Linear Encoder-Decoder-Controller Design over Channels with Packet Loss and Quantization Noise

We consider a decentralized multisensor estimation problem where L sensor nodes observe noisy versions of a possibly correlated random source. The sensors amplify and forward their observations over a fading coherent multiple access channel (MAC) to a fusion center (FC). The FC is equipped with a large array of N antennas, and adopts a minimum mean square error (MMSE) approach for estimating the source. We optimize the amplification factor (or equivalently transmission power) at each sensor node in two different scenarios: 1) with the objective of total power minimization subject to mean square error (MSE) of source estimation constraint, and 2) with the objective of minimizing MSE subject to total power constraint. For this purpose, we apply an asymptotic approximation based on the massive multiple-input-multiple-output (MIMO) favorable propagation condition (when L ≪ N). We use convex optimization techniques to solve for the optimal sensor power allocation in 1) and 2). In 1), we show that the total power consumption at the sensors decays as 1/N, replicating the power savings obtained in Massive MIMO mobile communications literature. Through numerical studies, we also illustrate the superiority of the proposed optimal power allocation methods over uniform power allocation

Optimal LQG Control Across a Packet-Dropping Link

We examine optimal Linear Quadratic Gaussian control for a system in which communication between the sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend the familiar LQG separation principle to this problem that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. We present one such optimal algorithm, which consists of a Kalman Filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design

On the effect of quantization on performance at high rates

We study the effect of quantization on the performance of a scalar dynamical system in the high rate regime. We evaluate the LQ cost for two commonly used quantizers: uniform and logarithmic and provide a lower bound on performance of any centroid-based quantizer based on entropy arguments. We also consider the case when the channel drops data packets stochastically