Assume a monostatic radar is transmitting a pulsed waveform. The pulse has been modulated by a Barker code with$\ N$ chips or bits. The waveform chip rate is $\tau_c $, the radar receiver's detection bandwidth is $\beta_c = 1/\tau_c$, and the waveform's pulsewidth is $\ N*\tau_c$.
I've heard conflicting opinions about a signal processing gain,$\ P_g$, due to compressing the pulse that is proportional to the waveform's time-bandwidth (or pulse compression ratio (PCR)) product (or equivalently the product of the uncompressed pulsewidth $\tau_p$ and the compressed bandwidth $\beta_c$) of the pulse: $\ P_g = \tau_p*\beta_c=N\tau_c*\beta_c$
Is it appropriate to add a$\ P_g$ term to the power form of the SNR radar range equation?
(Pulse compression allows a radar to transmit a longer pulse to get more energy on the target while simultaneously achieving the range resolution of a much shorter pulse.)
FWIW, I have the same question about the energy form of the radar range SNR equation: