A method of suppressing side-lobes on at least one side of a principal lobe in the beam pattern of a phased antenna array having a plurality of antenna elements (10, 10') and phase control circuitry (111, 113, 14), the method including: for each antenna element (10, 10'), adjusting the phase of radio frequency signals that may be fed to and/or received by the element (10, 10') by a phase correction Φ(α,r) as a function of the position of the element within the array to generate an asymmetric side-lobe pattern, such that side-lobes on at least one side of the principal lobe are suppressed, characterised in that: the phase correction Φ(α,r) applied to any one antenna element (10, 10') is defined according to the expression: Φ r α = sin α ∑ k = 1 p a 2 k + 1 r 2 k + 1 where α is the angular position of the antenna element, r is the radial position of that antenna element, p is a variable and a 2k+1 are coefficients of the phase function Φ; wherein at least one coefficient a 2k+1 is non-zero and the coefficients are pre-determined on fabrication of said phased antenna array by, pre-selecting a template of beam pattern with a desired asymmetric side-lobe configuration, and for a selection of variables p, minimising the mean square error between a beam pattern generated with said polynomial and said template by adjusting the coefficients a 2k+1 until the mean square error is less than a prescribed level. for each antenna element (10, 10'), adjusting the phase of radio frequency signals that may be fed to and/or received by the element (10, 10') by a phase correction Φ(α,r) as a function of the position of the element within the array to generate an asymmetric side-lobe pattern, such that side-lobes on at least one side of the principal lobe are suppressed, characterised in that: the phase correction Φ(α,r) applied to any one antenna element (10, 10') is defined according to the expression: Φ r α = sin α ∑ k = 1 p a 2 k + 1 r 2 k + 1 where α is the angular position of the antenna element, r is the radial position of that antenna element, p is a variable and a 2k+1 are coefficients of the phase function Φ; wherein at least one coefficient a 2k+1 is non-zero and the coefficients are pre-determined on fabrication of said phased antenna array by, pre-selecting a template of beam pattern with a desired asymmetric side-lobe configuration, and for a selection of variables p, minimising the mean square error between a beam pattern generated with said polynomial and said template by adjusting the coefficients a 2k+1 until the mean square error is less than a prescribed level. the phase correction Φ(α,r) applied to any one antenna element (10, 10') is defined according to the expression: Φ r α = sin α ∑ k = 1 p a 2 k + 1 r 2 k + 1 where α is the angular position of the antenna element, r is the radial position of that antenna element, p is a variable and a 2k+1 are coefficients of the phase function Φ; wherein at least one coefficient a 2k+1 is non-zero and the coefficients are pre-determined on fabrication of said phased antenna array by, pre-selecting a template of beam pattern with a desired asymmetric side-lobe configuration, and for a selection of variables p, minimising the mean square error between a beam pattern generated with said polynomial and said template by adjusting the coefficients a 2k+1 until the mean square error is less than a prescribed level.