Robust detection of random variables using sparse measurements

We look at the problem of estimating k discrete random variables from n noisy and sparse measurements where k = nR, with a ‘rate’ R. The model is motivated by problems studied in diverse areas including compressed sensing, group testing, multiple access channels and sensor networks. In particular, we study uncertainty and mismatch in the measurement functions and the noise model and quantify the effect of these faults on detection performance, in the large system limit as n → ∞, while R remains constant. We characterize the performance of mismatched and uncertain detectors, design and analyze robust detectors and present an illustrative example where the analysis presented can be used to guide the design of robust measurement ensembles.