Communications-Inspired Projection Design with Application to Compressive Sensing

We consider the recovery of an underlying signal x \in C^m based on projection measurements of the form y=Mx+w, where y \in C^l and w is measurement noise; we are interested in the case l < m. It is assumed that the signal model p(x) is known, and w CN(w;0,S_w), for known S_W. The objective is to design a projection matrix M \in C^(l x m) to maximize key information-theoretic quantities with operational significance, including the mutual information between the signal and the projections I(x;y) or the Renyi entropy of the projections h_a(y) (Shannon entropy is a special case). By capitalizing on explicit characterizations of the gradients of the information measures with respect to the projections matrix, where we also partially extend the well-known results of Palomar and Verdu from the mutual information to the Renyi entropy domain, we unveil the key operations carried out by the optimal projections designs: mode exposure and mode alignment. Experiments are considered for the case of compressive sensing (CS) applied to imagery. In this context, we provide a demonstration of the performance improvement possible through the application of the novel projection designs in relation to conventional ones, as well as justification for a fast online projections design method with which state-of-the-art adaptive CS signal recovery is achieved.Comment: 25 pages, 7 figures, parts of material published in IEEE ICASSP 2012, submitted to SIIM

Robust Transceiver Design Based on Interference Alignment for Multi-User Multi-Cell MIMO Networks with Channel Uncertainty

In this paper, we firstly exploit the inter-user interference (IUI) and inter-cell interference (ICI) as useful references to develop a robust transceiver design based on interference alignment for a downlink multi-user multi-cell multiple-input multiple-output (MIMO) interference network under channel estimation error. At transmitters, we propose a two-tier transmit beamforming strategy, we first achieve the inner beamforming direction and allocated power by minimizing the interference leakage as well as maximizing the system energy efficiency, respectively. Then, for the outer beamformer design, we develop an efficient conjugate gradient Grassmann manifold subspace tracking algorithm to minimize the distances between the subspace spanned by interference and the interference subspace in the time varying channel. At receivers, we propose a practical interference alignment based on fast and robust fast data projection method (FDPM) subspace tracking algorithm, to achieve the receive beamformer under channel uncertainty. Numerical results show that our proposed robust transceiver design achieves better performance compared with some existing methods in terms of the sum rate and the energy efficiency.Comment: 12 pages, 8 figure