相位编码信号码元宽度估计的修正克拉美—罗限

Modified Cramer-Rao lower bound for symbol width estimation from a phase-shift-keying signal

推导了相位编码信号码元宽度估计的修正克拉美—罗限(MCRB)。采用Parseval定理将单位冲激函数δ(t)平方的积分转换到频域计算,得到脉冲成形函数是矩形脉冲时码元宽度估计的修正克拉美—罗限。当脉冲成形函数是升余弦脉冲时则进行了数值计算。计算表明,当滚降系数为0.5时,升余弦脉冲和矩形脉冲对应的码元宽度估计性能相差1dB左右。

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 difference was about 1 dB.