Active Sensing for Reciprocal MIMO Channels

TL;DR

This work tackles the overhead of obtaining full channel state information for massive MIMO by proposing a learning-based active sensing framework that directly designs transmit precoders and receive combiners from interactive, reciprocity-based pilot exchanges. Using ping-pong pilots, recurrent neural networks summarize history into compact state representations, which are then mapped by dense networks to sensing beamformers and, ultimately, the data precoders and combiners for $N_{ m s}$ streams, applicable to both fully digital and hybrid architectures. The approach replaces conventional channel estimation with a data-driven policy that optimizes the $N_{ m s}$-dimensional subspace of interest, demonstrated to outperform LMMSE+SVD, vanilla power-iteration, and other baselines, especially in low-SNR regimes and with limited pilots, while providing interpretable alignment with the dominant singular vectors. The method also generalizes to realistic mmWave ray-tracing channels and maintains strong performance when trained on different channel models, underscoring its practical impact for scalable, low-overhead reciprocal MIMO systems.

Abstract

This paper addresses the design of transmit precoder and receive combiner matrices to support $N_{\rm s}$ independent data streams over a time-division duplex (TDD) point-to-point massive multiple-input multiple-output (MIMO) channel with either a fully digital or a hybrid structure. The optimal precoder and combiner design amounts to finding the top-$N_{\rm s}$ singular vectors of the channel matrix, but the explicit estimation of the entire high-dimensional channel would require significant pilot overhead. Alternatively, prior works suggest to find the precoding and combining matrices directly by exploiting channel reciprocity and by using the power iteration method, but its performance degrades in the low SNR regime. To tackle this challenging problem, this paper proposes a learning-based active sensing framework, where the transmitter and the receiver send pilots alternately using sensing beamformers that are actively designed as functions of previously received pilots. This is accomplished by using recurrent neural networks to summarize information from the historical observations into hidden state vectors, then using fully connected neural networks to learn the appropriate sensing beamformers in the next pilot stage and finally the transmit precoding and receive combiner matrices for data communications. Simulations demonstrate that the learning-based method outperforms existing approaches significantly and maintains superior performance even in the low SNR regime for both the fully digital and hybrid MIMO scenarios.

Figures (10)

• Figure 1: Ping-pong pilot transmission protocol of $L$ rounds for digital MIMO. The sensing matrices adaptively designed at agent A and agent B are highlighted as green (e.g., $\bm W_{0}^{\rm B}$) and blue (e.g., $\bm W_{1}^{\rm A}$), respectively.
• Figure 2: Proposed active sensing unit in the $\ell$-th pilot round for digital MIMO.
• Figure 3: Performance comparison under the Rayleigh fading channel model for a fully digital MIMO system with $M_{\rm t}=M_{\rm r}=64$.
• Figure 4: Achievable rate vs. pilot SNR.
• Figure 5: Performance comparison under a ray-tracing channel model for a fully digital MIMO system with $M_{\rm t}=64, M_{\rm r}=16$ and $N_{\rm s}=2$.