Consider a desired signal that is a sum of harmonic random processes: with fixed amplitudes { A k } and frequencies { f k } , and IID random phases { 𝜙 k } , uniformly distributed on the interval...

Consider a desired signal that is a sum of harmonic random processes:

with fixed amplitudes { A_k
} and frequencies { f_k
} , and IID random phases { 𝜙_k
} , uniformly distributed on the interval from 0 to 2𝜋. Assume that the interference u(t) is colored noise that is uncorrelated with x(t), with the autocorrelation sequence:

a) Compute the fullmode input SNR.

b) Assume that the desired signal impinges on the ULA from the broadside direction. Describe the steps to find the correlation matrix 𝐑_𝐱
m
.

c) Assume that the desired signal impinges on the ULA from the direction 𝜃. Describe the steps to find the correlation matrix 𝐑_𝐱
m
.

d) Assume that the sampling interval satisfies Ts = d∕c, and the interference impinges on the ULA from the endfire direction. Describe the steps to find the correlation matrix 𝐑_𝐮
m
 .