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Deep Learning for TDD and FDD Massive MIMO: Mapping Channels in Space and Frequency

Muhammad Alrabeiah, Ahmed Alkhateeb

arXiv:1905.03761v2cs.ITeess.SP

TL;DR

Massive MIMO channel acquisition can incur substantial training, feedback, and fronthaul overhead, motivating whether channels can be mapped across antenna sets and frequency bands. The paper proves existence under a bijective position-to-channel condition and uses deep neural networks to learn the mapping. Simulations show strong achievable-rate performance from mapped channels with only a subset of antennas.

  • Problem

    Massive MIMO requires channel knowledge across many antennas, creating training, feedback, and fronthaul overhead; prior frequency-transfer methods rely on imperfectly resolved spatial parameters.

  • Method

    The paper proves channel-mapping existence under a bijective mapping from candidate user positions to first-set channels, then trains deep neural networks to approximate the mapping.

  • Results

    With 4 antennas, about 6% of 64, predicted downlink channels achieve more than 4 bits/sec/Hz and come within 7% of the upper bound; the gap approaches the upper bound with 8 antennas.

  • Takeaways & Limitations

    Channel mapping can reduce channel-training, feedback, and fronthaul overhead in co-located, distributed, and cell-free massive MIMO systems.

Abstract

from arXiv · show

Can we map the channels at one set of antennas and one frequency band to the channels at another set of antennas---possibly at a different location and a different frequency band? If this channel-to-channel mapping is possible, we can expect dramatic gains for massive MIMO systems. For example, in FDD massive MIMO, the uplink channels can be mapped to the downlink channels or the downlink channels at one subset of antennas can be mapped to the downlink channels at all the other antennas. This can significantly reduce (or even eliminate) the downlink training/feedback overhead. In the context of cell-free/distributed massive MIMO systems, this channel mapping can be leveraged to reduce the fronthaul signaling overhead as only the channels at a subset of the distributed terminals need to be fed to the central unit which can map them to the channels at all the other terminals. This mapping can also find interesting applications in mmWave beam prediction, MIMO radar, and massive MIMO based positioning. In this paper, we introduce the new concept of channel mapping in space and frequency, where the channels at one set of antennas and one frequency band are mapped to the channels at another set of antennas and frequency band. First, we prove that this channel-to-channel mapping function exists under the condition that the mapping from the candidate user positions to the channels at the first set of antennas is bijective; a condition that can be achieved with high probability in several practical MIMO communication scenarios. Then, we note that the channel-to-channel mapping function, even if it exists, is typically unknown and very hard to characterize analytically as it heavily depends on the various elements of the surrounding environment. With this motivation, we propose to leverage the powerful learning capabilities of deep neural networks ....

I. INTRODUCTION

The paper introduces channel mapping across antenna sets and frequency bands to reduce channel-acquisition overhead in massive MIMO. It establishes the mapping's existence under a bijectivity condition and proposes deep learning to model it despite environmental complexity.

  • Massive MIMO's antenna scaling requires channel knowledge, but training and feedback overhead can limit system scalability.
  • The proposed mapping can reduce downlink training and feedback in FDD systems and fronthaul signaling in TDD cell-free systems.Applications also include mmWave beam prediction, MIMO radar, and massive MIMO positioning.
  • Prior frequency-extrapolation methods estimate spatial parameters such as angles of arrival and path delays before constructing channels at another band.Their performance is limited by system and hardware capability to resolve those parameters.
  • Channel mapping uses channels at one antenna set and frequency band to predict channels at another set and frequency band.The general model allows the antenna sets and frequencies to be co-located, distributed, identical, or different.
  • The paper proves that a channel-to-channel mapping exists when candidate user positions map bijectively to channels at the first antenna set.It then uses deep neural networks to learn an approximate mapping from observed channel pairs.

II. SYSTEM AND CHANNEL MODELS

The system model maps a user's channel vector from antenna set M1 at frequency f1 to set M2 at frequency f2. The section formulates existence and modeling questions while allowing arbitrary relations between antenna sets and frequencies.

  • System Model: The model considers a user communicating with antenna set M1 at f1 or antenna set M2 at f2, without constraining their locations or frequencies.It includes shared antennas and the same-frequency case f1 = f2.
  • Channel Model: Each multipath channel depends on path distance, delay, complex gain, frequency, antenna gains, and scatterer properties.Path phase additionally depends on scatterer materials and wave incidence angles.
  • Channel Mapping Problem: The channel mapping problem asks whether hu,M1(f1) can estimate hu,M2(f2) for the same user.The paper separately poses existence and modeling problems for the mapping function ΦM1,f1→M2,f2(.).
  • Motivation: If the mapping is available, only one antenna subset needs channel estimation while its channels predict those at other antennas or frequencies.In cell-free systems, a subset can be fed to the central unit to reduce front-haul control overhead.
  • Problem Formulation: The paper next investigates mapping existence and deep-learning approaches for modeling the mapping function.

IV. THE EXISTENCE OF CHANNEL MAPPING

The paper establishes channel-to-channel mapping across antenna sets and frequencies when the first position-to-channel mapping is bijective. This existence result supports reduced training, feedback, and fronthaul overhead in several massive MIMO settings, while practical prediction errors remain possible.

  • Existence condition: Bijectiveness means every candidate user position has a unique channel vector at the first antenna set.Its likelihood depends on antenna placement, candidate locations, and the surrounding environment, and is reported to be high in many practical scenarios.
  • Existence condition: A channel-to-channel mapping exists when the position-to-channel mapping at the first antenna set is bijective.The mapping is constructed through channel-to-position inversion followed by position-to-channel mapping at the target set.
  • Scope: The mapping can connect channels across co-located or distributed antennas and across different frequencies.The general model imposes no required relationship between antenna sets or frequencies.
  • Applications: In FDD massive MIMO, uplink channels at a subset of antennas can map to downlink channels at all antennas, reducing training and feedback overhead.The special case uses M1 ⊆ M2 with uplink and downlink frequencies.
  • Applications: In TDD cell-free massive MIMO, forwarding channels from only a subset of distributed antennas can reduce channel feed-forward overhead to the central unit.The central unit maps the forwarded channels to those at the remaining antennas.
  • Practical considerations: Measurement noise, limited ADC bandwidth, and time-varying fading can introduce probabilistic channel-prediction error.The paper identifies evaluating these effects as an important future extension.

V. DEEP LEARNING BASED CHANNEL MAPPING: THE MAIN MOTIVATION

The channel-mapping function exists under a stated condition but is difficult to characterize analytically because it incorporates the communication environment. The paper therefore uses deep neural networks to approximate it from channel observations.

  • Motivation: The mapping is hard to characterize analytically because it convolves geometry, materials, and other aspects of the communication environment.The paper motivates a learned approximation rather than an explicit analytical characterization.
  • Approach: Deep neural networks are proposed to learn and approximate the channel-to-channel mapping function.The approach leverages neural networks as universal function approximators for complex functions.
  • Approach: The network takes the source channel vector as input and learns weights that approximate the target channel mapping from paired observations.Training data contain channel vectors at both antenna sets and frequencies.

VI. DEEP LEARNING BASED CHANNEL MAPPING IN CELL-FREE MASSIVE MIMO SYSTEMS

The paper applies deep-learning channel mapping to a cell-free, distributed massive MIMO system and structures the treatment around the system model, its application, and the learning model.

  • Section organization: The cell-free setup is modeled with distributed massive MIMO terminals connected to a central processing unit.The section first introduces the model, then explains channel-mapping operation and the proposed machine-learning model.
  • Section organization: The section presents the adopted cell-free model before describing how deep-learning channel mapping is applied.The detailed learning model is presented after the application procedure.

A. Cell-Free Massive MIMO Model

The cell-free model uses geographically distributed antennas and an OFDM uplink/downlink with potentially different center frequencies. Uplink and downlink signals are modeled with noise, power constraints, and conjugate beamforming.

  • System model: The system contains M geographically distributed antenna terminals connected to a central processing unit and uses K OFDM subcarriers.The uplink and downlink center frequencies, fUL and fDL, may differ.
  • Uplink: The uplink received signal is modeled per antenna and subcarrier for a user transmission, with additive receive noise and transmit power Pu.The subcarrier spacing is Δf = BW/K.
  • Downlink: The downlink model assumes joint transmission from all M antennas and uses total base-station transmit power PT.The downlink bandwidth is assumed equal to the uplink bandwidth for simplicity.
  • Beamforming: Conjugate beamforming sets each transmit weight proportional to the conjugate channel and normalizes the beamforming vector to unit norm.The normalization factor κ enforces the transmit-vector power constraint.
  • Performance metric: The downlink achievable rate is averaged over the K subcarriers and uses an SNR determined by PT, K, and the receive-noise variance.This rate follows the specified signal and beamforming model.

B. Proposed Channel Mapping with Deep Learning

The proposed system learns to map uplink channels at a subset of distributed antennas to downlink channels at all antennas, reducing training, feedback, and fronthaul overhead.

  • The central unit learns a mapping from uplink channels at antenna subset M1 to downlink channels at all M distributed antennas.The mapped channels may generally use a different frequency.
  • For an example with M = 64 antennas, only 4–8 antennas in M1 provide very good channel prediction quality while reducing training, feedback, and fronthaul overhead.
  • Learning mode: During learning mode, conventional uplink and downlink training acquires paired channels used to train the deep learning model.
  • Prediction mode: During prediction mode, one uplink pilot estimates channels at M1, which are fed to the central unit to predict downlink channels at all antennas.The predicted downlink channels are then used to design the downlink precoding matrix.

C. Deep Learning Model

The channel-mapping model uses masked space-frequency channel arrays, preprocessing, and supervised learning with a fully connected neural network trained by normalized mean squared error.

  • Neural Network Architecture: The proposed architecture is a fully connected multilayer network whose neurons access all outputs from the previous layer to learn spatial and frequency dependencies.
  • Neural Network Architecture: The network uses successive nonlinear transformations that compress the input into a lower-dimensional feature vector and project hidden features into the output space.ReLU nonlinearities follow the neurons in each layer.
  • Preprocessing: Inputs and outputs are centralized using the dataset mean and normalized to the interval [−1, 1].
  • Preprocessing: The model processes channel arrays organized across antenna space, subcarriers, and real/imaginary components, with selected antennas retained through masking.The masked array is flattened for the fully connected network.
  • Preprocessing: A binary mask selects antenna rows while preserving channel values across all subcarriers and both real and imaginary components.Element-wise multiplication produces the masked input array.
  • Model Training: Supervised training fits channel-array reconstruction using normalized mean squared error between the model output and desired response.The vectorized output and target each have length n, where n equals antennas multiplied by subcarriers.

VII. EXPERIMENTAL RESULTS AND ANALYSIS

The paper evaluates its deep-learning channel-mapping solution and illustrates its potential to reduce channel training and feedback overhead.

  • The experiments evaluate the proposed solution’s performance and potential gains for reducing channel training and feedback overhead.The evaluation covers the scenario, deep learning parameters, and simulation results.

A. Scenario and Dataset

The experiments use an indoor distributed massive MIMO ray-tracing scenario with 64 ceiling antennas, two user grids, and channels at 2.4 GHz and 2.5 GHz.

  • The adopted indoor distributed massive MIMO scenario is DeepMIMO ’I1’, generated using the Wireless InSite 3D ray-tracing simulator.
  • Users occupy two x-y grids positioned 1 m above the floor.
  • Channels are generated between every candidate user location and antenna terminal at the 2.4 GHz and 2.5 GHz operating frequencies.These frequencies emulate uplink and downlink carrier frequencies.
  • The generated dataset is shuffled and split into training and testing subsets with an 80%/20% ratio.The subsets train the deep learning model and evaluate the proposed solution.

B. Model Training and Testing

The proposed model is trained on channels from a randomly selected antenna subset and evaluated by predicting full downlink channels and achievable rates. Across single- and multipath settings, mapped channels approach the full-channel upper bound with relatively few antennas and training samples.

  • Model Training and Testing: The fully connected network uses four layers and is trained for about 17 epochs on approximately 121 thousand samples.Testing uses approximately 30 thousand unseen samples.
  • Model Training and Testing: The model maps uplink channels at the antenna subset M1 to full downlink channels, which are then used to construct conjugate beamforming vectors.The subset antennas are randomly chosen from the 64-antenna array.
  • Performance Evaluation: With 4 antennas, around 6% of the total, predicted channels achieve more than 4 bits/sec/Hz and come within 7% of the full-channel upper bound.The gap approaches the upper bound with 8 subset antennas; performance depends strongly on antenna selection when the subset is small.
  • Performance Evaluation: With 8 subset antennas, about 30% of the full training dataset is enough to approach the upper bound.The network is retrained for each dataset size and evaluated on a fixed-size test set.
  • Performance Evaluation: In multipath channels using the 5 strongest paths, predicted-channel rates converge very closely to the upper bound with only 8–16 antennas.The evaluation compares within-band mapping at 2.5 GHz with cross-band mapping from 2.4 GHz uplink channels to 2.5 GHz downlink channels.

VIII. CONCLUSION

The paper introduces channel mapping across antenna sets and frequency bands, proves when the mapping exists, and uses deep neural networks to learn it. Simulations indicate that a small antenna subset can efficiently predict channels for 64 distributed antennas while reducing training, feedback, and fronthaul overhead.

  • VIII. CONCLUSION: Channel mapping transfers channels from one antenna set and frequency band to another antenna set and frequency band.The antenna sets and frequencies need not have any particular relation.
  • VIII. CONCLUSION: The mapping function exists when user positions map bijectively to channels at the first antenna set, a condition often attainable in practical scenarios.The paper states this condition can be satisfied with high probability in several practical communication scenarios.
  • VIII. CONCLUSION: Deep neural networks are proposed to learn the complex channel-to-channel mapping shaped by environmental elements.The approach is applied to FDD/TDD cell-free massive MIMO systems.
  • VIII. CONCLUSION: For 64 distributed antennas, results show that channels from only 4–8 antennas can efficiently predict the remaining channels.The reported applications include reducing downlink training, feedback, and fronthaul signaling overhead.
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