System, method and apparatus for multi-input multi-output communications over per-transmitter power-constrained channels

A method for transmitting information comprising:

• providing a communication system having, n transmitting antennas and m receiving antennas, n≦m wherein said communication system is subject to a per-antenna power constraint, said communication system operating to produce a received signal characterized by a vector y, the elements of vector y corresponding to said m receiving antennas respectively, in response to a transmitted signal characterized by a vector x, the elements of vector x corresponding to said n transmitting antennas respectively, said signal being transmitted through a channel characterized by a channel matrix H of circular complex multiplicative factors and in the presence of Gaussian white noise characterized by a vector z according to the relationship:
• y=Hx+z;
• operating a linear precode device to derive, in real time, a linear precode for a communication channel based on said antenna power constraint and a channel state information matrix, said operating said linear precode device including iteratively performing the following method steps, where variable index i identifies the values associated with a particular iteration of the iterative method:
• 1) forming a temporary matrix F, where Fi=K{hacek over (D)}iK†−In,
• Fi being the value of a temporary matrix F at a current iteration,
• K being a matrix such that K=VHΣnVH†, where VH is a unitary matrix containing a plurality of right singular values obtained by singular value decomposition of the channel matrix H, and VH† is the hermitian conjugate transpose of VH,
• Σn being a diagonal matrix containing said corresponding (real) singular values in decreasing order,
• {hacek over (D)}i being the value of the matrix {hacek over (D)} at the ith iteration of the method, where {hacek over (D)} is the inverse of a matrix D, D being a diagonal matrix consisting of Lagrangian multipliers for respective per-antenna power constraints of said n transmitter antennas, K† being the hermitian conjugate transpose of K, and
• In being an identity matrix of dimension n;
• 2) performing an eigenvalue decomposition of said temporary matrix F, where
• Fi=UFΛUF†,
• UF being a matrix consisting of the resulting eigenvectors,
• Λ being a matrix of eigenvalues,
• UF† being the hermitian conjugate transpose of UF, and;
• 3) discarding non-positive eigenvalues of said temporary matrix F;
• 4) forming a matrix Si, where Si=−UFkΛFkUFk†, and where
• k is the number of said non-positive eigenvalues and Si being a matrix consisting of non-positive eigenmodes of (F−In),
• ΛFk is the k×k diagonal matrix of all k non-positive eigenvalues of Fi and where
• UFk consists of the corresponding k eigenvectors and where
• UFk† is the hermitian conjugate transpose of UFk;
• 5) forming a matrix Zi where Zi={hacek over (K)}Si{hacek over (K)}†
• Zi being the value of a matrix Z at the ith iteration of the method, where {hacek over (K)} is the inverse matrix of matrix K and {hacek over (K)}† is the hermitian conjugate transpose of {hacek over (K)};
• 6) forming a transmitted signal covariant matrix Qi where
• Qi={hacek over (D)}i−{hacek over (G)}+Zi;
• Qi being the value of the transmitted signal covariant matrix at the ith iteration of the method, and
• {hacek over (G)} being a subsidiary matrix equal to {hacek over (K)}{hacek over (K)}†;
• and
• encoding information to be transmitted according to said linear precode by applying, as a linear precode, a resulting transmitted signal covariance matrix Qi of the final iteration, to modify an encoded signal to be transmitted from said transmitting antennas.