THIRD-ORDER CUMULANTS RECONSTRUCTION FROM COMPRESSIVE MEASUREMENTS

Estimation of popular third-order statistics hinges on the availability of a huge amount of data records, which brings severe challenges on the data collecting hardware in terms of considerable storage costs, overwhelming energy consumption and unaffordably high sampling rate especially when dealing with wideband signals. To overcome these challenges, we propose a systematic approach to estimate the third-order statistics of wide-sense stationary signals under the compressive sampling framework. Without any sparsity constraints on the signal or cumulants, we provide the sufficient conditions for lossless third-order statistics recovery via solving simple least-squares, and analyze the strongest achievable compression ratio in closed-form.