More Like this

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. 

   more » « less
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. 

   more » « less
3. 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)

   Abstract 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. 

   more » « less
4. Robust Multi-User Analog Beamforming in mmWave MIMO Systems

   Jiang, Lisi; Jafarkhani, Hamid (November 2018, IEEE Global Conference on Signal and Information Processing)

   In this paper, we propose a robust analog-only beamforming scheme for the downlink multi-user systems, which not only suppresses the interference and enhances the beamforming gain, but also provides robustness against imperfect channel state information (CSI). We strike a balance between the average beamforming gain and the inter-user interference by formulating a multi-objective problem. A probabilistic objective of leakage interference power is formulated to alleviate the effects of the channel estimation and feedback quantization errors. To solve the problem, we first use the sum-weighted method to transform the multi-objective problem into a single-objective problem. Then, we use the semi-definite programing technique to make the constantmagnitude constraints of the analog beamforming tractable. Simulation results show that our proposed robust beamformer can provide up to 120% improvement in the sum-rate compared to the beam selection method. 

   more » « less
5. Joint Jammer Mitigation and Data Detection for Smart, Distributed, and Multi-Antenna Jammers

   https://doi.org/10.1109/ICC45041.2023.10278647  

   Marti, Gian; Studer, Christoph (May 2023, IEEE International Conference on Communications)

   Multi-antenna (MIMO) processing is a promising solution to the problem of jammer mitigation. Existing methods mitigate the jammer based on an estimate of its subspace (or receive statistics) acquired through a dedicated training phase. This strategy has two main drawbacks: (i) it reduces the communication rate since no data can be transmitted during the training phase and (ii) it can be evaded by smart or multi-antenna jammers that are quiet during the training phase or that dynamically change their subspace through time-varying beamforming. To address these drawbacks, we propose joint jammer mitigation and data detection (JMD), a novel paradigm for MIMO jammer mitigation. The core idea is to estimate and remove the jammer interference subspace jointly with detecting the transmit data over multiple time slots. Doing so removes the need for a dedicated rate-reducing training period while enabling the mitigation of smart and dynamic multi-antenna jammers. We instantiate our paradigm with SANDMAN, a simple and practical algorithm for multi-user MIMO uplink JMD. Extensive simulations demonstrate the efficacy of JMD, and of SANDMAN in particular, for jammer mitigation. 

   more » « less