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Massive MIMO and Small Cells: Improving Energy Efficiency by Optimal Soft-Cell Coordination
Emil Björnson, Marios Kountouris, Mérouane Debbah
TL;DR
Cellular densification must improve energy efficiency without violating user QoS, balancing dynamic savings against added hardware power. This paper combines massive-MIMO macro BSs with operator-deployed SCAs, formulates coordinated non-coherent multiflow transmission, and solves the resulting power-minimization problem. The formulation is convex after relaxation, and simulations show substantial total-power benefits from combining massive MIMO and small cells, with many benefits retained by low-complexity beamforming.
Problem
Classical macro-cell topology cannot efficiently handle rapidly increasing user numbers and QoS expectations, motivating densification through massive MIMO and small cells.
Method
The paper minimizes total dynamic and static power under QoS and transmitter constraints for coordinated non-coherent multiflow transmission using massive-MIMO BSs and SCAs.
Results
The power-minimization problem has a convex reformulation solvable in polynomial time, and its optimal solution usually assigns each user to only the BS or one SCA.
Takeaways & Limitations
Combining massive MIMO and small cells can greatly improve total power consumption, with most benefits also achievable using low-complexity Multiflow-RZF beamforming.
Abstract
from arXiv · showhide
To improve the cellular energy efficiency, without sacrificing quality-of-service (QoS) at the users, the network topology must be densified to enable higher spatial reuse. We analyze a combination of two densification approaches, namely "massive" multiple-input multiple-output (MIMO) base stations and small-cell access points. If the latter are operator-deployed, a spatial soft-cell approach can be taken where the multiple transmitters serve the users by joint non-coherent multiflow beamforming. We minimize the total power consumption (both dynamic emitted power and static hardware power) while satisfying QoS constraints. This problem is proved to have a hidden convexity that enables efficient solution algorithms. Interestingly, the optimal solution promotes exclusive assignment of users to transmitters. Furthermore, we provide promising simulation results showing how the total power consumption can be greatly improved by combining massive MIMO and small cells; this is possible with both optimal and low-complexity beamforming.
I. INTRODUCTION
Classical macro-cell networks provide wide-area coverage but struggle with rising user numbers and QoS expectations, motivating densification through massive MIMO and small cells. The paper combines these approaches with coordinated operator-deployed SCAs to reduce total power while preserving QoS.
- Densification is motivated by the classical topology’s low energy efficiency under rapidly increasing user numbers and QoS expectations.
- Massive MIMO improves energy efficiency by using large antenna arrays to focus emitted energy precisely on intended users.Its channel estimation accuracy is limited by the number of users rather than BS antennas when channel reciprocity is exploited through TDD.
- Small-cell access points reduce propagation losses and improve energy efficiency by shortening average user–transmitter distances.They also create a heterogeneous topology in which inter-user interference is difficult to control and coordinate.
- Operator-deployed SCAs enable reliable backhaul and joint BS–SCA control, including spatial soft-cell coordination that can be transparent to users.
- Dense deployments must optimize both dynamic emitted power and static hardware power because densification can improve the former while increasing the latter.
- The paper minimizes total power under QoS and transmitter-power constraints, proves hidden convexity, and compares optimal and low-complexity beamforming through simulations.The optimal solution dynamically assigns users to transmitters.
II. SYSTEM MODEL
The system is a single-cell downlink with one macro BS, an optional overlay of small-cell access points, and single-antenna users. Users may receive independently coded signals from multiple transmitters through non-coherent spatial multiflow transmission.
- The model contains a macro BS with NBS antennas, S arbitrarily deployed SCAs with NSCA antennas each, and K single-antenna users.Typically 1 ≤ NSCA ≤ 4, while NBS ranges from 8 to several hundred; NBS ≫ K is the massive-MIMO regime.
- The macro BS has generous power constraints for broad coverage, whereas SCA power constraints are stricter and limit their coverage areas.
- Channels are modeled as block fading on a single flat-fading subcarrier and are assumed perfectly known at both sides of each channel.
- Joint backhaul coordination supports spatial multiflow transmission, allowing each user to receive independent non-coherent signals from multiple transmitters.This can supplement users that are barely covered by an SCA with signals from the BS or other SCAs.
- Independent Gaussian information symbols are multiplied by transmitter-specific beamforming vectors to form the transmitted signals.The beamforming vectors are optimization variables, and zero vectors identify transmitters that do not serve a user.
A. Problem Formulation
The problem minimizes total power consumption while requiring every user to meet a fixed information-rate target. Rates are expressed through aggregate SINR, with co-user signals treated as noise and no phase synchronization required across transmitters.
- The optimization minimizes total power consumption subject to user QoS constraints and transmitter power constraints.
- Each user’s QoS constraint requires an information rate measured in bits/s/Hz to be achieved in parallel.
- The rate constraint is log2(1 + SINRk) ≥ γk, where γk is the fixed QoS target.
- The aggregate SINR supports successive interference cancellation of each user’s own symbols while treating co-user symbols as noise.This rate requires no phase synchronization between transmitters, unlike coherent joint transmission.
- Total per-subcarrier power is modeled as Pdynamic + Pstatic, combining emitted-power and hardware-related consumption.
C NSCA,
The formulation minimizes dynamic emitted power plus static circuitry power under generalized transmitter constraints. Its hidden convexity enables polynomial-time solution, while the optimal solution usually assigns each user to only one transmitter; adaptive sleep modes remain outside scope.
- The dynamic power term aggregates emitted beamforming powers, with each transmitter weighted by its power-amplifier inefficiency factor ρj.
- Static power is proportional to antenna count and models dissipation in circuits such as filters, mixers, converters, and baseband processing.
- BSs and SCAs are subject to positive-semidefinite quadratic power constraints that can represent per-antenna, per-array, or soft-shaping limits.
- The optimization can be reformulated as a convex problem solvable in polynomial time using standard algorithms.
- The optimal power-minimizing solution is self-organizing, with each user served by only one or a few transmitters.
- Adaptive sleep modes for inactive SCAs and antennas are excluded because mobility sensing, user arrivals, and switching transients are outside the paper’s scope.
III. ALGORITHMS FOR NON-COHERENT COORDINATION
The non-convex beamforming problem is reformulated through semidefinite relaxation into a convex optimization problem solvable in polynomial time. Its optimal structure usually assigns each user to one transmitter, with multiflow transmission mainly appearing in SCA transition areas.
- Convex reformulation: Semidefinite relaxation exposes an underlying convex structure in the original non-convex beamforming problem.The reformulation removes rank constraints and preserves optimality.
- Convex reformulation: The relaxed problem is a convex semidefinite optimization problem with an optimal rank-one solution.Therefore, the relaxation does not lose optimality relative to the original formulation.
- Convex reformulation: The original power-minimization problem can be solved as a convex optimization problem in polynomial time using standard algorithms.The paper gives SeDuMi's interior-point toolbox as an example.
- Optimal assignment: The optimal solution usually assigns one transmitter per user, although multiflow transmission can occur when SCA power constraints limit coverage.Users near an SCA are typically served exclusively by it, while most other users are served by the BS.
- Optimal assignment: Removing power constraints eliminates the transition areas in which multiflow transmission is used.Those areas arise because an SCA cannot fully support some users' QoS targets.
A. Low-Complexity Algorithm
The paper proposes Multiflow-RZF, a non-iterative low-complexity beamforming method that coordinates the BS and SCAs through limited scalar exchanges. It is intended as a practical alternative to centralized optimal beamforming while retaining most energy-efficiency improvements.
- A. Low-Complexity Algorithm: Theorem 1 provides a centralized polynomial-time benchmark but becomes impractical for real-time use as NBS and S grow.It requires centralized channel knowledge at the BS; distributed alternatives require iterative backhaul signaling.
- A. Low-Complexity Algorithm: Multiflow-RZF is a low-complexity, non-iterative beamforming algorithm proposed for non-coherent coordination.It uses heuristic RZF beamforming to transform the problem into power allocation.
- A. Low-Complexity Algorithm: Each transmitter computes local quantities, SCAs send scalar parameters to the BS, and the resulting power allocation is returned for beamforming.The coordination exchanges are designed to enable joint resource allocation without iterative operation.
- A. Low-Complexity Algorithm: The power-allocation problem has the same low complexity regardless of the number of antennas.In practice, only users near an SCA require nonzero exchanged parameters.
IV. NUMERICAL EVALUATIONS
The numerical evaluation studies a macro cell overlaid with small cells, varying antenna counts, QoS targets, and beamforming methods. Combining massive MIMO with small cells substantially reduces total power consumption, while low-complexity beamforming captures much of the benefit.
- Evaluation setup: The evaluation averages performance over user locations and channel realizations in a macro cell overlaid by four small cells serving ten active users.Six users are uniformly distributed across the macro cell, while each small-cell access point has one user within 40 meters.
- Antenna configurations: The study varies NBS from 20 to 100 and NSCA from 0 to 3 under 2 bits/s/Hz QoS constraints.Average total power consumption per subcarrier is evaluated using optimal spatial multiflow transmission.
- Antenna configurations: Adding hardware can substantially decrease total power consumption because reduced dynamic power outweighs increased static circuitry power.The simulations identify saturation points where additional hardware no longer reduces total power.
- Antenna configurations: Massive MIMO alone provides large energy-efficiency improvements, while a few single-antenna SCAs can achieve the same power consumption with half as many BS antennas or fewer.Multi-antenna SCAs provide further improvements, making combined massive MIMO and small-cell topologies desirable with little additional hardware.
- User assignment: Only 0–3% of users are served by multiple transmitters; with NSCA = 3, each SCA serves more than one user exclusively with 20–45% probability, decreasing as NBS increases.The low multiflow probability agrees with the paper's structural result favoring exclusive transmitter assignment.
- Beamforming comparison: With NBS = 50 and NSCA = 2, optimal spatial soft-cell coordination improves energy efficiency, while proposed Multiflow-RZF achieves most of those gains with lower complexity.The comparison includes BS-only optimal beamforming, Multiflow-RZF, and optimal spatial soft-cell coordination.
V. CONCLUSION
The conclusion combines massive MIMO and operator-deployed small cells through non-coherent soft-cell coordination and optimizes total power under QoS constraints. The resulting convex formulation dynamically assigns users to transmitters, while simulations show large total-power gains and substantial benefits from low-complexity beamforming.
- V. CONCLUSION: The paper analyzes massive MIMO at macro BSs and overlaid SCAs using non-coherent beamforming from multiple transmitters.Users are dynamically assigned to optimal transmitters, usually only the BS or one SCA.
- V. CONCLUSION: Power-minimizing spatial multiflow transmission under QoS constraints is obtained by solving a convex optimization problem.The optimization accounts for total power consumption while determining transmitter assignments.
- V. CONCLUSION: Combining massive MIMO and small cells can greatly improve total power consumption, including both dynamic emitted power and static hardware consumption.Most benefits are also achievable with low-complexity beamforming such as Multiflow-RZF.
APPENDIX
The appendix supports the convex reformulation and characterizes the structure of optimal solutions. Its eigenvalue argument explains why users are generally served by a single transmitter, with multiflow needed only in constrained tie cases.
- Theorem 1: Removing rank constraints from the semi-definite relaxation yields a convex semi-definite optimization problem with an optimal rank-one solution.This establishes that the original problem can be solved through convex optimization in polynomial time.
- Eigenvalue characterization: The optimal beamforming direction is the dominating eigenvector of a matrix derived from the uplink SINR formulation.The relevant multipliers are associated with the QoS and power constraints.
- Optimal assignment: Because the matrices are block-diagonal, the dominating eigenvector is nonzero in one transmitter block, favoring service of each user by one transmitter.An additional transmitter is needed only under eigenvalue multiplicity when single-transmitter solutions violate power constraints.