In massive grant-free transmission, joint user activity detection (UAD) and channel estimation (CE) is essential for data recovery at the receiver, which has been extensively researched in frequency-flat fading scenarios. However, in practical orthogonal frequency division multiplexing (OFDM)-based systems, frequency-selective fading (FSF) leads to a significant increase in the number of channel coefficients to be estimated, imposing new challenges for the design of joint UAD and CE algorithms. Therefore, this paper investigates joint UAD and CE for OFDM-based massive grant-free transmission over FSF channels. Firstly, by employing the discrete cosine transform (DCT), the joint estimation problem is formulated as the compressed sensing (CS) problem with the reduced dimension of the DCT-domain channel response vector. Then, based on the low-dimension sparse channel model, we develop a hybrid message passing (HMP) algorithm under the constrained Bethe free energy (BFE) minimization framework to achieve efficient joint UAD and CE. To deal with the lack of the DCT-domain prior information in practical scenarios, we parameterize it as the Cauchy distribution or the Laplacian distribution and learn their parameters by the proposed HMP algorithm. Numerical results confirm the superior joint UAD and CE performance of the proposed algorithm over FSF channels.

中文翻译：

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基于 OFDM 的频率选择性衰落信道上的大规模无授权传输


在大规模无授权传输中，联合用户活动检测（UAD）和信道估计（CE）对于接收器处的数据恢复至关重要，这在频率平坦衰落场景中已得到广泛研究。然而，在实际的基于正交频分复用（OFDM）的系统中，频率选择性衰落（FSF）导致需要估计的信道系数数量显着增加，给联合UAD和CE算法的设计带来了新的挑战。因此，本文研究了联合 UAD 和 CE，用于 FSF 信道上基于 OFDM 的大规模无授权传输。首先，通过采用离散余弦变换（DCT），联合估计问题被表述为具有DCT域信道响应向量的降维的压缩感知（CS）问题。然后，基于低维稀疏信道模型，我们在约束Bethe自由能（BFE）最小化框架下开发了混合消息传递（HMP）算法，以实现高效的联合UAD和CE。为了解决实际场景中 DCT 域先验信息的缺乏，我们将其参数化为柯西分布或拉普拉斯分布，并通过所提出的 HMP 算法学习它们的参数。数值结果证实了所提出的算法在 FSF 通道上具有优越的联合 UAD 和 CE 性能。