In this letter, we consider a novel problem of blind source separation from observed magnitude-only measurements of their convolutive mixture in different communication systems. The problem setups correspond to a blind receiver architecture that either does not have phase information in the measurements or has excessive phase noise that cannot be easily recovered. We have formulated the problem as a matrix recovery problem by using the lifting technique and proposed a convex programming-based solution for joint recovery of the unknown channel and source signals. We have implemented the proposed solution using the alternating direction method of multipliers (ADMM). We have plotted a phase transition diagram for random Gaussian subspaces that shows, for s source signals each of length n and channel of length k, the minimum measurements required for exact recovery are \(m \ge 1.19 (sn+k) \log ^{2}m\) that is in accord with our theoretical result. We have also plotted a phase transition diagram for the case where the channel delays matrix is deterministic (consisting of the first k columns of the identity matrix) that shows the minimum measurements required for exact recovery are \(m \ge 2.86 (sn+k) \log ^{2}m\) which are higher than random subspaces.

在这封信中，我们考虑了一个新问题，即盲源分离与观察到的仅在不同通信系统中的卷积混合的幅度测量。问题设置对应于盲接收器架构，该架构要么在测量中没有相位信息，要么具有无法轻易恢复的过多相位噪声。我们通过使用提升技术将该问题表述为矩阵恢复问题，并提出了一种基于凸规划的解决方案，用于联合恢复未知通道和源信号。我们已经使用乘法器的交替方向方法 (ADMM) 实现了所提出的解决方案。我们绘制了随机高斯子空间的相变图，显示了对于s个源信号，每个长度为n和长度为k的通道，精确恢复所需的最小测量值为\(m \ge 1.19 (sn+k) \log ^{2}m\)，这与我们的理论结果一致。我们还绘制了通道延迟矩阵是确定性（由单位矩阵的前k列组成）的情况的相变图，显示精确恢复所需的最小测量值为\(m \ge 2.86 (sn+k ) \log ^{2}m\)高于随机子空间。