A method in a wireless device of reporting multi-beam channel state information, CSI, in uplink control information, UCI, and in an uplink shared channel, UL-SCH, the method including: providing an indication of a plurality of beam index pairs, (l k, m k), in the UCI in a first transmission, each beam index pair corresponding to a beam k; and providing an indication of a beam power, a beam rotation and a channel quality index, CQI, in the UL-SCH in a second transmission, wherein a beam power p k of a beam k is a real number such that a cophasing factor c k is expressed c k = c' k p k, where c k ′ 2 = 1, and beam rotations r 1 and r 2 are real numbers such that beam directions for beam k, Δ 1,k and Δ 2,k are expressed as Δ 1,k = Δ' 1,k + r 1 and Δ 2,k Δ' 2,k + r 2, and wherein each beam is a k th beam, d(k), that comprises a set of complex numbers and has index pair (l k, m k), each element of the set of complex numbers being characterized by at least one complex phase shift such that: (i) d n (k) = d i (k)α i,n e j2π(pΔ 1,k+qΔ2,k); (ii) d n (k), and d i (k) are the i th and n th elements of d(k), respectively; (iii) α i,n is a real number corresponding to an i th and n th elements of d(k); (iv) p and q are integers; (v) beam directions Δ 1,k and Δ 2,k are real numbers corresponding to beams with index pair (l k, m k) that determine the complex phase shifts e j2πΔ 1,k and e j2πΔ 2,k respectively; and (vi) each beam cophasing coefficient is a complex number c k for d(k) that is used to adjust a phase of an i th element of d(k) according to c k d i (k). providing an indication of a plurality of beam index pairs, (l k, m k), in the UCI in a first transmission, each beam index pair corresponding to a beam k; and providing an indication of a beam power, a beam rotation and a channel quality index, CQI, in the UL-SCH in a second transmission, wherein a beam power p k of a beam k is a real number such that a cophasing factor c k is expressed c k = c' k p k, where c k ′ 2 = 1, and beam rotations r 1 and r 2 are real numbers such that beam directions for beam k, Δ 1,k and Δ 2,k are expressed as Δ 1,k = Δ' 1,k + r 1 and Δ 2,k Δ' 2,k + r 2, and wherein each beam is a k th beam, d(k), that comprises a set of complex numbers and has index pair (l k, m k), each element of the set of complex numbers being characterized by at least one complex phase shift such that: (i) d n (k) = d i (k)α i,n e j2π(pΔ 1,k+qΔ2,k); (ii) d n (k), and d i (k) are the i th and n th elements of d(k), respectively; (iii) α i,n is a real number corresponding to an i th and n th elements of d(k); (iv) p and q are integers; (v) beam directions Δ 1,k and Δ 2,k are real numbers corresponding to beams with index pair (l k, m k) that determine the complex phase shifts e j2πΔ 1,k and e j2πΔ 2,k respectively; and (vi) each beam cophasing coefficient is a complex number c k for d(k) that is used to adjust a phase of an i th element of d(k) according to c k d i (k). (i) d n (k) = d i (k)α i,n e j2π(pΔ 1,k+qΔ2,k); (ii) d n (k), and d i (k) are the i th and n th elements of d(k), respectively; (iii) α i,n is a real number corresponding to an i th and n th elements of d(k); (iv) p and q are integers; (v) beam directions Δ 1,k and Δ 2,k are real numbers corresponding to beams with index pair (l k, m k) that determine the complex phase shifts e j2πΔ 1,k and e j2πΔ 2,k respectively; and (vi) each beam cophasing coefficient is a complex number c k for d(k) that is used to adjust a phase of an i th element of d(k) according to c k d i (k).