CSI-PPPNet: One-Sided Deep CSI Feedback

• CSI-PPPNet is a one-sided deep learning framework for CSI feedback in massive MIMO-OFDM systems, decoupling the UE from the neural network.
• It employs a random linear projection at the UE and an iterative plug-and-play deep denoising process at the BS to achieve state-of-the-art NMSE improvements.
• The framework minimizes computational load at the UE by using a simple matrix multiplication while supporting arbitrary compression ratios with a single denoiser.

CSI-PPPNet is a one-sided, one-for-all deep learning framework for channel state information (CSI) feedback in massive multiple-input multiple-output (MIMO) systems utilizing orthogonal frequency division multiplexing (OFDM). It addresses the challenge of efficient downlink CSI acquisition at the base station (BS) with minimal computational and storage burden at the user equipment (UE). CSI-PPPNet decouples the deep learning (DL) model from the encoder side, relying on a simple random linear projection at the UE and iterative plug-and-play (PnP) deep denoising at the BS. A single denoiser network supports arbitrary compression ratios, achieving state-of-the-art performance with substantially reduced system complexity and deployment overhead (Chen et al., 2022, Guo et al., 2024).

1. System Model and Mathematical Foundations

CSI-PPPNet is designed for single-cell frequency division duplexing (FDD) massive MIMO–OFDM downlinks, where the BS employs a uniform linear array (ULA) with $N_t$ antennas and the UE has a single antenna. For $N_s$ OFDM subcarriers, the frequency-domain downlink CSI is represented by the matrix $\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$. Sparsity in the angular-delay domain is exploited via two-dimensional DFTs:

$$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$

$\mathbf F_s$ and $\mathbf F_t$ are unitary DFT matrices for subcarriers and antennas, respectively. Only the leading $N_d\ll N_s$ delay taps are retained, and the truncated matrix is stacked into a real vector, $\mathbf h\in\mathbb{R}^N$, with $N=2N_dN_t$.

At the UE, the high-dimensional CSI $\mathbf h$ is compressed using a random linear projection:

$N_s$0

where $N_s$1 and $N_s$2 models quantization or noise. The compression ratio is $N_s$3. The projection matrix $N_s$4 (or its seed) is shared between the UE and the BS, ensuring consistency.

2. Plug-and-Play Recovery and Denoiser Design

CSI recovery at the BS is formulated as a penalized least squares problem:

$N_s$5

where $N_s$6 regularizes the angular-delay structure and $N_s$7 tunes the tradeoff.

CSI-PPPNet adopts a plug-and-play (PnP) alternating minimization scheme, using an auxiliary variable and alternating between a gradient data step and a deep denoising step:

• Data (gradient) step:

$N_s$8

where $N_s$9 is a step size.

• Denoising (prior) step:

$\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$0

$\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$1 is a shallow CNN, replacing the proximal operator, and is trained on synthetic CSI with AWGN contamination. After a fixed number of iterations $\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$2, the output is taken as the reconstructed CSI.

The denoiser adopts an FFDNet-inspired architecture, operating on tensors of shape $\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$3, incorporates a pixel-(un)shuffle scheme, and concatenates a scalar noise-level $\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$4 as a feature channel. Eight convolutional layers are used (ReLU for the first, batch normalization and ReLU for six intermediates, Tanh for the final). The denoiser is trained using MSE loss normalized by the ground-truth Frobenius norm, optimized via Adam.

3. One-Sided, One-for-All Framework and Deployment

A central feature of CSI-PPPNet is the complete offloading of all DL operations to the BS:

• The UE stores only the random seed or index indicating the projection rows used (requiring negligible memory) and implements the linear map $\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$5.
• The BS maintains a single trained denoiser $\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$6 of roughly 175,000 parameters.
• The same denoiser supports all choices of $\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$7 (compression ratio) and all random projections, completely decoupling the DL model from the encoder and eliminating per-rate model training and delivery.
• During inference, the UE transmits $\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$8 and the seed/index $\tilde{\mathbf H}\in\mathbb{C}^{N_s\times N_t}$9 to the BS, which reconstructs $$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$0 using the plug-and-play loop and the corresponding measurement submatrix.
• No neural network is present at the UE.

This architecture avoids the interoperability, privacy, and joint-training impediments of two-sided approaches such as CsiNet or CsiNet+, and supports instant reconfiguration for different feedback overhead constraints (Chen et al., 2022, Guo et al., 2024).

4. Algorithmic Summary

The CSI-PPPNet BS-side recovery process can be summarized in pseudocode as follows:

$\mathbf F_t$5

$$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$1 is computed as a function of $$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$2 and the penalty parameter at iteration $$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$3. The initial estimate can also be refined with support selection and least-squares over the selected support.

5. Performance Analysis

Performance is benchmarked on simulated QuaDRiGa channels (3GPP TR 38.901) in indoor and urban macro (UMa) scenarios, each with $$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$4, $$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$5 ($$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$6). Key metrics include:

• Normalized mean squared error (NMSE):

$$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$7

• Correlation coefficient (CoS):

$$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$8

CSI-PPPNet establishes the following results:

Compression Ratio	CsiNet (two-sided)	CS-CsiNet (fixed)	CSI-PPPNet (one-for-all)
1/2	−10 dB	−9 dB	−16 dB
1/4	−8 dB	−7 dB	−12 dB
1/8	−6 dB	−5 dB	−9 dB
1/16	−4 dB	−3 dB	−6 dB

At $$\mathbf H = \mathbf F_s\,\tilde{\mathbf H}\,\mathbf F_t,\quad \mathbf H\in\mathbb{C}^{N_s\times N_t}$$9, CSI-PPPNet surpasses CsiNet by more than 5 dB (Guo et al., 2024).

Further, CSI-PPPNet provides:

• NMSE improvement over TVAL3 and single-ratio one-sided CNNs (CS-CsiNet, ReNet) for $\mathbf F_s$0
• Graceful NMSE degradation at low $\mathbf F_s$1, with two-sided networks only slightly lower at $\mathbf F_s$2 (at cost of multiple models at UEs)
• Matched-filter downlink rates within 1–2% of two-sided DL models; always above classical CS-based methods
• Robustness under 3–6 bit quantization; NMSE/CoS degrade only $\mathbf F_s$3–$\mathbf F_s$4 dB, outperforming CsiNet+ at moderate–high $\mathbf F_s$5
• Convergence within 6–10 iterations and visual CSI quality approaching oracle reconstructions in $\mathbf F_s$610 PnP steps

6. Model Size, Complexity, and Deployment Characteristics

CSI-PPPNet demonstrates marked reductions in model and memory footprint:

• UE model: 1 integer to encode $\mathbf F_s$7 (or projection seed); no neural network or decoder
• BS model: 175 K parameters (single denoiser for all $\mathbf F_s$8)
• By comparison, CsiNet requires ≈2 033 K at UE and ≈2 062 K at BS for each CR, and CS-CsiNet/ReNet require 2.1 M/14.9 M at BS per CR
• CSI-PPPNet thus uses just 4.3% of parameters of two-sided CsiNet while supporting all compression ratios simultaneously

BS-side computational complexity scales as $\mathbf F_s$9, where $\mathbf F_t$0 is the cost of a denoiser pass ($\mathbf F_t$1175 K parameters); $\mathbf F_t$2 suffices for practical convergence. The UE-side complexity is limited to a single matrix–vector multiplication.

Deployment advantages include:

• Elimination of joint training and cross-vendor model management
• Absence of per-rate encoder models at UEs
• Immediate support for different feedback overheads without model updates
• Enhanced privacy, as UE is agnostic to BS-side DL models

7. Limitations and Extensions

Identified limitations are:

• Iterative PnP reconstruction introduces additional latency compared to a one-pass decoder
• Convergence and stability are sensitive to step size, iteration count, and the spectrum of $\mathbf F_t$3
• Assumes perfect instantaneous CSI at the UE; real-world estimation errors are not modeled
• Efficacy is contingent on close match between training data and operational channel statistics

Proposed extensions include:

• Joint “one-for-all” DL architectures incorporating channel coding, pilot/precoding design, and channel estimation
• Embedding temporal prediction to mitigate channel aging effects
• Exploration of learned or structured measurement matrices $\mathbf F_t$4 to exploit channel priors more efficiently
• Online PnP prior fine-tuning using small quantities of measured data to adapt to domain shifts

Further details and discussion appear in (Chen et al., 2022) and (Guo et al., 2024).