Asymptotic Optimality of Equal Power Allocation for Linear Estimation of   WSS Random Processes
  This letter establishes the asymptotic optimality of equal power allocation for measurements of a continuous wide-sense stationary (WSS) random process with a square-integrable autocorrelation function when linear estimation is used on equally-spaced measurements with periodicity meeting the Nyquist criterion and with the variance of the noise on any sample inversely proportional to the power expended by the user to obtain that measurement. 
Boulat A. Bash, Dennis Goeckel, Don Towsley
cs.IT math.IT