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Deep CNN-Based Channel Estimation for mmWave Massive MIMO Systems

Peihao Dong, Hua Zhang, Geoffrey Ye Li, Ivan Simoes Gaspar, Navid NaderiAlizadeh

arXiv:1904.06761v2cs.IT

TL;DR

Hybrid processing makes channel estimation difficult in mmWave massive MIMO systems because it connects many antennas through fewer RF chains. The paper develops CNN estimators that exploit spatial, frequency, and temporal correlation, and reports improved estimation with lower complexity or reduced pilot overhead. Overall, the proposed methods remain effective across propagation scenarios while SPR-CNN uses about one third of the spatial pilot overhead.

  • Problem

    Hybrid architecture makes channel estimation challenging in mmWave massive MIMO systems, while conventional methods can perform poorly in complicated channel models and have high complexity.

  • Method

    The paper develops SF-CNN, SFT-CNN, and SPR-CNN channel estimators that exploit spatial, frequency, and temporal channel correlation, with SPR-CNN grouping successive coherence intervals using a channel-estimation unit with memory.

  • Results

    The proposed SF-CNN and SFT-CNN outperform non-ideal MMSE with lower complexity and approach ideal MMSE performance, while SPR-CNN achieves comparable performance with about one third of the spatial pilot overhead.

  • Takeaways & Limitations

    Deep CNNs efficiently exploit channel correlation for accurate mmWave massive MIMO channel estimation, including under different propagation statistics.

Abstract

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For millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, hybrid processing architecture is usually used to reduce the complexity and cost, which poses a very challenging issue in channel estimation. In this paper, deep convolutional neural network (CNN) is employed to address this problem. We first propose a spatial-frequency CNN (SF-CNN) based channel estimation exploiting both the spatial and frequency correlation, where the corrupted channel matrices at adjacent subcarriers are input into the CNN simultaneously. Then, exploiting the temporal correlation in time-varying channels, a spatial-frequency-temporal CNN (SFT-CNN) based approach is developed to further improve the accuracy. Moreover, we design a spatial pilot-reduced CNN (SPR-CNN) to save spatial pilot overhead for channel estimation, where channels in several successive coherence intervals are grouped and estimated by a channel estimation unit with memory. Numerical results show that the proposed SF-CNN and SFT-CNN based approaches outperform the non-ideal minimum mean-squared error (MMSE) estimator but with reduced complexity, and achieve the performance close to the ideal MMSE estimator that is very difficult to be implemented in practical situations. They are also robust to different propagation scenarios. The SPR-CNN based approach achieves comparable performance to SF-CNN and SFT-CNN based approaches while only requires about one third of spatial pilot overhead at the cost of complexity. Our work clearly shows that deep CNN can efficiently exploit channel correlation to improve the estimation performance for mmWave massive MIMO systems.

I. INTRODUCTION

Hybrid architecture reduces the complexity and cost of mmWave massive MIMO but makes channel estimation challenging. This paper uses deep CNNs to exploit spatial, frequency, and temporal channel correlations, with a pilot-reduced design for lower overhead.

  • Motivation: Hybrid architecture connects many antennas to fewer RF chains, reducing complexity and cost in mmWave massive MIMO systems.The architecture uses phase shifters at both transmitter and receiver sides.
  • Motivation: Channel estimation remains challenging because conventional methods perform poorly in complicated channel models and have high complexity.Deep CNNs are presented as a way to extract channel structure while enabling efficient parallel computation.
  • Proposed approaches: SF-CNN simultaneously processes tentatively estimated channel matrices at adjacent subcarriers to exploit spatial and frequency correlation.The approach targets mmWave massive MIMO-OFDM channel estimation.
  • Proposed approaches: SFT-CNN additionally uses channel information from the previous coherence interval to exploit temporal correlation in time-varying channels.It incorporates spatial, frequency, and temporal correlation within the channel-estimation process.
  • System model: The system inserts pilots across frequency and time, with adjacent pilot subcarriers forming blocks and remaining time slots used for data transmission.This pilot structure supports estimation at corresponding time-frequency positions.

III. SF-CNN BASED CHANNEL ESTIMATION

This section introduces the SF-CNN channel-estimation approach and describes its offline training, online deployment, and online computational-complexity analysis.

  • III. SF-CNN based channel estimation: The SF-CNN section covers the proposed approach, offline training, online deployment, and computational complexity for online estimation.The section is organized around the complete estimation workflow rather than a single implementation component.

A. Algorithm Description

For adjacent subcarriers, the channel-estimation procedure first forms pilot observations and coarse channel estimates, then jointly refines them with SF-CNN.

  • Channel Estimation Procedure: Pilot observations Y_k are processed by a tentative-estimation module using combining and beamforming matrices to produce coarse estimates of H_k.The module uses matrices G_L and G_R to process Y_k.
  • Channel Estimation Procedure: The tentative estimates from two adjacent subcarriers are input simultaneously into SF-CNN, which outputs the corresponding estimated channel matrices.The CNN performs the refinement through a learned mapping parameterized by Φ.

2) SF-CNN Offline Training:

SF-CNN is trained offline to map tentative channel estimates to scaled true channels, using a convolutional denoising architecture tailored to the channel matrix.

  • SF-CNN Offline Training: The training set contains N_tr samples pairing input data R_i with target channel data H_i generated under a specified channel model.R_i is the CNN input and H_i is the corresponding target.
  • SF-CNN Offline Training: The input comprises tentative channel matrices from two adjacent subcarriers, represented with separate real and imaginary components.The matrices correspond to subcarriers k′_0 and k′_0 + 1.
  • SF-CNN Offline Training: A scaling constant matches target-channel values to the output activation range before SF-CNN approximates the scaled true channels.The output is later scaled back and recombined into complex-valued channel estimates.
  • SF-CNN Offline Training: For the example NT = 32 and NR = 16, the network processes four real-valued 16 × 32 matrices and maintains dimensions through zero-padded convolutions.The network uses ReLU and batch normalization in its convolutional layers, with a tanh output layer.
  • SF-CNN Offline Training: The offline-training objective is to minimize the mean-squared-error loss function.The loss is defined over the training samples and their target channel data.
  • SF-CNN Offline Training: The architecture uses nine convolutional hidden layers with 3 × 3 filters and feature-map dimensions NR × NT for channel denoising.Small filters are selected to maintain good estimation performance with low complexity.

3) Online Deployment Issue:

The offline-trained SF-CNN and its TE module are deployed at the receiver to jointly process pilot matrices and estimate adjacent-subcarrier channels. The approach is evaluated by computational complexity and can avoid costly online fine-tuning when channel statistics change.

  • After offline training, the SF-CNN and TE module jointly process pilot matrices to output estimated channel matrices at adjacent subcarriers.
  • Online fine-tuning uses more power or longer pilot sequences to improve estimated channels, but increases online overhead.
  • Offline-trained SF-CNN is robust to most previously unobserved channel statistics, so further online fine-tuning may provide only marginal improvement.
  • Testing-stage complexity is measured using floating-point operations from the TE module and SF-CNN processing.

QNTNR(NT + NR) + NTNR

The paper extends SF-CNN channel estimation with temporal correlation and analyzes its computational complexity against MMSE. The proposed CNN approach uses substantially fewer operations and much shorter reported runtime under the stated parameter settings.

  • Under NT = 32, NR = 16, and Q = 2, SF-CNN complexity is on the order of 10^8, whereas MMSE requires 10^9.
  • The SF-CNN runtime is 1.47 × 10^-4 seconds per channel realization on an NVIDIA GeForce GTX 1080 Ti GPU, compared with 6.14 × 10^-2 seconds for MMSE on an Intel Core i7-3770 CPU.
  • The SFT-CNN further incorporates temporal correlation into SF-CNN, while SPR-CNN reduces spatial pilot overhead caused by large-scale antenna arrays.
  • The SFT-CNN refines tentative channel matrices by simultaneously exploiting spatial, frequency, and temporal channel correlations across successive coherence intervals.
  • Temporal correlation between successive coherence intervals is modeled with a Gauss-Markov distribution, where 0 ≤ ρ ≤ 1 is the correlation coefficient.

A. SFT-CNN based Channel Estimation

SFT-CNN jointly refines tentative channel estimates across adjacent subcarriers and successive coherence intervals, exploiting spatial, frequency, and temporal correlation. Its temporal extension adds limited complexity while improving estimation efficiency.

  • A. SFT-CNN based Channel Estimation: SFT-CNN jointly processes tentative channel matrices from adjacent subcarriers and successive coherence intervals to exploit spatial, frequency, and temporal correlation.A cache stores prior-interval matrices for joint processing in the next coherence interval.
  • A. SFT-CNN based Channel Estimation: The same SFT-CNN is reused across coherence intervals because it learns general temporal correlation rather than interval-specific relationships.
  • A. SFT-CNN based Channel Estimation: Training uses tentative estimates as inputs and scaled true channel matrices as targets under an offline MSE objective.
  • A. SFT-CNN based Channel Estimation: SFT-CNN increases only the first convolutional layer's complexity by S times relative to SF-CNN, a minor portion of total complexity.The comparison is based on the stated architecture and complexity analysis.
  • A. SFT-CNN based Channel Estimation: With temporal correlation included, MMSE complexity increases significantly even when S = 2, whereas SFT-CNN provides a simple alternative.

B. SFT-CNN or LSTM-CNN?

SFT-CNN and LSTM-CNN achieve nearly identical channel-estimation accuracy, but LSTM-CNN requires substantially more training and testing time. The paper therefore favors the simpler SFT-CNN architecture.

  • B. SFT-CNN or LSTM-CNN?: LSTM-CNN consumes much more time than SFT-CNN in both training and testing stages.Table IV reports time complexity for both methods on an NVIDIA GeForce GTX 1080 Ti GPU.
  • B. SFT-CNN or LSTM-CNN?: SFT-CNN and LSTM-CNN achieve almost the same NMSE performance across the whole SNR regime.The comparison involves two and four coherence intervals, respectively.
  • B. SFT-CNN or LSTM-CNN?: Because LSTM-CNN has no performance advantage but higher complexity, the paper prefers SFT-CNN for channel estimation.

3) Training and Testing Complexity:

SPR-CNN reduces spatial pilot overhead by grouping successive coherence intervals and using cached channel information, while adding only moderate computational complexity. Full pilots initialize each group, followed by reduced pilots.

  • C. SPR-CNN based Channel Estimation: SPR-CNN groups D successive coherence intervals into a channel estimation unit and exploits their correlation to reduce spatial pilot overhead.Different channel estimation units are non-overlapping.
  • C. SPR-CNN based Channel Estimation: The first coherence interval in each group uses full spatial pilot overhead, while subsequent intervals use reduced overhead.The first interval supplies complete channel information for estimating the group.
  • C. SPR-CNN based Channel Estimation: For later coherence intervals, current and previously received pilots are jointly used to estimate the current channels.Tentative channel matrices from earlier intervals are retained in a cache.
  • C. SPR-CNN based Channel Estimation: Reducing the numbers of transmit or receive beamforming and combining vectors lowers spatial pilot overhead.The relevant dimensions are MT[n] and MR[n].
  • C. SPR-CNN based Channel Estimation: SPR-CNN saves spatial pilot overhead effectively while increasing complexity moderately.The highest-complexity SPR-CNN variant increases only the first convolutional layer's complexity by D = 4 times relative to SF-CNN.

V. NUMERICAL RESULTS

The numerical-results section evaluates the proposed CNN estimators against MMSE baselines under a specified mmWave MIMO-OFDM simulation setup. It also documents pilot, channel-model, dataset, and training configurations.

  • V. NUMERICAL RESULTS: The simulations compare the proposed CNN channel estimators with non-ideal MMSE using estimated covariance and ideal MMSE using true covariance.
  • V. NUMERICAL RESULTS: The channel data follow the 3GPP TR 38.901 Release 15 clustered delay line model at fc = 28 GHz with K = 64 subcarriers.The sampling rate is fs = 100 MHz and the number of main paths is L = 3.
  • V. NUMERICAL RESULTS: For SF-CNN, the training, validation, and testing sets contain 81,000, 9,000, and 19,000 samples, respectively.
  • V. NUMERICAL RESULTS: Training uses 800 epochs with learning rates 10^-4, 5 × 10^-5, and 10^-5 over successive epoch ranges, and batch size 128.The scaling constant is c = 2.

A. SF-CNN based Channel Estimation

SF-CNN and SFT-CNN exploit spatial, frequency, and temporal channel correlation to improve mmWave massive MIMO channel estimation. The approaches outperform non-ideal MMSE with lower complexity, approach ideal MMSE in key conditions, and show robustness to mismatched scenarios and path counts.

  • SF-CNN performance: SF-CNN jointly estimates channels over adjacent subcarriers, using frequency correlation to improve NMSE over single-subcarrier estimation.The comparison is performed in the UMi street NLOS scenario.
  • SF-CNN performance: SF-CNN significantly outperforms non-ideal MMSE with lower estimation complexity and approaches ideal MMSE, especially at low and medium SNRs.The result is reported for joint estimation over two adjacent subcarriers.
  • Robustness: SF-CNN remains effective under UMi-to-UMa channel-statistics mismatch, outperforming non-ideal MMSE without mismatch while MMSE performance degrades significantly.MMSE depends strongly on the covariance statistics used for estimation.
  • SFT-CNN performance: SFT-CNN improves NMSE by incorporating temporal correlation from the previous coherence interval alongside adjacent-subcarrier information.SFT-CNN jointly estimates current channels over two subcarriers and outperforms non-ideal MMSE in performance and complexity.
  • Robustness: SFT-CNN remains more robust than ideal and non-ideal MMSE when both propagation scenario and maximum Doppler spread are mismatched.The matched setting uses UMi NLOS with fd = 1,400 Hz; the mismatched setting uses UMa NLOS with fd = 1,800 Hz.
  • Robustness: Temporal correlation improves SFT-CNN accuracy even when the tested number of main paths differs from training.This conclusion follows from comparing the SF-CNN and SFT-CNN robustness evaluations.

C. SPR-CNN based Channel Estimation

SPR-CNN reduces spatial pilot overhead by grouping successive coherence intervals and estimating them with a channel estimation unit with memory. It achieves comparable performance to full-pilot CNN approaches while requiring about one third of the pilot overhead, at increased complexity.

  • Pilot reduction: SPR-CNN groups D = 4 successive coherence intervals into one channel estimation unit and varies antenna-side pilot dimensions across intervals.The settings use MT[n] = NT = 32 and MR[n] = NR = 16 for d = 1, then MT[n] = 16 and MR[n] = 4 for d = 2, 3, 4.
  • Pilot reduction: The SPR-CNN average spatial pilot overhead is pSPR-CNN = 88, with ratio r = pSPR-CNN / pfull = 88 / 256 ≈ 1/3.The comparison uses full pilot overhead pfull = 256.
  • Performance and trade-off: SPR-CNN achieves comparable performance to SF-CNN and SFT-CNN, especially at low and medium SNRs, while requiring about one third of pilot overhead.This reduction comes at the cost of increased complexity.
  • Performance and trade-off: SPR-CNN tolerates reduced spatial pilot overhead more effectively than ideal and non-ideal MMSE under the same channel-correlation information.The MMSE approaches perform poorly in this reduced-overhead comparison.
  • Conclusion: The paper concludes that SF-CNN, SFT-CNN, and SPR-CNN provide lower-complexity or lower-overhead alternatives while retaining competitive channel-estimation accuracy.The conclusion reports performance close to ideal MMSE for SF-CNN and SFT-CNN and minor performance loss for SPR-CNN.
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