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Deep Learning for Direct Hybrid Precoding in Millimeter Wave Massive MIMO Systems

Xiaofeng Li, Ahmed Alkhateeb

arXiv:1905.13212v1cs.ITeess.SPmath.IT

TL;DR

MmWave channel estimation and hybrid precoding can require substantial training overhead, while conventional compressive sensing often uses random measurement vectors. The paper’s auto-precoder jointly learns channel sensing and direct RF beam prediction; with 4 or 8 channel measurements, exact prediction of the three transmit and three receive beams reaches nearly 90% sample-wise accuracy.

Abstract

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This paper proposes a novel neural network architecture, that we call an auto-precoder, and a deep-learning based approach that jointly senses the millimeter wave (mmWave) channel and designs the hybrid precoding matrices with only a few training pilots. More specifically, the proposed machine learning model leverages the prior observations of the channel to achieve two objectives. First, it optimizes the compressive channel sensing vectors based on the surrounding environment in an unsupervised manner to focus the sensing power on the most promising spatial directions. This is enabled by a novel neural network architecture that accounts for the constraints on the RF chains and models the transmitter/receiver measurement matrices as two complex-valued convolutional layers. Second, the proposed model learns how to construct the RF beamforming vectors of the hybrid architectures directly from the projected channel vector (the received sensing vector). The auto-precoder neural network that incorporates both the channel sensing and beam prediction is trained end-to-end as a multi-task classification problem. Thanks to this design methodology that leverages the prior channel observations and the implicit awareness about the surrounding environment/user distributions, the proposed approach significantly reduces the training overhead compared to classical (non-machine learning) solutions. For example, for a system of 64 transmit and 64 receive antennas, with 3 RF chains at both sides, the proposed solution needs only 8 or 16 channel training pilots to directly predict the RF beamforming/combining vectors of the hybrid architectures and achieve near-optimal achievable rates. This highlights a promising solution for the channel estimation and hybrid precoding design problem in mmWave and massive MIMO systems.

I. INTRODUCTION

The paper targets the training overhead of mmWave channel estimation and hybrid precoding, proposing environment-adapted sensing and direct beam prediction. It places this approach in a hybrid analog/digital transceiver and a sparse, geometric channel model.

I. INTRODUCTION

  • Random compressive sensing spreads power across spatial directions, while useful directions depend on the environment and likely user locations.The introduction motivates using surrounding-environment and user-distribution information to design measurement vectors.Source: §I · p. 1
  • The auto-precoder jointly optimizes channel measurement vectors toward promising directions and predicts hybrid beamforming vectors directly from the received sensing vector.This avoids explicitly estimating or reconstructing the channel in the proposed prediction approach.Source: §I · p. 1

II. SYSTEM AND CHANNEL MODELS

  • The transceiver divides precoding and combining between baseband and RF components, with constant-modulus entries assumed for the RF matrices.The model also normalizes the baseband precoder to enforce a total-power constraint.Source: §II · p. 2
  • The geometric channel model represents the channel through paths with complex gains and arrival and departure angles, and mmWave channels are typically sparse in the angular domain.The passage reports a typical range of 3–5 paths.Source: §II · p. 2

III. PROBLEM DEFINITION

The problem is to design hybrid precoders and combiners that maximize achievable rate while minimizing channel-training overhead.

III. PROBLEM DEFINITION

  • The general objective is to maximize system achievable rate while minimizing channel-training overhead.The section introduces the achievable-rate expression for analog/digital precoders and combiners.Source: §III · p. 2

n WHHFFHHHW

With orthogonal RF codebooks, the baseband design can be determined for fixed RF precoders and combiners, leaving an exhaustive search over RF choices.

n WHHFFHHHW

  • For orthogonal RF codebooks, including DFT codebooks, the optimal baseband precoders and combiners are defined from the effective channel’s singular vectors.The passage identifies V and U as the right and left singular-vector matrices, respectively.Source: n WHHFFHHHW · p. 2
  • The resulting hybrid-precoding design reduces to exhaustive search over candidate RF precoding and combining matrices.Source: n WHHFFHHHW · p. 2

I + SNRWH

The channel is normally unknown, so explicit estimation creates substantial training overhead; the proposed network instead maps sensing measurements to RF beam choices.

I + SNRWH

  • Explicit channel estimation creates substantial training overhead, motivating direct selection of RF precoding and combining vectors.The stated objective is to approach the optimal achievable rate with low training overhead.Source: I + SNRWH · p. 2
  • The auto-precoder uses a channel encoder to produce a received sensing vector and a precoder network to predict RF beamforming and combining codebook indices.The encoder uses two complex-valued convolutional layers, followed by fully connected layers and two codebook-sized output layers.Source: Figure 2 · p. 3

IV. MMWAVE AUTO-PRECODER: A NOVEL NEURAL NETWORK FOR DIRECT HYBRID PRECODING DESIGN

The auto-precoder replaces the classical channel-estimation and hybrid-precoding pipeline with learned channel sensing and direct beam prediction. It uses prior channel observations to adapt sensing and reduce training overhead while aiming for near-optimal rates.

IV. MMWAVE AUTO-PRECODER: A NOVEL NEURAL NETWORK FOR DIRECT HYBRID PRECODING DESIGN

  • The proposed auto-precoder learns measurement vectors from the environment and predicts hybrid beamforming vectors directly from compressed channel measurements.This contrasts with classical workflows that sense, reconstruct, and then use the channel to design hybrid precoders.Source: §IV · p. 3
  • Learned sensing focuses measurement power on promising spatial directions based on user distribution and the surrounding environment.The approach is presented as reducing training overhead while achieving near-optimal achievable rates.Source: §IV · p. 3
  • The section introduces the auto-precoder concept before detailing channel sensing and hybrid beam prediction.The two components are described in Sections IV-B and IV-C.Source: §IV · p. 3

A. mmWave Auto-Precoder: The Main Concept

The auto-precoder has a channel encoder that learns compressive measurements and a precoder that predicts hybrid RF beams from the resulting sensing vector. Its channel encoder implements transmitter and receiver measurements as complex-valued convolutional layers whose weights become the measurement matrices.

A. mmWave Auto-Precoder: The Main Concept

  • End-to-end training uses target RF precoding and combining matrices to supervise beam-index prediction while teaching the channel encoder to optimize sensing vectors.The target matrices are constructed using the near-optimal Gram-Schmidt hybrid beamforming algorithm [11], though other hybrid beamforming algorithms can also be used.Source: A. mmWave Auto-Precoder: The Main… · pp. 3–4
  • At prediction time, trained channel-encoder convolutional weights implement RF measurement matrices, and the resulting receive sensing vector feeds the baseband precoder.The precoder directly predicts RF beamforming and combining indices; after those are selected, the low-dimensional effective channel can be estimated with a few pilots for baseband design.Source: A. mmWave Auto-Precoder: The Main… · p. 4, Figure 3 · p. 4

B. mmWave Compressive Channel Sensing

  • Classical compressive sensing typically uses random measurements, whereas the proposed encoder adapts transmitter and receiver measurements to the environment and user distribution.The motivation is that classical approaches generally do not use prior observations to identify promising spatial directions.Source: B. mmWave Compressive Channel Sensing · p. 4
  • The channel encoder emulates the joint channel-measurement operation with two consecutive complex-valued convolutional layers whose kernels represent receive and transmit measurement vectors.The first layer uses Mr kernels of size Nr and stride Nr; the second uses Mt kernels to implement the transmit measurement matrix.Source: B. mmWave Compressive Channel Sensing · pp. 4–5
  • After training, the encoder’s kernels serve as measurement matrices, and its receive sensing vector becomes the precoder’s input for RF beam prediction.End-to-end training teaches the encoder in an unsupervised way to optimize the transmit and receive compressive measurements.Source: B. mmWave Compressive Channel Sensing · p. 5

C. Hybrid beam predictions

The precoder maps the receive measurement vector to indices of RF beamforming and combining vectors selected from codebooks. It predicts both sets of indices jointly as related tasks.

C. Hybrid beam predictions

  • RF beamforming and combining vectors are predicted as codebook indices in a multi-label classification problem.The focus is on RF vectors because their design requires large training overhead; once selected, the low-dimensional effective channel can be estimated to construct baseband precoders and combiners.Source: C. Hybrid beam predictions · p. 5
  • The precoder network has two fully connected layers followed by separate transmit-beam and receive-combiner output layers.Each output dimension equals the cardinality of its corresponding codebook, so candidate beams correspond to classes.Source: C. Hybrid beam predictions · p. 5
  • Multi-task training treats RF precoding and combining as related tasks to account for their dependence.The network optimizes both tasks simultaneously.Source: C. Hybrid beam predictions · p. 5

D. Deep Learning Model Training and Prediction

The auto-precoder jointly optimizes channel measurements and predicts hybrid RF beams from the resulting sensing vectors. It is trained end-to-end on channel vectors and target RF beam labels, with a shared loss and sample-wise accuracy evaluation.

D. Deep Learning Model Training and Prediction

  • Training uses channel vectors paired with target RF precoding and combining vectors calculated by the near-optimal Gram-Schmidt algorithm [11].Channel vectors are globally normalized so their largest absolute element equals one, and beam labels are represented as one-hot vectors.Source: D. Deep Learning Model Training and… · p. 5
  • Binary cross entropy is used for each beam-prediction task, and the total loss is the arithmetic mean of the transmit and receive losses.The two tasks are treated as equally important in the hybrid precoding/combining objective.Source: D. Deep Learning Model Training and… · p. 5
  • Sample-wise accuracy compares predicted and true label sets; with fixed label counts, precision and recall reduce to this measure.The overall sample-wise accuracy is averaged over the number of samples.Source: D. Deep Learning Model Training and… · p. 5
  • The network jointly optimizes transmitter and receiver measurement vectors to focus sensing on promising directions and predicts RF beams directly from the measurements.The measurement vectors are weights of the channel encoder’s two convolutional layers; beam prediction is performed by the precoder network.Source: D. Deep Learning Model Training and… · p. 5

V. SIMULATION RESULTS

The paper evaluates its direct hybrid precoding design using realistic 3D ray-tracing simulations.

V. SIMULATION RESULTS

  • The evaluation studies the performance of the proposed deep-learning-based direct hybrid precoding design.The simulations use realistic 3D ray tracing.Source: §V · p. 6
  • Realistic 3D ray-tracing simulations provide the setting for the performance evaluation.The passage specifies the simulation approach but no results.Source: §V · p. 6
  • The evaluated approach is the proposed deep-learning-based direct hybrid precoding design.The supplied passage identifies the evaluation subject, not its outcomes.Source: §V · p. 6

A. Dataset and Training

The evaluation uses a DeepMIMO outdoor uplink dataset with 64 antennas and three RF chains at each end. With four measurements per side, the proposed approach nearly matches the perfect-channel upper bound using 16 pilots.

A. Dataset and Training

  • The DeepMIMO dataset uses BS 4 in outdoor scenario O1, users in rows R1200–R1500, and an uplink setup.Both ends use 64 antennas and three RF chains; noisy channels are paired with target beam indices generated using the near-optimal Gram-Schmidt algorithm [11].Source: A. Dataset and Training · p. 6
  • The model is trained on the constructed dataset with cross-entropy loss, using Adam with momentum 0.5, batch size 512, and learning rate 0.005.The implementation uses Keras with a Theano backend.Source: A. Dataset and Training · p. 6

B. Achievable Rates

  • Achievable rate is calculated from predicted RF precoding and combining indices using the baseband design, then compared with rates obtained using perfect channel knowledge.The perfect-knowledge comparison uses the precoding and combining design described in Section V-A.Source: B. Achievable Rates · p. 6
  • 4 measurements at each end (16 pilots) achieve nearly the same spectral efficiency as the perfect-channel upper bound.The comparison is against 4096 pilots for exhaustive search and approximately 300–400 for compressive-sensing solutions.Source: Figure 4 · p. 6, B. Achievable Rates · p. 6
  • The rate comparison varies total transmit power and includes the proposed approach’s results for 2, 4, and 8 channel measurements at each end.The figure also compares rates with an upper bound based on perfect channel knowledge.Source: B. Achievable Rates · p. 6, Figure 4 · p. 6

C. Sample-Wise Accuracy

With four or eight channel measurements, the model predicts the exact three transmit and three receive beams with nearly 90% sample-wise accuracy. The conclusion describes the auto-precoder as combining learned channel sensing with direct RF beam prediction.

C. Sample-Wise Accuracy

  • Nearly 90% sample-wise accuracy is reached for predicting the exact three transmit and three receive beams with four or eight channel measurements.The table reports beam-index prediction accuracy versus SNR; transmit and receive accuracy are reported as almost the same.Source: Table II · p. 7, C. Sample-Wise Accuracy · p. 7
  • Transmit and receive beam prediction accuracies are almost equal, consistent with the model treating both tasks as equally important during training.Sample-wise accuracy measures whether the predicted set of RF beams is correct.Source: C. Sample-Wise Accuracy · pp. 6–7

VI. CONCLUSION

  • The auto-precoder combines a channel encoder that learns sensing vectors with a precoder network that predicts RF beams from the received sensing vector.The conclusion states that the design accounts for RF-chain constraints and uses complex-valued neural networks.Source: §VI · p. 7
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