Consider a desired signal that is a harmonic pulse of T samples: with fixed amplitude A and frequency f 0 , and random phase 𝜙, uniformly distributed on the interval from 0 to 2𝜋. Suppose that the...

Consider a desired signal that is a harmonic pulse of T samples:

with fixed amplitude A and frequency f₀, and random phase 𝜙, uniformly distributed on the interval from 0 to 2𝜋. Suppose that the desired signal impinges on a ULA of M sensors from the direction 𝜃₀.

a) Show that the variance of ( f ) is

Where

b) Assume an interference u(t) ∼ N ( 0, 𝜎²
_u
) that impinges on the ULA from the endfire direction. Show that

c) Compute the narrowband and broadband input SNRs.

d) Show that with the maximum SNR filter the narrowband gain in SNR can be written as