Low-overhead Communications in IoT Networks: Structured Signal Processing Approaches

Preface
	Acknowledgements
Contents
Mathematical Notations
1 Introduction
	1.1 Low-Overhead Communications in IoT Networks
		1.1.1 Grant-Free Random Access
		1.1.2 Pilot-Free Communications
		1.1.3 Identification-Free Communications
	1.2 Structured Signal Processing
		1.2.1 Example: Compressed Sensing
		1.2.2 General Structured Signal Processing
	1.3 Outline
	References
2 Sparse Linear Model
	2.1 Joint Activity Detection and Channel Estimation
	2.2 Problem Formulation
		2.2.1 Single-Antenna Scenario
		2.2.2 Multiple-Antenna Scenario
	2.3 Convex Relaxation Approach
		2.3.1 Method: p-Norm Minimization
		2.3.2 Algorithm: Smoothed Primal-Dual First-Order Methods
		2.3.3 Analysis: Conic Integral Geometry
			2.3.3.1 Conic Integral Geometry for the Sparse Linear Model
			2.3.3.2 Computation and Estimation Trade-Offs
			2.3.3.3 Simulation Results
	2.4 Iterative Thresholding Algorithm
		2.4.1 Algorithm: Approximate Message Passing
		2.4.2 Analysis: State Evolution
			2.4.2.1 State Evolution
			2.4.2.2 Denoiser Designs
			2.4.2.3 Asymptotic Performance of Device Activity Detection
			2.4.2.4 Simulation Results
	2.5 Summary
	References
3 Blind Demixing
	3.1 Joint Data Decoding and Channel Estimation
	3.2 Problem Formulation
		3.2.1 Cyclic Convolution
		3.2.2 System Model
		3.2.3 Representation in the Fourier Domain
	3.3 Convex Relaxation Approach
		3.3.1 Method: Nuclear Norm Minimization
		3.3.2 Theoretical Analysis
	3.4 Nonconvex Approaches
		3.4.1 Regularized Wirtinger Flow
		3.4.2 Regularization-Free Wirtinger Flow
		3.4.3 Riemannian Optimization Algorithm
			3.4.3.1 An Example on Riemannian Optimization
			3.4.3.2 Riemannian Optimization on Product Manifolds for Blind Demixing
		3.4.4 Simulation Results
	3.5 Summary
	References
4 Sparse Blind Demixing
	4.1 Joint Device Activity Detection, Data Decoding, and Channel Estimation
	4.2 Problem Formulation
		4.2.1 Single-Antenna Scenario
		4.2.2 Multiple-Antenna Scenario
	4.3 Convex Relaxation Approach
	4.4 Difference-of-Convex-Functions (DC) Programming Approach
		4.4.1 Sparse and Low-Rank Optimization
		4.4.2 A DC Formulation for Rank Constraint
		4.4.3 DC Algorithm for Minimizing a DC Objective
		4.4.4 Simulations
	4.5 Smoothed Riemannian Optimization on Product Manifolds
		4.5.1 Optimization on Product Manifolds
		4.5.2 Smoothed Riemannian Optimization
		4.5.3 Simulation Results
	4.6 Summary
	References
5 Shuffled Linear Regression
	5.1 Joint Data Decoding and Device Identification
	5.2 Problem Formulation
	5.3 Maximum Likelihood Estimation Based Approaches
		5.3.1 Sorting Based Algorithms
		5.3.2 Approximation Algorithm
	5.4 Algebraic-Geometric Approach
		5.4.1 Eliminating Π via Symmetric Polynomials
		5.4.2 Theoretical Analysis
			5.4.2.1 Exact Data
			5.4.2.2 Corrupted Data
		5.4.3 Algebraically Initialized Expectation-Maximization
		5.4.4 Simulation Results
	5.5 Summary
	References
6 Learning Augmented Methods
	6.1 Structured Signal Processing Under a Generative Prior
	6.2 Joint Design of Measurement Matrix and Sparse Support Recovery
	6.3 Deep-Learning-Based AMP
		6.3.1 Learned AMP
		6.3.2 Learned Vector-AMP
		6.3.3 Learned ISTA for Group Row Sparsity
			6.3.3.1 Simulations Results
	6.4 Summary
	References
7 Conclusions and Discussions
	7.1 Summary
	7.2 Discussions
	References
8 Appendix
	8.1 Conic Integral Geometry
		8.1.1 The Kinematic Formula for Convex Cones
		8.1.2 Intrinsic Volumes and the Statistical Dimension
		8.1.3 The Approximate Kinematic Formula
		8.1.4 Computing the Statistical Dimension
	8.2 Proof of Proposition 2.1
	8.3 Proof of Theorem 3.3
		8.3.1 Proof of Lemma 8.4
	8.4 Theoretical Analysis of Wirtinger Flow with Random Initialization for Blind Demixing
	8.5 The Basic Concepts on Riemannian Optimization
	8.6 Proof of Theorem 3.4
	8.7 Basic Concepts in Algebraic–Geometric Theory
		8.7.1 Geometric Characterization of Dimension
	References