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Dilated Convolution based CSI Feedback Compression for Massive MIMO Systems

Shunpu Tang, Junjuan Xia, Lisheng Fan, Xianfu Lei, Wei Xu, Arumugam Nallanathan

arXiv:2106.04043v1cs.ITeess.SPmath.IT

TL;DR

FDD massive MIMO needs downlink CSI for base-station precoding, but large CSI matrices make feedback challenging. DCRNet uses dilated convolutions and redesigned encoder and decoder blocks for CSI compression and reconstruction. It achieves near-SOTA performance with lower computational complexity in the reported settings.

Abstract

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Although the frequency-division duplex (FDD) massive multiple-input multiple-output (MIMO) system can offer high spectral and energy efficiency, it requires to feedback the downlink channel state information (CSI) from users to the base station (BS), in order to fulfill the precoding design at the BS. However, the large dimension of CSI matrices in the massive MIMO system makes the CSI feedback very challenging, and it is urgent to compress the feedback CSI. To this end, this paper proposes a novel dilated convolution based CSI feedback network, namely DCRNet. Specifically, the dilated convolutions are used to enhance the receptive field (RF) of the proposed DCRNet without increasing the convolution size. Moreover, advanced encoder and decoder blocks are designed to improve the reconstruction performance and reduce computational complexity as well. Numerical results are presented to show the superiority of the proposed DCRNet over the conventional networks. In particular, the proposed DCRNet can achieve almost the state-of-the-arts (SOTA) performance with much lower floating point operations (FLOPs). The open source code and checkpoint of this work are available at https://github.com/recusant7/DCRNet.

I. INTRODUCTION

In FDD massive MIMO, users must return downlink CSI for base-station precoding, but large CSI matrices make feedback costly. The paper introduces DCRNet, while the feedback model transforms, compresses, and reconstructs CSI.

I. INTRODUCTION

  • Large CSI matrices make FDD feedback costly, while users also face limited transmit power and uplink bandwidth.The base station needs downlink CSI for precoding, but weak reciprocity makes it difficult to obtain directly.Source: §I · p. 1, §II · p. 1
  • Earlier deep-learning methods used larger convolutions to expand receptive fields, increasing computational complexity; DCRNet instead uses dilated convolutions and redesigned blocks.The paper reports near-SOTA performance with lower FLOPs.Source: §I · p. 1

II. CSI FEEDBACK IN MASSIVE MIMO SYSTEMS

  • The feedback model transforms CSI into angular and delay domains, retains the sparse, compressible component, and uses an encoder and decoder to transmit and reconstruct it.The stated objective is to minimize average reconstruction error.Source: §II · p. 2

III. DILATED CONVOLUTIONS BASED CSI FEEDBACK

This section introduces DCRNet’s structure and its dilated encoder and decoder blocks for extracting features from block-sparse CSI matrices.

III. DILATED CONVOLUTIONS BASED CSI FEEDBACK

  • DCRNet’s dilated encoder and decoder blocks are designed to extract features from block-sparse CSI matrices efficiently.Source: §III · p. 2

A. Structure of the proposed DCRNet

DCRNet uses a CNN-based autoencoder to compress CSI at the user and recover it at the base station. Its encoder and decoder combine convolutional processing with fully connected layers and reshaping.

A. Structure of the proposed DCRNet

  • DCRNet uses a dilated CNN-based autoencoder to extract spatially local correlations in CSI matrices.Source: A. Structure of the proposed DCRNet · p. 2
  • The encoder processes the real and imaginary CSI channels with a 5×5 head convolution and one encoder block, then compresses the flattened features into a codeword.Using one encoder block, rather than ACRNet’s two, reduces implementation complexity.Source: A. Structure of the proposed DCRNet · p. 2
  • At the base station, fully connected layers and reshaping restore the CSI dimensions before a 5×5 head convolution and two sequential dilated decoder blocks recover the information.Batch normalization and PReLU are appended to all convolutions.Source: A. Structure of the proposed DCRNet · p. 2

B. Critical design on dilated encoder and decoder blocks

DCRNet uses dilated convolutions to expand the receptive field without increasing convolution size, with encoder and decoder blocks as its main components.

B. Critical design on dilated encoder and decoder blocks

  • Dilated convolution samples input features at intervals set by rate d, and its effective kernel size grows with that rate.The operation is defined over a 2D input and convolution kernel.Source: B. Critical design on dilated encoder… · p. 2
  • For d > 1, dilated convolution provides a larger receptive field than a standard convolution of the same kernel size, enabling sparse sampling of block-sparse CSI.At d = 1, it reduces to standard convolution.Source: B. Critical design on dilated encoder… · p. 2
  • DCRNet’s encoder and decoder blocks are its main components, with the figure showing the network and block structures separately.Panels (a) and (b) show the encoder and decoder; panels (c) and (d) show their blocks.Source: Figure 2 · p. 3

1) Encoder block design:

The encoder block combines asymmetric dilated and standard convolutions to capture multi-scale CSI features while limiting computational complexity. Its dilated path reaches a 13×13 receptive field without the gridding effect described for equal-rate dilated convolutions.

1) Encoder block design:

  • The asymmetric 3×3 convolutions with dilation rates 1, 2, and 3 yield a 13×13 receptive field while avoiding the gridding effect.The paper says this receptive field equals that of CsiNet+ and the design decreases computational complexity.Source: 1) Encoder block design · p. 3
  • A parallel standard 3×3 convolution complements the dilated path, and concatenation combines their outputs into multi-resolution CSI features.The concatenated output has 4 × Na × Nt dimensions, then a 1×1 convolution reduces channels to 2; residual learning adds the input identity.Source: 1) Encoder block design · p. 3
  • Residual learning adds the input identity to the encoder block’s final 1×1 convolution output.The block concatenates the parallel-branch outputs before this convolution.Source: 1) Encoder block design · p. 3

2) Decoder block design:

The decoder uses parallel branches, dilated and group convolutions, and width expansion to balance reconstruction performance and computational complexity. Its evaluation uses COST 2100 samples from indoor and outdoor scenarios.

2) Decoder block design:

  • The decoder block has two parallel branches and an identity map; its first branch uses a 3×3 dilated convolution (d=2) to expand features to 8ρ, with ρ≥1 adjustable for devices with different computational capacities.Group convolutions use 3×1 and 1×3 DConvs with d=3.Source: 2) Decoder block design · p. 3
  • The second decoder branch uses group convolutions and width expansion; the two branches are concatenated and passed through a 1×1 convolution.The paper describes the wider-than-ACRNet decoder as having lower FLOPs and a fine trade-off between performance and computational complexity.Source: 2) Decoder block design · p. 3

1) Data generation:

  • The evaluation uses COST 2100 indoor 5.3GHz and outdoor 300MHz-bandwidth scenarios, with 100,000 training, 30,000 validation, and 20,000 test samples.The original 2 × 32 × 1024 CSI matrix is transformed to the angular-delay domain and truncated to 2 × 32 × 32.Source: 1) Data generation · p. 3

2) Training setting:

The training setup uses Kaiming initialization and Adam, with cosine annealing for the learning rate. Training uses 30 warm-up epochs and 2500 total epochs.

2) Training setting:

  • Weights for each convolution and fully connected layer use Kaiming initialization, and Adam updates the weights.Source: 2) Training setting · p. 3
  • Cosine annealing sets the learning rate, which ranges from γmin = 5e−5 to γmax = 2e−3.Source: 2) Training setting · p. 4
  • Training uses 30 warm-up epochs and 2500 total epochs for the learning-rate schedule.The schedule denotes the current learning rate as γt and t as the training-epoch index.Source: 2) Training setting · p. 4

3) Evaluation criteria:

The evaluation measures reconstruction with NMSE and also tracks FLOPs and parameter count. Across the reported scenarios and compression rates, DCRNet variants approach state-of-the-art performance with lower computational complexity.

3) Evaluation criteria:

  • NMSE evaluates reconstruction between the input and decoder-restored CSI matrices; the experiments also measure FLOPs and parameter count.Source: 3) Evaluation criteria · p. 4

B. Performance of the proposed DCRNet

C. Ablation experiments

The ablation compares dilated-convolution configurations at a compression rate of 1/16 and reports the strongest reconstruction performance when dilation is used in both encoder and decoder.

C. Ablation experiments

  • The ablation tests the effect of replacing dilated convolutions in both network blocks with standard convolutions, alongside an encoder-only dilation variant.Source: C. Ablation experiments · p. 5
  • At compression rate 1/16, joint use of dilated convolution in the encoder and decoder achieves the best reconstruction performance.Table II reports the NMSE comparison.Source: C. Ablation experiments · p. 5, Table II · p. 5
  • DCRNet-M1, which uses dilated convolution only in the encoder, outperforms the standard-convolution baseline.The authors attribute this result to the encoder's use of dilated convolution.Source: C. Ablation experiments · p. 5

V. CONCLUSIONS

The conclusion presents DCRNet as a dilated-convolution CSI-feedback network that increases receptive field while reducing computational complexity. Its lightweight variant is competitive, while its higher-performance variant approaches state-of-the-art reconstruction with lower complexity.

V. CONCLUSIONS

  • DCRNet uses dilated convolution to increase receptive field while reducing computational complexity.Source: §V · p. 5
  • DCRNet-1× outperforms the competitive lightweight networks when computational resources are limited.Source: §V · p. 5
  • DCRNet-10× achieves almost-SOTA reconstruction performance with much lower computational complexity than conventional networks.Source: §V · p. 5
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