Covariance of narrow-band noise in multiple beams of a phased-array system

Covariance of narrow-band noise among two simultaneous beams, looking toward different directions with identical power patterns, for a phased array system is formally analyzed. It is shown that the noise correlation coefficient as a function of the angle of separation between two beams is the same as the normalized beam power pattern. This result is independent of the way the beams are formed, in particular these conclusions for both the total power beam systems and the correlator beam systems are examined in detail.