Activity detection is an important task in the next generation grant-free
multiple access. While there are a number of existing algorithms designed for
this purpose, they mostly require precise information about the network, such
as large-scale fading coefficients, small-scale fading channel statistics,
noise variance at the access points, and user activity probability. Acquiring
these information would take a significant overhead and their estimated values
might not be accurate. This problem is even more severe in cell-free networks
as there are many of these parameters to be acquired. Therefore, this paper
sets out to investigate the activity detection problem without the
above-mentioned information. In order to handle so many unknown parameters,
this paper employs the Bayesian approach, where the unknown variables are
endowed with prior distributions which effectively act as regularizations.
Together with the likelihood function, a maximum a posteriori (MAP) estimator
and a variational inference algorithm are derived. Extensive simulations
demonstrate that the proposed methods, even without the knowledge of these
system parameters, perform better than existing state-of-the-art methods, such
as covariance-based and approximate message passing methods.

本文研究了在不需要网络信息的情况下进行活动检测的问题，并采用了贝叶斯方法，该方法使用先验分布作为正则化，结合似然函数，得出了一种最大后验估计器和变分推断算法。广泛的模拟结果表明，即使没有这些系统参数的知识，所提出的方法仍然优于现有的协方差 - based 和近似传递信息方法。

基于贝叶斯方法的无线全覆盖网络中的大规模连接活动检测

Activity Detection for Massive Connectivity in Cell-free Networks with  Unknown Large-scale Fading, Channel Statistics, Noise Variance, and Activity  Probability: A Bayesian Approach

In this paper we compare and contrast the behavior of the posterior
predictive distribution to the risk of the maximum a posteriori estimator for
the random features regression model in the overparameterized regime. We will
focus on the variance of the posterior predictive distribution (Bayesian model
average) and compare its asymptotics to that of the risk of the MAP estimator.
In the regime where the model dimensions grow faster than any constant multiple
of the number of samples, asymptotic agreement between these two quantities is
governed by the phase transition in the signal-to-noise ratio. They also
asymptotically agree with each other when the number of samples grow faster
than any constant multiple of model dimensions. Numerical simulations
illustrate finer distributional properties of the two quantities for finite
dimensions. We conjecture they have Gaussian fluctuations and exhibit similar
properties as found by previous authors in a Gaussian sequence model, which is
of independent theoretical interest.

本文研究了超参数区域内随机特征回归模型的后验预测分布的行为与最大后验估计风险的比较，证明当模型维度增长快于样本数的任何常数倍时，两者的演化存在信噪比的相变现象。