Optimal Estimation with Limited Measurements and Noisy Communication

This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as to whether or not to send this measurement to the estimator. The sensor and the estimator have the common objective of minimizing expected distortion in the estimation of the state of the process, over a finite time horizon, with the constraint that the sensor can transmit its observation only a limited number of times. As opposed to the prior work where communication between the sensor and the estimator was assumed to be perfect (noiseless), in this work an additive noise channel with fixed power constraint is considered; hence, the sensor has to encode its message before transmission. For some specific source and channel noise densities, we obtain the optimal encoding and estimation policies in conjunction with the optimal transmission schedule. The impact of the presence of a noisy channel is analyzed numerically based on dynamic programming. This analysis yields some rather surprising results such as a phase-transition phenomenon in the number of used transmission opportunities, which was not encountered in the noiseless communication setting.Comment: X. Gao, E. Akyol, and T. Basar. Optimal estimation with limited measurements and noisy communication. In 54th IEEE Conference on Decision and Control (CDC15), 2015, to appea

Matrix-Monotonic Optimization for MIMO Systems

For MIMO systems, due to the deployment of multiple antennas at both the transmitter and the receiver, the design variables e.g., precoders, equalizers, training sequences, etc. are usually matrices. It is well known that matrix operations are usually more complicated compared to their vector counterparts. In order to overcome the high complexity resulting from matrix variables, in this paper we investigate a class of elegant multi-objective optimization problems, namely matrix-monotonic optimization problems (MMOPs). In our work, various representative MIMO optimization problems are unified into a framework of matrix-monotonic optimization, which includes linear transceiver design, nonlinear transceiver design, training sequence design, radar waveform optimization, the corresponding robust design and so on as its special cases. Then exploiting the framework of matrix-monotonic optimization the optimal structures of the considered matrix variables can be derived first. Based on the optimal structure, the matrix-variate optimization problems can be greatly simplified into the ones with only vector variables. In particular, the dimension of the new vector variable is equal to the minimum number of columns and rows of the original matrix variable. Finally, we also extend our work to some more general cases with multiple matrix variables.Comment: 37 Pages, 5 figures, IEEE Transactions on Signal Processing, Final Versio

Optimal Sensing and Transmission in Energy Harvesting Sensor Networks

Sensor networks equipped with energy harvesting (EH) devices have attracted great attentions recently. Compared with conventional sensor networks powered by batteries, the energy harvesting abilities of the sensor nodes make sustainable and environment-friendly sensor networks possible. However, the random, scarce and non-uniform energy supply features also necessitate a completely different approach to energy management. A typical EH wireless sensor node consists of an EH module that converts ambient energy to electrical energy, which is stored in a rechargeable battery, and will be used to power the sensing and transmission operations of the sensor. Therefore, both sensing and transmission are subject to the stochastic energy constraint imposed by the EH process. In this dissertation, we investigate optimal sensing and transmission policies for EH sensor networks under such constraints. For EH sensing, our objective is to understand how the temporal and spatial variabilities of the EH processes would affect the sensing performance of the network, and how sensor nodes should coordinate their data collection procedures with each other to cope with the random and non-uniform energy supply and provide reliable sensing performance with analytically provable guarantees. Specifically, we investigate optimal sensing policies for a single sensor node with infinite and finite battery sizes in Chapter 2, status updating/transmission strategy of an EH Source in Chapter 3, and a collaborative sensing policy for a multi-node EH sensor network in Chapter 4. For EH communication, our objective is to evaluate the impacts of stochastic variability of the EH process and practical battery usage constraint on the EH systems, and develop optimal transmission policies by taking such impacts into consideration. Specifically, we consider throughput optimization in an EH system under battery usage constraint in Chapter 5