Milind Rao

MGF Approach to the Analysis of Generalized Two-Ray Fading Models

We analyze a class of generalized two-ray (GTR) fading channels that consist of two line-of-sight (LOS) components with random phase plus a diffuse component. We derive a closed-form expression for the moment-generating function of the signal-to-noise ratio (SNR) for this model, which greatly simplifies its analysis. This expression arises from the observation that the GTR fading model can be expressed in terms of a conditional underlying Rician distribution. We illustrate the approach to derive simple expressions for statistics and performance metrics of interest, such as the amount of fading, the level crossing rate, the symbol error rate, and the ergodic capacity in GTR fading channels. We also show that the effect of considering a more general distribution for the phase difference between the LOS components has an impact on the average SNR.

Benefits of Storage Control for Wind Power Producers in Power Markets

We consider a wind power producer (WPP) participating in a dynamically evolving two settlement power market. We study the utility of energy storage for a WPP in maximizing its expected profit. With random wind and price processes, the optimal forward contract and storage charging/discharging decisions are formulated as solutions of an infinite horizon stochastic optimal control problem. For the asymptotically small storage capacity regime, we precisely characterize the maximum profit increase brought by utilizing energy storage. We prove that, in this regime, an optimal policy uses storage to compensate for power delivery shortfall/surplus in real time, without changing the forward contracts from the optimal ones in the absence of energy storage. This policy also serves as an approximately optimal policy for the case of relatively small storage capacity. We also design a policy based on model predictive control (MPC) that is approximately optimal for general storage capacities. We numerically evaluate the developed policies for wind and price processes with representative statistics from real world data. It is observed that, as expected, the simple small storage approximation policy performs closely to the optimum when storage is relatively small, while the more complex stochastic MPC policy performs better for larger storage capacities.

Statistics and system performance metrics for the Two Wave with Diffuse Power fading model

The Two Wave with Diffuse Power (TWDP) fading model was proposed by Durgin, Rappaport and de Wolf as a generalization of the Rayleigh and Rician fading models. This model can characterize a large range of fading behavior and has a geometric justification in terms of two dominant line of sight components in the presence of a diffuse component. The fact that the pdf of the TWDP model is not in closed-form has hindered the analytical characterization of this otherwise intuitive model. We show that any metric which is a linear function of the envelope statistics of the TWDP fading model can be computed as a finite integral of the corresponding metric for the Rice model. Employing this approach, we obtain simple expressions for some performance metrics for this fading model hitherto not found in the literature, such as the Amount of Fading, the Level Crossing Rate and the Moment Generating Function, by leveraging existing results for Rician fading.

On the capacity of diffusion-based molecular timing channels with diversity

This work introduces a class of molecular timing (MT) channels, where information is modulated on the release timing of multiple indistinguishable information particles and decoded from the times of arrival at the receiver. The particles are assumed to have a finite lifetime. The capacity of the MT channel, as well as an upper bound on this capacity, are derived for the case where information particles are released simultaneously by the transmitter. Two lower bounds for this capacity are also discussed.

MGF approach to the capacity analysis of Generalized Two-Ray fading models

We propose a class of Generalized Two-Ray (GTR) fading channels that consists of two line of sight (LOS) components with random phase and a diffuse component. Observing that the GTR fading model can be expressed in terms of the underlying Rician distribution, we derive a closed-form expression for the moment generating function (MGF) of the signal-to-noise ratio (SNR) of this model. We then employ this approach to compute the ergodic capacity with receiver side information. The impact of the underlying phase difference between the LOS components on the average SNR of the signal received is also illustrated.

Value of storage for wind power producers in forward power markets

Wind power producers (WPPs) that sell power in forward power markets would like to minimize their operating costs which increase with generation uncertainty. In this work, the value of energy storage for reducing such costs is studied. In particular, profit maximization is considered for a WPP who participates in a two-settlement (forward and real time) market and utilizes energy storage by charging/discharging it strategically. An infinite horizon discounted cost minimization problem for the optimal use of energy storage is formulated as a dynamic programming (DP) problem that includes the past unfulfilled forward contracts in the state space. The optimal storage operation policy is shown to have a structure with two thresholds: after delivering its contracted power, if a WPPs energy falls below a lower threshold, it buys energy and charges its storage up to this threshold; if its energy exceeds a higher threshold, it sells the excess energy and maintains its storage level at this threshold. Several heuristics for solving the DP are derived based on approximating the problem model: a) a discrete policy based on discretizing the state and action space, and b) affine and look ahead policies derived by solving a Linear Quadratic (LQ) controller whose parameters are fit from the DP. The heuristics are tested both with simulated and real world wind and price data. It is observed that while the discrete optimal policy performs better on simulated data than either the look ahead or the affine policies (except with a very high battery capacity), the look ahead policy performs much better with real world data. This suggests that the performance of look ahead approximate optimal policy is more robust to the modeling errors and mismatch between analytic models and real data traces. The appropriate heuristic to use thus depends on modeling fidelity, available computational resources and variability of wind and price forecasts.

Estimation in autoregressive processes with partial observations

We consider the problem of estimating the covariance matrix and the transition matrix of vector autoregressive (VAR) processes from partial measurements. This model encompasses settings where there are limitations in the data acquisition of the underlying measurement systems so that data is lost or corrupted by noise. An estimator for the covariance matrix of the observations is first presented. More refined estimators, factoring in structural constraints on the covariance matrix such as sparsity, bandedness, sparsity of the inverse and low-rankness are then introduced that are particularly useful in the high-dimensional regime. These estimates are then used to perform system identification by estimating the state transition matrix with or without further structural assumptions. Non-asymptotic guarantees are presented for all estimators.

Fundamental estimation limits in autoregressive processes with compressive measurements

We consider the problem of estimating the parameters of a vector autoregressive (VAR) process from low-dimensional random projections of the observations. This setting covers the cases where we take compressive measurements of the observations or have limits in the data acquisition process associated with the measurement system and are only able to subsample. We first present fundamental bounds on the convergence of any estimator for the covariance or state-transition matrices with and without considering structural constraints of sparsity and low-rankness. We then construct an estimator for these matrices or the parameters of the VAR process and show that it is order optimal.

System identification from partial samples: Non-asymptotic analysis

The problem of learning the parameters of a vector autoregressive (VAR) process from partial random measurements is considered. This setting arises due to missing data or data corrupted by multiplicative bounded noise. We present an estimator of the covariance matrix of the evolving state-vector from its partial noisy observations. We analyze the non-asymptotic behavior of this estimator and provide an upper bound for its convergence rate. This expression shows that the effect of partial observations on the first order convergence rate is equivalent to reducing the sample size to the average number of observations viewed, implying that our estimator is order-optimal. We then present and analyze two techniques to recover the VAR parameters from the estimated covariance matrix applicable in dense and in sparse high-dimensional settings. We demonstrate the applicability of our estimation techniques in joint state and system identification of a stable linear dynamic system with random inputs.