【OFDM】OFDM Radar Algorithms in Mobile Communication Networks

[1] Maximum Likelihood Speed and Distance
Estimation for OFDM Radar

1-CRB估计

1-初步形式

首先单频信号频率估计的CRB，也就是原文Eq.(3.53)
$$\mathrm{var}[\hat{\omega }]\ge \frac{6{\sigma }_N^2}{(N^2-1)N}$$

然后论文里说，利用Eq.(3.32), Eq.(3.53)可以得到距离的CRB，即Eq.(3.54)

var ⁡ { d ^ } ≥ 6 σ N 2 ( N 2 − 1 ) N ( c 0 4 π Δ f ) 2 \operatorname{var}\{\hat{d}\}\geq\frac{6\sigma_N^2}{(N^2-1)N}\left(\frac{c_0}{4\pi\Delta f}\right)^2 var{d^}≥(N2−1)N6σN2​​(4πΔfc0​​)2

其实是根据Eq.(3.22)
$$\hat{d}=\frac{1}{2}\hat{\tau }{c}_0=\frac{{\hat{\Omega }}_d{c}_0}{2(2\pi )\Delta f}$$