PaperlayerView exact revision on arXiv

Source-linked AI summary

Content-Centric Sparse Multicast Beamforming for Cache-Enabled Cloud RAN

Meixia Tao, Erkai Chen, Hao Zhou, Wei Yu

arXiv:1512.06938v2cs.IT

TL;DR

The paper addresses how to jointly cluster BSs and design multicast beamformers for cache-enabled cloud RAN when users share content but differ in channel conditions and cache availability. It formulates a cost-minimization problem, proves a cache-based clustering property, and reformulates the design as sparse multicast beamforming. The proposed content-centric design achieves a significant reduction in total network cost versus conventional user-centric clustering and unicast beamforming under the considered content-request model.

  • Problem

    The paper asks how BS clustering can be made simultaneously channel-aware and cache-aware for content-centric multicast delivery in cloud RAN.

  • Method

    The paper formulates a weighted backhaul-and-power MINLP, proves that caching BSs may join the relevant cluster, and solves an equivalent sparse multicast beamforming formulation through DC programming and CCP algorithms.

  • Results

    The content-centric design offers significant reduction in total network cost compared with conventional user-centric clustering and unicast beamforming under the considered content-request model.

  • Takeaways & Limitations

    Content-centric BS clustering and multicast beamforming provide a joint transmission design that incorporates requested content and caching into cloud-RAN delivery.

Abstract

from arXiv · show

This paper presents a content-centric transmission design in a cloud radio access network (cloud RAN) by incorporating multicasting and caching. Users requesting a same content form a multicast group and are served by a same cluster of base stations (BSs) cooperatively. Each BS has a local cache and it acquires the requested contents either from its local cache or from the central processor (CP) via backhaul links. We investigate the dynamic content-centric BS clustering and multicast beamforming with respect to both channel condition and caching status. We first formulate a mixed-integer nonlinear programming problem of minimizing the weighted sum of backhaul cost and transmit power under the quality-of-service constraint for each multicast group. Theoretical analysis reveals that all the BSs caching a requested content can be included in the BS cluster of this content, regardless of the channel conditions. Then we reformulate an equivalent sparse multicast beamforming (SBF) problem. By adopting smoothed $\ell_0$-norm approximation and other techniques, the SBF problem is transformed into the difference of convex (DC) programs and effectively solved using the convex-concave procedure algorithms. Simulation results demonstrate significant advantage of the proposed content-centric transmission. The effects of three heuristic caching strategies are also evaluated.

I. INTRODUCTION

The paper proposes content-centric BS clustering and multicast beamforming for cache-enabled cloud RAN, jointly adapting transmission to requested content, channel conditions, and caching status. It formulates and solves the resulting sparse beamforming problem while showing that multicast delivery can improve energy and spectral efficiency.

  • Content-centric transmission: Users requesting the same content form multicast groups served cooperatively by content-specific BS clusters that may overlap.The design replaces user-centric unicast service with content-centric multicast transmission.
  • Solution approach: Content-centric multicast transmission can improve energy and spectral efficiency and provide efficient content delivery compared with user-centric unicast transmission.The paper also evaluates three heuristic caching strategies through simulation.
  • Content-centric transmission: The proposed clustering must account for both channel conditions and the caching state of each BS.Geographically separated users in one group make channel-aware clustering insufficient by itself.
  • Optimization formulation: The optimization minimizes a weighted sum of backhaul cost and transmit power subject to each multicast group’s QoS constraint, yielding an MINLP.Backhaul cost is based on data transferred from the CP to BSs, while transmit power captures wireless delivery cost.
  • Optimization formulation: All BSs caching a multicast group’s requested content can be included in that content’s cluster without loss of optimality, regardless of channel conditions.This result reduces the search space for jointly optimizing clustering and multicast beamforming.
  • Solution approach: The equivalent sparse multicast beamforming problem uses smoothed ℓ0-norm approximations, DC reformulations, and convex-concave procedure algorithms.The paper compares logarithmic, exponential, and arctangent smooth functions and develops two DC programming forms.

II. NETWORK MODEL AND ASSUMPTIONS

The network model considers dynamic, frame-level multicast service in which users requesting the same content are grouped and served by possibly overlapping BS clusters. Cached content is obtained locally, while uncached content is fetched from the CP through backhaul links.

  • System model: Users requesting the same content are grouped together and served using multicast transmission.Each multicast group is cooperatively served by a BS cluster that may overlap with other groups’ clusters.
  • System model: Content-centric BS clustering and multicast beamforming are dynamically optimized by the CP on a transmission-frame basis.Channels remain constant within a frame and vary across frames.
  • System model: A binary clustering matrix records whether each BS belongs to a multicast group’s serving cluster, and each group beamformer is sparse across BSs.The beamforming vector for a BS outside the cluster is zero.
  • QoS model: The model defines each group’s target SINR as the minimum received SINR required by its users and uses fixed-rate transmission R_m = B log2(1 + γ_m).Every user k in group G_m must satisfy SINR_k ≥ γ_m.

B. Cache Model

Each BS has finite local storage represented by a fixed cache-placement matrix, and requested content is served locally when cached or fetched from the CP otherwise. The cost model combines backhaul usage and transmission power.

  • Cache placement: The CP stores F normalized-size contents, while BS n can cache at most Y_n contents.The local storage limit satisfies Y_n < F.
  • Cache placement: The binary cache-placement matrix C records whether each content is cached at each BS, subject to each BS’s storage capacity.Cache placement is fixed according to a chosen caching strategy and is optimized on a slower timescale than transmission.
  • Cost model: The total network cost combines backhaul cost and transmission power, with η controlling the trade-off between backhaul capacity and power.η can be interpreted as a pricing factor for exchanging power against backhaul capacity.
  • Cost model: For a serving BS, cached requested content is accessed locally without backhaul cost, whereas uncached content is fetched from the CP through the backhaul link.The backhaul transfer rate is modeled using the corresponding multicast group’s content-delivery rate.

III. PROBLEM FORMULATION AND ANALYSIS

The paper jointly designs content-centric BS clustering and multicast beamforming to minimize total network cost under QoS constraints. Its analysis shows cached BSs can join the serving cluster without loss of optimality, while exact clustering remains computationally difficult.

  • III. PROBLEM FORMULATION AND ANALYSIS: The optimization jointly designs content-centric BS clustering and multicast beamforming to minimize total network cost under QoS constraints.CSI, user requests, and cache placement are assumed available at the central processor.
  • A. Joint content-centric BS clustering and multicast beamforming: Peak power constraints are omitted because they are convex and do not change the problem’s nature or algorithm design.The study therefore focuses on the backhaul-power tradeoff in total network cost.
  • A. Joint content-centric BS clustering and multicast beamforming: The formulation is combinatorial, with 2^MN possible BS clustering matrices, and each fixed-clustering subproblem is a nonconvex QCQP.Exhaustive search can select the globally best clustering, but multicast beamforming is NP-hard in general.
  • A. Joint content-centric BS clustering and multicast beamforming: The original problem can become infeasible when SINR requirements are too stringent or users across multicast groups have highly correlated channels.Determining feasibility is itself difficult for this NP-hard problem.
  • A. Joint content-centric BS clustering and multicast beamforming: If a BS caches a requested content, it can be included in that content’s cluster without loss of optimality, regardless of channel conditions.Adding such a BS causes no extra backhaul cost and may reduce transmit power through additional cooperative-transmission degrees of freedom.
  • A. Joint content-centric BS clustering and multicast beamforming: A cached BS need not transmit positive power: the optimized beamformer can remain zero even when the BS is included in the cluster.Cluster inclusion and strictly positive transmission are distinct decisions.
  • A. Joint content-centric BS clustering and multicast beamforming: The proposition reduces global-search complexity by restricting deactivated BSs to those that do not cache the requested content.When some requested content is uncached except at the CP, the remaining search space is on the order of 2^N, which can still be prohibitively large for many BSs.
  • A. Joint content-centric BS clustering and multicast beamforming: The authors propose a cache-aware greedy clustering algorithm that starts with full cooperation and successively deactivates noncaching BSs.Its worst-case iterations grow quadratically with MN, and each iteration solves a nonconvex QCQP.

B. Sparse multicast beamforming

The paper reformulates dynamic content-centric clustering as an equivalent sparse multicast beamforming problem. It replaces the discontinuous sparsity term with smooth concave approximations and solves the resulting DC programs using CCP-based algorithms.

  • B. Sparse multicast beamforming: The sparse multicast beamforming formulation represents active serving BSs through the nonzero entries of each content’s beamformer.The formulation is equivalent to the original joint clustering problem while making the cluster matrix implicit.
  • B. Sparse multicast beamforming: The sparse formulation remains challenging because it contains nonconvex QoS constraints and a discontinuous ℓ0-norm objective.The ℓ0-norm counts nonzero vector elements and becomes an indicator function in the scalar case.
  • B. Sparse multicast beamforming: CCP finds local optima of DC programs by replacing each concave component with its first-order Taylor expansion and solving successive convex problems.The procedure starts from an initial feasible point and updates the convexified subproblem iteratively.
  • B. Sparse multicast beamforming: The authors convert the sparse problem into DC programs by replacing the ℓ0-norm with continuous smooth concave functions and applying additional transformations.The resulting CCP-based algorithms are designed to obtain effective solutions of the sparse beamforming problem.
  • B. Sparse multicast beamforming: The generalized CCP formulation applies to traditional multi-group multicast beamforming as a special case.The paper identifies this as the first application of CCP to multi-group multicast beamforming.
  • B. Sparse multicast beamforming: Three smooth concave approximations are considered: logarithmic, exponential, and arctangent functions.The smoothness parameter θ controls the approximation trade-off: larger θ gives smoother but less accurate approximations.

C. SDR-based CCP Algorithm

The SDR-based CCP algorithm lifts beamforming vectors to matrix variables, removes rank-one constraints, and solves convexified semidefinite subproblems. This approach can incur relaxation and computational costs as system size grows.

  • C. SDR-based CCP Algorithm: The SDR approach converts the sparse beamforming problem into a relaxed matrix optimization problem by removing rank-one constraints.The resulting SINR constraint becomes affine, while the objective is represented as a difference of convex functions.
  • C. SDR-based CCP Algorithm: CCP convexifies only the objective in the SDR formulation, so each iteration solves an SDP using a generic SDP solver.The constraints are convex after the SDR transformation.
  • C. SDR-based CCP Algorithm: If the SDR solution is rank-one, eigenvalue decomposition directly recovers the beamformer; otherwise, randomization and scaling produce a suboptimal solution.The recovery procedure depends on whether the relaxed matrix solution has rank one.
  • C. SDR-based CCP Algorithm: The SDR relaxation is more reliable for small user counts, whereas rank-one solutions become unlikely as users or antennas increase.Randomization-based recovery can then be far from optimal.
  • C. SDR-based CCP Algorithm: SDR roughly squares the variable count from MNL to M(NL)^2, making the method computationally inefficient for larger systems.The generalized formulation instead avoids this rank relaxation.
  • C. SDR-based CCP Algorithm: The generalized formulation introduces auxiliary variables so both objective and constraints have DC structure, yielding convex QCQP subproblems under CCP.Unlike SDR, this transformation does not incur loss of optimality and uses roughly MN(L+1) variables.

E. Discussions and Algorithm Outlines

The paper develops initialization and smoothing-parameter strategies for its CCP algorithms, including an annealing scheme for θ. It also explains how the generalized algorithm extends to conventional multicast beamforming.

  • E. Discussions and Algorithm Outlines: CCP requires a feasible starting point, which the paper obtains by solving a full-BS-cooperation power minimization problem.The resulting solution can initialize the SDR-based CCP algorithm, with eigenvalue decomposition or randomization used when needed.
  • E. Discussions and Algorithm Outlines: If the initialization problem is infeasible, the original problem is infeasible; however, feasibility of initialization does not guarantee feasibility of the original problem.The latter qualification is stated explicitly in the paper’s footnote.
  • E. Discussions and Algorithm Outlines: The θ schedule is motivated by using larger θ for large x and smaller θ for small x, so the approximation approaches ℓ0 behavior near zero.An earlier adaptive rule selected θ to maximize the approximation-function gradient, while this work implements annealing.
  • E. Discussions and Algorithm Outlines: The paper uses annealing for θ: it starts with a large smoothness value, then decreases θ by a factor β while reusing the previous solution.The process continues until θ is sufficiently small.
  • E. Discussions and Algorithm Outlines: The generalized CCP algorithm avoids repeated final-stage randomization by using randomization and scaling during initialization until a feasible point is found.SDR-CCP may require many randomization trials when its relaxed solution is not rank one.
  • E. Discussions and Algorithm Outlines: As η approaches infinity, the original and sparse problems reduce to total-power minimization for multi-group multicast beamforming.This identifies the total-power problem as an extreme backhaul-power weighting case.
  • E. Discussions and Algorithm Outlines: The generalized CCP algorithm remains applicable to traditional multi-group multicast beamforming, while SDR-CCP reduces to the traditional SDR method under full cooperation.No smoothness-parameter update is needed in the generalized algorithm for that special case.

Initialization:

The simulation initializes feasible beamforming solutions and evaluates the proposed algorithms in a seven-BS cloud RAN under specified channel, traffic, popularity, and caching settings.

  • Algorithm initialization: SDR-CCP and G-CCP initialize from feasible solutions obtained by solving PINI, with rank-based extraction or randomization and scaling when necessary.Both algorithms reduce the smoothness factor until θ < ǫ.
  • Simulation setting: The simulations use N = 7 BSs with L = 4 antennas, K = 30 active users, and F = 100 contents.Each BS caches Y = 10 contents by default.
  • Simulation setting: The channel model uses uniformly distributed users, 500m adjacent-BS spacing, 10dBi antenna gain, 10MHz bandwidth, pathloss PL(dB) = 148.1 + 37.6log10(d), 8dB shadowing, and normalized Rayleigh fading.Users are excluded from inner 50m circles around BSs.
  • Content popularity: The default request model has one trending-news content with probability 0.5 and the remaining probability distributed across 99 contents by a Zipf law with α = 1.Equal popularity is also evaluated.
  • Caching strategies: The evaluated caching strategies are Popularity-aware Caching, Random Caching, and Probabilistic Caching.Popularity-aware caching stores the same most-popular contents at equal-sized BS caches; probabilistic caching increases storage probability with popularity.
  • Caching strategies: Popularity-aware caching can enable strong cooperation under highly non-uniform popularity, whereas probabilistic caching balances cache-hit rate and cooperative transmission gain.Popularity-aware caching may impose large backhaul burden under equal popularity, while probabilistic caching is designed to balance the two effects.

A. Comparison between SDR-CCP and Generalized CCP algorithms

The simulations compare SDR-CCP and G-CCP across convergence, backhaul-power tradeoffs, smooth functions, and caching strategies. G-CCP achieves better tradeoffs with lower computational cost, while caching effects depend on popularity, user density, and objective weighting.

  • Algorithm comparison: Both SDR-CCP and G-CCP converge within fewer than 10 iterations in all considered cases.The convergence comparison uses θ = 0.01.
  • Algorithm comparison: At the same backhaul cost, G-CCP achieves 1 ∼5 dB lower power cost than SDR-CCP.The backhaul-power curves are generated by varying η, the weight governing backhaul cost versus transmit power.
  • Algorithm comparison: G-CCP saves 0.5dB power cost relative to the SDR method in the transmit-power-minimization limit η →+∞.In this limit, the proposed problem reduces to the multi-group QoS multicast beamforming problem.
  • Smooth-function comparison: The three smooth functions have similar performance across a wide range of η, while the arctangent function has slightly lower backhaul cost as η →0.The arctangent function is therefore used in the remaining simulations.
  • Caching effects: With equal popularity and K = 20, PopC and ProC perform almost identically across the backhaul-power tradeoff curve.For K = 7, ProC retains a significant minimum-backhaul advantage.
  • Caching effects: All caching strategies have the same minimum transmit power because it is determined by the multicast groups’ 10dB target SINR constraints.A reasonably designed cache can nevertheless dramatically reduce backhaul cost and improve the backhaul-power tradeoff.

D. Multicast versus Unicast

Multicast transmission exploits shared content requests to design fewer beamformers than unicast transmission. In the considered cloud RAN, this gives a substantial advantage except in the orthogonal-channel special case.

  • Overall comparison: The simulations demonstrate a significant advantage of the proposed content-centric design over conventional user-centric transmission for the considered setting.The comparison uses popularity-aware caching and accounts for backhaul cost and transmit power.
  • Performance comparison: Multicast transmission performs well by exploiting content popularity among users and designing fewer beamformers.When active-user count decreases, unicast improves but remains considerably inferior to multicast.
  • Performance comparison: At η →+∞ with K = 20, unicast transmission requires 3 dB higher power than multicast transmission.The comparison uses unequal content popularity with α = 1.
  • Special case: If same-content users occupy geographically disjoint BS areas, their network-wide channel vectors can be orthogonal, making unicast and multicast beamforming equivalent.This is identified as a special case rather than the typical considered setting.
  • Small-network benchmark: In a small network, the smooth-function sparse beamforming algorithm is very close to exhaustive-search global optimum, with slightly higher minimum backhaul cost as η →0.The small-network benchmark uses N = 3 BSs, K = 6 users, and F = 4 files.
  • Small-network benchmark: Exhaustive search and greedy clustering become computationally expensive as BS or user counts increase, while the number of convex QCQP problems in G-CCP is not directly affected.Their problem counts grow exponentially and quadratically, respectively.

F. Effect of Peak Power Constraints

Under per-antenna and per-BS peak power constraints, stricter limits increase the minimum achievable backhaul cost because they reduce the power–backhaul tradeoff freedom.

  • Experimental setting: 35dBm and 40dBm per-antenna peak powers are evaluated alongside per-BS limits scaled by the number of antennas.The comparison uses K = 30 users and one channel realization with popularity-aware caching.
  • Performance effect: When η is small, imposing peak power constraints incurs additional backhaul cost.Small η places more weight on backhaul cost in the objective.
  • Performance effect: More stringent peak power constraints produce a higher minimum achievable backhaul cost.The constraints reduce freedom to trade total transmit power against backhaul cost.
  • Performance comparison: Figure 12 compares performance under per-antenna constraints, per-BS constraints, and no power constraint.These are the three constraint settings used for the performance comparison.

APPENDIX A: PROOF OF PROPOSITION 1

The proof shows that any BS caching a multicast group's requested content can be added to that content's cluster without increasing total network cost, regardless of channel conditions.

  • Proof construction: For an arbitrary clustering that excludes a caching BS, the proof constructs another clustering that includes it.The modified clustering changes the relevant BS–content association from zero to one.
  • Backhaul cost: Adding the caching BS does not increase backhaul cost because its requested content is locally available.The corresponding backhaul term is zero when the caching indicator equals one.
  • Cost comparison: The feasible set of the original power-minimization problem is a subset of the modified problem's feasible set.Therefore, the modified clustering can achieve a total network cost no larger than the original.
  • Conclusion: Thus, without loss of optimality, the clustering variable for every caching BS–content association can be set to one.This establishes the proposition that caching BSs can always belong to the corresponding content cluster.
Loading 1512.06938v2…