MIMO Channel as a Neural Function: Implicit Neural Representations for Extreme CSI Compression in Massive MIMO Systems

TL;DR

This work treats the CSI compression problem in the context of implicit neural representations as a neural function that maps the CSI coordinates (antenna number and subchannel) to the corresponding channel gains through a meta-learning algorithm.

Abstract

Acquiring and utilizing accurate channel state information (CSI) can significantly improve transmission performance, thereby holding a crucial role in realizing the potential advantages of massive multiple-input multiple-output (MIMO) technology. Current prevailing CSI feedback approaches improve precision by employing advanced deep-learning methods to learn representative CSI features for a subsequent compression process. Diverging from previous works, we treat the CSI compression problem in the context of implicit neural representations. Specifically, each CSI matrix is viewed as a neural function that maps the CSI coordinates (antenna number and subchannel) to the corresponding channel gains. Instead of transmitting the parameters of the implicit neural functions directly, we transmit modulations based on the CSI matrix derived through a meta-learning algorithm. Modulations are then applied to a shared base network to generate the elements of the CSI matrix. Modulations corresponding to the CSI matrix are quantized and entropy-coded to further reduce the communication bandwidth, thus achieving extreme CSI compression ratios. Numerical results show that our proposed approach achieves state-of-the-art performance and showcases flexibility in feedback strategies.

Figures (7)

• Figure 1: Illustration of alternative CSI feedback methodologies in a MIMO-OFDM system, involving the compression of the CSI matrix $\bm{H}$ into a codeword index $\bm{M}$, which is transmitted to the BS and used to reconstruct the estimated CSI matrix $\bm{\hat{H}}$. Top: Block diagram of feature learning-based methods guo2022overviewsun2020ancinetwen2018deepguo2020convolutionalcao2021lightweightsun2021lightweightji2021clnettang2022dilatedcui2022transnetchen2021deep, where a pair of encoder and decoder is adopted to learn a low-dimensional latent representation for compression. Middle: Illustration of the potential INR-based CSI compression scheme, where a neural network $f_{\bm{\theta}}$ is employed to map the CSI matrix from corresponding coordinates and thus $\bm{H}$ is converted into a neural function $f_{\bm{\theta}}$ with the compressed feedback codewords $\bm{M}\triangleq\bm{\theta}$. Bottom: Illustration of the proposed CSI-INR scheme, where CSI data points are generated via a shared base network, and the specific information of each CSI instance is modulated into the base network as codeword $\bm{M}$.
• Figure 2: (a). Basic blocks of our CSI-INR structure, where each data point $\bm{H^i}$ is modulated into $\bm{M^i}$ to generate the modulation factors $\bm{\phi^i}\triangleq\left[ \bm{\phi^i_1},\cdots,\bm{\phi^i_{L_{t}}}\right]$, each element of which is defined as $\bm{\phi^i_k}\triangleq\left[\bm{\gamma^i_k}, {\bm{\eta^i_k}}\right]$, representing the modulation factors of $i$-th sample for the $k$-th layer of the base network. The FiLM modulation operations are employed with the above factors and denoted as $\bigotimes$. Modulations are operated over the intermediate feature output $\bm{E^i_k}$ of the base network, resulting in modulated features $\bm{F^i_k}$, to map the coordinate input $\bm{x}$ into the distinct CSI data $\bm{H^i}$. (b). The illustration of the training process of the CSI-INR scheme. Specifically, the network $\bm{\theta}$ is optimized through a meta-learning strategy, where $\bm{\theta}$ and $\bm{M}$ are frozen and optimized in turns until it converges into the optimal network parameters $\bm{\theta^*}$.
• Figure 3: Inner architecture of the CSI-INR model, where $\bigodot$ is the element-wise multiplication operation and $\bigoplus$ is the adding operation.
• Figure 4: The NMSE performance of different schemes over varying feedback dimensions.
• Figure 5: The rate-distortion performance of CSI-INR schemes across varying feedback lengths when the modulations are quantized with various bit widths. The data points on each curve denote the model performance across a range of quantization levels, ordered from highest ($14$ bits) to lowest ($3$ bits).

Theorems & Definitions (1)

• Lemma 3.1