Threshold Effects in Parameter Estimation from Compressed Data (1505.07431v1)

Abstract: In this paper, we investigate threshold effects associated with swapping of signal and noise subspaces in estimating signal parameters from compressed noisy data. The term threshold effect refers to a sharp departure of mean-squared error from the Cramer-Rao bound when the signal-to-noise ratio falls below a threshold SNR. In many cases, the threshold effect is caused by a subspace swap event, when the measured data (or its sample covariance) is better approximated by a subset of components of an orthogonal subspace than by the components of a signal subspace. We derive analytical lower bounds on the probability of a subspace swap in compressively measured noisy data. These bounds guide our understanding of threshold effects and performance breakdown for parameter estimation using compression. As a case study, we investigate threshold effects in maximum likelihood (ML) estimation of directions of arrival of two closely-spaced sources using co-prime subsampling. Our results show the impact of compression on threshold SNR. A rule of thumb is that every doubling of compression ratio brings a penalty in threshold SNR of 3 dB.