Abstract-This paper studies the ergodic capacity of timeand frequency-selective multipath fading channels in the ultrawideband (UWB) regime when training signals are used for channel estimation at the receiver. Motivated by recent measurement results on UWB channels, we propose a model for sparse multipath channels. A key implication of sparsity is that the independent degrees of freedom (DoF) in the channel scale sub-linearly with the signal space dimension (product of signaling duration and bandwidth). Sparsity is captured by the number of resolvable paths in delay and Doppler. Our analysis is based on a training and communication scheme that employs signaling over orthogonal short-time Fourier (STF) basis functions. STF signaling naturally relates sparsity in delayDoppler to coherence in time-frequency. We study the impact of multipath sparsity on two fundamental metrics of spectral efficiency in the wideband/low-SNR limit introduced by Verdu: first-and second-order optimality conditions. Recent results by Zheng et. al. have underscored the large gap in spectral efficiency between coherent and non-coherent extremes and the importance of channel learning in bridging the gap. Building on these results, our results lead to the following implications of multipath sparsity: 1) The coherence requirements are shared in both time and frequency, thereby significantly relaxing the required scaling in coherence time with SNR; 2) Sparse multipath channels are asymptotically coherent -for a given but large bandwidth, the channel can be learned perfectly and the coherence requirements for first-and second-order optimality met through sufficiently large signaling duration; and 3) The requirement of peaky signals in attaining capacity is eliminated or relaxed in sparse environments.

This paper studies the ergodic capacity of wideband multipath channels with limited feedback. Our work builds on recent results that have established the possibility of significant capacity gains in the wideband/low-SNR regime when there is perfect channel state information (CSI) at the transmitter.Furthermore, the perfect CSI benchmark gain can be obtained with the feedback of just one bit per channel coefficient. However, the input signals used in these methods are peaky, that is, they have a large peak-to-average power ratios. Signal peakiness is related to channel coherence and many recent measurement campaigns show that, in contrast to previous assumptions, wideband channels exhibit a sparse multipath structure that naturally leads to coherence in time and frequency. In this work, we first show that even an instantaneous power constraint is sufficient to achieve the benchmark gain when perfect CSI is available at the receiver. In the more realistic non-coherent setting, we study the performance of a training-based signaling scheme. We show that multipath sparsity can be leveraged to achieve the benchmark gain under both average as well as instantaneous power constraints as long as the channel coherence scales at a sufficiently fast rate with signal space dimensions. We also present rules of thumb on choosing signaling parameters as a function of the channel parameters so that the full benefits of sparsity can be realized.

The ability of modern power plant data acquisition systems to provide a continuous real-time data feed can be exploited to carry out interesting research studies. In the first part of this study, real-time data from a power plant is used to carry out a comprehensive heat balance calculation. The calculation involves application of the first law of thermodynamics to each powerhouse component. Stoichiometric combustion principles are applied to calculate emissions from fossil fuel consuming components. Exergy analysis is carried out for all components by the combined application of the first and second laws of thermodynamics. In the second part of this study, techniques from the field of System Identification and Linear Programming are brought together in finding thermoeconomically optimum plant operating conditions one step ahead in time. This is done by first using autoregressive models to make short-term predictions of plant inputs and outputs. Then, parameter estimation using recursive least squares is used to determine the relations between the predicted inputs and outputs. The estimated parameters are used in setting up a linear programming problem which is solved using the simplex method. The end result is knowledge of thermoeconomically optimum plant inputs and outputs one step ahead in time.

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