Signal Estimation Via Averaging of Coarsely Quantised Signals

It is well known that averaging N independently noisy versions of an otherwise constant signal, x, reduces the rms value of the noise by a factor of radicN, regardless of the distribution of the noise. However, this result applies exactly only if each noisy version of the signal can be added together with infinite precision. If averaging is performed after digitisation, the nonlinearity imposed by quantisation affects the performance of the averaging. For the case of averaging after a coarse (two-state) quantisation, it is demonstrated that the resultant mean square error performance is highly dependent on the noise distribution. Lower bounds on the performance are found using a generalisation of the Cramer-Rao lower bound.