Joint Activity Detection and Channel Estimation for Massive Connectivity: Where Message Passing Meets Score-Based Generative Priors

TL;DR

The paper tackles the challenge of joint activity detection and channel estimation (JADCE) in massive connectivity scenarios for MIMO-OFDM grant-free uplinks. It introduces STMP-JADCE, a turbo message passing framework that threads a score based generative prior for the channel into a non separable, super node denoiser, enabling efficient Bayesian inference. Learning is performed via two score networks that provide the first order score for MMSE denoising and the second order score for variance estimation, trained with score matching across noise levels. Empirical results on CDL channel models show substantial NMSE gains and improved activity detection over state of the art baselines, with strong generalization across pilot designs and channel realizations, and data efficiency in training. This work demonstrates a principled integration of data driven priors into Bayesian inference for wireless sensing and communications, offering a scalable path to close to performance limits in JADCE with practical complexity.

Abstract

Massive connectivity supports the sporadic access of a vast number of devices without requiring prior permission from the base station (BS). In such scenarios, the BS must perform joint activity detection and channel estimation (JADCE) prior to data reception. Message-passing algorithms have emerged as a prominent solution for JADCE under a Bayesian inference framework. The existing message-passing algorithms, however, typically rely on some hand-crafted and overly simplistic priors of the wireless channel, leading to significant channel estimation errors and reduced activity detection accuracy. In this paper, we focus on the problem of JADCE in a multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) grant-free random access network. We propose to incorporate a more accurate channel prior learned by score-based generative models into message passing, so as to push towards the performance limit of JADCE. Specifically, we develop a novel turbo message passing (TMP) framework that models the entire channel matrix as a super node, rather than factorizing it element-wise. This design enables the seamless integration of score-based generative models as a minimum mean-squared error (MMSE) denoiser. The variance of the denoiser, which is essential in message passing, can also be learned through score-based generative models. Our approach, termed score-based TMP for JADCE (STMP-JADCE), takes full advantages of the powerful generative prior and, meanwhile, benefits from the fast convergence speed of message passing. Numerical simulations show that STMP-JADCE drastically enhances the activity detection and channel estimation performance compared to the state-of-the-art baseline algorithms.

Figures (13)

• Figure 1: System model of the MIMO-OFDM grant-free random access network.
• Figure 2: Factor graph representation of the joint posterior distribution $p(\mathbf{X}, \{\mathbf{H}_k\}_{k=1}^K, \{\alpha_k\}_{k=1}^K|\mathbf{Y})$. The variables are represented by the "variable nodes" that appear as circles, while the distributions are represented by the "factor nodes" that appear as black filled squares. We use different colors to differentiate $\mathbf{x}_m$ and $\mathbf{X}_k$ in vector-matrix reorganization.
• Figure 3: Diagram of the STMP-JADCE algorithm. The real and imaginary parts of the wireless channel matrix are concatenated as two feature channels (analogous to the RGB channels in images) when fed into the score networks. For the $k$-the device, the input tensor is constructed by stacking the real and imaginary parts of $\mathbf{H}_k$ into a tensor of size $(N,M,2)$. Across multiple devices, these tensors are further batched along the user dimension. In this figure, the first and the second devices are active, whereas the $K$-th device is inactive. Therefore, the input to the score networks takes the form of $\mathbf{H}_k^\mathtt{pri} = \mathbf{H}_{k} + \mathbf{W}_{k}$ for $k=1,2$, while $\mathbf{H}_K^\mathtt{pri}$ is a random noise. Note that, for brevity, we omitted the skip connections (dependences) from the prior messages to both the the posterior and extrinsic messages. Please refer to eqns. \ref{['eqn:stmp_post_mean']}, \ref{['eqn:stmp_post_var']}, \ref{['eqn:tau_ext']}, and \ref{['eqn:H_ext']} for the rigorous relationships.
• Figure 4: Comparison of the denoising performance under AWGN by different denoisers.
• Figure 5: NMSE in channel estimation versus the iteration number, where $\lambda = 0.05$, $T=30$, and the SNR is $10$ dB. Left: $K=800$ and we set the damping factor $\gamma = 0.8$ for all schemes; right: $K=1600$ and we set $\gamma = 0.6$ for all schemes.