外辐射源雷达信号模型

【 1. 发射端 】

基带

• 发射信号基带
  $$u_{基}(t)$$

调制

• 发射信号调制后
  u 调 ( t ) = u 基 ( t ) exp ⁡ { j 2 π f c t } u_{调}(t)=u_{基}(t)\exp\{j2\pi f_ct\} u调​(t)=u基​(t)exp{ j2πfc​t}
  • 第 m 个脉冲调制后的波形
    u 调 ( t ^ , t m ) = u 基 ( t ^ , t m ) exp ⁡ { j 2 π f c t ^ } u_{调}(\widehat{t},t_m)=u_{基}(\widehat{t},t_m)\exp\{j2\pi f_c\widehat{t}\} u调​(t ,tm​)=u基​(t ,tm​)exp{ j2πfc​t }
    其中，快时间 $\hat{t}=t-t_m$，慢时间 $t_m=m{T}_r$。

【 2. 接收端 】

采样

• 回波信号（仅考虑目标回波）
  e c h o ( t ) = A u 调 ( t − τ ) = A u 基 ( t − τ ) exp ⁡ { j 2 π f c ( t − τ ) } = A u 基 ( t − τ ) exp ⁡ { j 2 π f c [ t − 2 ( R 0 − V t ) c ] } = A u 基 ( t − τ ) exp ⁡ { j 2 π f c t } exp ⁡ { − j 4 π f c R 0 − V t c } = A u 基 ( t − τ ) exp ⁡ { j 2 π f c t } exp ⁡ { − j 4 π f c R 0 c } exp ⁡ { j 4 π f c V t c }
  echo(t)=Au调(t−τ)=Au基(t−τ)exp⁡{j2πfc(t−τ)}=Au基(t−τ)exp⁡{j2πfc[t−2(R0−Vt)c]}=Au基(t−τ)exp⁡{j2πfct}exp⁡{−j4πfcR0−Vtc}=Au基(t−τ)exp⁡{j2πfct}exp⁡{−j4πfcR0c}exp⁡{j4πfcVtc}" role="presentation" style="position: relative;">echo(t)=Au调(t−τ)=Au基(t−τ)exp{j2πfc(t−τ)}=Au基(t−τ)exp{j2πfc[t−2(R0−Vt)c]}=Au基(t−τ)exp{j2πfct}exp{−j4πfcR0−Vtc}=Au基(t−τ)exp{j2πfct}exp{−j4πfcR0c}exp{j4πfcVtc}$$\begin{array}{rl}echo(t)& =A{u}_{调}(t-\tau )\\ & =A{u}_{基}(t-\tau )\exp \{j2\pi f_c(t-\tau )\}\\ & =A{u}_{基}(t-\tau )\exp \{j2\pi f_c[t-\frac{2(R_0-Vt)}{c}]\}\\ & =A{u}_{基}(t-\tau )\exp \{j2\pi f_{c}t\}\exp \{-j4\pi f_c\frac{R_0-Vt}{c}\}\\ & =A{u}_{基}(t-\tau )\exp \{j2\pi f_{c}t\}\exp \{-j4\pi f_c\frac{R_0}{c}\}\exp \{j4\pi f_c\frac{Vt}{c}\}\end{array}$$
  echo(t)​=Au调​(t−τ)=Au基​(t−τ)exp{ j2πfc​(t−τ)}=Au基​(t−τ)exp{ j2πfc​[t−c2(R0​−Vt)​]}=Au基​(t−τ)exp{ j2πfc​t}exp{ −j4πfc​cR0​−Vt​}=Au基​(t−τ)exp{ j2πfc​t}exp{ −j4πfc​cR0​​}exp{ j4πfc​cVt​}​
  其中，A为衰减后的幅度，目标的延时 $\tau =\frac{2(}{c}$