A method implemented by a computer for maximizing a sum rate of a Millimeter wave communication system, said communication system enabling both analog and digital beamforming, said communication system including a transmitter being able to serve a plurality of receivers, wherein each receiver among the plurality of receivers is associated to a set of analog precoding codewords, wherein is the set of analog precoding codewords associated to the k th receiver, wherein each analog precoding codeword F is a column of a predetermined matrix having a number of rows equal to a number of antennas (121, 12Nt) of the transmitter and a number of columns greater or equal than L r k, said matrix being a Discrete Fourier Transform, DFT, matrix or a matrix obtained by re-normalizing a sub-matrix extracted from a DFT matrix, L r k being a number of receiving analog chains at said receiver; said method comprising: - for each receiver among the plurality of receivers, computing, at said receiver, an analog precoding matrix F RF,k associated to said receiver, wherein F RF,k is the analog precoding matrix associated to the k th receiver; and - using at least one computed analog precoding matrix for processing at least one signal to transmit from the transmitter to at least one receiver; wherein the computation of the analog precoding matrix associated to a receiver among the plurality of receivers comprises: /a/ performing a Singular Value Decomposition, SVD, on a channel matrix associated to said receiver; /b/ determining a first decomposition matrix V k based on the relative SVD; characterized in that the computation of the analog precoding matrix associated to a receiver among the plurality of receivers further comprises: /c/ selecting a column f i from the predetermined matrix which is different from the columns of C i -1 and which maximizes a first function g 1 ( V k, F) of V k and F, said first function being function of: F H V ̅ k V ̅ k H F + λ min C i − 1 H V ̅ k V ̅ k H C i − 1 2 − F H V ̅ k V ̅ k H F − λ min C i − 1 H V ̅ k V ̅ k H C i − 1 2 4 + F H V ̅ k V ̅ k H C i − 1 C i − 1 H V ̅ k V ̅ k H F where: • C i -1 is composed from at least one column of said predetermined matrix; • F is different from all the columns of C i -1; • A H denotes a conjugate transpose matrix of a matrix A; and • λ min denotes a minimal eigenvalue of a matrix A; wherein /c/ is performed iteratively for i = 2,..., L r, with C 1 = f 1, where f 1 is a column of said predetermined matrix which maximizes a function F H V ̅ k V ̅ k H F of V k and F, for a plurality of and C i is the concatenated matrix whose first columns are all columns of C i -1, and last column is f i, and the analogue combining matrix associated to receiver k is F RF, k = C L r k, where C L r k is the C i matrix after L r k iterations. wherein each receiver among the plurality of receivers is associated to a set of analog precoding codewords, wherein is the set of analog precoding codewords associated to the k th receiver, wherein each analog precoding codeword F is a column of a predetermined matrix having a number of rows equal to a number of antennas (121, 12Nt) of the transmitter and a number of columns greater or equal than L r k, said matrix being a Discrete Fourier Transform, DFT, matrix or a matrix obtained by re-normalizing a sub-matrix extracted from a DFT matrix, L r k being a number of receiving analog chains at said receiver; said method comprising: - for each receiver among the plurality of receivers, computing, at said receiver, an analog precoding matrix F RF,k associated to said receiver, wherein F RF,k is the analog precoding matrix associated to the k th receiver; and - using at least one computed analog precoding matrix for processing at least one signal to transmit from the transmitter to at least one receiver; - for each receiver among the plurality of receivers, computing, at said receiver, an analog precoding matrix F RF,k associated to said receiver, wherein F RF,k is the analog precoding matrix associated to the k th receiver; and - using at least one computed analog precoding matrix for processing at least one signal to transmit from the transmitter to at least one receiver; wherein the computation of the analog precoding matrix associated to a receiver among the plurality of receivers comprises: /a/ performing a Singular Value Decomposition, SVD, on a channel matrix associated to said receiver; /b/ determining a first decomposition matrix V k based on the relative SVD; /a/ performing a Singular Value Decomposition, SVD, on a channel matrix associated to said receiver; /b/ determining a first decomposition matrix V k based on the relative SVD; characterized in that the computation of the analog precoding matrix associated to a receiver among the plurality of receivers further comprises: /c/ selecting a column f i from the predetermined matrix which is different from the columns of C i -1 and which maximizes a first function g 1 ( V k, F) of V k and F, said first function being function of: F H V ̅ k V ̅ k H F + λ min C i − 1 H V ̅ k V ̅ k H C i − 1 2 − F H V ̅ k V ̅ k H F − λ min C i − 1 H V ̅ k V ̅ k H C i − 1 2 4 + F H V ̅ k V ̅ k H C i − 1 C i − 1 H V ̅ k V ̅ k H F • C i -1 is composed from at least one column of said predetermined matrix; • F is different from all the columns of C i -1; • A H denotes a conjugate transpose matrix of a matrix A; and • λ min denotes a minimal eigenvalue of a matrix A;