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Machine Learning Inspired Energy-Efficient Hybrid Precoding for MmWave Massive MIMO Systems

Xinyu Gao, Linglong Dai, Ying Sun, Shuangfeng Han, I Chih-Lin

arXiv:1708.07022v2cs.ITmath.IT

TL;DR

Hybrid precoding reduces RF-chain requirements for mmWave massive MIMO, but common phase-shifter networks still consume substantial energy. The paper proposes a switch-and-inverter architecture with an adaptive cross-entropy precoding scheme. It reports near-optimal sum-rate performance and higher energy efficiency than traditional schemes.

  • Problem

    Existing hybrid precoding schemes commonly rely on complicated phase-shifter networks that retain high energy consumption.

    Source: §I · p. 1

  • Method

    The paper combines a switch-and-inverter hybrid precoding architecture with an ACE scheme that adapts precoder-element probability distributions using cross-entropy optimization.

    Source: §I · p. 1, §V · p. 6

  • Results

    The proposed scheme achieves satisfying sum-rate performance and much higher energy efficiency than traditional schemes.

    Source: §V · p. 6

  • Takeaways & Limitations

    The SI architecture provides a low-energy alternative whose performance gap from the traditional near-optimal architecture remains limited and constant as antenna count grows.

    Source: §V · p. 6

Abstract

from arXiv · show

Hybrid precoding is a promising technique for mmWave massive MIMO systems, as it can considerably reduce the number of required radio-frequency (RF) chains without obvious performance loss. However, most of the existing hybrid precoding schemes require a complicated phase shifter network, which still involves high energy consumption. In this paper, we propose an energy-efficient hybrid precoding architecture, where the analog part is realized by a small number of switches and inverters instead of a large number of high-resolution phase shifters. Our analysis proves that the performance gap between the proposed hybrid precoding architecture and the traditional one is small and keeps constant when the number of antennas goes to infinity. Then, inspired by the cross-entropy (CE) optimization developed in machine learning, we propose an adaptive CE (ACE)-based hybrid precoding scheme for this new architecture. It aims to adaptively update the probability distributions of the elements in hybrid precoder by minimizing the CE, which can generate a solution close to the optimal one with a sufficiently high probability. Simulation results verify that our scheme can achieve the near-optimal sum-rate performance and much higher energy efficiency than traditional schemes.

I. INTRODUCTION

Hybrid precoding reduces the need for RF chains by splitting a fully digital precoder into analog and digital parts, but common phase-shifter networks remain costly. The paper proposes a switch-and-inverter architecture and an adaptive cross-entropy scheme to address that trade-off.

I. INTRODUCTION

  • Hybrid precoding decomposes a fully digital precoder into a large analog beamformer and a small digital precoder, reducing RF-chain requirements while retaining near-optimal performance through low-rank mmWave channels.The RF-chain burden of fully digital processing becomes costly as antenna counts grow.Source: §I · p. 1
  • Finite-resolution phase shifters reduce energy use but still require many phase shifters, whereas switch networks lower cost and energy at the expense of performance.Traditional high-resolution phase-shifter networks require hundreds or thousands of components.Source: §I · p. 1
  • The proposed switch-and-inverter architecture uses a small number of switches and inverters, while its ACE scheme adaptively updates precoder-element distributions to seek high-sum-rate solutions.It samples candidate precoders, weights them by achievable sum-rate, and refines the distributions by minimizing cross-entropy.Source: §I · p. 1

II. SYSTEM MODEL

The system model considers a base station serving single-antenna users with hybrid precoding and a geometric mmWave channel. It specifies the precoder dimensions, power constraint, noise model, and planar-array steering structure.

II. SYSTEM MODEL

  • The model has a base station with N antennas and N_RF RF chains serving K single-antenna users, and assumes N_RF = K to fully achieve multiplexing gains.The text notes that extension to users with multiple antennas is possible.Source: §II · pp. 1–2
  • The received signal uses channel matrix H, analog beamformer F_RF, and digital precoder F_BB, with the total transmit power constrained by ρ and additive white Gaussian noise.F_RF has size N × N_RF and F_BB has size N_RF × K.Source: §II · p. 2
  • User channels follow a geometric mmWave model, with a uniform planar array formed from horizontal and vertical antenna dimensions and corresponding steering vectors.At mmWave frequencies, the stated typical antenna spacing is half a wavelength in both dimensions.Source: §II · p. 2

III. ENERGY EFFICIENT HYBRID PRECODING

The energy-efficient precoding section proceeds from the proposed SI architecture to an ACE-based scheme, then analyzes computational complexity.

III. ENERGY EFFICIENT HYBRID PRECODING

  • The section first describes the proposed SI-based hybrid precoding architecture.Source: §III · p. 2
  • It next presents an ACE-based hybrid precoding scheme for the SI architecture.Source: §III · p. 2
  • The section concludes with a computational complexity analysis.Source: §III · p. 2

A. The proposed SI-based hybrid precoding architecture

The SI architecture uses switches and inverters to reduce hardware and energy costs while retaining array-gain performance close to a phase-shifter architecture. Its array-gain gap remains limited and constant as the antenna count grows.

A. The proposed SI-based hybrid precoding architecture

  • Traditional PS precoding uses a phase-shifter network, while SW precoding uses switches but activates only N_RF antennas simultaneously and incurs an obvious performance loss.The PS architecture may require N × N_RF phase shifters; the text gives 64 × 16 = 1024 as an example.Source: A. The proposed SI-based hybrid… · pp. 2–3
  • Each RF chain in the SI architecture connects to an M-antenna subarray through one inverter and M switches rather than N phase shifters.Here M = N/N_RF; the architecture is presented as a trade-off between near-optimal PS precoding and energy-efficient switch-based precoding.Source: A. The proposed SI-based hybrid… · p. 3
  • The proposed SI architecture is reported to consume much less energy than the PS architecture while using all antennas to retain their potential array gains.The inverter energy consumption is described as similar to that of a switch.Source: A. The proposed SI-based hybrid… · p. 3
  • The SI analog beamformer is block diagonal, and its nonzero elements are constrained to the two values −1 and +1.These hardware constraints distinguish it from the traditional architectures.Source: A. The proposed SI-based hybrid… · p. 3
  • With a single-path user channel and N → ∞ at fixed N/M = N_RF, the SI-to-PS array-gain ratio has a limited, constant performance gap that does not grow with the number of base-station antennas.The comparison is against a PS-based architecture with sufficiently high-resolution phase shifters.Source: A. The proposed SI-based hybrid… · p. 3

B. ACE-based hybrid precoding scheme

The scheme optimizes analog and digital precoders for achievable sum-rate under the analog beamformer's constraints. ACE replaces an infeasible-scale exhaustive search with iterative candidate evaluation and probability updates, weighting elite candidates by their sum-rates.

B. ACE-based hybrid precoding scheme

  • The design objective is to maximize achievable sum-rate while satisfying the analog beamformer's non-convex constraints.Because the allowed analog-beamformer elements come from a finite set, exhaustive search can in principle find the optimum.Source: B. ACE-based hybrid precoding scheme · pp. 3–4
  • Exhaustive search over 2^N possible analog beamformers is computationally unaffordable for large N, motivating the proposed ACE alternative.For each analog candidate, the digital precoder can be computed from the effective channel without the analog constraints.Source: B. ACE-based hybrid precoding scheme · p. 4
  • ACE iteratively samples candidates, evaluates their sum-rates, selects elites, and updates the sampling distribution to seek a near-optimal solution.Conventional CE treats all elites equally; ACE instead weights them adaptively according to achievable sum-rate.Source: B. ACE-based hybrid precoding scheme · p. 4
  • In the described implementation, zero-forcing is used as the digital precoder for each candidate analog beamformer.The paper notes that other digital precoder schemes could also be used.Source: B. ACE-based hybrid precoding scheme · p. 4
  • For users with multiple antennas, ACE can jointly search the base-station and user analog beamformers.Source: B. ACE-based hybrid precoding scheme · p. 5

C. Computational complexity analysis

The complexity analysis identifies candidate evaluation and probability updates as major computational steps. The authors characterize total complexity as acceptable and comparable to simple least squares when K is small and I and S need not be very large.

C. Computational complexity analysis

IV. SIMULATION RESULTS

Simulations evaluate achievable sum-rate and energy efficiency for ACE-based hybrid precoding, including comparisons with alternative schemes and tests of candidate and iteration counts.

Sum-rate comparison

  • ACE-based precoding has a limited, constant sum-rate gap from two-stage precoding and outperforms antenna selection; ACE also beats conventional CE by about 1 dB in SNR gap.The Fig. 2 comparison uses N = 64, NRF = K = 4, S = 200, Selite = 40, and I = 20.Source: Figure 2 · p. 5, §IV · pp. 5–6

Parameter sensitivity

  • At SNR = 10 dB, increasing candidate count S improves sum-rate when S is small, but gains become less apparent at larger S; S = 200 is sufficient.The tested setting uses Selite/S = 0.2, N = 64, and NRF = K = 4.Source: Figure 3 · p. 5, §IV · p. 6

Simulation setup

  • The channel simulations use Lk = 3 paths, uniformly distributed path angles over (−π, π), and define SNR as ρ/σ².The simulation evaluates achievable sum-rate and energy efficiency.Source: §IV · p. 5

Energy efficiency

  • The SI-based ACE scheme achieves much higher energy efficiency than the compared schemes, especially when K ≤ 12.The comparison fixes N = 64 and varies NRF = K from 1 to 16.Source: Figure 4 · p. 6, §IV · p. 6

Parameter sensitivity

  • The ACE-based scheme converges with a small number of iterations, with I = 20 given as an example.These observations support the Algorithm 1 parameters used in the Fig. 2 comparison.Source: §IV · p. 6

V. CONCLUSIONS

The conclusion presents an SI-based architecture, analyzes its performance gap from traditional near-optimal precoding, and reports simulation evidence for ACE-based precoding.

V. CONCLUSIONS

  • The SI-based analog architecture uses a small number of switches and inverters to reduce hardware cost and energy consumption.Source: §V · p. 6
  • The performance gap between the proposed SI architecture and the traditional near-optimal architecture is limited and remains constant.Source: §V · p. 6
  • The ACE-based scheme is low complexity and achieves satisfying sum-rate performance and much higher energy efficiency than traditional schemes in simulations.Source: §V · p. 6
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