Efficient Multiple-Input–Multiple-Output Channel State Information Feedback: A Semantic-Knowledge-Base- Driven Approach

Abstract

Massive multiple-input–multiple-output (MIMO) systems encounter substantial challenges in relation to channel state information (CSI) feedback; this is particularly the case in frequency division duplex systems, where the lack of channel reciprocity necessitates high-dimensional CSI transmission, resulting in substantial feedback overheads. Most existing deep learning methods have improved compression efficiency but still suffer from high feedback overheads due to their transmission of entire compressed vectors. To address this, we propose SKBNet, an innovative semantic knowledge base (SKB)-driven framework for efficient MIMO CSI feedback. By sharing the SKB between the transmitter and receiver, SKBNet transmits only index values, significantly reducing feedback overheads while achieving efficient CSI compression and accurate reconstruction. The simulation results demonstrate that SKBNet outperforms many existing methods in normalized mean square error, cosine similarity, and feedback bit-count at various compression ratios. This framework offers a promising solution for low-overhead, high-precision CSI feedback for future semantic communication networks.

1. Introduction

1.1. Motivations

With the rapid development of massive multiple-input–multiple-output (MIMO) systems, traditional channel state information (CSI) feedback mechanisms face significant challenges. In frequency division duplex (FDD) systems, due to the lack of channel reciprocity, user equipment (UE) must estimate the downlink CSI and report it to the base station (BS). As the number of antennas increases, the dimensionality of the CSI also grows, resulting in prohibitively high feedback overheads [1]. This severely limits the scalability and efficiency of massive MIMO systems. Although compressed sensing (CS) algorithms [2,3,4] have been widely adopted to reduce feedback overhead, they still struggle to meet the performance demands in dynamic and complex wireless environments. The limitations of conventional CSI feedback approaches necessitate the exploration of more efficient and intelligent solutions.

To address these challenges, semantic communication [5] has emerged as a promising paradigm. Unlike traditional communication systems that primarily focus on the accurate transmission of raw bits, semantic communication emphasizes the extraction, processing, and transmission of the essential semantic features of information. By reducing redundancy and preserving the underlying meaning of the data, semantic communication enables more efficient transmission; while existing semantic communication systems have achieved remarkable advancements in handling high-level semantic information such as text [6,7,8], images [9,10,11], and videos [12,13], research on semantic communication at the physical layer, particularly for CSI, is still in its early stages [14]. CSI plays a pivotal role in physical layer semantic communication, providing detailed insights into wireless propagation environments, including fading characteristics, signal power, and interference levels. Accurate acquisition and processing of CSI are crucial for optimizing transmission strategies such as beamforming [15], precoding, resource allocation [16], and spatial multiplexing in massive MIMO systems. Furthermore, CSI is essential for channel equalization, which ensures the accurate recovery of the original transmitted signals. In the context of CSI feedback, physical layer semantic communication allows systems to capture and transmit the essential features of wireless channels rather than the entire high-dimensional data, thereby significantly reducing feedback overheads while maintaining high reconstruction accuracy at the BS.

Recent advances in deep learning (DL) offer novel solutions for CSI compression [17,18]. By leveraging deep neural networks (DNNs) to learn compact representations of high-dimensional data, researchers have successfully reduced CSI feedback overheads while preserving high-quality reconstruction. Particularly, the integration of semantic communication principles, along with advanced techniques such as semantic encoding and semantic knowledge base (SKB), has demonstrated great potential for further optimizing CSI feedback, paving the way for the development of next-generation intelligent communication systems.

1.2. Related Works

Deep-learning-based methods for MIMO CSI feedback have advanced compression and reconstruction efficiency. Wen et al. [19] introduced CsiNet in 2018, using an autoencoder to compress CSI into continuous representations, reducing feedback overheads. In 2020, Lu et al. [20] proposed CRNet with multi-resolution feature extraction, while Tolba et al. [21] developed DCGAN, enhancing robustness via generative adversarial networks. Cao et al. [22] presented ACCsiNet in 2021, optimizing feature extraction, and Cui et al. [23] introduced TransNet in 2022, leveraging Transformers for better performance. However, these methods do not consider compatibility with modern digital communication systems, which require the conversion of UE feedback latent vectors into finite-length bit sequences.

Recent studies have adopted VQ-VAE [24] to address this quantization need. Rizzello et al. [25] applied VQ-VAE to MIMO CSI feedback in 2023, introducing ordered vector quantization with a nested dropout layer to enable adaptive, variable-length feedback. However, this approach overlooks the computational complexity of comparing latent vectors to all codewords, which scale with codebook size. To this end, Shin et al. [26] proposed Shape-Gain VQ in 2024, reducing this complexity through shape-gain vector quantization, achieving better reconstruction with lower demands. Despite these advances, both non-VQ-based and VQ-based methods require transmitting the entire compressed latent vector, causing significant feedback overheads in massive MIMO systems with high-dimensional CSI.

In this paper, we propose SKBNet, the first framework to introduce an SKB into MIMO CSI feedback, addressing the feedback overhead challenge. By sharing the SKB between the transmitter and receiver, SKBNet uses vector quantization to compress CSI into discrete codewords and transmits only their indices, drastically reducing feedback overheads while maintaining high reconstruction accuracy. Unlike prior Shape-Gain VQ methods focusing on computational efficiency, SKBNet prioritizes communication efficiency, offering a balanced solution for low-overhead, high-precision CSI feedback in massive MIMO systems.

1.3. Contributions

In MIMO CSI feedback, existing methods often incur high feedback overheads by transmitting entire compressed latent vectors, posing a challenge for bandwidth-constrained massive MIMO systems. This paper introduces SKBNet, a novel SKB-driven framework that addresses this issue through efficient compression and low-overhead transmission. The main contributions of this work are as follows:

• We are the first to introduce an SKB into MIMO CSI feedback, leveraging a shared SKB between the transmitter and receiver to compress CSI into discrete codewords using vector quantization, transmitting only their indices and significantly reducing feedback overhead.
• We propose a systematic approach for analyzing feedback overheads in MIMO CSI systems, evaluating the impact of transmission mechanisms on communication efficiency in bandwidth-constrained scenarios.
• We conduct extensive experiments to validate the feasibility of SKBNet. Experimental results show that SKBNet outperforms many existing methods in reconstruction accuracy and feedback efficiency across various compression ratios. Additionally, we analyze the impact of SKB size on feedback bit-count (FBC), NMSE, and cosine similarity, revealing the relationship between codebook size and performance metrics.

The remainder of this paper is organized as follows: Section 2 presents the system model; Section 3 details our proposed SKB-enabled design for massive MIMO CSI feedback; Section 4 provides the feedback overhead analysis; Section 5 discusses the experimental setup and results, including a comparison with existing CSI feedback methods and the impact of codebook size; and Section 6 concludes the paper and outlines future research directions.

2. System Model

In this paper, we establish a system model for a single-cell FDD massive MIMO system focusing on CSI feedback. As shown in Figure 1, we consider a cell with a single BS equipped with $N_b$ antennas and a UE with $N_r$ antennas, assuming $N_r=1$ and $N_b\ge 1$. The system adopts orthogonal frequency division multiplexing (OFDM) with $N_f$ subcarriers. For FDD systems, the uplink and downlink transmissions operate on different frequency bands. Thus, the BS requires the UE to measure a channel state described via a vector $\mathbf{h}$ and feed it back to the BS. During downlink transmission, the signal received by a UE on the n-th subcarrier can be denoted as follows:

$${\mathbf{y}}_n={\tilde{\mathbf{h}}}_n^H{\mathbf{w}}_n{\mathbf{H}}_{a,n}^{\prime }+{\mathbf{q}}_n,$$

(1)

where ${\tilde{\mathbf{h}}}_n\in {\mathbb{C}}^{N_b\times 1}$ denotes the channel vector, ${\mathbf{w}}_n\in {\mathbb{C}}^{N_b\times 1}$ is the precoding vector, ${\mathbf{H}}_{a,n}^{\prime }\in \mathbb{C}$ represents the transmitted symbol, and ${\mathbf{q}}_n\in \mathbb{C}$ is the additive noise. Here, ${\mathbf{w}}_n$ is set based on ${\tilde{\mathbf{h}}}_n$ to achieve high-efficiency transmission. Therefore, accurate knowledge of ${\tilde{\mathbf{h}}}_n$ is crucial for optimal transmission performance. However, in FDD systems, ${\tilde{\mathbf{h}}}_n$ cannot be measured by the BS because the uplink and downlink operate on different frequency bands.

Typically, the UE sends the channel vectors for all $N_f$ subcarriers at once to the BS, which can be represented by a matrix in the spatial–frequency domain:

$$\tilde{\mathbf{H}}={[{\tilde{\mathbf{h}}}_1,{\tilde{\mathbf{h}}}_2,\dots ,{\tilde{\mathbf{h}}}_{N_f}]}^H.$$

(2)

The size of the CSI matrix, $\tilde{\mathbf{H}}$, which is $N_f\times N_b$, grows with the number of BS antennas $N_b$ in massive MIMO systems. This results in a prohibitively high feedback overheads that cannot be accommodated by the limited feedback link. Fortunately, the channel matrix exhibits sparsity in the angle-delay domain [19]. To reduce the feedback overhead, the CSI matrix $\tilde{\mathbf{H}}$ is commonly transformed from the spatial–frequency domain to the angle-delay domain using discrete Fourier transform (DFT):

$$\mathbf{H}={\mathbf{F}}_f\tilde{\mathbf{H}}{\mathbf{F}}_b^H,$$

(3)

where ${\mathbf{F}}_f$ and ${\mathbf{F}}_b$ are DFT matrices of dimensions $N_f\times N_f$ and $N_b\times N_b$, respectively. Notably, only the first $N_a(N_a<N_f)$ rows of $\mathbf{H}$ contain significant values, while the elements of the remaining $N_f-N_a$ rows are close to zero and can be safely ignored without substantial information loss. Consequently, the UE only needs to transmit the first $N_a$ rows of $\mathbf{H}$, denoted as ${\mathbf{H}}_a$, reducing the total feedback parameter count to $2N_a{N}_b$.

3. The Proposed Method

This section presents an SKB-driven MIMO CSI feedback method. As shown in Figure 2, the proposed approach leverages semantic feature extraction, quantization, and reconstruction to significantly reduce communication overhead while improving reconstruction accuracy. The framework integrates a transmitter, a receiver, and an SKB shared between them. All these modules are working collaboratively to minimize the differences between the transmitted and received ${\mathbf{H}}_a$ through a carefully designed training process. Below, we first introduce the components, and then present the processes of their training.

3.1. Component Design

As illustrated in Figure 2, the proposed method utilizes a framework that consists of three components: a DNN-based encoder $\mathcal{E}$ located at the UE, a DNN-based decoder $\mathcal{G}$ located at the BS, and an SKB shared between the encoder and decoder. Below, we explain these components.

Semantic knowledge base: The SKB is defined as a codebook comprising a set of vectors, ${\mathbf{Z}}_{\mathrm{SKB}}={\left\{{\mathbf{e}}_k\in {\mathbb{R}}^{n_q}\right\}}_{k=1}^B$, each consisting of $n_q$ elements. These vectors are trainable, to be explained in Section 3.2.

Encoder: The encoder first reshapes the angular channel matrix ${\mathbf{H}}_a$ to a tensor ${\mathbf{H}}_a^{\prime }\in {\mathbb{R}}^{N_a\times N_b\times 2}$, where the two channels, respectively, correspond to the real and imaginary parts of ${\mathbf{H}}_a$. Then, the encoder extracts the semantic feature of ${\mathbf{H}}_a^{\prime }$, denoted as $\mathbf{Z}\in {\mathbb{R}}^{h\times w\times n_q}$. That is,

$$\mathbf{Z}=\mathcal{E}\left({\mathbf{H}}_a^{\prime }\right).$$

(4)

Then, based on the ${\mathbf{Z}}_{\mathrm{SKB}}$, the encoder quantizes $\mathbf{Z}$ into ${\mathbf{Z}}^q\in {\mathbb{R}}^{h\times w\times n_q}$:

$${\mathbf{Z}}_q=q\left(\mathbf{Z}\right),$$

(5)

More specifically, let ${\mathbf{z}}_i$ and ${\mathbf{z}}_i^q$ denote the i-th vector of $\mathbf{Z}$ and ${\mathbf{Z}}^q$, respectively. For $i=1,...,h\times w$, ${\mathbf{z}}_i^q$ is obtained by

$${\mathbf{z}}_i^q={\mathbf{e}}_{k^{*}}\in {\mathbb{R}}^{n_q},\mathrm{where}{k}^{*}=arg\underset{k}{min}\left|\right|{\mathbf{z}}_i-{\mathbf{e}}_k{\left|\right|}_2.$$

(6)

Let $\mathcal{K}$ denote the indices $k^{*}$s for each quantization. The encoder converts these indices into a bit sequence and feeds them to the physical layer of the UE for transmission to the BS.

Decoder: Upon receiving $\mathcal{K}$, the BS retrieves ${\mathbf{Z}}_q$ according to ${\mathbf{Z}}_{\mathrm{SKB}}$. Then, its decoder performs tensor reconstruction as follows:

$${\widehat{\mathbf{H}}}_a^{\prime }=\mathcal{G}\left({\mathbf{Z}}_q\right).$$

(7)

Finally, the decoder reshapes ${\widehat{\mathbf{H}}}_a^{\prime }$ to ${\widehat{\mathbf{H}}}_a\in {\mathbb{R}}^{N_a\times N_b}$, which is very close to ${\mathbf{H}}_a$.

3.2. Training Procedure

The training process is primarily focused on optimizing a CNN-based semantic autoencoder with additional adversarial and perceptual loss functions to achieve high-quality CSI reconstruction. The training procedure involves three components: the autoencoder, the codebook, and the discriminator. The SKB (codebook) is a set of key–value pairs, where the keys are codewords and the values are features. During the quantization stage, the autoencoder compresses the CSI matrix into an integer index sequence $\mathbf{s}$, and the decoder $\mathcal{G}$ reconstructs the new feature map from the codebook. The overall loss is given by

$$L=L_1+L_2,$$

(8)

where $L_1$ is the loss function of the semantic autoencoder and $L_2$ is the loss of GAN.

In the loss function of the semantic autoencoder, to address the non-differentiability of the quantization process, which hinders gradient backpropagation, the gradient of the decoder is directly copied to the encoder. Consequently, the loss function for this process is expressed as:

$$L_1(\mathcal{E},\mathcal{G},\mathbf{Z})=L_{\mathrm{NMSE}}+\parallel \mathrm{sg}[\mathcal{E}\left({\mathbf{H}}_a^{\prime }\right)-{\mathbf{z}}_q]{\parallel }_2^2+{\parallel \mathrm{sg}\left[{\mathbf{z}}_q\right]-\mathcal{E}\left({\mathbf{H}}_a^{\prime }\right)\parallel }_2^2,$$

(9)

where $\mathrm{sg}[·]$ represents the stop-gradient operation. The autoencoder is trained to minimize the discrepancy between the reconstructed tensor $\widehat{{\mathbf{H}}_a^{\prime }}$ and the original tensor ${\mathbf{H}}_a^{\prime }$. For the CSI tensor, an NMSE-based loss function is adopted to constrain the difference between the original and reconstructed CSI tensor, which is given by

$$L_{\mathrm{NMSE}}=\mathbb{E}\left\{{\displaystyle \frac{\parallel {\mathbf{H}}_a^{\prime }-{\widehat{\mathbf{H}}}_a^{\prime }{\parallel }_2^2}{\parallel {\mathbf{H}}_a^{\prime }{\parallel }_2^2}}\right\}.$$

(10)

To enhance the realism of the reconstructed CSI tensor, a PatchGAN-based discriminator [27] is employed, introducing patch-level adversarial loss for discrimination. Furthermore, a perceptual loss is incorporated to replace conventional reconstruction loss. The adversarial component of the loss function is formulated as:

$$L_2(\{\mathcal{E},\mathcal{G},\mathbf{Z}\},\mathcal{D})=log\mathcal{D}\left({\mathbf{H}}_a^{\prime }\right)+log(1-\mathcal{D}\left({\widehat{\mathbf{H}}}_a^{\prime }\right)).$$

(11)

Here, it should be noted that the GAN is employed solely during the training phase to enhance the decoder’s reconstruction performance, and it is not involved in the inference stage, avoiding introducing additional computational burdens during deployment.

Remarks: Our design shares the fundamental computational structure of existing deep-learning-based CSI feedback methods, with two sources of additional operations: (i) the distance calculation in (5), which has a complexity of $O\left(B\right)$, where B is the codebook size; (ii) the codebook training processes in Section 3.2. The former adds negligible overheads compared to the convolutional operations in both encoder and decoder, while the latter is performed only once offline and does not affect deployments that require inference only. Nonetheless, as will be demonstrated in

Table 1. Performance comparison in terms of NMSE, $\rho$, and FBC.

Compression Ratio	1/16			1/64
Metrics	NMSE (dB)	$\mathbf{\rho }$	FBC (bits)	NMSE (dB)	$\mathbf{\rho }$	FBC (bits)
CsiNet [19]	−4.51	0.790	4096	−1.93	0.590	1024
CRNet [20]	−5.44	0.821	4096	−2.22	0.593	1024
DCGAN [21]	−8.07	-	4096	−4.01	-	1024
CF-FCFNN [28]	−9.12	0.920	4096	−7.25	0.880	1024
MRFNet [29]	−9.49	-	4096	−6.52	-	1024
ACCsiNet [22]	−11.76	0.944	4096	−7.11	0.876	1024
TransNet [23]	−7.82	-	4096	−2.62	-	1024
SKBNet	−12.45	0.969	704	−10.69	0.954	176

, this slight increase in computational complexity yields a significant reduction in feedback overheads while maintaining high reconstruction accuracy.

4. Feedback Overhead Analysis

This section calculates the feedback overhead of SKBNet. We focus on the feedback bit-count (FBC) which is measured in bits per channel instance.

Let $N_e$ denote the number of elements needed to be transmitted from a UE to a BS for each channel instance. Let $N_{\mathrm{bpe}}$ denote the number of bits representing each element. Then, we have

$$\mathrm{FBC}=N_e\times N_{\mathrm{bpe}}.$$

(12)

Recall that we reshape the ${\mathbf{H}}_a$ with $H_a\times H_b$ complex elements into a tensor ${\mathbf{H}}_a^{\prime }$ with $H_a\times H_b\times 2$ real elements and employ the encoder, $\mathcal{E}$, to compress it into $\mathbf{Z}$ with $h\times w$ vectors, each having $n_q$ elements. Then, employ ${\mathbf{Z}}_{\mathrm{SKB}}$ to quantize $\mathbf{Z}$ into ${\mathbf{Z}}_q$, with $h\times w$$n_q$-long vectors, as shown in (5). Instead of transmitting all elements belonging to ${\mathbf{Z}}_q$, we only need to transmit the indices, $\mathcal{K}$, of these vectors. Thus,

$$N_e=h\times w.$$

(13)

The number of bits used to represent each index in $\mathcal{K}$ depends on the number of vectors in ${\mathbf{Z}}_{\mathrm{SKB}}$. Thus, we have

$$N_{\mathrm{bpe}}={log}_{2}B.$$

(14)

5. Experiments

This section presents the experimental setup, evaluation metrics, and performance analysis for the proposed SKBNet, a semantic-knowledge-base-driven approach for massive MIMO CSI feedback. The evaluation demonstrates its effectiveness in outdoor scenarios at a 300 MHz frequency band, showcasing significant performance improvements over existing methods.

5.1. Experimental Setup

We evaluate the proposed SKBNet under the following experimental setup:

• Channel model configuration: We used an outdoor rural scenario operating in the 300 MHz frequency band. The BS is positioned at the center of a square area with each side spanning 400 meters, simulating an outdoor scenario. UEs are randomly scattered across this area for each sample. The BS is equipped with a Uniform Linear Array comprising 32 antennas ($N_b=32$), and the system is configured with 1024 subcarriers ($N_f=1024$). We generate the channel matrices using the default settings from COST2100 [30]. When transforming the channel matrix into the angle-delay domain, we retain the first 32 rows ($N_a=32$).
• Training implementation: The dataset is partitioned into 100,000 training samples, 30,000 validation samples, and 20,000 test samples, ensuring that all test samples are distinct from the training and validation sets. The models are trained for 1000 epochs with a batch size of 200. The simulation platform is implemented using PyTorch (https://pytorch.org/, accessed on 29 March 2025) and executed on an NVIDIA RTX 4090 GPU.
• CSI feedback assumption: In all experiments, we assume that CSI feedback is successfully delivered through reliable transmission mechanisms commonly employed in modern communication systems, allowing us to isolate and evaluate the fundamental compression-reconstruction performance of the proposed method.

5.2. Performance Evaluation

Now, we evaluate our proposed approach. We first outline our evaluation metrics, then compare the proposed approach with existing ones, and finally evaluate the impact of codebook size.

5.2.1. Evaluation Metrics

We assess the fidelity of the reconstructed CSI using these metrics:

• NMSE: NMSE quantifies the reconstruction accuracy by measuring the difference between the original angular-delay domain CSI matrix, ${\mathbf{H}}_a$, and its reconstructed counterpart, ${\widehat{\mathbf{H}}}_a$, defined as below. A lower NMSE indicates better reconstruction quality.

  $$\mathrm{NMSE}=\mathbb{E}\left\{{\displaystyle \frac{\parallel {\mathbf{H}}_a-{\widehat{\mathbf{H}}}_a{\parallel }_2^2}{\parallel {\mathbf{H}}_a{\parallel }_2^2}}\right\}.$$

  (15)
• Cosine similarity ($\rho$): In addition to NMSE, we employ the cosine similarity defined in [19] to measure the alignment between the original and reconstructed channel matrices. The cosine similarity is computed as

  $$\rho ={\displaystyle \frac{\langle {\mathbf{H}}_a,{\widehat{\mathbf{H}}}_a\rangle }{\parallel {\mathbf{H}}_a{\parallel }_2{\parallel {\widehat{\mathbf{H}}}_a\parallel }_2}},$$

  (16)

  where $\langle ·,·\rangle$ denotes the inner product. Higher values of $\rho$ indicate better preservation of angular-delay domain features.
• FBC: Recall that we have calculated the FBC of SKBNet in Section 4. Here, we would like to emphasize that the existing approaches directly transmit the compressed tensor for CSI feedback. Without loss of generality, we assume each tensor element is converted into 32 bits for transmission, as the data type of these elements is usually float32. Thus, for their FBC calculation,

  $$N_e=h\times w\times n_q\mathrm{and}{N}_{\mathrm{bpe}}=32.$$

  (17)

5.2.2. Comparison with Existing Methods

To demonstrate the superiority of our proposed SKBNet method, we conducted a comprehensive performance comparison with representative existing deep-learning-based CSI feedback methods, including CsiNet [19], CRNet [20], ACCsiNet [22], CF-FCFNN [28], MRFNet [29], DCGAN [21], and TransNet [23], under different CRs. According to [19], CR is defined as:

$$\begin{array}{cc}\hfill \mathrm{CR}& ={\displaystyle \frac{\mathrm{Size}\left(\mathbf{Z}\right)}{\mathrm{Size}\left({\mathbf{H}}_a^{\prime }\right)}}\hfill \\ \hfill & ={\displaystyle \frac{h\times w\times n_q}{H_a\times H_b\times 2}}.\hfill \end{array}$$

(18)

We perform experiments under two CRs, 1/16 and 1/64, in outdoor scenarios, as shown in Table 1. The performance metrics include normalized mean square error (NMSE), cosine similarity ($\rho$), and feedback bit-count (FBC). For SKBNet, all experiments are conducted with a fixed codebook size of $B=2048$.

Table 1 highlights two key trends in MIMO CSI feedback performance. First, as the CR decreases from 1/16 to 1/64, the NMSE and $\rho$ of all methods worsen, while their FBC decreases. The worsening of NMSE and $\rho$ occurs because the compressed feature vector becomes smaller at lower CRs, representing less information and reducing the ability to capture CSI details, which degrades reconstruction performance. The decrease in FBC results from the smaller number of elements transmitted as the feature vector size shrinks with lower compression. Second, SKBNet consistently outperforms all existing methods in NMSE and $\rho$ at both CRs, while requiring significantly lower FBC. This advantage stems from the SKB-driven framework, which leverages a shared SKB and index-based transmission to enhance reconstruction quality and minimize feedback overhead, even under stringent compression conditions. However, for SKBNet, there exists a trade-off relationship between performance and feedback overhead, as higher reconstruction accuracy at CR = 1/16 comes with increased FBC compared to CR = 1/64.

5.2.3. Impact of Codebook Size

In evaluating the performance of SKBNet for MIMO CSI feedback, the codebook size, denoted as B, plays a pivotal role. We analyze the effects of varying B at values of $2^8$, $2^9$, $2^{10}$, and $2^{11}$ on three critical metrics, FBC, NMSE, and $\rho$, with experiments conducted at CRs of 1/16 and 1/64.

Figure 3 illustrates the NMSE performance of SKBNet at CRs of 1/16 and 1/64 across different codebook sizes. A key observation is that as the codebook size B increases from $2^8$ to $2^{11}$, the NMSE initially worsens and then improves for both CRs. Specifically, the NMSE exhibits non-monotonic behavior, with a noticeable performance drop at $B=2^9$, which can be attributed to codebook collapse [31,32], where underutilized codewords during training reduce the model’s representation ability, leading to temporary degradation. Despite this, the overall trend shows that NMSE improves with larger codebook sizes, as a greater B enhances quantization granularity, allowing SKBNet to better capture the semantic features of CSI data and improve reconstruction accuracy.

Figure 4 illustrates the cosine similarity ($\rho$) performance of SKBNet at CRs of 1/16 and 1/64 across different codebook sizes. A key observation is that as the codebook size B increases from $2^8$ to $2^{11}$, $\rho$ initially decreases and then increases for both CRs, exhibiting non-monotonic behavior with a noticeable decline at $B=2^9$. This dip at $B=2^9$ mirrors the codebook collapse phenomenon observed in the NMSE analysis [31,32], where underutilized codewords during training reduce the model’s ability to preserve CSI structure, leading to temporary degradation. Despite this, the overall trend of improving $\rho$ with larger codebook sizes demonstrates that a greater B enhances quantization granularity, allowing SKBNet to better capture the semantic structure of CSI and improve structural similarity.

Figure 5 illustrates some observations regarding the FBC of SKBNet. First, at both CRs of 1/16 and 1/64, the FBC exhibits an upward trend as the codebook size B increases from $2^8$ to $2^{11}$. This is because a larger B increases the ${log}_{2}B$ term in the FBC formula ($\mathrm{FBC}=h\times w\times {log}_{2}B$), requiring more bits to represent each index. Second, for a given codebook size, the FBC at CR = 1/16 is higher than at CR = 1/64. This occurs because a lower CR results in a larger number of transmitted elements ($h\times w$), directly increasing the FBC. Third, as the codebook size increases, the FBC at CR = 1/16 grows faster than at CR = 1/64. This is due to the combined effect of a larger $h\times w$ at CR = 1/16 and the increasing ${log}_{2}B$, amplifying the growth rate of FBC compared to the smaller $h\times w$ at CR = 1/64.

6. Conclusions

We propose SKBNet, a semantic knowledge-driven framework for MIMO CSI feedback, addressing the challenge of high feedback overhead in FDD massive MIMO systems. By introducing a shared SKB and utilizing vector quantization with index-based transmission, SKBNet achieves efficient CSI compression, low-overhead feedback, and high-precision reconstruction, outperforming many existing deep learning methods in NMSE, cosine similarity, and feedback bit-count across various compression ratios. This work highlights the potential of SKB-sharing in advancing semantic communication networks. Future work will explore bandwidth–accuracy trade-offs, investigate performance under diverse SNR conditions, imperfect feedback scenarios, and non-ideal channel scenarios, conduct experiments across multiple datasets and scenarios, perform comparisons with the recent literature, quantify codebook size impacts on hardware resources, develop adaptive SKB maintenance strategies for channel time variation and device heterogeneity, and integrate dynamic codebook adaptation, multi-user scenarios, and channel noise to enhance SKBNet’s adaptability and robustness in real-world deployments.