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Deep Learning Power Allocation in Massive MIMO

Luca Sanguinetti, Alessio Zappone, Merouane Debbah

arXiv:1812.03640v2eess.SPcs.ITcs.LGmath.IT

TL;DR

Traditional downlink power allocation requires Monte Carlo averaging and can be too costly for real-time use as UE positions change. The paper trains neural networks to map UE positions to max-min and max-prod power policies; the reported results are near-optimal for max-prod and closely match theoretical curves for max-min with both precoders.

  • Problem

    Traditional power-allocation solutions require Monte Carlo computation and can be too costly to recompute in real time as UE positions change.

    Source: §III · pp. 2–3

  • Method

    The framework trains neural networks to learn power allocations from UE positions for max-min and max-prod strategies.

    Source: §I · p. 1, §VI · p. 5

  • Results

    Max-prod achieves near-optimal performance with MR and M-MMSE, while max-min matches almost exactly the theoretical curves with both precoders.

    Source: A. Max-prod · p. 4, B. Max-min · p. 5

  • Takeaways & Limitations

    UE positions alone are used to allocate powers, substantially reducing optimization complexity and processing time.

    Source: §VI · p. 5

    The max-min network has 509,829 trainable parameters and lacks scalability as network size increases.

    Source: B. Max-min · p. 5

Abstract

from arXiv · show

This work advocates the use of deep learning to perform max-min and max-prod power allocation in the downlink of Massive MIMO networks. More precisely, a deep neural network is trained to learn the map between the positions of user equipments (UEs) and the optimal power allocation policies, and then used to predict the power allocation profiles for a new set of UEs' positions. The use of deep learning significantly improves the complexity-performance trade-off of power allocation, compared to traditional optimization-oriented methods. Particularly, the proposed approach does not require the computation of any statistical average, which would be instead necessary by using standard methods, and is able to guarantee near-optimal performance.

I. INTRODUCTION

The introduction proposes learning max-min and max-prod downlink power allocation from UE positions, while the network section specifies the Massive MIMO setting and notes a spatial-consistency concern in the shadowing model.

I. INTRODUCTION

  • Massive MIMO uses base stations with many antennas to serve many UEs through spatial multiplexing,.The introduction also notes its integration into 5G New Radio and the resolution of pilot contamination under specific conditions.Source: §I · p. 1
  • Deep learning is proposed for max-min and max-prod downlink power allocation, using UE positions to predict near-optimal policies.The positions can be obtained by GPS, and training samples can be generated with off-the-shelf optimization algorithms.Source: §I · p. 1

II. MASSIVE MIMO NETWORK

  • The considered network has L cells, each with a base station equipped with M antennas and serving K UEs.Source: §II · p. 1
  • Log-normal shadowing can make channel models spatially inconsistent, so nearby UEs may experience different channels; ray tracing or recorded measurements are proposed alternatives.Source: §II · p. 1

A. Channel Estimation

The channel-estimation setup uses pilot-based training in a synchronized TDD system, with one reused pilot per UE index across cells and MMSE channel estimation.

A. Channel Estimation

  • Channel estimation uses a TDD protocol with uplink training before downlink data transmission, assuming perfect synchronization.Source: A. Channel Estimation · p. 1
  • The setup uses τp = K pilots with reuse factor 1, and UE i uses the same pilot in every cell.Source: A. Channel Estimation · p. 1
  • Each base station estimates channel vectors using standard MMSE techniques, with the estimation error independent of the channel estimate.Source: A. Channel Estimation · p. 2

B. Downlink Spectral Efficiency

Downlink spectral efficiency is evaluated using a hardening-bound lower bound whose validity depends on how well the channel hardens.

B. Downlink Spectral Efficiency

  • The downlink ergodic channel capacity is lower-bounded using the hardening bound.The bound's spectral-efficiency expression includes a pre-log factor accounting for the fraction of the coherence block used for downlink data.Source: B. Downlink Spectral Efficiency · p. 2
  • The lower bound assumes that the UE treats the mean of its precoded channel as the true channel, a reasonable assumption when channels exhibit hardening.Source: B. Downlink Spectral Efficiency · p. 2
  • The bound incurs some loss for channels with little or no hardening; explicit or implicit precoded-channel estimation is noted as an alternative not considered here,.Source: B. Downlink Spectral Efficiency · p. 2

C. Precoder Design

Downlink precoder design is difficult because each UE's spectral efficiency depends on precoders throughout the network, so the paper uses uplink combining vectors as a heuristic basis.

C. Precoder Design

  • Downlink spectral efficiency depends on every UE's precoding vector in the network, making optimal precoder selection challenging.Source: C. Precoder Design · p. 2
  • A common heuristic, motivated by uplink-downlink duality, selects downlink precoders using the corresponding uplink combining vectors.The considered combining choices are MR and M-MMSE,,.Source: C. Precoder Design · p. 2
  • M-MMSE is optimal but computationally expensive, whereas MR has the lowest complexity among the receive-combining schemes but is suboptimal, including as M → ∞.Source: C. Precoder Design · p. 2

III. POWER ALLOCATION

The section formulates max-min fairness and max-product SINR power allocation and outlines the conventional procedure for finding optimal powers. These problems use averaged channel and interference gains, but their optimization can be too slow for real-time updates.

III. POWER ALLOCATION

  • The downlink spectral efficiency is expressed using average channel and interference gains, with averages over small-scale fading leaving it dependent on large-scale statistics and precoding.This averaging simplifies power allocation compared with single-antenna systems.Source: §III · p. 2
  • Max-min fairness and max-product SINR are presented as prominent downlink power-allocation policies.The optimal powers are obtained by solving the corresponding allocation problems.Source: §III · p. 2
  • The conventional Monte Carlo procedure samples UE positions and propagation effects, generates estimated channels, computes spectral efficiency, and then allocates power.The procedure includes precoding-vector computation and averaging over estimated channels to obtain the required gain terms.Source: §III · pp. 2–3
  • Max-min allocation uses bisection over convex problems, while max-product allocation uses geometric programming; either may be too slow for real-time updates.The methods have polynomial or quasi-polynomial complexity, and a solution may be needed before UE positions change again.Source: §III · p. 3

IV. DEEP LEARNING BASED POWER ALLOCATION

The proposed approach learns a mapping from geographical UE positions to optimal power allocations. A feedforward neural network is trained on position-allocation examples and can predict powers for inputs outside the training set.

IV. DEEP LEARNING BASED POWER ALLOCATION

  • UE positions are proposed as a proxy for optimal powers, replacing traditional methods’ need for average channel and interference gains.The paper motivates this proxy by arguing that positions capture main features of propagation and interference.Source: §IV · p. 3
  • A fully connected feedforward network maps the 2KL-dimensional position input to an estimate of each cell’s K-dimensional power allocation.Its K + 1 outputs also include the sum of allocated powers to satisfy the power constraint and improve estimation accuracy.Source: §IV · p. 3
  • Training uses position samples paired with optimal power allocations produced by conventional optimization, and adjusts network weights to minimize a loss.The loss compares the network’s estimated allocations with the optimal allocations in the training set.Source: §IV · p. 3
  • After training, the network estimates allocations for unseen position inputs, allowing updates without solving the conventional optimization problems again.The stated workflow feeds new UE positions into the configured network.Source: §IV · p. 3

A. Online implementation and complexity

The approach shifts substantial computation to generating training data, while making power prediction inexpensive once the network is configured. This supports real-time allocation updates as UE positions change.

A. Online implementation and complexity

  • Network inference requires only the activation functions across its layers, while training uses standard gradient descent with back-propagation.The stated inference count is the sum of the neurons in the network’s layers.Source: A. Online implementation and complexity · p. 3
  • Training-set generation remains the main computational burden because it solves the conventional power-allocation problems for many UE-position realizations.The authors argue this is manageable because generation can be performed offline and updated less frequently than UE positions change.Source: A. Online implementation and complexity · p. 3
  • The approach is stated to reduce complexity enough to update power allocation from UE positions in real time.The training set can be refreshed on a longer timescale than the power-control problem would need under traditional allocation.Source: A. Online implementation and complexity · p. 3

V. PERFORMANCE EVALUATION

The evaluation uses randomly distributed UEs in a four-cell Massive MIMO network and tests neural networks trained on optimization-generated allocations. The supplied passages describe the evaluation setup and training data, but provide no performance results.

V. PERFORMANCE EVALUATION

  • The evaluation uses four cells with five randomly and uniformly distributed UEs per cell, averaged over 100 UE distributions.Each cell covers a 250 × 250 m square, and UEs are placed more than 35 m from the base station.Source: §V · p. 3
  • The training dataset contains 340,000 UE-position samples paired with optimal allocations, with 90% used for training and 10% for validation.An additional 10,000 independent samples form the test dataset; Adam and relative MSE are used for training.Source: §V · pp. 3–4
  • The reported neural-network layout has 6,373 trainable parameters.The supplied passage identifies this value with Table II’s network layout.Source: Table II · p. 4

A. Max-prod

With max-prod power allocation, the deep-learning approach maintains near-optimal performance with both MR and M-MMSE while offering a significant computational-complexity advantage over traditional approaches.

A. Max-prod

  • With the Table II network, average SE MSE is 0.007 with M-MMSE and 0.051 with MR; the M-MMSE MSE CDF lies to the left of MR's.The figure presents CDFs of downlink SE and SE MSE for MR and M-MMSE precoding.Source: A. Max-prod · p. 4, Figure 1 · p. 4
  • Average SE MSE falls to 0.003 with M-MMSE and 0.015 with MR using the more complex neural network.The network has 202,373 trainable parameters.Source: A. Max-prod · p. 4, Table III · p. 4
  • With max-prod, deep-learning power allocation maintains near-optimal performance with MR and M-MMSE while offering a significant computational-complexity advantage over traditional approaches.The larger network increases trainable parameters to 202,373 from 6,373, at the cost of computational complexity and training time.Source: A. Max-prod · p. 4

B. Max-min

The max-prod network was inadequate for max-min allocation, so the authors used a larger recurrent network that closely matched theoretical curves. The conclusions note that max-min was harder to learn and that the evaluation covered a small network.

B. Max-min

  • The max-prod network was inadequate for max-min, but a two-layer LSTM network matched theoretical curves with both MR and M-MMSE; its 509,829 parameters limit scalability.The reported network was evaluated for L = 4 cells and K = 5 UEs per cell.Source: B. Max-min · pp. 4–5, Table IV · p. 5

VI. CONCLUSIONS

  • The framework learns max-min and max-prod power allocation from UE positions; the conclusions report better performance with M-MMSE than MR and greater learning difficulty for max-min.The max-min policy required recurrent neural networks with a relatively high number of trainable parameters.Source: §VI · p. 5
  • The analysis used a relatively small network of L = 4 cells and K = 5 UEs per cell, leaving performance as network size increases for further investigation.The authors also note that handling varying UE counts with multiple NNs per BS is not scalable.Source: §VI · p. 5
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