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Joint Antenna Selection and Hybrid Beamformer Design using Unquantized and Quantized Deep Learning Networks

Ahmet M. Elbir, Kumar Vijay Mishra

arXiv:1905.03107v2eess.SP

TL;DR

The paper addresses the computational burden of antenna-subarray selection and hybrid beamformer design in large mm-Wave MIMO systems. It uses twin CNNs trained offline on noisy channel data to select antennas and predict beamformers, achieving improved performance over conventional methods while supporting low-memory deployment through quantization.

  • Problem

    Large mm-Wave MIMO arrays make separate RF chains costly, while searching all antenna subsets in real time remains computationally complex.

  • Method

    A twin-CNN framework classifies the best antenna subarray from the channel matrix and predicts the corresponding RF and baseband beamformers using offline-generated noisy training pairs.

  • Results

    The CNN approach provides significantly better performance than conventional beamformer-design techniques, with classification accuracy reaching 100% in the reported training setup.

  • Takeaways & Limitations

    The framework reduces online computation by replacing real-time antenna-subset search and beamformer computation with channel-matrix classification and prediction.

  • Takeaways & Limitations

    The network must be retrained when full-array parameters such as N_T, N_R, N_RS, or N_S change because they determine the input and output dimensions.

Abstract

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In millimeter-wave communications, multiple-input-multiple-output (MIMO) systems use large antenna arrays to achieve high gain and spectral efficiency. These massive MIMO systems employ hybrid beamformers to reduce power consumption associated with fully digital beamforming in large arrays. Further savings in cost and power are possible through the use of subarrays. Unlike prior works that resort to large latency methods such as optimization and greedy search for subarray selection, we propose a deep-learning-based approach in order to overcome the complexity issue without causing significant performance loss. We formulate antenna selection and hybrid beamformer design as a classification/prediction problem for convolutional neural networks (CNNs). For antenna selection, the CNN accepts the channel matrix as input and outputs a subarray with optimal spectral efficiency. The resultant subarray channel matrix is then again fed to a CNN to obtain analog and baseband beamformers. We train the CNNs with several noisy channel matrices that have different channel statistics in order to achieve a robust performance at the network output. Numerical experiments show that our CNN framework provides an order better spectral efficiency and is 10 times faster than the conventional techniques. Further investigations with quantized-CNNs show that the proposed network, saved in no more than 5 bits, is also suited for digital mobile devices.

I. INTRODUCTION

The paper addresses costly mm-Wave hardware and computationally demanding antenna-selection and hybrid-beamforming problems with CNNs. It uses noisy channel data to jointly select antennas and design beamformers, while also investigating quantized networks for low-memory devices.

  • Motivation: Massive MIMO compensates mm-Wave propagation losses through beamforming gain from large antenna arrays.Mm-Wave signals experience penetration, diffraction, scattering, and path-loss challenges.
  • Motivation: 15-795 mW per full-resolution ADC and large-array RF hardware motivate hybrid beamforming to reduce cost and power overhead.The cited ADC range corresponds to 36 MHz-1.8 GHz bandwidths.
  • Motivation: Subarrays with analog switches can further reduce energy use compared with phase-shifter-based architectures, while antenna selection trades off cost and performance.Optimal subarray selection reduces phase-shifter and LNA power consumption.
  • Problem: Branch-and-bound and related optimization methods impose high computational burden for optimum massive-MIMO subarray selection.The paper introduces deep learning to reduce complexity when an optimum solution is still obtainable.
  • Approach: The proposed CNNs sequentially classify the antenna subarray and predict hybrid beamformers from the selected channel matrix.The first CNN selects the subarray; a second CNN chooses the RF beamformer and constructs the baseband beamformer.
  • Results: 10 times faster than conventional antenna-selection and hybrid-beamformer techniques, with classification accuracy quickly reaching 100%.Training uses approximately 240000 noisy channel-matrix samples, with offline data generation and training overhead included.
  • Deployment: Quantized-CNNs are investigated to reduce memory and computational demands for deployment on digital mobile devices.The paper positions this as an extension of the joint antenna-selection and beamformer-design framework.

III. JOINT ANTENNA AND RF CHAIN SELECTION

The joint design focuses on selecting an optimized antenna subarray and designing the associated transmit and receive hybrid beamformers. The formulation uses a selection matrix together with analog and baseband beamforming variables.

  • Joint design: Scheme 3 jointly selects NRS antennas from the full array and designs transmit and receive analog and baseband beamformers.The selected antennas are outputs of the full-array receiver.
  • Optimization: The optimization maximizes Q over antenna selection and the analog and baseband beamformers.The displayed formulation includes Q, FRF, FBB, WRF, and WBB.

RF WRF WBB

The paper replaces real-time exhaustive subarray and RF-chain search with an offline-trained classification network. The network then selects the best subarray and corresponding RF beamformers for a given channel matrix.

  • Complexity: The joint optimization is difficult because it contains several matrix variables, including Q, FRF, WRF, FBB, and WBB.This motivates avoiding direct real-time solution of the optimization problem.
  • Deep-learning formulation: The antenna-selection stage is cast as a classification problem to obtain an optimum solution with lower computational complexity.The approach uses deep learning instead of solving the optimization directly in real time.

A. Antenna Selection

The paper formulates antenna subarray selection as maximizing spectral efficiency over candidate configurations, then recasts the task as classification to reduce exhaustive-search complexity.

  • Classification formulation: Antenna selection is therefore cast as a classification problem with Q_A classes representing all possible subarray configurations.For very large arrays, branch-and-bound and block partitioning are used to manage the computational burden of enumerating candidate subsets.
  • Selected subarray model: The selected subarray extracts rows from the full channel and received signal, producing a reduced channel for subsequent hybrid processing.The selected channel has dimensions N_RS × N_T, while analog and baseband combiners process the resulting signal.
  • Antenna-selection objective: A candidate subarray is selected by maximizing the spectral efficiency R(q_A) over all antenna configurations.The selected index identifies the antenna positions that provide maximum spectral efficiency.
  • Joint optimization: Joint selection with hybrid beamformers evaluates each candidate subarray using its corresponding beamformer design rather than unconstrained beamformers alone.The paper notes that the best subarray can change when hybrid beamformers are included in the optimization.
  • Classification formulation: Similar channel matrices can share the same optimal subarray, yielding far fewer maximizing configurations than the full candidate set.The paper denotes this reduced set by Q̄_A and states Q̄_A ≪ Q_A.

B. Hybrid Beamformer Design

The hybrid beamformer design problem jointly optimizes analog and baseband precoders and combiners for a selected channel subarray.

  • Hybrid beamformer design: For a selected channel matrix H_qA, the design problem optimizes F_RF, F_BB, W_RF, and W_BB subject to hybrid beamforming constraints.The formulation treats precoders and combiners as the design variables for the selected subarray.
  • Hybrid beamformer design: The selected subarray channel determines the hybrid beamformer design problem solved after antenna selection.Thus, beamformer design is conditioned on the antenna configuration q_A.

RF HqAFRF FBBFH

The paper converts hybrid beamformer design into constrained precoder and combiner optimization, then uses the resulting solutions to create neural-network labels and motivate offline training.

  • Optimization formulation: The precoder and combiner problems are decoupled and minimize Euclidean distance between unconstrained and hybrid beamformers.This provides a tractable design route for obtaining analog and baseband beamformers.
  • Label generation: Manifold optimization solves the precoder and combiner subproblems, producing F_RF, F_BB, W_RF, and W_BB for network labeling.The resulting beamformer parameters form the output representation used by CNN_RF.
  • Offline training: The trained classifier replaces real-time exhaustive search with offline computation followed by fast prediction of the best subarray and RF beamformers.The offline process includes all possible subarray and RF-chain combinations.

IV. TRAINING THE DL NETWORK

The training framework uses two CNNs and noisy, statistically varied channel realizations: one selects the antenna subarray, while the other predicts RF beamformer parameters.

  • Network architecture: Two CNNs operate sequentially: CNN_AS selects the antenna subarray, and CNN_RF uses the selected channel rows to choose RF beamformers.Both networks are trained from channel realizations paired with their corresponding output classes.
  • Input representation: The network input encodes each imperfect channel matrix through absolute, real, and imaginary components.These form a three-channel input tensor X with dimensions N_R × N_T × 3.
  • Training-data generation: Training channels vary user locations, channel gains, cluster counts, and synthetic AWGN realizations to enrich the data distribution.The noise variance is tied to SNR_TRAIN, and the resulting samples are paired with offline-optimal subarrays and beamformers.
  • Training-data generation: The generated input-output pairs label CNN_AS with subarray indices and CNN_RF with RF beamformer representations.The algorithm constructs pairs (X, q̄_A) for CNN_AS and (X, z) for CNN_RF.
  • Network architecture: The CNNs use 14-layer architectures with convolutional, fully connected, dropout, and ReLU components, while CNN_RF ends with a G × 1 regression output.The architecture was selected through optimization analysis for performance and computational cost.

V. NUMERICAL EXPERIMENTS

The experiments evaluate the CNN framework under specified channel, noise, and training configurations, using stochastic-gradient optimization and a fixed number of RF chains.

  • Experimental setup: The networks are trained and tested with synthetic noise to reduce similarity between training and test data.Testing uses a noise-based SNR definition, while training uses stochastic gradient descent with momentum, a 0.01 learning rate, mini-batches of 500, and 50 epochs.
  • Experimental setup: All simulations select N_RF = 4 RF chains.
  • Channel model: The simulations use four clusters and five rays per cluster for each channel realization.The angle spread is fixed at σ2_Θ = 5°, with transmit and receive azimuth and elevation angles sampled uniformly from the stated intervals.

A. Performance of Unquantized CNN

The unquantized CNN is assessed for training size, noise level, and channel-statistics variation. Training across multiple noisy realizations and statistics yields robust performance, but changing array dimensions requires retraining.

  • Training and noise robustness: Validation loss becomes satisfactory for L ≥ 150 noisy channel realizations, so the simulations use L = 200.The reported assessment uses N = 100, N_T = N_R = 64, and N_S = 4.
  • Training and noise robustness: Both networks attain satisfactory accuracy for SNR_TEST ≥ 0 dB, while low-SNR inputs produce poor classification performance.Training over multiple SNR_TRAIN levels improves robustness, although excessive noise limits the network’s ability to distinguish inputs.
  • Channel-statistics robustness: The CNN framework provides robust performance against different channel statistics.The authors attribute this robustness to training with several channel statistics and synthetic noise at multiple SNR_TRAIN values.
  • Scope boundary: Changing full-array parameters such as N_T, N_R, N_RS, or N_S requires retraining because they determine the network input and output dimensions.

B. Antenna Selection Performance

The experiments compare CNN-based antenna selection and hybrid beamforming with conventional methods across spectral-efficiency, imperfect-channel, and beamformer-error evaluations.

  • Antenna selection: CNNAS performs close to BAS, which uses branch-and-bound to obtain an optimum antenna-selection solution, and outperforms the other reported algorithms and schemes.The comparison uses N_T = N_R = 256 and N_RS = 16, with hybrid beamforming performed by manifold optimization for all antenna-selection techniques.
  • Hybrid beamforming: CNNRF outperforms the compared hybrid beamforming algorithms and performs very close to MO-Alt-Min for N_S = 1 and N_S = 4.The comparison includes SOMP, Wang et al., Sohrabi et al., and an MLP trained with the same data; CNNRF receives the channel selected by CNNAS.
  • Imperfect-channel robustness: The proposed CNN approach performs more robustly than the other algorithms with imperfect channel matrices.The robustness analysis varies SNR_TEST while simulations use SNR = 10 dB and provide all algorithms with imperfect channel inputs.
  • Beamformer-design error: CNN-based RF-chain selection produces less precoder and combiner error than the other algorithms in the reported beamformer-design evaluation.The evaluation covers N_S = {1, 2, 3}; most algorithms, including CNN, achieve lower γ_F and γ_W at N_S = 3 than at N_S = 1.

D. Binarized and Quantized CNN

The paper examines CNN compression for mobile deployment, focusing on binarized and quantized weights, performance loss, and computational considerations. At least 5 bits preserve the best subarray and RF-chain performance, while training-data generation can remain costly for large arrays.

  • Motivation: Network quantization compresses CNN weights and can reduce memory usage and computational cost for mobile deployment.The paper motivates quantization because larger CNNs may exceed mobile devices’ memory and latency constraints.
  • Quantized performance: Binarized-CNN performance is poorer than SOMP for hybrid beamforming.The binarized network uses parameters restricted to 0 or 1.
  • Quantized performance: At least 5 bits are required for CNN to attain the best subarray and best RF chain performance.This result comes from evaluating quantized weights and biases across different bit widths.
  • Computational considerations: The CNN approach has lower computation time than the compared algorithms, while MO-Alt-Min has the highest computation cost.The reported runtime comparison uses N_R = 64, N_S = 4, and N_RS ∈ {8, 16}.
  • Computational considerations: Training-data generation takes about two days for 256 × 256 × 3 × 30000 data and 40 minutes for 25 × 25 × 3 × 30000 data.Large antenna arrays also create memory-allocation challenges during training-data generation.
  • Quantized performance: The proposed framework is reported to provide significant capacity improvement over conventional beamformer-design techniques while requiring no more than 5 bits for digital storage.The paper presents this as a low-memory, low-overhead deployment option.
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