Fading Channel Signal-to-Noise Ratio Limitation for Closed-Loop Stabilizability

摘要

Explicit communication channels in the feedback loop introduce new key elements such as channel input power, channel variable gain, channel bandwidth, additive channel noise, transmission rate, quantization, packet losses, etc. In this article, we propose a stationary signal-to-noise ratio (SNR) analysis for the fading channel model. The channel SNR can be connected with most communication issues such as channel input power, additive channel noise, and quantization noise. Recently, a power analysis has also been used to characterize for every instant the effect of packet losses and channel fading. Here, we propose an equivalent average channel model that preserves the first and second moments of a fading channel output in steady state. The proposed equivalency is stated initially in an open loop, and then, with the assumption of a plant model with a relative degree greater or equal to one, extended to the closed-loop feedback allowing a stationary SNR analysis. As a result, we can compute the fading channel SNR for closed-loop stabilizability limitation, and then consider the presence of disturbance and setpoint signals.