Linear Precoding and Equalization for Network MIMO with Partial Cooperation

A cellular multiple-input multiple-output (MIMO) downlink system is studied in which each base station (BS) transmits to some of the users, so that each user receives its intended signal from a subset of the BSs. This scenario is referred to as network MIMO with partial cooperation, since only a subset of the BSs are able to coordinate their transmission towards any user. The focus of this paper is on the optimization of linear beamforming strategies at the BSs and at the users for network MIMO with partial cooperation. Individual power constraints at the BSs are enforced, along with constraints on the number of streams per user. It is first shown that the system is equivalent to a MIMO interference channel with generalized linear constraints (MIMO-IFC-GC). The problems of maximizing the sum-rate(SR) and minimizing the weighted sum mean square error (WSMSE) of the data estimates are non-convex, and suboptimal solutions with reasonable complexity need to be devised. Based on this, suboptimal techniques that aim at maximizing the sum-rate for the MIMO-IFC-GC are reviewed from recent literature and extended to the MIMO-IFC-GC where necessary. Novel designs that aim at minimizing the WSMSE are then proposed. Extensive numerical simulations are provided to compare the performance of the considered schemes for realistic cellular systems.Comment: 13 pages, 5 figures, published in IEEE Transactions on Vehicular Technology, June 201

Exponential Lower Bounds for Polytopes in Combinatorial Optimization

We solve a 20-year old problem posed by Yannakakis and prove that there exists no polynomial-size linear program (LP) whose associated polytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric. Moreover, we prove that this holds also for the cut polytope and the stable set polytope. These results were discovered through a new connection that we make between one-way quantum communication protocols and semidefinite programming reformulations of LPs.Comment: 19 pages, 4 figures. This version of the paper will appear in the Journal of the ACM. The earlier conference version in STOC'12 had the title "Linear vs. Semidefinite Extended Formulations: Exponential Separation and Strong Lower Bounds

Inference of Sparse Networks with Unobserved Variables. Application to Gene Regulatory Networks

Networks are a unifying framework for modeling complex systems and network inference problems are frequently encountered in many fields. Here, I develop and apply a generative approach to network inference (RCweb) for the case when the network is sparse and the latent (not observed) variables affect the observed ones. From all possible factor analysis (FA) decompositions explaining the variance in the data, RCweb selects the FA decomposition that is consistent with a sparse underlying network. The sparsity constraint is imposed by a novel method that significantly outperforms (in terms of accuracy, robustness to noise, complexity scaling, and computational efficiency) Bayesian methods and MLE methods using l1 norm relaxation such as K-SVD and l1--based sparse principle component analysis (PCA). Results from simulated models demonstrate that RCweb recovers exactly the model structures for sparsity as low (as non-sparse) as 50% and with ratio of unobserved to observed variables as high as 2. RCweb is robust to noise, with gradual decrease in the parameter ranges as the noise level increases.Comment: 8 pages, 5 figure