CLOUD RADIO ACCESS NETWORK WITH OPTIMIZED BASE-STATION CACHING

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1 CLOUD RADIO ACCESS NETWORK WITH OPTIMIZED BASE-STATION CACHING Binbin Dai and Wei Yu Ya-Feng Liu Department of Eectrica and Computer Engineering University of Toronto, Toronto ON, Canada M5S 3G4 Emais: {bdai, LSEC, ICMSEC, AMSS Chinese Academy of Sciences, Beijing , China Emai: ABSTRACT The performance of coud radio access networks C- RAN) is imited by the finite capacities of the backhau inks connecting the coud with the base-stations BSs). A promising approach to improving the performance of C-RAN is to augment the backhau through BS caching, where the BSs pre-store some of the popuar contents. In this paper, we first derive a muticast backhau rate expression based on a joint cache-channe coding scheme, and show that, as compared to the uniform cache aocation, it is better to aocate arger cache sizes to the weaker BSs. Then, by everaging the sampe approximation method and the aternating direction method of mutipiers, we deveop an efficient agorithm to optimize the cache aocation by maximizing the BS expected fie downoading rate from the coud. Numerica resuts show considerabe performance improvement of the optimized cache aocation scheme over heuristic schemes. Index Terms Caching, C-RAN, muticast backhau 1. INTRODUCTION Coud radio access network C-RAN) has been recognized as one of the enabing technoogies for the next generation wireess networks [1, 2, 3]. In C-RAN, the base-stations BSs) are connected to a centraized processor CP) through the backhau inks. A main advantage of C-RAN is that it enabes cooperation among the BSs for inter-ce interference canceation. The cooperation gain brought by C-RAN is however imited by the capacities of the backhau inks [4, 5]. In particuar, this paper focuses on the data-sharing strategy for the downink C-RAN, where the user messages are shared with mutipe BSs for cooperative transmission. In this case, the BS cooperation custer size is imited by the backhau. This paper proposes the use of caching at the BSs for aeviating backhau traffic in the downink C-RAN. Caching at the network edge has attracted extensive research interests. For exampe, the pioneering work of [6] uses network coding to simutaneousy deiver mutipe fies through a commmon noiseess channe to mutipe receivers, each caching different parts of the fies. This paper studies a different scenario in which the same content is required at mutipe BSs, but the backhau is wireess with different channe conditions to different BSs. In particuar, we consider a practica C-RAN mode where each BS ony caches a fraction of each fie and requests the rest from the CP via noisy wireess backhau channe. Under a tota cache size constraint, we investigate the optima cache size aocation strategy at each BS and the transmission strategy at the coud such that the fie requests can be deivered most efficienty from the coud to the BSs. As reated works, wireess muticast backhau for C-RAN has been considered in [7, 8]. However, [7] does not consider BS caching, whie [8] considers network coded muticasting with fixed cache sizes. This paper differs from the above works in optimizing the cache aocation among the BSs to further improve the efficiency of wireess muticast backhau. This paper is motivated by the information theoretica study of [9], which shows that it is advantageous to aocate different cache sizes to different BSs depending on the channe conditions. In addition, [9] proposes a joint cache-channe coding scheme that optimay utiizes the caches at the BSs. We take the findings in [9] one step coser to the practice and consider the cache aocation probem under a reaistic downink C-RAN setup with a singe BS custer. This paper first derives a new muticast backhau rate expression with BS caching, then formuates the cache aocation probem which s the expected fie deivering rate from the coud to the BSs under a tota cache size constraint. By taking advantage of the sampe approximation method and the aternating direction method of mutipiers ADMM), we propose an efficient cache aocation scheme that together with transmit optimization consideraby outperforms the uniform cache aocation scheme and the heuristic scheme of aocating cache in proportion to the ong term channe statistics. 2. CACHING IN C-RAN BACKHAUL Consider a downink C-RAN mode in which a the BSs are connected to a coud center through shared wireess backhau. The coud empoys a data-sharing strategy which deivers each user s intended message to a predefined custer of BSs and the BS custer subsequenty serves the user through cooperative beamforming. The performance of C-RAN is argey

2 imited by the capacities of the backhau [4, 5]. In order to mitigate the demand for high backhau capacities needed for arge cooperation gain, we assume that each BS is equipped with a oca cache and can pre-store content during off-peak traffic time to reduce the peak time backhau traffic. For simpicity, we consider a network consisting of a singe custer of cooperative BSs. A fie of size F needs to be deivered to a the BSs in order to enabe cooperation. Each BS L := {1, 2,..., L} is equipped with a oca storage unit of size C that can cache some contents of the fie, where L C C. In this paper, the backhau connecting the coud with the BSs is assumed to be a shared wireess medium. We address the question of how to distribute the tota cache size C among the BSs and design transmission strategies at the coud such that the coud can deiver the fie to the BSs in the most effective way. We assume a bock-fading mode for the wireess backhau channe from the coud to the BSs. The coud transmitter has M transmit antennas, whie a the BSs are equipped with a singe antenna. Let h C M 1 denote the channe vector between the coud transmitter and BS within a coherent bock. The received signa at BS can be written as y = h H x + z 1) where x C M 1 is the transmit signa of the coud transmitter, y C is the received signa at BS, and z CN 0, ) is the background noise at BS. We optimize the transmit covariance matrix for each channe reaization. 3. EFFECTIVE DOWNLOAD RATE WITH CACHING 3.1. Broadcast Channe with Uncoded Caching The downink C-RAN wireess backhau network with a singe BS custer can be modeed as a broadcast channe BC) with common message, the capacity of which is given as R 0 min {I x; y )}, 2) where R 0 denotes the muticast rate, I x; y ) is the mutua information between the transmit signa x at the coud and the received signa y at BS. It can be seen from 2) that the common information rate is imited by the worst channe. With caching at the BSs and assuming that BS fis up its cache by naivey caching the C /F fraction of the fie, the coud then ony needs to deiver the rest 1 C /F fraction of the fie to each BS. However, since the BSs are served through muticasting, the coud has to send the maximum of the rest of the request fie, i.e., max {1 C /F }, to make sure that the BS with east cache size can get the entire fie. Therefore, the effective fie downoading rate is D 0 = min {I x; y )} max {1 C /F }. 3) Under this naive caching strategy, it is optima to aocate the cache size uniformy, i.e., C = C/L, L BC with Joint Cache-Channe Coding The above downoading rate can be improved if a joint cachechanne coding scheme is empoyed, in which BSs use the cached bits to faciitate the decoding of the received signa. From an information theoretic anaysis, we have: Lemma 3.1 [9]) In a broadcast channe with common message, if each receiver caches m bits, the common message rate R c bits per channe use is achievabe if and ony if R c I x; y ) + m, L. 4) Now if the BS caches C /F fraction of the fie, it ony needs to have its channe to be abe to support the rest 1 C /F fraction of the fie. By 4), this condition needs to be satisfied for each BS individuay. This gives the effective downoading rate with caching as D c = min { I x; y ) 1 C /F }. 5) Ceary, the effective downoading rate in 5) is stricty arger than the one in 3) except when a I x; y ) are equa. Instead of aocating the cache size C uniformy, 5) shows that it is advantageous to aocate more cache to the BS with weaker channe to achieve an overa higher muticast rate. In the next section, we formuate an optimization probem to find the optima cache aocation among the BSs. 4. OPTIMIZING BS CACHE ALLOCATION Based on 5) and the channe mode 1) and by further incuding the optimization of the transmit covariance matrix, we now formuate the optima muticast downoading rate probem with BS caching as ) og 1 + TrH W) Dc = max min W W 1 C /F, 6) where H = h h H, W is the covariance matrix of the transmit signa x, and W = {W 0 Tr W) P } with P being the transmit power budget. Note that the optima muticast rate in 6) is a function of both the channe condition and the cache aocation. In practice, the transmit covariance matrix is adapted to each channe reaization, but the cache aocation is determined at the cache depoyment phase so can ony adapt to the channe statistics. We therefore take expectation of Dc in 6) over the channe distribution, and aim to find an optima cache aocation that s the ong-term expected effective downoading rate. The overa optimization probem is now formuated as: {C } E {H } [D c ] C C, 0 C F, L. L 7a) 7b)

3 In the fu version of this paper [10], we aso consider the expected fie downoading time as the objective function. Finding a cosed-form expression for the objective function in 7a) is in genera chaenging. This paper proposes to repace the objective function of the above with its sampe approximation [11] and to reformuate the probem as: {C, W n } ) 1 og 1 + TrHn Wn ) σ min 2 N 1 C /F C C, 0 C F, L, Tr W n ) P, W n 0, n N, 8a) 8b) 8c) where N := {1, 2,..., N}, {H n } n N are the sampes drawn according to the distribution of H, and W n is the covariance matrix adapted to the sampes {H n } L. Probem 8) is sti not easy to sove mainy due to the foowing two reasons. First, the objective function of probem 8) is nonsmooth and nonconvex, athough a of its constraints are convex. Second, the sampe size N generay needs to be sufficienty arge such that the sampe average is a good approximation to the origina expected rate [11], eading to a high compexity for soving probem 8) directy. In the next section, we first reformuate probem 8) as a smooth probem, then inearize the nonconvex term, and finay everage the ADMM to decoupe the probem into N ow-compexity convex subprobems. 5. ADMM WITH SAMPLE APPROXIMATION Dropping the constant 1/N and introducing the auxiiary variabes { }, we first reformuate probem 8) as {C, W n, } og Hn Wn ) 8b) and 8c). 9a) 1 C /F ), L, n N, 9b) The above probem 9) is smooth but sti nonconvex due to the term 1 C /F ). To dea with the nonconvex term, we approximate it by its first-order Tayor expansion at some appropriate point, C ), i.e., 1 C /F ) 1 C /F ) + [ 1 C /F, /F ] [, C C ] T = 1 C /F ) + 1 C /F ) ). An iterative first-order approximation eads to the Agorithm 1 for soving probem 8) shown on the next page. More specificay, et { t), C t)} be the iterates at the t-th iteration, the agorithm soves {C, W n, } og Hn Wn ) 10a) t) 1 C /F ) + 1 C t)/f ) t)), L, n N, 10b) t) rt), n N, 10c) 8b) and 8c), where 10c) is the trust region constraint i.e., within the region the inear approximation in 10b) is trusted to be of good quaity) and rt) is the radius of the trust region at the t-th iteration; then the agorithm updates the parameters for the next iteration as t + 1) = min L ) og 1 + TrHn Wn t)) 1 C t)/f, n N, 11) C t + 1) = C t), L, 12) where W n t) and C t) are soutions to probem 10). For the initia point, we can set C 1) to be C/L for a L, and decoupe probem 9) into N convex optimization subprobems to sove for 1) for a n N. It remains to sove probem 10). Note that probem 10) is a convex probem but with a potentiay) arge number of variabes due to the arge sampe size). We propose to use the ADMM [12] to sove probem 10), which decoupes the high-dimensiona probem into many sma-dimensiona subprobems. In particuar, we introduce the so-caed consensus constraints C n = C,, n and reformuate probem 10) as {, W n, C n, C } og Hn Wn ) 13a) t) 1 C n /F ) + 1 C t)/f ) t)), L, n N, 13b) C n = C, L, n N, 13c) t) rt), n N, 13d) 8b) and 8c). The partia augmented Lagrangian of probem 13) is L ρ, W n, C n, C ; λ n ) = L n N + [ λ n C n C ) + ρ 2 Cn C ) 2], 14)

4 Agorithm 1 Proposed Agorithm for Probem 8) Initiaization: Initiaize C 1) = C/L, L, and 1) as the soution to probem 8) with C = C 1); set t = 1; Repeat: 1. Use the ADMM to sove probem 10); 2. Update { t + 1), C t + 1)} according to 11) and 12), respectivey; 3. Set t = t + 1; Unti convergence Cumuative Distribution Function Uniform, C = 100 Proportiona, C = 100 Optimized, C = 100 Upper Bound, C = 100 Uniform, C = 200 Proportiona, C = 200 Optimized, C = 200 Upper Bound, C = Muticast Rate in bps/hz Fig. 1. CDF of muticast rates under different caching schemes. where λ n is the Lagrange mutipier corresponding to the constraint C = C n and ρ > 0 is the penaty parameter. To sove the origina probem, the ADMM sequentiay updates the prima variabes via minimizing the augmented Lagrangian, foowed by an update of the dua variabe. In our case, at each iteration, the ADMM first minimizes 14) 13b), 13d), and 8c) over the variabes {, W n, C n } ; then minimizes 14) 8b) over {C } ; and finay updates the Lagrange mutipier. A subprobems at each iteration of the ADMM here are easy to sove. In particuar, the subprobem of minimizing 14) 13b), 13d), and 8c) over the variabes {, W n, C n } automaticay decoupes into N ow-dimensiona convex probems. 6. SIMULATION RESULTS We consider a downink C-RAN mode with L = 5 BSs ocated at distances 398, 278, 473, 286, 267) meters from the coud. The coud transmitter is equipped with M = 10 transmit antennas. We generate 1000 sets of channe reaizations according to h = K 1/2 v, where K is fixed and generated in the same fashion as in [13] with path-oss component modeed as og 10 d) db and d is the distance be- Tabe 1. Cache aocations for BS 1,..., BS 5 ) at distances 398, 278, 473, 286, 267) meters from the coud transmitter with fie size F = 100. C = 100 C = 200 Uniform 20, 20, 20, 20, 20) 40, 40, 40, 40, 40) Proportiona 23, 17, 26, 18, 16) 42, 38, 45, 38, 37) Optimized 25, 10, 45, 13, 7) 44, 33, 58, 35, 30) tween the coud and the BS; v is a Gaussian random vector with each eement independenty and identicay distributed as CN 0, 1). The first N = 100 sets of channe reaizations are used in probem 8) to optimize the cache aocation whie the rest 900 are used to evauate the muticast rates under the optimized cache aocation. The transmit power at the coud is set to be 40 watts and the background noise eve is set to be 150 dbm/hz. The fie size is set as F = 100. We compare our proposed cache aocation scheme with the foowing two benchmarks: the uniform cache aocation scheme and the proportiona aocation scheme which aocates cache such that og 1 + P TrK ) L ) / 1 C /F ) for a are equaized if possibe). We aso simuate an impractica) scheme of dynamicay and optimay aocating cache based on each channe reaization, which provides a generay not achievabe) upper bound of the optima muticast rate in probem 8). Note that the cache aocation probem based on each channe reaization is a convex optimization probem. In Tabe 1, we ist the cache size aocated to each BS under two different settings of the tota cache size C = 100 and 200 for the proposed optimized scheme as compared to the two benchmarks. Fig. 1 pots the cumuative distribution functions CDF) of the effective muticast rates under the cache aocation in Tabe 1. As we can see from Fig. 1, the proposed optimized caching scheme exhibits considerabe performance improvement as compared to the other two naive baseine schemes i.e., the uniform and proportiona aocation schemes). The improvement is due to that the BSs farther away from the coud are more aggressivey aocated arger amount of cache under the optimized scheme. 7. CONCLUSION This paper studies the optima BS cache aocation probem in the downink C-RAN with edge caching. We first derive the optima fie downoading rate with given BS cache size, then formuate the cache optimization probem of maximizing the expected downoading rate over channe fading reaizations the tota cache size constraint. By everaging the sampe approximation method and the ADMM, we propose an efficient cache aocation agorithm. Simuation resuts show that the optimized cache aocation scheme significanty outperforms the heuristic caching schemes.

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