Nearly-optimal compression matrices for signal power estimation

We present designs for compression matrices minimizing the Cramér-Rao bound for estimating the power of a stationary Gaussian process, whose second-order statistics are known up to a scaling factor, in the presence of (possibly colored) Gaussian noise. For known noise power, optimum designs can be found assuming either low or high signal-to-noise ratio (SNR). In both cases the optimal schemes sample the frequency bins with highest SNR, suggesting near-optimality for all SNR values. In the case of unknown noise power, optimal patterns in both SNR regimes sample two subsets of frequency bins with lowest and highest SNR, which also suggests that they are nearly-optimal for all SNR values.