14 research outputs found
Waterfilling Theorems for Linear Time-Varying Channels and Related Nonstationary Sources
The capacity of the linear time-varying (LTV) channel, a continuous-time LTV
filter with additive white Gaussian noise, is characterized by waterfilling in
the time-frequency plane. Similarly, the rate distortion function for a related
nonstationary source is characterized by reverse waterfilling in the
time-frequency plane. Constraints on the average energy or on the squared-error
distortion, respectively, are used. The source is formed by the white Gaussian
noise response of the same LTV filter as before. The proofs of both
waterfilling theorems rely on a Szego theorem for a class of operators
associated with the filter. A self-contained proof of the Szego theorem is
given. The waterfilling theorems compare well with the classical results of
Gallager and Berger. In the case of a nonstationary source, it is observed that
the part of the classical power spectral density is taken by the Wigner-Ville
spectrum. The present approach is based on the spread Weyl symbol of the LTV
filter, and is asymptotic in nature. For the spreading factor, a lower bound is
suggested by means of an uncertainty inequality.Comment: 13 pages, 5 figures; channel model in Section III now restricted to
LTV filters with real-valued kerne
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A Geometric Framework for Analyzing the Performance of Multiple-Antenna Systems under Finite-Rate Feedback
We study the performance of multiple-antenna systems under finite-rate feedback of some function of the current channel realization from a channel-aware receiver to the transmitter. Our analysis is based on a novel geometric paradigm whereby the feedback information is modeled as a source distributed over a Riemannian manifold. While the right singular vectors of the channel matrix and the subspace spanned by them are located on the traditional Stiefel and Grassmann surfaces, the optimal input covariance matrix is located on a new manifold of positive semi-definite matrices - specified by rank and trace constraints - called the Pn manifold. The geometry of these three manifolds is studied in detail; in particular, the precise series expansion for the volume of geodesic balls over the Grassmann and Stiefel manifolds is obtained. Using these geometric results, the distortion incurred in quantizing sources using either a sphere-packing or a random code over an arbitrary manifold is quantified. Perturbative expansions are used to evaluate the susceptibility of the ergodic information rate to the quality of feedback information, and thereby to obtain the tradeoff of the achievable rate with the number of feedback bits employed. For a given system strategy, the gap between the achievable rates in the infinite and finite-rate feedback cases is shown to be for Grassmann feedback and for other cases, where is the dimension of the manifold used for quantization and is the number of bits used by the receiver per block for feedback. The geometric framework developed enables the results to hold for arbitrary distributions of the channel matrix and extends to all covariance computation strategies including, waterfilling in the short-term/long-term power constraint case, antenna selection and other rank-limited scenarios that could not be analyzed using previous probabilistic approaches
Distributed field estimation in wireless sensor networks
This work takes into account the problem of distributed estimation of a physical field of interest through a wireless sesnor networks
Distributed field estimation in wireless sensor networks
This work takes into account the problem of distributed estimation of a physical field of interest through a wireless sesnor networks
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An optimization paradigm for wideband antenna arrays : integrating electromagnetics and information theory
As larger bandwidths are used in multiple-antenna wireless systems, the frequency selectivity of the antenna arrays starts to impact rate. Therefore, optimizing the achievable rate in compact antenna arrays becomes important especially for future wireless networks that can require octaves of bandwidth. With the emergence of 6G technologies, using terahertz (THz) frequency bands become inevitable to achieve terabit rates. Hence, in this dissertation, we focus on combining wireless communication theory and electromagnetics theory to provide a new platform that addresses the challenges in future wireless networks. In this dissertation, we introduce a circuit-level analysis of compact wideband antennas at sub-6GHz bands. We present an approach that combines the mathematics of information theory with the physics behind antenna theory. Then, we focus on designing antenna arrays for future 6G technologies that can maintain a full rank channel in the presence of a line-of-sight (LoS) component. Lastly, we introduce a passive reflective intelligent surface (RIS) that helps in redirecting the signal efficiently to the intended user. In Chapter 2 of the dissertation, we focus on optimizing the achievable rate in compact antenna arrays. We present a system model that incorporates the effects of mutual coupling (MC) of wideband physically realizable single-input multiple-output (SIMO) and multiple-input single-output (MISO) antenna systems. For the SIMO system setup, we extract the noise correlation matrices for two different antenna array configurations (parallel and co-linear). We optimize the inter-element spacing in each alignment while maximizing the achievable rate and fixing the transmit power. Then, we compare the two compact antenna designs to a perfectly matched single omni-directional antenna while accounting for MC. Likewise, for the MISO antenna system, we derive the optimal beamformer that maximizes the achievable rate using the same antenna configurations as the SIMO system. Then, we study the impact of MC and develop a new single-port matching technique for wideband antenna arrays. Finally, we provide reciprocity plots to compare the performance of the SIMO-MISO systems using different channel models. In Chapter 3 of the dissertation, we present an optimized antenna port switching technique for a LoS multiple-input multiple-output (MIMO) system operating at THz frequencies. MIMO technology usually requires a rich scattering environment to work properly and uses non-line-of-sight (NLoS) components. When MIMO is used in high-frequency point-to-point microwave links, however, the channel will have a dominant LoS component. For a LoS MIMO system to maintain spatial diversity, the signal streams should remain orthogonal to each other. Therefore, we design an optimally spaced uniform linear array (ULA) and non-uniform linear array (NULA) that preserves the orthogonality between the signals in a mesh grid network. We present a novel technique that selects the proper antenna ports to be activated which results in preserving the signal stream orthogonality and achieves a good condition number for the channel matrix. Finally, we provide bit error rate (BER) plots to show the performance and flexibility of this novel approach. In Chapter 4 of the dissertation, we design a reconfigurable intelligent surface, which controls the state of the imposing electromagnetic waves at THz frequencies. Since at THz frequencies there is significant and severe path loss, current beamforming techniques use costly phased arrays or bulky reflector antennas that hinder and limit their applications. Furthermore, THz frequencies are highly susceptible to frequent link outages due to misalignment and obstruction thus severely affecting the overall system throughput and reliability. As a result, the designed RIS controls the properties of an electromagnetic signal and acts as a reflector and directs the impinging wave to its proper receiver (i.e. user equipment, base station). The reflective surface controls the phase of the reflected wave from each unit-cell, hence steers the reflected signal from the surface of the array to reach the intended user equipment and improves the user’s signal-to-noise ratio (SNR). To show the effectiveness of our design, we provide plots of the beam-steering angle of the RIS.Electrical and Computer Engineerin