Information Theory and Reliable Communication

A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison across architectural alternatives of modularized network design. Decomposition theory naturally provides the mathematical language to build an analytic foundation for the design of modularized and distributed control of networks. In this tutorial paper, we first review the basics of convexity, Lagrange duality, distributed subgradient method, Jacobi and Gauss-Seidel iterations, and implication of different time scales of variable updates. Then, we introduce primal, dual, indirect, partial, and hierarchical decompositions, focusing on network utility maximization problem formulations and the meanings of primal and dual decompositions in terms of network architectures. Finally, we present recent examples on: systematic search for alternative decompositions; decoupling techniques for coupled objective functions; and decoupling techniques for coupled constraint sets that are not readily decomposable

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A tutorial on decomposition methods for network utility maximization

Sphere Packings, Lattices and Groups

Generalized Linear Models (2nd ed.)

This paper considers a multi-cell multiple antenna system with precoding used at the base stations for downlink transmission. Channel state information (CSI) is essential for precoding at the base stations. An effective technique for obtaining this CSI is time-division duplex (TDD) operation where uplink training in conjunction with reciprocity simultaneously provides the base stations with downlink as well as uplink channel estimates. This paper mathematically characterizes the impact that uplink training has on the performance of such multi-cell multiple antenna systems. When non-orthogonal training sequences are used for uplink training, the paper shows that the precoding matrix used by the base station in one cell becomes corrupted by the channel between that base station and the users in other cells in an undesirable manner. This paper analyzes this fundamental problem of pilot contamination in multi-cell systems. Furthermore, it develops a new multi-cell MMSE-based precoding method that mitigates this problem. In addition to being linear, this precoding method has a simple closed-form expression that results from an intuitive optimization. Numerical results show significant performance gains compared to certain popular single-cell precoding methods.

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Pilot Contamination and Precoding in Multi-Cell TDD Systems

Multiple-input multiple-output (MIMO) technology constitutes a breakthrough in the design of wireless communications systems, and is already at the core of several wireless standards. Exploiting multipath scattering, MIMO techniques deliver significant performance enhancements in terms of data transmission rate and interference reduction. This book is a detailed introduction to the analysis and design of MIMO wireless systems. Beginning with an overview of MIMO technology, the authors then examine the fundamental capacity limits of MIMO systems. Transmitter design, including precoding and space-time coding, is then treated in depth, and the book closes with two chapters devoted to receiver design. Written by a team of leading experts, the book blends theoretical analysis with physical insights, and highlights a range of key design challenges. It can be used as a textbook for advanced courses on wireless communications, and will also appeal to researchers and practitioners working on MIMO wireless systems.

https://assets.cambridge.org/97805211/37096/frontmatter/9780521137096_frontmatter.pdf

MIMO Wireless Communications

Compressed sensing theory suggests that successful inversion of an image of the physical world from its modal parameters can be achieved at measurement dimensions far lower than the image dimension, provided that the image is sparse in an a priori known basis The assumed basis for sparsity typically corresponds to a gridding of the parameter space, eg, an DFT grid in spectrum analysis However, in reality no physical field is sparse in the DFT basis or in an a priori known basis No matter how finely we grid the parameter space the sources may not lie in the center of the grid cells and there is always mismatch between the assumed and the actual bases for sparsity In this paper, we study the sensitivity of compressed sensing (basis pursuit to be exact) to mismatch between the assumed and the actual sparsity bases Our mathematical analysis and numerical examples show that the performance of basis pursuit degrades considerably in the presence of basis mismatch

/pdf/sensitivity-to-basis-mismatch-in-compressed-sensing-2l8u3zva29.pdf

Sensitivity to basis mismatch in compressed sensing

Compressed Sensing aims to capture attributes of k-sparse signals using very few measurements. In the standard compressed sensing paradigm, the N × C measurement matrix ? is required to act as a near isometry on the set of all k-sparse signals (restricted isometry property or RIP). Although it is known that certain probabilistic processes generate N × C matrices that satisfy RIP with high probability, there is no practical algorithm for verifying whether a given sensing matrix ? has this property, crucial for the feasibility of the standard recovery algorithms. In contrast, this paper provides simple criteria that guarantee that a deterministic sensing matrix satisfying these criteria acts as a near isometry on an overwhelming majority of k-sparse signals; in particular, most such signals have a unique representation in the measurement domain. Probability still plays a critical role, but it enters the signal model rather than the construction of the sensing matrix. An essential element in our construction is that we require the columns of the sensing matrix to form a group under pointwise multiplication. The construction allows recovery methods for which the expected performance is sub-linear in C, and only quadratic in N, as compared to the super-linear complexity in C of the Basis Pursuit or Matching Pursuit algorithms; the focus on expected performance is more typical of mainstream signal processing than the worst case analysis that prevails in standard compressed sensing. Our framework encompasses many families of deterministic sensing matrices, including those formed from discrete chirps, Delsarte-Goethals codes, and extended BCH codes.

Construction of a Large Class of Deterministic Sensing Matrices That Satisfy a Statistical Isometry Property

https://www.ese.wustl.edu/~nehorai/MURI/publications/Applebaum_2009.pdf

Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery

Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any n-dimensional vector that is k-sparse can be fully recovered using O(klogn) measurements and only O(klogn) simple recovery iterations. In this paper, we improve upon this result by considering expander graphs with expansion coefficient beyond 3 / 4 and show that, with the same number of measurements, only O(k) recovery iterations are required, which is a significant improvement when n is large. In fact, full recovery can be accomplished by at most 2k very simple iterations. The number of iterations can be reduced arbitrarily close to k, and the recovery algorithm can be implemented very efficiently using a simple priority queue with total recovery time O(nlog(n/k))). We also show that by tolerating a small penalty on the number of measurements, and not on the number of recovery iterations, one can use the efficient construction of a family of expander graphs to come up with explicit measurement matrices for this method. We compare our result with other recently developed expander-graph-based methods and argue that it compares favorably both in terms of the number of required measurements and in terms of the time complexity and the simplicity of recovery. Finally, we will show how our analysis extends to give a robust algorithm that finds the position and sign of the k significant elements of an almost k-sparse signal and then, using very simple optimization techniques, finds a k-sparse signal which is close to the best k-term approximation of the original signal.

/pdf/efficient-and-robust-compressed-sensing-using-optimized-4piiom2e8n.pdf

Robert Calderbank

Papers

MIMO Wireless Communications

Sensitivity to basis mismatch in compressed sensing

Construction of a Large Class of Deterministic Sensing Matrices That Satisfy a Statistical Isometry Property

Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery

Efficient and Robust Compressed Sensing Using Optimized Expander Graphs