Robust predictive deconvolution system and method

Abstract

A method for processing a received, modulated pulse (i.e. waveform) that requires predictive deconvolution to resolve a scatterer from noise and other scatterers includes receiving a return signal; obtaining L+(2M−1)(N−1) samples y of the return signal, where y(l)={tilde over (x)}(l) s+v(l); applying RMMSE estimation to each successive N samples to obtain initial impulse response estimates [{circumflex over (x)}{−(M−1)(N−1)}, . . . , {circumflex over (x)}{−1}, {circumflex over (x)}{0}, . . . , {circumflex over (x)}{L−1}, . . . , {circumflex over (x)}{L}, {circumflex over (x)}{−1 +(M−1)(N−1)}]; computing power estimates {circumflex over (ρ)}(l)=|{circumflex over (x)}(l)|for l=−(M−1)(N−1), . . . , L−1+(M−1)(N−1) and 0<α≦2; computing MMSE filters according to w(l)=ρ(l) (C(l)+R)s, where ρ(l)=E[|x(l)|] is the power of x(l), for 0<α≦2, and R=E[v(l) v(l)] is the noise covariance matrix; applying the MMSE filters to y to obtain [{circumflex over (x)}{−(M−2)(N−1)}, . . . , {circumflex over (x)}{−1}, {circumflex over (x)}{0}, . . . , {circumflex over (x)}{L−1}, {circumflex over (x)}{L}, . . . , {circumflex over (x)}{L−1+(M−2)(N−1)}]; and repeating (d)–(f) for subsequent reiterative stages until a desired length-L range window is reached, thereby resolving the scatterer from noise and other scatterers. The RMMSE predictive deconvolution approach provides high-fidelity impulse response estimation. The RMMSE estimator can reiteratively estimate the MMSE filter for each specific impulse response coefficient by mitigating the interference from neighboring coefficients that is a result of the temporal (i.e. spatial) extent of the transmitted waveform. The result is a robust estimator that adaptively eliminates the spatial ambiguities that occur when a fixed receiver filter is used.