A Note on Compressed Sensing for Low Latency

With the intention of contributing to the ongoing debate on ultra-low latency within the context of 5G networked control systems, this short note highlights one example of how increased computation capabilities can soften up demands for ultra-low latency. One fundamental problem in control theory is the state observation: in a networked system, the latency for transporting signals delays the samples of inputs and outputs and consequently degrades the accuracy of the estimator of the hidden state. Though, in broad classes of systems the state vector is known to be sparse under some representation. Compressed sensing can exploit this sparseness and this note presents a quantitative analysis of the possibilities offered by compressed sensing to largely reduce latency and increase accuracy of state estimators for systems bearing sparse states.