Receiver, communication system, and method implemented by computer for enabling both analog and digital beamforming in communication system

A method implemented by a computer for maximizing a sum rate of a 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 relative set prec,k of analog precoding codewords, wherein prec,k is the set of analog precoding codewords associated to the kth 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 of the transmitter and a number of columns greater or equal than Lrk, said matrix being a Discrete Fourier Transform, DFT, matrix or a matrix obtained by re-normalizing a sub-matrix extracted from a DFT matrix;
• said method comprising:
• for each receiver among the plurality of receivers, computing, at said receiver, an analog precoding matrix FRF,k associated to said receiver, wherein FRF,k is the analog precoding matrix associated to the 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 Vk 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/ determining an analog precoding codeword which maximizes a first function g1 (Vk,F) of Vk and F, said first function being function of:
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• where:
• Ci−1 is composed from at least one column of said predetermined matrix;
• F is different from all the columns of Ci−1;
• AH denotes a conjugate transpose matrix of a matrix A;
• and
• λmin(A) denotes a minimal eigenvalue of a matrix A;
• wherein /c/ is performed iteratively for i=2 . . . Lr, with C1=f1, where f1 is column of said predetermined matrix which maximizes a function FHVkVkHF of Vk and F, for a plurality of F∈prec,k.

A receiver configured to receive data from a transmitter able to serve a plurality of receivers, in a communication system enabling both analog and digital beamforming,

• said receiver being associated to a set prec,k of analog precoding codewords,
• said receiver comprising a circuit for maximizing a sum rate of the communication system, said maximization including a computation of an analog precoding matrix FRF,k,
• wherein the computation of the analog precoding matrix comprises:
• /a/ performing a Singular Value Decomposition, SVD, on a channel matrix;
• /b/ determining a first decomposition matrix Vk based on said SVD;
• and
• characterized in that the computation of the analog precoding matrix associated to a receiver among the plurality of receivers further comprises:
• /c/ determining an analog precoding codeword which maximizes a first function g1(Vk,F)=λmin(VkHFFHVk) of Vk and F, for a plurality of F∈prec,k,
• where:
• AH denotes a conjugate transpose matrix of a matrix A;
• and
• λmin(A) denotes a minimal eigenvalue of a matrix A.

A communication system enabling both analog and digital beamforming, said system comprising a transmitter being able to serve a plurality of receivers, wherein each receiver is configured to receive data from said transmitter,

• said receiver being associated to a set prec,k of analog preceding codewords,
• said receiver comprising a circuit for maximizing a sum rate of the communication system, said maximization including a computation of an analog precoding matrix FRF,k,
• wherein the computation of the analog precoding matrix comprises:
• /a/ performing a Singular Value Decomposition, SVD, on a channel matrix:
• /b/ determining a first decomposition matrix Vk based on said SVD;
• and
• characterized in that the computation of the analog precoding matrix associated to a receiver among the plurality of receivers further comprises:
• /c/ determining an analog precoding, codeword which maximizes a first function g1(Vk, F)=λmin(VkHFFHVk) of Vk and F, for a plurality of F∈prec,k,
• where:
• AH denotes a conjugate transpose matrix of a matrix A;
• and
• λmin (A) denotes a minimal eigenvalue of a matrix A.

A computer program product, comprising instructions for performing a method implemented by a computer for maximizing a sum rate of a 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 relative set prec,k of analog precoding codewords wherein prec,k is the set of analog precoding codewords associated to the kth receiver,
• said method comprising:
• for each receiver among the plurality of receivers, computing, at said receiver, an analog precoding matrix FRF,k associated to said receiver,
• wherein FRF,k is the analog precoding matrix associated to the kth 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 Vk 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/ determining an analog precoding codeword which maximizes a first function g1(Vk, F)=λmin(VkHFFHVk) of Vk and F, for a plurality of F∈prec,k,
• where:
• AH denotes a conjugate transpose matrix of a matrix A;
• and
• λmin(A) denotes a minimal eigenvalue of a matrix A.

A computer program product, comprising instructions for performing a method implemented by a computer for maximizing a sum rate of a 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 relative set prec,k of analog precoding codewords, wherein prec,k is the set of analog precoding codewords associated to the kth receiver,
• said method comprising:
• for each receiver among the plurality of receivers, computing, at said receiver, an analog precoding matrix FRF,k associated to said receiver,
• wherein FRF,k is the analog precoding matrix associated to the kth 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 Vk 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/ determining an analog precoding codeword which maximizes a first function g1(Vk, F)=λmin(VkHFFHVk) of Vk and F, for a plurality of F∈prec,k,
• where:
• AH denotes a conjugate transpose matrix of a matrix A;
• and
• λmin(A) denotes a minimal eigenvalue of a matrix A.