The optimal array, which maximizes = S ( 6 )a(t) + w(t)(1.1) the signal to interference plus noise ratio (SINR), is beam-formed by the following weigh vector: jd,e jd2 e jdN;] t -~~~~~~~~where s (9 ) [eJd eJd ,.eJd Tis the =c[R_ ls(5)~m j = c[R s(s0)0 steering vector from an interference source such as jamming, clutter or target return at arriving where R is the covariance matrix of interference and receiver noise, and where s() is the steering angle 9 , 4 = (2m/2)sin 0 , X is the wavelength, vector from a desired direction 0. The optimal and dn is the distance between the n-th sensor array is well known and fundamental in the literature of adaptive array and signal processing and a reference poit i the array. In (2), S (6) but has not been actually applied to real radar [S( e )... s(o )] is a NxM matrix, formed by because of huge computation burden for inverting 1 M R, which is on the order of N3 / Ar. Here N is the steering vectors from 9 ...0 9 and 6 the number of sensors in an array and Al' is the [0 ]T a(t) =[a (t) a (t)] is the update interval. Typically, N = 1,000 in a planar 1 M a ) M( array and Al = 1 IS . In order to reduce the vector of complex amplitudes of interference at computational burden, Brookner and Howells time t. a(t) is assumed to be stationary in t and proposed 111 the technique of adaptive-adaptive satisfies array, which transforms the large array of N E a(t) = O E a(t) a (t) = O sensors to a small array of M+1 beams of pointing H t to M interference sources and the desired direction E a(t) a (t) = P. (1.2) 0. The optimal array based on M+1 beams Hereafter, E denotes the statistical expectation, requires a computation burden only on the order of (.) , (.) and (.)H denote the complex M3 / AT . The adaptive-adaptive array in [1] is an conjugate, transpose and conjugated transpose of ingenious conjecture rather than a solid technique, a complex number or a matrix, respectively. because no solid method for tracking the directions P d lt th . 2 of M interference sources is given. In this paper, S aiagonamarixwi ,the angle-tracking adaptive array (ATAA) in 121 is along its diagonal (so Pm the power of the m-th introduced to implement the adaptive-adaptive array processing. The ATAA offers an even higher interference source, m = 1,2... M). SINR than the well-known optimal array at a w (t) is the complex Gaussian receiver noise computational burden only on the order of vector at time t and is assumed to be white and N M2 / A 17. The ATAA is providing a solid basis stationary in t, satisfying for the adaptive-adaptive array and is superior E w (t) =O,E w (t) w (t) = 0, over the well known optimal array in both SINR H 2 and computation burden, suggesting a remarkable E w (t) w (t) = J7 I.(1.3) new direction to the adaptive array processing in Data snapshots x(t) are assumed to follow model the eve of digital beam-forming era.