Chapter 15: Compressed Sensing for Communications

Learning Objectives

• Formulate wireless channel estimation as a sparse recovery problem in the delay and angular domains, and justify pilot-overhead savings
• Explain massive-access activity detection as compressed sensing with user-specific pilot signatures and analyse ROC behaviour
• Connect DOA estimation to sparse recovery on an angular grid, contrast on-grid and off-grid methods, and state the atomic-norm formulation
• Use group sparsity and $\ell_{2,1}$-norm regularization to jointly estimate channels with shared support across subcarriers or antennas
• Describe hierarchical sparsity for massive-MIMO channels and its role in the unsourced random access and massive-MTC research lines of the CommIT group