Diffusion-based Generative Prior for Low-Complexity MIMO Channel Estimation

Diffusion-based Generative Prior for Low-Complexity MIMO Channel Estimation

2024 | Benedikt Fesl, Michael Baur, Florian Strasser, Michael Joham, Wolfgang Utschick
This paper proposes a novel channel estimator based on diffusion models (DMs), which are currently among the top-rated generative models. The proposed estimator uses a lightweight convolutional neural network (CNN) with positional embedding of the signal-to-noise ratio (SNR) information to learn the channel distribution in the sparse angular domain. This approach reduces computational complexity and memory overhead compared to existing generative prior-based estimators. The estimator avoids stochastic resampling and truncates reverse diffusion steps that account for lower SNR than the given pilot observation, resulting in a low-complexity and memory-efficient estimator. Numerical results show that the proposed DM-based estimator outperforms state-of-the-art generative prior-based channel estimators. Generative models have shown great success in learning complex data distributions and leveraging this prior information for wireless communication applications. The development of advanced channel estimation methodologies has relied on state-of-the-art generative models such as Gaussian mixture models (GMMs), mixture of factor analyzers (MFAs), generative adversarial networks (GANs), and variational autoencoders (VAEs). Recently, diffusion models (DMs) and score-based models have been identified as the most powerful generative models. However, their high computational overhead makes them difficult to apply in real-time applications like channel estimation. DMs have been used in wireless communications, such as for channel coding and joint source-channel coding. However, the approach of using a score-based model for channel estimation has several disadvantages, including a high number of network parameters and a large number of reverse steps. A deterministic denoising strategy utilizing a DM, where the observation's SNR level is matched with the corresponding timestep of the DM, drastically reduces the necessary number of reverse steps without requiring resampling. This strategy is asymptotically mean square error (MSE)-optimal if the number of total diffusion timesteps grows large. The proposed DM-based channel estimator is designed to leverage the structural properties of MIMO channels, such as sparsity in the angular/beamspace domain, to design lightweight neural networks. The estimator is shown to be asymptotically MSE-optimal and achieves strong denoising performance close to the utopian bound of the conditional mean estimator (CME). The proposed estimator is evaluated on different channel models, showing its versatile applicability and better estimation performance compared to existing techniques based on generative priors. The DM-based channel estimator is trained using a dataset transformed into the angular domain. The online estimation phase involves computing a least squares (LS) estimate, normalizing the observation's variance, transforming into the angular domain, and initializing the DM reverse process. The DM's reverse process is then iteratively applied to estimate the channel. The resulting estimate is transformed back into the spatial domain. The asymptotic optimality of the DM-based estimator is proven under certain assumptions. The estimator's performance is evaluated on two different channel models, showing that it outperforms state-of-the-art generThis paper proposes a novel channel estimator based on diffusion models (DMs), which are currently among the top-rated generative models. The proposed estimator uses a lightweight convolutional neural network (CNN) with positional embedding of the signal-to-noise ratio (SNR) information to learn the channel distribution in the sparse angular domain. This approach reduces computational complexity and memory overhead compared to existing generative prior-based estimators. The estimator avoids stochastic resampling and truncates reverse diffusion steps that account for lower SNR than the given pilot observation, resulting in a low-complexity and memory-efficient estimator. Numerical results show that the proposed DM-based estimator outperforms state-of-the-art generative prior-based channel estimators. Generative models have shown great success in learning complex data distributions and leveraging this prior information for wireless communication applications. The development of advanced channel estimation methodologies has relied on state-of-the-art generative models such as Gaussian mixture models (GMMs), mixture of factor analyzers (MFAs), generative adversarial networks (GANs), and variational autoencoders (VAEs). Recently, diffusion models (DMs) and score-based models have been identified as the most powerful generative models. However, their high computational overhead makes them difficult to apply in real-time applications like channel estimation. DMs have been used in wireless communications, such as for channel coding and joint source-channel coding. However, the approach of using a score-based model for channel estimation has several disadvantages, including a high number of network parameters and a large number of reverse steps. A deterministic denoising strategy utilizing a DM, where the observation's SNR level is matched with the corresponding timestep of the DM, drastically reduces the necessary number of reverse steps without requiring resampling. This strategy is asymptotically mean square error (MSE)-optimal if the number of total diffusion timesteps grows large. The proposed DM-based channel estimator is designed to leverage the structural properties of MIMO channels, such as sparsity in the angular/beamspace domain, to design lightweight neural networks. The estimator is shown to be asymptotically MSE-optimal and achieves strong denoising performance close to the utopian bound of the conditional mean estimator (CME). The proposed estimator is evaluated on different channel models, showing its versatile applicability and better estimation performance compared to existing techniques based on generative priors. The DM-based channel estimator is trained using a dataset transformed into the angular domain. The online estimation phase involves computing a least squares (LS) estimate, normalizing the observation's variance, transforming into the angular domain, and initializing the DM reverse process. The DM's reverse process is then iteratively applied to estimate the channel. The resulting estimate is transformed back into the spatial domain. The asymptotic optimality of the DM-based estimator is proven under certain assumptions. The estimator's performance is evaluated on two different channel models, showing that it outperforms state-of-the-art gener
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