 2 for user 2 are chosen by the RCC or by the RRSs, epening on the functional splits, so that no outage occurs. The aaptive sum-rate is the average of the sum rates R 1 + R 2. We will also consier, as iscusse below, a generalize metric, terme aaptive outage sum-rate, in which a (small) outage probability ε is allowe, where an outage event is cause by the imperfect knowlege of the CSI.

3 3 III. ANALYSIS OF THE CONTROL-DATA FUNCTIONAL SPLITS In this section, we analyze the performance in terms of the aaptive sum-rates of the mentione control-ata functional splits between RCC an RRSs in the presence of the fronthaul transmission elay. Throughout, we efine C xy as C xy E[log 2 et(i + H xy H xy)], (5) for x, y {L, H}, where H xy = [ Se jθ11 Ix e jθ12 ; Iy e jθ21 Se jθ 22 ] an the expectation is taken over the ranom phases θ = [θ 11,θ 12,θ 21,θ 22 ] which are mutually inepenent an uniformly istribute in the interval [0, 2π]. Note that this is the maximum achievable sum-rate in a timeslot with I 1 (t) =I x an I 2 (t) =I y if joint ata ecoing is performe at the RCC (see, e.g., [14, Ch. 4]). We will also use the notation C I1I 2 for C xy when I 1 = I x an I 2 = I y. We also observe that C LH = C HL. A. Decentralize Control - Decentralize Data (DC-DD) Here, we stuy the conventional cellular implementation base on DC-DD. Accoringly, each RRS i selects the transmission rate R i for the user i in its cell base on the available current CSI I i (t) an performs local ata ecoing. We further assume the stanar approach of treating interference from the out-of-cell user as noise for local ecoing. Base on the mentione assumptions, the rate for each user can be aapte at each RRS base on the CSI I i (t) =I x by choosing the transmission rate R i = R x log 2 (1 + S/(1 + I x )). This choice guarantees no outage. The resulting maximum aaptive sum-rate R DC DD is summarize in the following lemma. Note that this rate oes not epen on the fronthaul elay, which oes not affect the performance of DC-DD. Lemma 1: With DC-DD, the maximum aaptive sum-rate is given by R DC DD =2π 2 LR L +2π L π H (R L + R H )+2π 2 HR H. (6) B. Decentralize Control - Centralize Data (DC-CD) With DC-CD, the transmission rate R i for user i is selecte by each RRS i base on the available current CSI I i (t) as for DC-DD, while the RCC performs centralize joint ata ecoing on behalf of the RRSs. The set of achievable rate pairs (R 1,R 2 ) with joint ecoing at the RCC is given by the capacity region C I1(t)I 2(t) of the ergoic multiple access channel between the two users at the two RRSs. Using stanar results in network information theory (see, e.g., [14, Ch. 4]), we have R 1 log 2 (1 + S + I 2 (t)) C I1(t)I 2(t) = (R 1,R 2 ) R 2 log 2 (1 + S + I 1 (t)). R 1 + R 2 C I1(t)I 2(t) (7) The capacity regions C LL, C LH, C HL, C HH are illustrate in Fig. 3. We efine as R L an R H the rates selecte by each RRS i when I i (t) =I L an I i (t) =I H, respectively. The outage probability is the probability that the rate pair (R I1(t),R I2(t)) R 2 A, a c C b B (a) C LH C LL /2+log 2 (1 + S + I L ) c A, a E D, b R 2 A, a c C B b (b) C LL /2+log 2 (1 + S + I L ) < C LH 2log 2 (1 + S + I L ) E B (c) 2log 2 (1 + S + I L ) <C LH Fig. 3. Capacity regions C xy in (7) when the interference realizations are I 1 = I x an I 2 = I y if (a) C LH C LL /2+log 2 (1 + S + I L );(b) C LL /2+log 2 (1 + S + I L ) < C LH 2log 2 (1 + S + I L );an(c) 2log 2 (1 + S + I L ) <C LH. The points a, b, c, an inicate the four rate pairs (R x,r y) selecte by the DC-CD scheme in Sec. III-B an the points A, B, C, D, E, an E enote the rates selecte by the RCC in the CC-CD scheme iscusse in Sec. III-C. oes not belong to the capacity region C I1(t)I 2(t). The next proposition provies the maximum aaptive sum-rate for DC- CD base on an optimize choice of the rates R L an R H. Specifically, it shows that the optimal rate pairs (R L,R L ), (R L,R H ), (R H,R L ) an (R H,R H ) are given by the points a, b, c an, respectively, in Fig. 3. Proposition 1: With DC-CD, the maximum aaptive sumrate R DC CD is given as R DC CD =2π 2 LR L +2π L π H (R L + R H )+2π 2 HR H, (8) where R L is given as C LL /2 if C LH >C LL /2+log 2 (1+S+I L ), R L = C LL /2 if C LH C LL /2+log 2 (1+S+I L ) an πl 2 >π2 H, C LH log 2 (1 + S + I L ) otherwise, (9) an R H is given as log 2 (1 + S + I L ) if C LH >C LL /2+log 2 (1+S+I L ), R H = C LH C LL /2 if C LH C LL /2+log 2 (1+S+I L ) an πl 2 >π2 H, log 2 (1 + S + I L ) otherwise. (10) Proof: The etails are available in [9, Proposition 1]. C. Centralize Control - Centralize Data (CC-CD) With the C-RAN moe of CC-CD processing, at any transmission interval t, the RCC performs rate aaptation in a centralize manner base on the available elaye CSI, namely {I 1 (t ),I 2 (t )}. Furthermore, the RCC performs centralize joint ata ecoing on behalf of the connecte RRSs. Due to joint ecoing, an outage occurs at time t if the rate pair (R 1,xy,R 2,xy ) selecte by the RCC when the elaye CSI is I 1 (t ) =I x an I 2 (t ) =I y is outsie the capacity region C I1(t)I 2(t) in (7). Accoringly, the outage probability Pxy out in a time slot t for which the CSI available

4 4 at the scheuler is I 1 (t ) =I x an I 2 (t ) =I y can be compute as 5 CC-CD ( =0) P out xy =Pr [ (R 1,xy,R 2,xy )/ C I1(t)I 2(t) I 1 (t )=I x,i 2 (t )=I y ]. (11) For reference, we first observe the case of no fronthaul elay, i.e., =0, the RCC has perfect CSI I i (t) for all i {1, 2}. Therefore, the RCC can aapt the transmission rates to the current CSI to achieve the maximum sum-rate C I1(t)I 2(t) ue to joint ecoing at the RCC. The resulting aaptive sum-rate is given as =0 = π 2 LC LL +2π L π H C LH + π 2 HC HH. (12) This follows since, when I 1 (t) =I x an I 2 (t) =I y, the RCC can select the rates R 1,xy an R 2,xy such that the selecte rates are insie the capacity region C xy an R 1,xy + R 2,xy = C xy (see Fig. 3). In contrast to the case with no fronthaul elay, if the fronthaul link has elay, the RCC has elaye CSI, namely {I 1 (t ),I 2 (t )}, an is hence not informe about the current capacity region C I1(t)I 2(t) in (7). An outage event can thus be generally avoie only if transmitting always at the minimum sum-rate C LL, since the latter yiels rate pairs that are within the capacity region in all other states. Therefore, with > 0, the aaptive sum-rate of CC-CD is given by = C LL. Base on the iscussion above, CC-CD is outperforme by DC-CD when >0in terms of aaptive sum-rate. To enable aitional insights into the performance of CC-CD, we then consier a generalize performance metric, terme aaptive outage sum-rate, that allows for an outage probability (11) no larger than ε. We note that this efinition is sensible for CC-CD since outage event can occur in this case ue to the, typically small, uncertainty about the CSI at the RCC in the practical case when is not large. This is not the case with DC in which each RRS has no CSI about the cross-channel relative to the other RRS. To formulate the resulting aaptive outage sum-rate, we efine the probabilities Pxy HH = β H x ()β H y (), Pxy LH = β L x ()β H y (), Pxy HL = β H x ()β L y (), an Pxy LL = β L x ()β L y (), where the notation P x y xy inicates the probability of transitioning from elaye states {I 1 (t ) = I x,i 2 (t ) = I y } to current states {I 1 (t) =I x,i 2 (t) =I y }. The next proposition provies an achievable outage aaptive sum-rate. Proposition 2: With CC-CD, the outage aaptive sum-rate (ε) is achievable with outage probability ε, where (ε) =π 2 LR LL +2π L π H R LH + π 2 HR HH, (13) with R xy being efine as R xy = C LL C LH C HH if ε Pxy LL, if Pxy LL <ε 1 P HH if 1 Pxy HH <ε 1, xy, (14) Aaptive sum-rate DC-CD CC-CD (ɛ =0, 0.05, 0.1, 0.15) DC-DD Fronthaul elay Fig. 4. Aaptive sum-rate vs. fronthaul elay uner two-state Markov moel for the cross-channels (N S = N I =2, SNR =0B, SIR H = 10 B, SIR L =0B, μ =0.9, anp = q =(1 μ)/2). if C LH 2log 2 (1 + S + I L ), an as C LL if ε Pxy LL, 2log R xy = 2 (1 + S + I L ) if Pxy LL <ε P xy, C LH if Pxy <ε 1 Pxy HH, C HH if 1 Pxy HH <ε 1, (15) if C LH > 2log 2 (1+S +I L ), with P xy =min(pxy LH,Pxy HL )+ Pxy LL. Proof: The RCC chooses the rates R 1,xy an R 2,xy when I 1 (t ) =I x an I 2 (t ) =I y in such a way that the probability that the chosen rates are outsie the capacity region C I1(t)I 2(t) in (7) is less than ε. Specifically, referring to Fig. 3 for an illustration, the RCC selects the rate pair (R 1,xy,R 2,xy ) at the point A if ε Pxy LL ; at the point B if 1 Pxy HH <ε 1; at the point C if Pxy LL <ε 1 P xy HH an C LH 2log 2 (1+S+I L ); at the point D if Pxy LL <ε P xy an C LH >2log 2 (1+S+I L ); an at either the point E or E if P xy <ε 1 Pxy HH an C LH > 2log 2 (1+S+I L ), where the first rate pair is selecte when Pxy HL +Pxy LL <Pxy LH +Pxy LL an the other pair otherwise. The proof that the outage probability (11) with these choices is no larger than ε is available in [9, Appenix 1]. IV. NUMERICAL RESULTS In this section, we evaluate the performance of the consiere splits of control an ata functions between clou an ege in terms of the aaptive (outage) sum-rate as a function of key system parameters such as fronthaul elay an channel variability. We start by consiering the case stuie in Sec. III, in which the irect channels are fixe, ue to power control, while the cross-channels vary accoring to the two-state Markov chain in Fig. 2. Uner this moel, in Fig. 4 an Fig. 5, we set the SNR of the esire signal as SNR = S/N 0 =0B with noise power N 0 =1; an we assume that the SIR is SIR H = S/I H = 10 B when the cross-channel is in the high state I H, while it equals SIR L = S/I L =0B when the cross-channel is in the low state I L. Moreover, we parameterize the transition probabilities p an q as p = q =(1 μ)/2, with μ being the memory parameter iscusse in Sec. II. For the mentione conitions, Fig. 4 shows the aaptive sum-rate as function of the fronthaul elay when the memory

5 5 Aaptive sum-rate DC-CD CC-CD (ɛ =0.05, 0.1, 0.15) CC-CD ( =0) CC-CD (ɛ =0) DC-DD Memory parameter μ Fig. 5. Aaptive sum-rate vs. memory parameter μ uner two-state Markov moel for the cross-channels (N S = N I =2, SNR =0B, SIR H = 10 B, SIR L =0B, =1an p = q =(1 μ)/2). parameter is μ =0.9. With this choice, the average coherence time is 1/p =1/q =20transmission intervals. For reference, uner Clarke s moel, when the carrier frequency is c/λ =1 GHz, where c = m/s an λ is the wavelength, an the transmission interval is 0.5 ms, using the approximate expression for the coherence time λ/v, this correspons to a velocity v 46 km/h. From the figure, we first observe that, as expecte, the centralize ata ecoing performe by DC-CD strictly improves over the ecentralize ecoing of DC-DD, irrespective of the fronthaul elay, which oes not affect the performance of either scheme. In contrast, the centralize control carrie out by CC-CD is only able to enhance the sum-rate when the fronthaul latency is sufficiently small an the system allows for a non-zero outage. For example, for an outage level ε =0.05, CC-CD improves over DC-CD only as long as the fronthaul latency is no larger than two transmission intervals, i.e., <2. The impact of the memory parameter μ is stuie in Fig. 5, where the aaptive sum-rate is plotte versus μ with a fronthaul elay = 1. We only show the range μ > 0.5 since, for μ<0.5, the sum-rates o not change significantly as compare to μ =0.5. We note that, for Clarke s moel with the parameters iscusse above, the range [0.5, 1] for μ correspons approximately to interval of velocities [0, 230] (km/h). In keeping with the iscussion above, CC-CD is seen to outperform DC-CD for μ sufficiently large. For example, with ε =0.1 at μ =0.9, CC-CD provies a rate gain over the ecentralize schemes. Overall, this iscussion points to a conclusion for the problem of scheuling in a multi-hop network (see Sec. I): Centralize control base on global but elaye CSI can yiel a egrae performance as compare to ecentralize control base on local but timely CSI. We now turn to consier the more general case etaile in [9] in which both irect channel an cross-channel vary accoring to Markov chains with N S = N I > 2 states. Specifically, we aopt the equal-probability metho propose in [15] to approximate Clarke s moel with a finite-state Markov chain (see in etail [9]). In orer to obtain further insight into the operating requires in which ifferent functional splits are to be preferre, Fig. 6 shows the regions of the plane with coorinates given by the fronthaul elay an mobile Mobile velocity v (km/h) CC-CD DC-CD 20 1 ɛ =0 2 ɛ = Fronthaul elay Fig. 6. Regions of the plane (, v) in which DC-CD or CC-CD yiel a larger aaptive sum-rate when allowing an outage of ε =0(region 1 ) an ε =0.1 (region 2 ) uner the finite-state Markov moel [15] for both signal an interference processes (N S = N I =6, γ S = 5 B, an γ I =5B). velocity v in which each scheme offers the best aaptive sumrate. The DC-CD scheme is seen to be avantageous in the area above the uppermost soli line, while CC-CD with ε 0.1 is to be preferre in the complementary regime below this line. In particular, in the region 1 CC-CD outperforms DC-CD, an hence also DC-DD, even when allowing for no outage, while in the region 2 CC-CD outperforms DC-CD for ε =0.1. The uppermost bounary lines for each region hence provie the maximum fronthaul elay that can be tolerate by the CC- CD scheme for a given value of v while still yieling gains as compare to DC-CD scheme when ε =0or ε =0.1. V. CONCLUSIONS In this paper, we have analyze the relative merits of alternative functional splits for C-RAN base on control-ata separation. Our results show that moving the control functionality of rate selection at the ege while performing joint ata ecoing at the clou yiels potentially significant gains. This conclusion emonstrates the value of fog networking solutions in the evolution of C-RAN. REFERENCES [1] J. Huang an Y. Yuan, White paper of next generation fronthaul interface, [Online]. Available: labs.chinamobile.com/cran, ver. 1.0, China mobile Research Institute, Jun [2] D. Wubben, P. Rost, J. Bartelt, M. Lalam, V. Savin, M. Gorgoglione, A. Dekorsy, an G. Fettweis, Benefits an impact of clou computing on 5G signal processing: Flexible centralization through clou-ran, IEEE Sig. Proc. Mag., vol. 31, no. 6, pp , Nov [3] O. Simeone, A. Maeer, M. Peng, O. Sahin, an W. Yu, Clou raio access network: Virtualizing wireless access for ense heterogeneous networks, Journal of Communications an Networks, vol. 18, no. 2, pp , Apr [4] S. Khalili an O. Simeone, Uplink HARQ for clou ran via separation of control an ata planes, to appear in IEEE Trans. Veh. Techn., [5] A. Mohame, O. Onireti, M. Imran, A. Imran, an R. Tafazolli, Control-ata separation architecture for cellular raio access networks: A survey an outlook, IEEE Communications Surveys an Tutorials, vol. 18, no. 1, pp , Jun [6] U. Dotsch, M. Doll, H. P. Mayer, F. Schaich, J. Segel, an P. Sehier, Quantitative analysis of split base station processing an etermination of avantageous architectures for LTE, Bell Labs Technical Journal, vol. 18, no. 1, pp , Jun [7] P. Rost an A. Prasa, Opportunistic hybri ARQ: Enabler of centralize-ran over nonieal backhaul, IEEE Wireless Comm. Lett., vol. 3, no. 5, pp , Jul

6 [8] S. Sreekumar, B. Dey, an S. Pillai, Distribute rate aaptation an power control in faing multiple access channels, IEEE Trans. Info. Th., vol. 61, no. 10, pp , Oct [9] J. Kang, O. Simeone, J. Kang, an S. Shamai, Control-ata separation across ege an clou for uplink communications in C-RAN, arxiv: [10] G. Kramer, M. Gastpar, an P. Gupta, Cooperative strategies an capacity theorems for relay networks, IEEE Trans. Info. Th., vol. 51, no. 9, pp , Sep [11] S. A. Jafar, The ergoic capacity of phase-faing interference networks, IEEE Trans. Info. Th., vol. 57, no. 12, pp , Dec [12] NGMN Alliance, Further stuy on critical C-RAN technologies, [Online] Available: Mar [13] N. Nikaein, Processing raio access network functions in the clou: Critical issues an moeling, in Proc. of Int. Workshop on Mobile Clou Computing an Services, pp , Paris, France, Sep [14] A. E. Gamal an Y.-H. Kim, Network Information Theory. Cambrige University Press, [15] H. S. Wang an N. Moayeri, Finite-state Markov channel-a useful moel for raio communication channels, IEEE Trans. on Veh. Technol., vol. 44, no. 1, pp , Feb