PaperlayerView exact revision on arXiv

Source-linked AI summary

Joint Precoding and RRH selection for User-centric Green MIMO C-RAN

Cunhua Pan, Huiling Zhu, Nathan J. Gomes, Jiangzhou Wang

arXiv:1702.03346v1cs.IT

TL;DR

The paper studies joint active-RRH selection and precoding for minimizing NPC in a multiple-antenna user-centric C-RAN under rate and per-RRH power constraints, which may be infeasible. It proposes a two-stage low-complexity approach combining user selection with re-weighted l1-norm, WMMSE, Newton, and gradient-based optimization. The algorithms converge rapidly and achieve near-optimal NPC performance, while multiple receive antennas allow more users to be admitted.

  • Problem

    Joint RRH selection and precoding must minimize NPC in a multiple-antenna user-centric C-RAN despite conflicting rate and per-RRH power constraints that can make the problem infeasible.

  • Method

    A two-stage method selects the largest feasible user subset, then uses re-weighted l1-norm minimization, WMMSE, and low-complexity Newton- and gradient-based precoder updates.

  • Results

    The proposed algorithms converge rapidly and achieve near-optimal NPC performance, while more receive antennas enable more users to be admitted.

  • Takeaways & Limitations

    Joint active-RRH selection and precoding can reduce NPC while satisfying users’ rate requirements and per-RRH power constraints in the considered MIMO C-RAN.

Abstract

from arXiv · show

This paper jointly optimizes the precoding matrices and the set of active remote radio heads (RRHs) to minimize the network power consumption (NPC) for a user-centric cloud radio access network (C-RAN), where both the RRHs and users have multiple antennas and each user is served by its nearby RRHs. Both users' rate requirements and per-RRH power constraints are considered. Due to these conflicting constraints, this optimization problem may be infeasible. In this paper, we propose to solve this problem in two stages. In Stage I, a low-complexity user selection algorithm is proposed to find the largest subset of feasible users. In Stage II, a low-complexity algorithm is proposed to solve the optimization problem with the users selected from Stage I. Specifically, the re-weighted $l_1$-norm minimization method is used to transform the original problem with non-smooth objective function into a series of weighted power minimization (WPM) problems, each of which can be solved by the weighted minimum mean square error (WMMSE) method. The solution obtained by the WMMSE method is proved to satisfy the Karush-Kuhn-Tucker (KKT) conditions of the WPM problem. Moreover, a low-complexity algorithm based on Newton's method and the gradient descent method is developed to update the precoder matrices in each iteration of the WMMSE method. Simulation results demonstrate the rapid convergence of the proposed algorithms and the benefits of equipping multiple antennas at the user side. Moreover, the proposed algorithm is shown to achieve near-optimal performance in terms of NPC.

I. INTRODUCTION

This paper addresses network power consumption in multiple-antenna user-centric C-RAN by jointly selecting active RRHs and optimizing precoding under user-rate and per-RRH power constraints. Because these constraints can make the problem infeasible and the MAU rate formulation is nonconvex, the paper develops a two-stage low-complexity solution with near-optimal performance.

  • Motivation: Energy efficiency is important for 5G C-RAN because wireless communications consume more than 3 percent of worldwide electrical energy, while dense RRH deployment increases circuit power consumption.Traffic variation can allow lightly loaded RRHs to enter sleep mode while preserving users’ QoS requirements.
  • Problem formulation: The paper jointly optimizes precoding matrices and active RRHs to minimize NPC subject to users’ rate requirements and per-RRH power constraints.Each user may be served by an arbitrary subset of RRHs in the user-centric C-RAN.
  • Problem formulation: Conflicting rate and power constraints can make the optimization infeasible, while MAU rate constraints are nonconvex and cannot be transformed into the SOCP formulation used for SAU networks.Existing feasibility and solution techniques therefore cannot be directly extended to the MAU case.
  • Stage I: user selection: Stage I uses a low-complexity user-selection approach to maximize the number of admitted users whose QoS requirements can be satisfied.The approach requires at most K iterations and has lower complexity than exhaustive user selection; simulations show similar performance.
  • Stage II: optimization: Stage II applies re-weighted l1-norm minimization to convert the nonsmooth problem into weighted power minimization problems solved by WMMSE.With feasible initialization, the WMMSE precoder sequence converges to a KKT point of the weighted power minimization problem.
  • Results: The proposed low-complexity algorithms converge rapidly and achieve near-optimal NPC performance, while the BCD method has lower computational complexity than the interior point method.The WMMSE precoder-update subproblem is handled by exploiting its special structure.

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system models a user-centric multi-antenna C-RAN in which nearby RRHs cooperatively serve users, while RRH activation and precoding affect signal quality and network power consumption.

  • A. System model: Each RRH has M transmit antennas, each user has N receive antennas, and each user transmits d data streams through RRH precoding matrices.The channel and signal model includes per-RRH channels, aggregated CSI, received signals, interference-plus-noise, and achievable rates.
  • A. System model: The BBU pool has access to all users’ CSI and data, and every RRH connects to it through a fronthaul link.The network contains I RRHs and K users, with fronthaul connections between RRHs and the BBU pool.
  • A. System model: User-centric clustering assigns each admitted user to nearby RRHs, while unselected RRHs enter idle mode.Distant RRHs contribute less because of path loss, motivating nearby-RRH service and RRH deactivation.
  • A. System model: The candidate RRH sets and candidate served-user sets may overlap, so one RRH can jointly serve multiple users.The model defines I_k as the RRHs that can serve user k and U_i as the users that RRH i can serve.
  • A. System model: Each user’s achievable rate must exceed its minimum requirement, with rates determined from the received signal, interference-plus-noise covariance, and precoders.The rate expression is defined for the multi-antenna user model, and the precoding collection contains all RRH precoding matrices.
  • A. System model: Dense RRH deployment can substantially increase RRH and fronthaul power consumption, making selective RRH switching a potential NPC reduction strategy.The paper identifies RRH and corresponding fronthaul deactivation as important for modeling and reducing network power consumption.

B. NPC model

The NPC model combines RRH, fronthaul, and BBU consumption, while rate and per-RRH power constraints can make the joint optimization infeasible and motivate a two-stage design.

  • B. NPC model: The NPC includes power consumed at RRHs, fronthaul links, and the BBU pool, with the active RRH set determining the network configuration.The BBU consumption is modeled as a constant P_BBU for simplicity, while RRH and fronthaul terms depend on operation and traffic.
  • B. NPC model: An RRH’s consumption distinguishes active and sleep modes and accounts for transmit power, amplifier inefficiency, and per-antenna or RF-chain costs.The model uses η_i > 1 for amplifier inefficiency and separate active-mode and sleep-mode consumption terms.
  • B. NPC model: Fr onthaul power increases with supported data rates and is modeled with a proportional factor while also accounting for sleep-mode links.The paper modifies an earlier fronthaul model to include power consumption when links are in sleep mode.
  • B. NPC model: The BBU power model is a simplifying assumption because accurate computational-power modeling at the BBU pool and fronthaul links remains incompletely understood.The paper follows prior work by treating BBU consumption as constant P_BBU.
  • B. NPC model: Rate requirements may conflict with per-RRH power constraints, so the original optimization problem can be infeasible and some users may need removal.The paper therefore maximizes the number of admitted users in Stage I before optimizing RRH selection and precoding in Stage II.
  • B. NPC model: Exhaustive search over RRH and user selections has exponential complexity, motivating low-complexity algorithms for both stages.Stage II jointly selects active RRHs and precoders to minimize NPC for the users retained from Stage I.

III. STAGE I: LOW-COMPLEXITY USER SELECTION ALGORITHM

Stage I seeks the largest feasible user subset by testing rate feasibility through auxiliary scaling variables and iteratively removing the user furthest below its rate target.

  • III. STAGE I: LOW-COMPLEXITY USER SELECTION ALGORITHM: The user-selection problem introduces auxiliary variables α_k so that a user is admitted exactly when its optimal α_k equals one.Maximizing admitted users is therefore equivalent to finding the largest subset whose optimal α_k values all equal one.
  • III. STAGE I: LOW-COMPLEXITY USER SELECTION ALGORITHM: The formulation keeps the number of transmit antennas fixed; jointly optimizing that number could reduce NPC but is left for future work because it makes the problem harder.This scope boundary is stated in the model’s footnote.
  • III. STAGE I: LOW-COMPLEXITY USER SELECTION ALGORITHM: The USC algorithm initializes all users, solves the auxiliary problem, and terminates when every α_k equals one.If feasibility fails, it removes the user with the smallest α_k and repeats the solve.
  • III. STAGE I: LOW-COMPLEXITY USER SELECTION ALGORITHM: Removing the user with the smallest α_k targets the user with the largest gap to its rate target.This rule is the algorithm’s low-complexity heuristic for restoring feasibility while retaining as many users as possible.
  • III. STAGE I: LOW-COMPLEXITY USER SELECTION ALGORITHM: WMMSE reformulates rate expressions through auxiliary receiver and weight matrices, producing a lower-bound function that is concave in each block separately.The rate constraints are replaced by the lower-bound h_k(V,U_k,W_k), enabling block coordinate descent updates.
  • III. STAGE I: LOW-COMPLEXITY USER SELECTION ALGORITHM: Given receiver and weight matrices, the remaining optimization is transformed into an SOCP whose globally optimal solution can be obtained with interior-point methods.The iterative procedure alternates updates of α_k and V with updates of U and W.
  • III. STAGE I: LOW-COMPLEXITY USER SELECTION ALGORITHM: Algorithm 2 converges during its iterative procedure while updating precoders and auxiliary variables.The algorithm initializes feasible precoders, solves the SOCP subproblem, and updates receiver and weight matrices repeatedly.

B. Overall complexity to solve Problem (9) in Stage I

The paper analyzes Stage I complexity and then introduces Stage II’s low-complexity re-weighted l1-norm and WMMSE procedure for joint RRH selection and precoding optimization.

  • B. Overall complexity to solve Problem (9) in Stage I: Algorithm 2 runs at most K times within user selection, so the overall Stage I complexity combines the SOCP cost with up to K user-removal iterations.The paper provides the resulting total complexity expression under equal candidate-set sizes.
  • B. Overall complexity to solve Problem (9) in Stage I: The main per-iteration cost of Algorithm 2 is solving the SOCP subproblem, whose dimensions depend on users, RRHs, antennas, streams, and candidate-cluster size.The stated SOCP contains 2MKld+K real variables, K user-related SOC constraints, and I RRH-related SOC constraints.
  • B. Overall complexity to solve Problem (9) in Stage I: Stage II jointly selects RRHs and precoders for the selected users using a low-complexity algorithm.The method is designed to solve the NPC minimization problem after Stage I.
  • B. Overall complexity to solve Problem (9) in Stage I: The WMMSE-based subproblem satisfies the minimum-rate constraints with equality at the optimum under the stated formulation.The paper uses the resulting first-order conditions and iterative updates to solve the weighted problem.
  • B. Overall complexity to solve Problem (9) in Stage I: The re-weighted l1-norm method converts the original non-smooth objective into a sequence of smooth weighted power minimization problems.The weights are updated iteratively, with lower previous transmit power producing larger weights that encourage RRH shutoff.
  • B. Overall complexity to solve Problem (9) in Stage I: The RLN procedure is guaranteed to converge and produce sparse solutions, unlike the other smooth approximations in general.The sparse solution promotes RRH selection through the re-weighted l1-norm formulation.

B. Algorithm to Solve Problem (23)

The algorithm solves Problem (23) with WMMSE, then updates its precoders through a low-complexity block coordinate descent procedure for the dual problem. The resulting sequences converge to a KKT point, while the dual updates converge globally under the stated convexity conditions.

  • WMMSE algorithm: WMMSE transforms the non-convex rate-constrained problem into an iterative precoder-update procedure.The rate constraints are replaced by a lower bound, and the resulting problem is solved through alternating updates of U, W, and V.
  • WMMSE algorithm: The WMMSE-generated sequence of V converges to a KKT point of Problem (23).This convergence property is stated as Theorem 2.
  • Dual optimization: With fixed U and W, the remaining V update is solved through a convex reformulation and dual optimization.The matrices Gk are positive definite, making the reformulated problem convex; Newton’s method updates λ and gradient descent updates µ within BCD.
  • Complexity reduction: Gradient descent converges within five iterations while avoiding the Hessian and inverse-Hessian calculations required by Newton’s method.The paper reports lower computational complexity for gradient descent despite faster Newton convergence.
  • Dual optimization: The BCD algorithm alternates Newton updates of λ with gradient-descent updates of µ to solve the dual problem.A backtracking line search determines the Newton step size.
  • Convergence and optimality: The sequences of µ and λ converge to the globally optimal solution of the dual problem, yielding the globally optimal solution of Problem (27).The latter conclusion follows from the zero duality gap between the primal and dual problems.

D. Overall Complexity to Solve Problem (27) in Stage II

Stage II has three nested iteration layers: re-weighted l1-norm minimization, WMMSE for non-convex rate constraints, and BCD for the dual problem. Its complexity is dominated by the Newton update within BCD.

  • Iteration structure: Stage II comprises RLN, WMMSE, and BCD layers that respectively handle the non-smooth objective, non-convex rate constraints, and dual problem.The BCD layer uses Newton’s method for λ and gradient descent for µ.
  • BCD complexity: The BCD layer dominates the computational analysis because its updates require Newton and gradient-descent procedures.The main BCD complexity lies in updating λ and µ.

. Simulation results

The proposed algorithms converge rapidly in Stage II, with Newton’s method and the overall nested procedure typically reaching most of their final objective value within a small number of iterations.

  • Newton convergence: Newton’s method generally converges within five iterations.The paper reports this behavior from simulation results.
  • Gradient-descent convergence: The gradient-descent method also converges within five iterations but has lower computational complexity than Newton’s method.Its lower complexity comes from avoiding Hessian and inverse-Hessian calculations.
  • Overall convergence: The RLN, WMMSE, and BCD algorithms converge very fast, and generally five iterations achieve a large portion of the final objective value.The overall Stage II complexity depends on the average iteration counts of these three algorithms.

V. SIMULATION RESULTS

Simulations evaluate convergence, user selection, and power consumption in a wrap-around user-centric C-RAN model. The proposed methods converge quickly, closely match exhaustive or greedy baselines, and benefit from more receive antennas.

  • Simulation setup: The simulations use a wrap-around C-RAN region surrounded by eight uncoordinated macrocells, with users and RRHs uniformly distributed.The channel model includes path loss, shadowing, Rayleigh fading, and antenna gain.
  • Simulation setup: The default setup uses 12 RRHs, 8 users, 3 nearby serving RRHs per user, and 2 antennas at both each RRH and each user.Each RRH has a 4 W power constraint and each user has the same rate requirement.
  • Convergence behavior: The objective value decreases monotonically, and six iterations generally achieve a large proportion of the converged value under both initialization schemes.SVD-initial and rand-initial converge to almost the same value.
  • Convergence behavior: The converged objective value decreases as the number of receive antennas increases.The paper attributes this trend to the additional available degrees of freedom.
  • User selection: The boundary user is not selected because it is far from the serving configuration, and removing user 8 ensures feasibility for the remaining users.The converged state is illustrated for a randomly generated channel.
  • User selection: The number of admitted users decreases as rate requirements increase, while the greedy method nearly matches exhaustive search and USC has a negligible performance gap.The proposed USC algorithm’s complexity increases linearly with K, compared with quadratic greedy search and exponential exhaustive search.

3) Convergence behaviour of the RLN algorithm:

The RLN algorithm rapidly reduces active RRHs and NPC, with most convergence occurring within the first few iterations. Its WMMSE and BCD subroutines also converge quickly, supporting lower-complexity implementation.

  • RLN convergence: For all tested δ values, active RRHs and NPC decrease rapidly, with no additional decrease after the fifth iteration.The converged solution retains six active RRHs.
  • RLN convergence: Compared with full cooperation, the converged solution switches off distant RRHs and excludes users too far from the RRHs.RRH 2 and User 8 are specifically identified in the example.
  • WMMSE convergence: The WMMSE algorithm converges within ten iterations in the first RLN iteration, while later RLN iterations require almost no additional objective reduction.The second and third RLN iterations have nearly fixed objective values.
  • BCD convergence: One BCD iteration achieves 99.2% of the converged objective value in the reported example.The BCD algorithm is therefore observed to converge very quickly.
  • Subroutine complexity: The BCD algorithm has much lower computational complexity than directly solving the SOCP problem.Newton’s method needs several iterations only initially, whereas gradient descent converges in one initial iteration.

7) Impacts of the number of data streams:

The simulations examine how data streams and antenna dimensions affect admitted users and NPC. More streams or transmit antennas generally improve user support, but the gains diminish as dimensions increase.

  • Data streams: More data streams support more users and produce significant gains from d = 1 to d = 2, especially at high rate requirements.The gain from d = 4 over d = 2 is marginal and increases computational complexity.
  • Rate requirements: When Rmin increases from 3 to 6 nats/s/Hz, admitted users decrease dramatically, reducing transmit power and active RRHs.For Rmin ≤3 nats/s/Hz, admitted users remain nearly stable while fronthaul and active-RRH power increase.
  • Data streams: A greater number of data streams requires lower NPC, although the performance gain shrinks as the stream count grows.This trend is reported together with the corresponding active-RRH behavior.
  • Transmit antennas: Admitted users increase with transmit antennas because additional antennas provide more degrees of freedom.The gain is significant for M = 2 over M = 1, especially at high rates, but shrinks for M = 4 over M = 2.
  • Transmit antennas: Increasing M raises NPC while reducing active RRHs under the reported setup, although other parameter settings can reverse the NPC trend.The reported exception involves low per-antenna circuit power and high fronthaul power.
  • Candidate size: Candidate sizes above 4 are unnecessary for a good performance–complexity tradeoff because their additional gains diminish.Larger candidate sizes support more users, but distant RRHs contribute less to signal strength.

B. Performance comparison

The RLN method jointly selects RRHs and optimizes precoding with substantially lower complexity than exhaustive search. Simulations show near-optimal power consumption and advantages over several selection baselines.

  • Rate requirements: The RLN algorithm outperforms successive selection and full cooperation across all rate regimes.Greedy search is slightly better when Rmin ≤3 nats/s/Hz, while RLN is better in the high-rate regime.
  • Rate requirements: RLN power loss relative to optimal exhaustive search is at most 8% when Rmin = 1 nats/s/Hz, and the gap diminishes as rate requirements increase.At Rmin = 5 nats/s/Hz, exhaustive search provides negligible gain over RLN.
  • Baseline comparison: Full cooperation consumes the highest power because all selected RRHs remain active.This contrasts with RLN’s joint RRH selection and precoding optimization.
  • Network size: NPC decreases as the total number of RRHs increases because users’ average access distance decreases and transmit power is reduced.RLN remains superior to successive selection, while power-only RRH selection can incur significant loss.
  • Overall comparison: The proposed algorithm achieves much greater power savings than full cooperation, with insignificant loss compared with the optimal approach.The conclusion summarizes the observed near-optimal NPC performance.

APPENDIX A PROOF OF THEOREM 1

The appendix establishes convergence and optimality properties for the iterative WMMSE and BCD procedures. It also identifies dependence on initialization for the non-convex problem.

  • WMMSE convergence: The objective value decreases monotonically during the WMMSE iterations and is lower-bounded by zero, so the algorithm converges.The update preserves feasibility while producing a non-increasing objective.
  • WMMSE convergence: For fixed initial precoders, WMMSE converges to a unique solution because the BCD subproblem is strictly convex and has zero duality gap.The BCD procedure obtains the unique globally optimal solution of the convex precoder subproblem.
  • Scope of the guarantee: Because the associated non-convex problem may have multiple local optima, the WMMSE solution depends on the initial point.Uniqueness is guaranteed only for a fixed initialization of the precoders.
  • KKT conditions: The converged WMMSE solution satisfies the KKT conditions of the weighted power minimization problem.The appendix identifies the resulting equations as the KKT conditions.
  • Dual updates: Newton’s method and gradient descent solve the dual updates globally for fixed alternating variables under the stated convexity and Slater assumptions.The dual problem is convex in each multiplier block when the other block is fixed.
Loading 1702.03346v1…