Modified Cramer-Rao lower bound for symbol width estimation from a phase-shift-keying signal - DENG Zhen-miao; LIU Yu (Tongxin xuebao)
The modified Cramer-Rao lower bound（MCRB） on symbol width estimation of a phase-shift-keying signal was derived.When calculating the integration of the square of dirac delta function δ（t ）, Parseval’s theorem was used to transform the computation from time-domain to frequency-domain.Then the closed-form analytical solution of MCRB for symbol width estimation was derived when the pulse shaping function was the rectangle pulse.However when the pulse shaping function was the raised cosine（RC） pulse, the MCRB is evaluated by numerical simulation.The results show that the MCRB of rectangle pulse shape is higher than that of RC pulse with the roll-off factor to be 0.5 and the dif-ference was about 1 dB.