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

Abstract

A multipath communication system forms a complex weighted compound signal for transmission through a channel environment wherein the compound signal includes a complex variable weighted compound signal related to a count of available antennas, a power constraint related to each said antenna, and a channel state characteristic.

1 . A method for transmitting information comprising:
 providing a MIMO communication system having, a plurality of n transmitting antennas and a plurality of m receiving antennas, wherein said n transmitting antennas are subject to a per-antenna power constraint, said communication system operating to achieve the capacity of the system.   
     
     
         2 . Said MIMO system in  claim 1  producing 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 complex multiplicative factors and in the presence of 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, where in the case of n≦m, 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 F i =K{hacek over (D)} i K † −I n ,
 F i  being the value of a temporary matrix F at a current iteration, 
 K being a matrix such that K=V H Σ n V H   † , where V H  is a unitary matrix containing a plurality of right singular vectors obtained by singular value decomposition of the channel matrix H, and V H   †  is the Hermitian conjugate transpose of V H , 
 Σ n  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 
 I n  being an identity matrix of dimension n; 
 
 2) performing an eigenvalue decomposition of said temporary matrix F, where
     F   i   =U   F   ΛU   F   † , 
 U F  being a matrix consisting of the resulting eigenvectors, 
 Λ being a matrix of eigenvalues, 
 U F   †  being the Hermitian conjugate transpose of U F , and; 
 
 3) separating non-positive eigenvalues of said temporary matrix F; 
 4) forming a matrix S i , where S i =−U F   k  Λ F   k U F   k† , which contains the negative and zero eigenvalues and where k is the number of said non-positive eigenvalues and S i  is a matrix consisting of non-positive eigenmodes of F i ,
 Λ F   k  is the k×k diagonal matrix of all k non-positive eigenvalues of F i  and where 
 U F   k  consists of the corresponding k eigenvectors and where 
 U F   k†  is the Hermitian conjugate transpose of U F   k ; 
 
 5) forming a matrix Z i  where Z i ={hacek over (K)}S i {hacek over (K)} † 
 Z i  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 Q i  where
     Q   i   ={hacek over (D)}   i   −{hacek over (G)}+Z   i ; 
 
 Q i  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 Q i  of the final iteration, to modify an encoded signal to be transmitted from said transmitting antennas. 
     
     
         3 . A method for transmitting information as defined in  claim 2  wherein the values of said channel matrix H are acquired by evaluation of a pilot signal and subsequent receipt by the transmitter of a corresponding feedback signal. 
     
     
         4 . A method for transmitting information as defined in  claim 2  wherein the values of said channel matrix H are acquired by reciprocal information based on received general information signals. 
     
     
         5 . A method of transmitting information as defined in  claim 2  wherein an environment of said MIMO communication system includes colored noise, further comprising converting said colored noise to white noise. 
     
     
         6 . Said MIMO system in  claim 1  producing 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 complex multiplicative factors and in the presence of 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, where in the case of n>m, 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 F i =H {hacek over (D)} i H † −I m ,
 F i  being the value of a temporary matrix F at a current iteration, 
 {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, H †  being the Hermitian conjugate transpose of H, and 
 I m  being an identity matrix of dimension m; 
 
 2) performing an eigenvalue decomposition of said temporary matrix F, where
     F   i   =U   F   ΛU   F   † , 
 U F  being a matrix consisting of the resulting eigenvectors, 
 Λ being a matrix of eigenvalues, 
 U F   †  being the Hermitian conjugate transpose of U F , and; 
 
 3) separating non-positive eigenmodes of said temporary matrix F; 
 4) forming a matrix S i , where S i =−U F   k Λ F   k U F   k† , and where
 k is the number of said non-positive eigenmodes and S i  is a matrix consisting of non-positive eigenmodes of F i , 
 Λ F   k  is the k×k diagonal matrix of all k non-positive eigenvalues of F i  and where 
 U F   k  consists of the corresponding k eigenvectors and where 
 U F   k†  is the Hermitian conjugate transpose of U F   k ; 
 
 5) forming a matrix Z i  where Z i ={hacek over (H)}S i {hacek over (H)} † , Z i  being the value of a matrix Z at the ith iteration of the method, where {hacek over (H)} is the inverse matrix of matrix H and {hacek over (H)} †  is the Hermitian conjugate transpose of {hacek over (H)}; 
 6) form matrix D i  by taking the diagonal of matrix {hacek over (D)} i  bias a vector {hacek over (D)} i,jj , j=1 . . . n, and inverting resulting vector {hacek over (D)} i,jj  to produce D i ={hacek over (D)} i,jj   −1 ; 
 7) forming a temporary matrix B i =V 1   † (Z i −{hacek over (G)})D i V 2 (V 2   † D i V 2 ) −1  where matrix B i  is a m×(n−m) matrix representing the coupling among the modes to be dropped, {hacek over (G)} is a subsidiary matrix equal to {hacek over (K)}{hacek over (K)} †  where K is a matrix such that K=V H Σ n V H   † , where Σ n  is a diagonal matrix containing the singular values of H in decreasing order, V H  is a unitary matrix containing a plurality of right singular values obtained by singular value decomposition of the channel matrix H, V H   †  is the Hermitian conjugate transpose of V H , V 1   †  is a matrix formed of the first m columns of V H , V 2   †  is a matrix formed of the last n-m columns of V H , V 1   †  is the Hermitian conjugate transpose of V 1 , V 2   †  is the Hermitian conjugate transpose of V 2 , {hacek over (K)} is the inverse of matrix K, and {hacek over (K)} †  is the Hermitian conjugate transpose of {hacek over (K)}; 
 8) forming a temporary matrix A i =(I n-m −B i   † V 1   † D i V 2 ) −1  where A i  is a (n−m)×(n−m) Hermitian matrix representing the modes to be dropped; 
 9) forming a temporary matrix X i =V 2 A i V 2   † +V 1 B i V 2   † +V 2 B i   † V 2   †  where X i  is a Hermitian matrix representing the portion to be subtracted out of the transmit signal covariance matrix for said covariance matrix to remain positive semi-definite at each iteration; 
 10) forming a transmitted signal covariant matrix Q i  where
 Q i ={hacek over (D)} i −{hacek over (G)}+Z i −X i , Q i  being the value of the transmitted signal covariant matrix at the ith iteration of the method; and 
 
 
       encoding information to be transmitted according to said linear precode by applying, as a linear precode, a resulting transmitted signal covariance matrix Q i  of the final iteration, to modify an encoded signal to be transmitted from said transmitting antennas. 
     
     
         7 . A method for transmitting information as defined in  claim 6  wherein the values of said channel matrix H are acquired by evaluation of a pilot signal and subsequent receipt by the transmitter of a corresponding feedback signal. 
     
     
         8 . A method for transmitting information as defined in  claim 6  wherein the values of said channel matrix H are acquired by reciprocal information based on received general information signals. 
     
     
         9 . A method of transmitting information as defined in  claim 6  wherein an environment of said MIMO communication system includes colored noise, further comprising converting said colored noise to white noise.