Two convergence results for an alternation maximization procedure

Andresen and Spokoiny's (2013) ``critical dimension in semiparametric estimation`` provide a technique for the finite sample analysis of profile M-estimators. This paper uses very similar ideas to derive two convergence results for the alternating procedure to approximate the maximizer of random functionals such as the realized log likelihood in MLE estimation. We manage to show that the sequence attains the same deviation properties as shown for the profile M-estimator in Andresen and Spokoiny (2013), i.e. a finite sample Wilks and Fisher theorem. Further under slightly stronger smoothness constraints on the random functional we can show nearly linear convergence to the global maximizer if the starting point for the procedure is well chosen

Downlink Power Control in User-Centric and Cell-Free Massive MIMO Wireless Networks

Recently, the so-called cell-free Massive MIMO architecture has been introduced, wherein a very large number of distributed access points (APs) simultaneously and jointly serve a much smaller number of mobile stations (MSs). A variant of the cell-free technique is the user-centric approach, wherein each AP just decodes the MSs that it receives with the largest power. This paper considers both the cell-free and user-centric approaches, and, using an interplay of sequential optimization and alternating optimization, derives downlink power-control algorithms aimed at maximizing either the minimum users' SINR (to ensure fairness), or the system sum-rate. Numerical results show the effectiveness of the proposed algorithms, as well as that the user-centric approach generally outperforms the CF one.Comment: presented at the 28th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE PIMRC 2017), Montreal (CA), October 201

On best rank one approximation of tensors

In this paper we suggest a new algorithm for the computation of a best rank one approximation of tensors, called alternating singular value decomposition. This method is based on the computation of maximal singular values and the corresponding singular vectors of matrices. We also introduce a modification for this method and the alternating least squares method, which ensures that alternating iterations will always converge to a semi-maximal point. (A critical point in several vector variables is semi-maximal if it is maximal with respect to each vector variable, while other vector variables are kept fixed.) We present several numerical examples that illustrate the computational performance of the new method in comparison to the alternating least square method.Comment: 17 pages and 6 figure