This paper investigates the mean square error (MSE)-optimal conditional estimator (CME) in one-bit quantized systems context of channel estimation with jointly Gaussian inputs. We analyze relationship generally nonlinear CME to linear Bussgang estimator, a well-known method based on Bussgang's theorem. highlight novel observation that is equal for different special cases, including case univari...

We show that, on the Riemann hypothesis, lim supX→∞I(X)/X2⩽0.8603, where I(X)=∫X2X(ψ(x)−x)2dx. This proves (and improves on) a claim by Pintz from 1982. also unconditionally that 1.86⋅10−4⩽I(X)/X2 for sufficiently large X, and I(X)/X2 has no limit as X→∞.

We consider the problem of estimating a function ( ) on the unit disk ( ): 2 + 2 1 , given a discrete and noisy data recorded on a regular square grid. An estimate of ( ) based on a class of orthogonal and complete functions over the unit disk is proposed. This class of functions has a distinctive property of being invariant to rotation of axes about the origin of coordinates yielding therefore...