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1. Constrained Subspace Estimation via Convex Optimization

   Santamaria, I ; Via, J ; Kirby, M ; Marrinan, T ; Peterson, C ; Scharf, L. ( July 2017 , 2017 25th European Signal Processing Conference (EUSIPCO))

   Given a collection of M experimentally measured subspaces, and a model-based subspace, this paper addresses the problem of finding a subspace that approximates the collection, under the constraint that it intersects the model-based subspace in a predetermined number of dimensions. This constrained subspace estimation (CSE) problem arises in applications such as beamforming, where the model-based subspace encodes prior information about the direction-of-arrival of some sources impinging on the array. In this paper, we formulate the constrained subspace estimation (CSE) problem, and present an approximation based on a semidefinite relaxation (SDR) of this non-convex problem. The performance of the proposed CSE algorithm is demonstrated via numerical simulation, and its application to beamforming is also discussed. 

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2. Optimal Structured Principal Subspace Estimation: Metric Entropy and Minimax Rates

   Cai, T. Tony ; Li, Hongzhe ; Ma, Rong ( January 2021 , Journal of machine learning research)

   null (Ed.)

   Driven by a wide range of applications, several principal subspace estimation problems have been studied individually under different structural constraints. This paper presents a uni- fied framework for the statistical analysis of a general structured principal subspace estima- tion problem which includes as special cases sparse PCA/SVD, non-negative PCA/SVD, subspace constrained PCA/SVD, and spectral clustering. General minimax lower and up- per bounds are established to characterize the interplay between the information-geometric complexity of the constraint set for the principal subspaces, the signal-to-noise ratio (SNR), and the dimensionality. The results yield interesting phase transition phenomena concern- ing the rates of convergence as a function of the SNRs and the fundamental limit for consistent estimation. Applying the general results to the specific settings yields the mini- max rates of convergence for those problems, including the previous unknown optimal rates for sparse SVD, non-negative PCA/SVD and subspace constrained PCA/SVD. 

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3. Universal MIMO Jammer Mitigation via Secret Temporal Subspace Embeddings

   G. Marti ; C. Studer ( October 2023 , Conference record Asilomar Conference on Signals Systems Computers)

   MIMO processing enables jammer mitigation through spatial filtering, provided that the receiver knows the spatial signature of the jammer interference. Estimating this signature is easy for barrage jammers that transmit continuously and with static signature, but difficult for more sophisticated jammers: Smart jammers may deliberately suspend transmission when the receiver tries to estimate their spatial signature, they may use time-varying beamforming to continuously change their spatial signature, or they may stay mostly silent and jam only specific instants (e.g., transmission of control signals). To deal with such smart jammers, we propose MASH, the first method that indiscriminately mitigates all types of jammers: Assume that the transmitter and receiver share a common secret. Based on this secret, the transmitter embeds (with a linear time-domain transform) its signal in a secret subspace of a higher-dimensional space. The receiver applies a reciprocal linear transform to the receive signal, which (i) raises the legitimate transmit signal from its secret subspace and (ii) provably transforms any jammer into a barrage jammer, which makes estimation and mitigation via MIMO processing straightforward. We show the efficacy of MASH for data transmission in the massive multi-user MIMO uplink. 

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4. Envelopes for multivariate linear regression with linearly constrained coefficients

   https://doi.org/10.1111/sjos.12690  

   Cook, R. Dennis ; Forzani, Liliana ; Liu, Lan ( November 2023 , Scandinavian Journal of Statistics)

   A constrained multivariate linear model is a multivariate linear model with the columns of its coefficient matrix constrained to lie in a known subspace. This class of models includes those typically used to study growth curves and longitudinal data. Envelope methods have been proposed to improve the estimation efficiency in unconstrained multivariate linear models, but have not yet been developed for constrained models. We pursue that development in this article. We first compare the standard envelope estimator with the standard estimator arising from a constrained multivariate model in terms of bias and efficiency. To further improve efficiency, we propose a novel envelope estimator based on a constrained multivariate model. We show the advantage of our proposals by simulations and by studying the probiotic capacity to reduced Salmonella infection.

    

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5. State Space Collapse in Resource Allocation for Demand Dispatch and its Implications for Distributed Control Design

   https://doi.org/10.1109/TAC.2023.3293037  

   Mathias, Joel ; Meyn, Sean ; Moye, Robert ; Warrington, Joseph ( January 2023 , IEEE Transactions on Automatic Control)

   Alessandro Astolfi (Ed.)

   Demand dispatch is the science of extracting virtual energy storage through the automatic control of deferrable loads to provide balancing or regulation services to the grid, while maintaining consumer-end quality of service.The control of a large collection of heterogeneous loads is in part a resource allocation problem, since different classes of loads are more valuable for different services. The goal of this paper is to unveil the structure of the optimal solution to the resource allocation problem, and investigate short-term market implications. It is found that the marginal cost for each load class evolves in a two-dimensional subspace: spanned by a co-state process and its derivative. The resource allocation problem is recast to construct a dynamic competitive equilibrium model, in which the consumer utility is the negative of the cost of deviation from ideal QoS. It is found that a competitive equilibrium exists with the equilibrium price equal to the negative of an optimal co-state process. Moreover, the equilibrium price is different than what would be obtained based on the standard assumption that the consumer's utility is a function of power consumption. 

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