Two-stage robust algorithm of antenna array adaptation

Abstract

Let us assume that at the antenna array (AA) input the desired signal periodically is absent, with arrival moments and length of a “passive pause” changing in accordance with a pseudorandom law. For the case of absence of the desired signal at AA input die problem of adaptation algorithm synthesis is represented in the form of

*,                       (1)

where W is the N-dimensional vector of weight coefficients; R_xx is the correlation matrix of input signals. An eigen matrix vector R_xx corresponding to its minimum eigen is the solution W, of the problem (1), and in this case W, defines characteristics of the nulled pattern in the noise-arrival directions. Consequently, transforming W_l we can define noise-arrival direction and form L (L being the number of noise sources) matrices of the form R_jj ⁼ *, φ_jl is the phase shift, caused by the noise delay at the l-th antenna element relative to the first one. In the case of the desired signal presence at AA input we formulate optimization problem

*    (2)

where *, θ_j1, θ_j2 are suppression sector bounds of the j-th noise; α_j is a positive real coefficient. We represent the problem solution in the form of recurrence procedures

*                               (3)

Y⁺ = *, μ_k is a step constant; Pr{•} – a projector into hypersphere of the unit radius. Algorithms (3) converge on a global scale and provide the efficiency of AA approaching the potentially achievable one.