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Deep Learning-based Channel Estimation for Beamspace mmWave Massive MIMO Systems

Hengtao He, Chao-Kai Wen, Shi Jin, Geoffrey Ye Li

arXiv:1802.01290v2cs.IT

TL;DR

Limited RF chains make channel estimation difficult in beamspace mmWave massive MIMO systems. The paper applies an LDAMP network that learns channel structure from training data and supplies an asymptotic performance analysis. LDAMP outperforms state-of-the-art compressed-sensing algorithms, including with a small number of RF chains.

  • Problem

    Channel estimation is challenging when beamspace mmWave massive MIMO receivers use limited RF chains.

  • Method

    The paper uses an LDAMP network with a DnCNN denoiser and analyzes its asymptotic performance using state evolution.

  • Results

    LDAMP outperforms state-of-the-art compressed-sensing algorithms and achieves excellent performance with a small number of RF chains.

  • Takeaways & Limitations

    The results indicate that deep learning is a powerful tool for channel estimation in mmWave communications.

Abstract

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Channel estimation is very challenging when the receiver is equipped with a limited number of radio-frequency (RF) chains in beamspace millimeter-wave (mmWave) massive multiple-input and multiple-output systems. To solve this problem, we exploit a learned denoising-based approximate message passing (LDAMP) network. This neural network can learn channel structure and estimate channel from a large number of training data. Furthermore, we provide an analytical framework on the asymptotic performance of the channel estimator. Based on our analysis and simulation results, the LDAMP neural network significantly outperforms state-of-the-art compressed sensingbased algorithms even when the receiver is equipped with a small number of RF chains. Therefore, deep learning is a powerful tool for channel estimation in mmWave communications.

I. INTRODUCTION

Beamspace mmWave massive MIMO reduces RF-chain requirements but makes channel estimation difficult, motivating learned recovery methods that exploit channel structure. The paper introduces LDAMP for this setting and reports strong performance with few RF chains.

  • I. INTRODUCTION: Limited RF chains reduce hardware cost and power consumption but make channel estimation challenging in large beamspace mmWave massive MIMO arrays.The architecture uses K RF chains with K ≪ MN antennas.
  • I. INTRODUCTION: Lens-array channels exhibit sparsity, concentration, and correlated adjacent elements, resembling 2D natural images.These properties motivate image-recovery-inspired channel estimators.
  • I. INTRODUCTION: LDAMP incorporates a DnCNN denoiser into iterative sparse signal recovery for beamspace channel estimation.The network learns from a large number of channel matrices and can support various selection networks.
  • I. INTRODUCTION: The study provides an analytical performance framework and reports that LDAMP outperforms state-of-the-art compressed-sensing algorithms, including under few-RF-chain operation.The paper presents these as initial deep-learning results for beamspace channel estimation.
  • I. INTRODUCTION: The paper formulates beamspace channel estimation as signal recovery from measurements collected through a selection network.The beamspace channel matrix is vectorized into h, and the receiver observes selected noisy measurements.

III. LDAMP-BASED CHANNEL ESTIMATION

The LDAMP-based method estimates the beamspace channel vector from received measurements and a known selection network. Its performance is also analyzed asymptotically using state evolution.

  • III. LDAMP-BASED CHANNEL ESTIMATION: LDAMP estimates the beamspace channel vector h from the received signal r and the receiver’s selection network W.The method treats channel estimation as a signal-recovery task.
  • III. LDAMP-BASED CHANNEL ESTIMATION: The analysis investigates LDAMP’s asymptotic performance using state evolution.The framework is applied to characterize channel-estimation behavior in the large-system regime.

A. LDAMP network

The paper proposes an LDAMP neural network for beamspace channel estimation, combining iterative sparse recovery with learned DnCNN denoising. Its layers estimate the channel from noisy inputs while using divergence estimation and Onsager correction to maintain an equivalent AWGN model.

  • LDAMP integrates a DnCNN denoiser into an iterative sparse signal recovery algorithm for beamspace channel estimation.
  • Each LDAMP layer uses the same denoiser, divergence estimator, and tied weights to update the channel estimate.
  • The denoiser treats x_l = ĥ_l + W^Tz_l as a noisy channel vector and estimates h by removing equivalent noise n̂_l.
  • The Onsager correction removes bias from intermediate solutions so the equivalent noise follows the expected AWGN model.
  • LDAMP estimates divergence using a Monte Carlo approximation with an independent Gaussian vector and a small perturbation parameter.
  • The DnCNN denoiser contains 20 convolutional layers and learns residual noise rather than mapping noisy inputs directly to denoised channels.

B. SE analysis

The paper develops a state-evolution framework that predicts LDAMP performance layer by layer in the large-system limit. Recursive equations connect denoiser MSE with equivalent noise variance.

  • The analytical framework uses state-evolution equations to predict LDAMP performance over layers as M, N → ∞.
  • The measurement ratio δ is defined as K/MN, while θ_l denotes the average MSE of the l-th-layer denoiser output.
  • The state-evolution equations are derived from prior analysis of D-AMP algorithms using different denoisers.
  • The state-evolution analysis relies on the equivalent AWGN model and computes denoiser MSE using a Monte Carlo expectation.
  • Analytical average MSE is obtained by recursively updating the state-evolution equations for denoiser error and equivalent noise variance.

IV. SIMULATION RESULTS

The simulations evaluate LDAMP on a four-path mmWave channel using 64 × 64 lens dimensions and a 10-layer network.

  • The simulation assumes one user with a four-path mmWave channel and sets both lens dimensions to 64, giving M = N = 64.
  • The LDAMP network uses 10 layers in the simulation.

A. Implementation details

The implementation trains LDAMP on Saleh–Valenzuela channel samples using MatCovNet, data scaling, stochastic gradient descent, and Adam optimization.

  • The implementation uses MatCovNet, with 16,640 training, 6,400 validation, and 10,000 testing samples generated from the Saleh–Valenzuela channel model.
  • The data are scaled to [0, 1], and training uses stochastic gradient descent with the Adam optimizer.
  • The learning rate starts at 0.001 and is reduced to 0.0001 and then 0.00001 when validation error stops improving.

B. Comparison with other methods

The study compares LDAMP with SD, SCAMPI, and D-AMP methods using NMSE at measurement ratio δ = 0.1. LDAMP outperforms the compared compressed-sensing approaches, attributed to its learned denoiser and extensive training data.

  • B. Comparison with other methods: NMSE compares LDAMP with SD, SCAMPI, and D-AMP channel-estimation algorithms.The evaluated measurement ratio is δ = 0.1.
  • B. Comparison with other methods: LDAMP and D-AMP outperform SD and SCAMPI because of the denoisers used in these methods.
  • B. Comparison with other methods: LDAMP outperforms the state-of-the-art D-AMP algorithms, including BM3D-AMP.The passage attributes LDAMP’s performance to training on a large number of data samples.

C. Analytical performance

The paper validates its state-evolution analytical framework for LDAMP across measurement ratios at SNR = 10 dB. The framework accurately predicts network performance, and LDAMP converges within five layers.

  • C. Analytical performance: SE equations precisely evaluate LDAMP performance across different measurement ratios at SNR = 10 dB.The analysis is validated against the network’s performance in Fig. 5.
  • C. Analytical performance: LDAMP converges within five layers, demonstrating reported simplicity and practicality.

D. Impact of measurement ratio

Increasing the measurement ratio improves LDAMP’s NMSE performance. LDAMP still achieves superior performance at δ = 0.05, indicating that only a small number of receiver RF chains are required.

  • D. Impact of measurement ratio: LDAMP’s NMSE performance improves as the measurement ratio increases.The measurement ratio corresponds to the number of RF chains.
  • D. Impact of measurement ratio: δ = 0.05 still yields superior LDAMP performance, indicating that few receiver RF chains are required.The paper states that this can significantly decrease hardware cost and power consumption.

V. CONCLUSIONS

The paper concludes that LDAMP provides practical beamspace mmWave massive MIMO channel estimation with few receiver RF chains, while its analytical framework predicts large-system performance efficiently.

  • V. CONCLUSIONS: LDAMP achieves excellent channel-estimation performance with a small number of receiver RF chains.The conclusion presents this as evidence of practicality and applicability.
  • V. CONCLUSIONS: The analytical framework accurately predicts LDAMP performance in a large-system regime within a short time.
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