In a monostatic radar, transmitter and receiver share the same antenna; the range equation gains simplify to what?

In a monostatic radar, transmitter and receiver share the same antenna; the range equation gains simplify to what?

• A. The gain terms cancel to zero; P_r ≈ …
• B. The gains add linearly; P_r ≈ …
• C. The transmitter and receiver share the same antenna so G_t = G_r and L_t = L_r, giving P_r ≈ (P_t G^2 λ^2 σ)/((4π)^3 R^4 L^2)
• D. The gains become external; P_r ≈ (P_t G_t G_r λ^3 σ)/…

Answer: (C)

In a monostatic radar, the same antenna handles both transmitting and receiving, so the transmitter and receiver gains are the same and must be multiplied together. That gives G_t G_r = G^2. Because the signal travels to the target and back, the geometric spreading is effectively squared, giving a 1/R^4 dependence for range. The receiving aperture relates to the wavelength by A_e = G λ^2 /(4π), which introduces a λ^2 factor into the received power. Including the two path losses, one on transmit and one on receive, yields the L^2 term in the denominator. Putting these pieces together, the received power is P_r ≈ (P_t G^2 λ^2 σ) / ((4π)^3 R^4 L^2). This is exactly the form shown in the correct option. The other forms mis-handle the gain combination, the range dependence, or the λ term.

In a monostatic radar, the same antenna handles both transmitting and receiving, so the transmitter and receiver gains are the same and must be multiplied together. That gives G_t G_r = G^2. Because the signal travels to the target and back, the geometric spreading is effectively squared, giving a 1/R^4 dependence for range. The receiving aperture relates to the wavelength by A_e = G λ^2 /(4π), which introduces a λ^2 factor into the received power. Including the two path losses, one on transmit and one on receive, yields the L^2 term in the denominator. Putting these pieces together, the received power is P_r ≈ (P_t G^2 λ^2 σ) / ((4π)^3 R^4 L^2). This is exactly the form shown in the correct option. The other forms mis-handle the gain combination, the range dependence, or the λ term.