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Cell-Free Massive MIMO: Uniformly Great Service For Everyone
Hien Quoc Ngo, Alexei Ashikhmin, Hong Yang, Erik G. Larsson, Thomas L. Marzetta
TL;DR
The paper addresses how distributed APs can jointly serve users in Cell-Free Massive MIMO despite imperfect channel estimates and nonorthogonal pilots. It derives achievable rates and designs max-min power control, finding substantially higher and more robust per-user throughput than small-cell systems.
Problem
A comparison between small-cell systems and distributed Massive MIMO was not yet available, while pilot nonorthogonality and channel-estimation effects require analysis.
Method
The paper derives a closed-form achievable rate and designs pilot assignment and max-min power-control schemes for distributed APs serving users cooperatively.
Results
The 95%-likely per-user throughput of Cell-Free Massive MIMO is almost 20 times higher than that of a small-cell system.
Takeaways & Limitations
Cell-Free systems significantly outperform small-cell systems in throughput and are more robust to shadow fading correlation.
Abstract
from arXiv · showhide
We consider the downlink of Cell-Free Massive MIMO systems, where a very large number of distributed access points (APs) simultaneously serve a much smaller number of users. Each AP uses local channel estimates obtained from received uplink pilots and applies conjugate beamforming to transmit data to the users. We derive a closed-form expression for the achievable rate. This expression enables us to design an optimal max-min power control scheme that gives equal quality of service to all users. We further compare the performance of the Cell-Free Massive MIMO system to that of a conventional small-cell network and show that the throughput of the Cell-Free system is much more concentrated around its median compared to that of the small-cell system. The Cell-Free Massive MIMO system can provide an almost $20-$fold increase in 95%-likely per-user throughput, compared with the small-cell system. Furthermore, Cell-Free systems are more robust to shadow fading correlation than small-cell systems.
I. INTRODUCTION
The paper introduces Cell-Free Massive MIMO, in which distributed APs jointly serve users without cells or cell boundaries. It develops rate analysis, pilot assignment, and max-min power control for this architecture.
- Distributed Massive MIMO spreads service antennas over a wide area, exploiting macro-diversity and path-loss differences to potentially improve coverage probability.
- Cell-Free Massive MIMO uses many distributed APs to cooperatively serve fewer users over the same time-frequency resource, without cells or cell boundaries.
- The system uses uplink pilots for channel estimation, but limited coherence intervals can require nonorthogonal pilots, causing pilot contamination.
- The paper derives a finite-AP closed-form achievable-rate expression that accounts for channel-estimation errors, power control, and nonorthogonal pilot sequences.
- Two pilot assignment schemes are designed—random and greedy—and the paper reports that greedy assignment performs better.
- Max-min power control maximizes the smallest user rate under per-AP power constraints and is formulated as a quasi-convex optimization problem.
B. Downlink Payload Data Transmission
During downlink payload transmission, APs use channel estimates and conjugate beamforming to send data to all users. Power-control coefficients satisfy per-AP average power constraints.
- APs treat channel estimates as true channels and use conjugate beamforming to transmit signals to the users.
- Power-control coefficients η_mk are selected to satisfy an average power constraint at each AP.
- Each user receives the combined downlink transmission plus additive Gaussian noise and detects its intended data symbol.
III. ACHIEVABLE RATE
The paper rewrites the received signal as a deterministic desired-signal factor plus effective noise, then derives an exact closed-form achievable rate for Cell-Free transmission with finitely many APs.
- III. ACHIEVABLE RATE: The received signal is decomposed into a deterministic factor scaling the desired signal and an effective-noise term.The effective noise equals the received-signal expression minus the desired-signal component.
- III. ACHIEVABLE RATE: The desired signal and effective noise are uncorrelated, enabling an achievable-rate bound using the Gaussian-worst-case-noise argument.
- III. ACHIEVABLE RATE: The paper provides a new exact closed-form achievable-rate expression for a finite number of APs.The result is stated as Theorem 1 for transmission from the APs to the kth user.
IV. PILOT ASSIGNMENT AND POWER CONTROL
Pilot assignment and power control are treated as decoupled design problems, with random and greedy schemes proposed for assigning pilots to users.
- IV. PILOT ASSIGNMENT AND POWER CONTROL: Pilot assignment and power control are decoupled because the pilot sequences are not power controlled.
- IV. PILOT ASSIGNMENT AND POWER CONTROL: Because the coherence interval permits only τ orthogonal pilots, the paper addresses pilot assignment when different users must reuse sequences.
- IV. PILOT ASSIGNMENT AND POWER CONTROL: Random assignment selects one of the τ orthogonal pilot sequences independently for each user.
- IV. PILOT ASSIGNMENT AND POWER CONTROL: Random assignment can place nearby users on the same pilot, producing high pilot contamination and poor performance for those users.
- IV. PILOT ASSIGNMENT AND POWER CONTROL: Greedy assignment iteratively lets the lowest-rate user update its pilot to minimize pilot contamination, and can run at a central processing unit.
2) Greedy Pilot Assignment:
The greedy pilot-assignment method targets the worst user by minimizing its aggregate pilot contamination across APs through an eigenvector update.
- 2) Greedy Pilot Assignment:: Pilot contamination at user k is represented by the variance of the interference term involving correlations between pilot sequences.
- 2) Greedy Pilot Assignment:: The worst user chooses a new pilot sequence that minimizes pilot contamination summed over all APs.
- 2) Greedy Pilot Assignment:: Because the optimization is a Rayleigh quotient, the updated pilot is the eigenvector associated with the smallest eigenvalue of the relevant matrix.
B. Power Control
The paper formulates max-min power control to maximize the minimum user rate under per-AP constraints, and solves the resulting quasi-concave problem efficiently.
- B. Power Control: Max-min power control chooses coefficients η_mk to maximize the minimum rate among all users.
- B. Power Control: The coefficients satisfy per-AP power constraints and nonnegativity constraints.
- B. Power Control: Slack variables are introduced to reformulate the power-control optimization problem.
- B. Power Control: The resulting optimization problem is quasi-concave.
- B. Power Control: Bisection solves the quasi-concave problem efficiently through a sequence of convex feasibility problems.
V. NUMERICAL RESULTS AND DISCUSSIONS
The numerical evaluation uses randomly distributed APs and users, a specified propagation model, and fixed system parameters. Figure 1 reports minimum per-user rates across pilot lengths without power control.
- Simulation setup: The simulations distribute M APs and K users uniformly at random within a 1000×1000 m^2 square.The large-scale fading coefficient models path loss and shadow fading.
- Simulation setup: The path-loss model uses exponents 3.5, 2, and 0 across three distance regions, with Hata-COST231 calibration beyond d1.The regions are determined by dmk relative to d1 and d0.
- Simulation setup: The evaluation uses 1.9 GHz carrier frequency, 200 mW AP radiated power, 9 dB noise figure, and σsh = 8 dB.It also sets AP and user antenna heights and distance thresholds.
A. Pilot Assignment
The numerical results compare pilot assignment and power-control choices in Cell-Free and small-cell systems. Greedy pilot assignment and max-min power control improve minimum-rate performance under the evaluated settings.
- Pilot Assignment: When τ increases, pilot contamination decreases and the minimum per-user rate increases without power control.The comparison uses random and greedy pilot assignment against an orthogonal-pilot bound.
- Pilot Assignment: At τ = 20, greedy pilot assignment doubles the 95%-likely minimum rate relative to random pilot assignment.The greedy result remains close to the orthogonal-pilot bound.
- Pilot Assignment: At τ = 5, Cell-Free Massive MIMO still provides good service for all users without power control.The passage describes the greedy scheme as fairly good for subsequent evaluations.
- Max-Min Power Control: Max-min power control significantly improves the achievable-rate distribution compared with no power control for M = 60, K = 20, and τ = 10 or 20.It also notably reduces the effect of pilot contamination.
- Max-Min Power Control: At τ = 10, max-min power allocation improves the 95%-likely rate by a factor of 15 over no power control.The result is reported for the cumulative distribution of achievable rates.
2) Spatial Shadowing Correlation Models:
The study models shadowing correlation at both AP and user sides and evaluates its effect on Cell-Free and small-cell throughput. Cell-Free throughput is more concentrated and less affected by correlation in the reported comparison.
- Throughput comparison: Figure 3 compares cumulative distributions of per-user throughput under correlated and uncorrelated shadow fading for Cell-Free and small-cell systems.The setting is M = 60, K = 20, and τ = 10.
- Spatial Shadowing Correlation Models: The modified shadowing model includes cross-correlation and spatial correlation from both APs and users.This extends models that neglect correlation effects from the base-station side.
- Spatial Shadowing Correlation Models: ρ1 represents AP-side cross-correlation, while 1 − ρ1 represents user-side cross-correlation.Spatial correlation is represented through correlations among AP-side am variables and user-side bk variables.
- Spatial Shadowing Correlation Models: The correlation coefficients depend on AP and user locations through their pairwise distances and a decorrelation distance ddecorr.The model is stated to have been validated by practical experiments.
- Throughput comparison: Without shadow fading correlation, Cell-Free 95%-likely throughput is about 15 Mbits/s, 17 times the small-cell value of about 0.85 Mbits/s.Both systems use K pilot sequences, so their pilot overhead is the same.
- Throughput comparison: Shadow fading correlation reduces 95%-likely throughput by factors of 4 for small-cell and 2 for Cell-Free systems.The factors are relative to uncorrelated shadowing in the reported example.
VI. CONCLUSION
The paper analyzes Cell-Free Massive MIMO with channel estimation and compares it with small-cell systems. Cell-Free systems achieve higher reported throughput and greater robustness to shadow fading correlation.
- Conclusion: The analysis accounts for channel-estimation effects and compares Cell-Free Massive MIMO with small-cell systems.The comparison concerns system performance under the paper’s evaluated settings.
- Conclusion: Almost 20 times higher 95%-likely per-user throughput is achieved by Cell-Free Massive MIMO than by a small-cell system.The conclusion reports a significant throughput advantage for Cell-Free systems.
- Conclusion: Cell-Free Massive MIMO systems are more robust to shadow fading correlation than small-cell systems.This is stated as a conclusion of the comparison.