Energy-Based Localization in Wireless Sensor Networks Using Second-Order Cone Programming Relaxation

Source localization in wireless sensor networks (WSNs) aims to determine the position of a source in a network, given inaccurate position-bearing measurements. This paper addresses the problem of locating a single source from noisy acoustic energy measurements in WSNs. Under the assumption of Gaussian energy measurement errors, the maximum likelihood (ML) estimator requires the minimization of a nonlinear and nonconvex cost function which may have multiple local optima, thus making the search for the globally optimal solution hard. In this work, an approximate solution to the ML location estimation problem is presented by relaxing the minimization problem to a convex optimization problem, namely second-order cone programming. Simulation results demonstrate the superior performance of the convex relaxation approach. More precisely, the new approach shows an improvement of 20 % in terms of localization accuracy when compared to the existing approaches at moderate to high noise levels. Simulation results further show comparable performance of the new approach and the state-of-art approaches at low noise levels.     

Space-Time Codebook Design for Spread Systems

The problem of designing space-time constellations for communication in spread multiple-antenna wireless systems over Rayleigh fading channel is addressed. Using the asymptotic union bound on error probability as design criterion, codes based on general complex-valued symbols are obtained with a gradient search optimization technique. New space-time constellations are constructed and their performance is assessed. Simulation results show that the proposed technique achieves significant performance gains over existing schemes. Since the designed codebooks do not seem to possess any structure that could reduce the memory requirements for storing the corresponding codebook, the problem of designing structured space-time constellations is also addressed. To overcome this problem, a discrete Fourier transform-based approach is adopted to design structured codebooks and their performance is evaluated. The new structured codebooks also demonstrate significant improvement over state-of-art structured schemes.     

Noncoherent Communication in Multiple-Antenna Systems: Receiver Design and Codebook Construction

In this paper, we address the problem of space-time codebook design for noncoherent communications in multiple-antenna wireless systems. In contrast with other approaches, the channel matrix is modeled as an unknown deterministic parameter at both the receiver and the transmitter, and the Gaussian observation noise is allowed to have an arbitrary correlation structure, known by the transmitter and the receiver. In order to handle the unknown deterministic space-time channel, a generalized likelihood ratio test (GLRT) receiver is considered. A new methodology for space-time codebook design under this noncoherent setup is proposed. It optimizes the probability of error of the GLRT receiver's detector in the high signal-to-noise ratio (SNR) regime by solving a high-dimensional nonlinear nonsmooth optimization problem in a two-step approach. First, a convex semidefinite programming (SDP) relaxation of the codebook design problem yields a rough estimate of the optimal codebook. This is then refined through a geodesic descent optimization algorithm that exploits the Riemannian geometry imposed by the power constraints on the space-time codewords. The results obtained through computer simulations illustrate the advantages of our method. For the specific case of spatio-temporal white observation noise, our codebook constructions replicate the performance of state-of-the-art known solutions. The main point here is that our methodology permits extending the codebook construction to any given correlated noise environment. The simulation results show good performance of these new designed codes in colored noise setups.