Reference no: EM131549895

Question: The range (distance from transmitter) of a radar target is determined from the delay between the transmitted and return signals. For targets of unknown range, the delay will be a random variable. The decision problem in this case can be modeled as

H₁: z(t) = y(t - τ) + v(t)          0 ≤ t ≤ T

H₀: z(t) = v(t)                        0 ≤ t ≤ T

where y (t) is a known waveform and τ is the unknown delay. Derive the likelihood ratio test for this problem under the assumption that vet) is zero mean, white, Gaussian, and τ is uniformly distributed in [τ0,τ1].