Sparse MIMO-OFDM Channel Estimation via RKHS Regularization

TL;DR

The work addresses MIMO-OFDM channel estimation by leveraging band-sparsity in the delay-beamspace domain through regularization in a reproducing kernel Hilbert space. A Representer Theorem converts the infinite-dimensional RKHS problem into a finite one, which is further reduced via a low-rank surrogate and solved efficiently with a forward-backward splitting algorithm; a debiasing step and a data-driven deep-unfolding extension enhance performance. Empirical results on SionnaRT ray-traced channels show substantial NMSE improvements over LS and LMMSE baselines, with DD-RKHS achieving comparable or better accuracy at lower computational cost, and corresponding gains in downlink achievable rate. The approach offers a principled, scalable framework for high-performance channel estimation in massive MIMO-OFDM systems with practical relevance for next-generation wireless networks.

Abstract

We propose a method for channel estimation in multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) wireless communication systems. The method exploits the band-sparsity of wireless channels in the delay-beamspace domain by solving a regularized optimization problem in a reproducing kernel Hilbert space (RKHS). A suitable representer theorem allows us to transform the infinite-dimensional optimization problem into a finite-dimensional one, which we then approximate with a low-dimensional surrogate. We solve the resulting optimization problem using a forward-backward splitting (FBS)-based algorithm. By exploiting the problem's modulation structure, we achieve a computational complexity per iteration that is quasi-linear in the number of unknown variables. We also propose a data-driven deep-unfolding based extension to improve the performance at a reduced number of iterations. We evaluate our channel estimators on ray-traced channels generated with SionnaRT. The results show that our methods significantly outperform linear methods such as linear minimum mean squared error (LMMSE) channel estimation based on aggregate channel statistics, both in terms of raw estimation accuracy as well as in downstream performance.

Figures (11)

• Figure 1: Paths between transmitter (shown in red) and receiver (shown in blue). The dashed circles highlight clusters of paths with similar angles of arrival and delays.
• Figure 2: Comparison between a convex regularizer (red) and a non-convex one (blue). Both regularizers have a kink at $x=0$ that promotes sparsity. However, the convex regularizer incurs a penalty that increases linearly with its argument, and thus creates a bias towards the origin. In contrast, the non-convex regularizer's penalty is close to constant for large arguments, and thus causes a much smaller bias.
• Figure 3: Visualization of our channel simulation environment in Sionna RT. The BS is placed at the blue dot, with its array facing the white dot. The red dots correspond to randomly sampled user locations.
• Figure 4: Accuracy of different channel estimators, measured in normalized mean squared error (NMSE) as a function of signal-to-noise ratio (SNR).
• Figure 5: Single-user downlink achievable rates when channel estimates of different estimators are used for maximum ratio combining (MRC) precoding.

Theorems & Definitions (5)

• Theorem 1: Representer Theorem
• Remark 1: Tikhonov Regularization
• Remark 2: LASSO
• Remark 3: Elastic Net Regularization
• Lemma 2