arXiv subjects

Rodney A. Kennedy

Publications and source records attributed to Rodney A. Kennedy.

43 records · Page 3Linked to original sources

arXiv2014

Slepian Spatial-Spectral Concentration on the Ball

We formulate and solve the Slepian spatial-spectral concentration problem on the three-dimensional ball. Both the standard Fourier-Bessel and also the Fourier-Laguerre spectral domains are considered since the latter exhibits a number of practical advantages (spectral decoupling and exact computation). The Slepian spatial and spectral concentration problems are formulated as eigenvalue problems, the eigenfunctions of which form an orthogonal family of concentrated functions. Equivalence between the spatial and spectral problems is shown. The spherical Shannon number on the ball is derived, which acts as the analog of the space-bandwidth product in the Euclidean setting, giving an estimate of the number of concentrated eigenfunctions and thus the dimension of the space of functions that can be concentrated in both the spatial and spectral domains simultaneously. Various symmetries of the spatial region are considered that reduce considerably the computational burden of recovering eigenfunctions, either by decoupling the problem into smaller subproblems or by affording analytic calculations. The family of concentrated eigenfunctions forms a Slepian basis that can be used be represent concentrated signals efficiently. We illustrate our results with numerical examples and show that the Slepian basis indeeds permits a sparse representation of concentrated signals.

math.CA↗

arXiv2014

Training-Based Synchronization and Channel Estimation in AF Two-Way Relaying Networks

Two-way relaying networks (TWRNs) allow for more bandwidth efficient use of the available spectrum since they allow for simultaneous information exchange between two users with the assistance of an intermediate relay node. However, due to superposition of signals at the relay node, the received signal at the user terminals is affected by \emph{multiple impairments}, i.e., channel gains, timing offsets, and carrier frequency offsets, that need to be jointly estimated and compensated. This paper presents a training-based system model for amplify-and-forward (AF) TWRNs in the presence of multiple impairments and proposes maximum likelihood and differential evolution based algorithms for joint estimation of these impairments. The Cramer-Rao lower bounds (CRLBs) for the joint estimation of multiple impairments are derived. A minimum mean-square error based receiver is then proposed to compensate the effect of multiple impairments and decode each user's signal. Simulation results show that the performance of the proposed estimators is very close to the derived CRLBs at moderate-to-high signal-to-noise-ratios. It is also shown that the bit-error rate performance of the overall AF TWRN is close to a TWRN that is based on assumption of perfect knowledge of the synchronization parameters.

cs.IT↗

arXiv2013

Structured Optimal Transmission Control in Network-coded Two-way Relay Channels

This paper considers a transmission control problem in network-coded two-way relay channels (NC-TWRC), where the relay buffers random symbol arrivals from two users, and the channels are assumed to be fading. The problem is modeled by a discounted infinite horizon Markov decision process (MDP). The objective is to find a transmission control policy that minimizes the symbol delay, buffer overflow and transmission power consumption and error rate simultaneously and in the long run. By using the concepts of submodularity, multimodularity and L-natural convexity, we study the structure of the optimal policy searched by dynamic programming (DP) algorithm. We show that the optimal transmission policy is nondecreasing in queue occupancies or/and channel states under certain conditions such as the chosen values of parameters in the MDP model, channel modeling method, modulation scheme and the preservation of stochastic dominance in the transitions of system states. The results derived in this paper can be used to relieve the high complexity of DP and facilitate real-time control.

eess.SY↗

arXiv2013

Spatio-spectral Formulation and Design of Spatially-Varying Filters for Signal Estimation on the 2-Sphere

In this paper, we present an optimal filter for the enhancement or estimation of signals on the 2-sphere corrupted by noise, when both the signal and noise are realizations of anisotropic processes on the 2-sphere. The estimation of such a signal in the spatial or spectral domain separately can be shown to be inadequate. Therefore, we develop an optimal filter in the joint spatio-spectral domain by using a framework recently presented in the literature --- the spatially localized spherical harmonic transform --- enabling such processing. Filtering of a signal in the spatio-spectral domain facilitates taking into account anisotropic properties of both the signal and noise processes. The proposed spatio-spectral filtering is optimal under the mean-square error criterion. The capability of the proposed filtering framework is demonstrated with by an example to estimate a signal corrupted by an anisotropic noise process.

astro-ph.IM↗

arXiv2013

Classification and construction of closed-form kernels for signal representation on the 2-sphere

This paper considers the construction of Reproducing Kernel Hilbert Spaces (RKHS) on the sphere as an alternative to the conventional Hilbert space using the inner product that yields the L^2(S^2) function space of finite energy signals. In comparison with wavelet representations, which have multi-resolution properties on L^2(S^2), the representations that arise from the RKHS approach, which uses different inner products, have an overall smoothness constraint, which may offer advantages and simplifications in certain contexts. The key contribution of this paper is to construct classes of closed-form kernels, such as one based on the von Mises-Fisher distribution, which permits efficient inner product computation using kernel evaluations. Three classes of RKHS are defined: isotropic kernels and non-isotropic kernels both with spherical harmonic eigenfunctions, and general anisotropic kernels.

cs.IT↗

arXiv2005

Spatial Precoder Design for Space-Time Coded MIMO Systems: Based on Fixed Parameters of MIMO Channels

In this paper, we introduce the novel use of linear spatial precoding based on fixed and known parameters of multiple-input multiple-output (MIMO) channels to improve the performance of space-time coded MIMO systems. We derive linear spatial precoding schemes for both coherent (channel is known at the receiver) and non-coherent (channel is un-known at the receiver) space-time coded MIMO systems. Antenna spacing and antenna placement (geometry) are considered as fixed parameters of MIMO channels, which are readily known at the transmitter. These precoding schemes exploit the antenna placement information at both ends of the MIMO channel to ameliorate the effect of non-ideal antenna placement on the performance of space-time coded systems. In these schemes, the precoder is fixed for given transmit and receive antenna configurations and transmitter does not require any feedback of channel state information (partial or full) from the receiver. Closed form solutions for both precoding schemes are presented for systems with up to three receiver antennas. A generalized method is proposed for more than three receiver antennas. We use the coherent space-time block codes (STBC) and differential space-time block codes to analyze the performance of proposed precoding schemes. Simulation results show that at low SNRs, both precoders give significant performance improvement over a non-precoded system for small antenna aperture sizes.

cs.IT↗

arXiv2005

MIMO Channel Correlation in General Scattering Environments

This paper presents an analytical model for the fading channel correlation in general scattering environments. In contrast to the existing correlation models, our new approach treats the scattering environment as non-separable and it is modeled using a bi-angular power distribution. The bi-angular power distribution is parameterized by the mean departure and arrival angles, angular spreads of the univariate angular power distributions at the transmitter and receiver apertures, and a third parameter, the covariance between transmit and receive angles which captures the statistical interdependency between angular power distributions at the transmitter and receiver apertures. When this third parameter is zero, this new model reduces to the well known "Kronecker" model. Using the proposed model, we show that Kronecker model is a good approximation to the actual channel when the scattering channel consists of a single scattering cluster. In the presence of multiple remote scattering clusters we show that Kronecker model over estimates the performance by artificially increasing the number of multipaths in the channel.

math-ph↗