MIMO maximum-likelihood space-time architecture
First Claim
Patent Images
1. A method for the design and implementation of maximum-likelihood (ML) architecture for MIMO systems with M receive antennas and N transmit antennas and with epoch T>
- 1, comprising the steps;
constructing the new space-time TM×
TN transmission matrix H0 as the matrix-diagonal matrix generated by the tensor product of the T×
T identity diagonal matrix with the M×
N transmission matrix H to generate the TM×
TN matrix H0 whose matrix elements on the diagonal are the H and zeros elsewhere and whereinsymbol “
T”
is the number of time epochs which are the number of repeated transmissions,symbol “
TM×
TN”
reads “
TM rows by TN columns”
,transmission matrix H has transmission elements hi,j which measure the transmitter, path, and receiver transmission loss from transmitter j in column j=1, . . . , M to receiver i in row i=1, . . . , M,transmission elements hi,j are complex measurements of the transmission loss from j to i, anda matrix-diagonal matrix has matrices along the diagonal and zeros elsewhere;
constructing the new space-time TN×
N code matrix C0 as the matrix product C0=A•
B of a TN×
TN matrix A with a TN×
N matrix B and whereinsymbol “
•
”
is a matrix or vector product,matrix A is the TN×
TN matrix-diagonal matrix whose diagonal matrix elements are the T N×
N diagonal matrices A1, . . . , AT,matrices An for n=1, . . . , T are orthogonal matrices satisfying An′
•
An=NIN wherein An′
is the conjugate transpose of An and IN is the N×
N identity diagonal matrix,matrix B=[B1;
. . . ;
BN] is the TN×
N matrix whose elements are the N×
N orthogonal matrices B1, . . . , BT each with elements including L and using the Matlab construction operator “
;
”
for stacking matrices, vectors, or elements in a column format,matrices Bn for n=1, . . . , T are orthogonal matrices with the property Bn′
•
Bn=NIN,matrix element “
L”
is the new complex-conjugate operator defined by the operation “
L(w)=w*=complex-conjugate of the element w” and
L(L(w))=w,space-time TN×
N code matrix C0 satisfies the orthogonality equation C0′
•
C0=NIN for the column vectors of C0 wherein “
(o)′
”
is the complex-conjugate transpose of (o),current space-time TN×
1 codes C combine the space-time codes and the transmitted data symbols,current space-time codes C cannot be factored into the product of a code matrix with the transmitted data symbol vector except for a few codes,space-time code matrix C0 architecture enables all known space-time codes C to be represented by the C0•
X architecture wherein X is the N×
1 transmitted signal column vector and which means there exists a C0 that satisfies the identity C=C0•
X for all existing space-time codes C and for all future space-time codes C, andfactorization of the code matrix and the transmitted data symbol vector is a requirement for a ML solution;
using an alternate construction of the new space-time TN×
N code matrix C0 as the matrix C0=[A1•
B1;
. . . ;
AN•
BN] whose elements are the N×
N matrix products An•
Bn for n=1 , , , , , T wherein the matrices An, Bn and the operator “
;
”
are defined in the previous;
constructing the new linear MIMO matrix transmission equation for the TM×
1 output received data symbol vector Y
Y=H0•
C0•
X+No which factors out the input transmitted N×
1 data symbol vector X and replaces the current MIMO matrix equation Y=HC+No whereincurrent MIMO practice does not factor the H and C into a matrix product since it is difficult to separate the elements of H and C and which means HC is the current MIMO TM×
1 encoded data vector input whose elements are the space-time encoded data symbol elements multiplied by the appropriate transmission elements,receive TM×
1 data symbol vector Y=[y(1,1);
. . . ;
y(M,1);
y(M,2);
. . . ;
y(M,T)] elements are the detected data symbol values y(m,i) indexed on the receive antenna m=1, . . . , M and the time epoch i−
1, . . . , T for the MIMO signal set being addressed,transmitted N×
1 data symbol column vector X=[X1;
. . . ;
XN] elements are the set of N data signals Xn being transmitted over T time epochs, andNo is the TM×
1 receive noise vector;
implementing a new ML solution to Y=H0•
C0•
X+No to derive the estimate {circumflex over (X)} of X by solving the ML equation when L is absent
{circumflex over (X)}=[(H0C0)′
Q−
1(H0C0)]−
1(H0C0)′
Q−
1Y wherein Q=E{N0N0′
} is the noise covariance, E{o} is the mathematical expectation of “
o”
, assuming the determinant det(H0′
•
H0)≠
0 and det(C0′
•
C0)≠
0, and when the TM×
1 receive noise vector No is zero-mean additive white Gaussian noise (AWGN) with no cross-correlation this estimate reduces to
{circumflex over (X)}=[(H0C0)′
(H0C0)]−
1(H0C0)′
Y and for the applications where (H0C0) is a square matrix and assuming the determinant det(H0C0)≠
0 reduces the solution to
{circumflex over (X)}=(H0C0)−
1Y; and
implementing a new ML solution to Y=H0•
C0•
X+No to derive the estimate {circumflex over (X)} of X by solving the ML equation with L present
{circumflex over (X)}=[H2−
1•
H1−
H1*−
1•
H2*]−
1•
[H2−
1−
H1*−
1•
L]•
Y wherein by definition
H0•
C0=H1+H2•
L assuming the determinant det((H0•
C0)′
(H0•
C0))≠
0, the TM×
1 receive noise vector No is AWGN with no cross-correlation, and the determinant det(H1′
•
H1)≠
0 and det(H2′
•
H2)≠
0.
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Abstract
A method for constructing architectures for multiple input transmit and multiple output receive (MIMO) systems with generalized orthogonal space-time codes (C0) and generalizations (H0) of the transmission matrix (H) that enable the MIMO equation to be written Y=H0∘C0∘X+No which factors out the input signal symbol vector X and allows a direct maximum-likelihood calculation of the estimate {circumflex over (X)} of X, and where Y is the received symbol vector and No is the received noise vector. The architectures spread the users uniformly over the transmission paths to provide improved bit error rate performance and are developed to support code division multiple access (CDMA) and variations including multi-carrier CDMA (MC-CDMA) for equalization, orthogonal frequency division multiple access (OFDMA), and orthogonal Wavelet division multiple access (OWDMA) using waveforms that include multi-resolution Wavelets and with Walsh, Hybrid Walsh, generalized Hybrid Walsh orthogonal and quasi-orthogonal codes for CDMA and MC-CDMA and variations.
-
Citations
5 Claims
-
1. A method for the design and implementation of maximum-likelihood (ML) architecture for MIMO systems with M receive antennas and N transmit antennas and with epoch T>
- 1, comprising the steps;
constructing the new space-time TM×
TN transmission matrix H0 as the matrix-diagonal matrix generated by the tensor product of the T×
T identity diagonal matrix with the M×
N transmission matrix H to generate the TM×
TN matrix H0 whose matrix elements on the diagonal are the H and zeros elsewhere and whereinsymbol “
T”
is the number of time epochs which are the number of repeated transmissions,symbol “
TM×
TN”
reads “
TM rows by TN columns”
,transmission matrix H has transmission elements hi,j which measure the transmitter, path, and receiver transmission loss from transmitter j in column j=1, . . . , M to receiver i in row i=1, . . . , M, transmission elements hi,j are complex measurements of the transmission loss from j to i, and a matrix-diagonal matrix has matrices along the diagonal and zeros elsewhere; constructing the new space-time TN×
N code matrix C0 as the matrix product C0=A•
B of a TN×
TN matrix A with a TN×
N matrix B and whereinsymbol “
•
”
is a matrix or vector product,matrix A is the TN×
TN matrix-diagonal matrix whose diagonal matrix elements are the T N×
N diagonal matrices A1, . . . , AT,matrices An for n=1, . . . , T are orthogonal matrices satisfying An′
•
An=NIN wherein An′
is the conjugate transpose of An and IN is the N×
N identity diagonal matrix,matrix B=[B1;
. . . ;
BN] is the TN×
N matrix whose elements are the N×
N orthogonal matrices B1, . . . , BT each with elements including L and using the Matlab construction operator “
;
”
for stacking matrices, vectors, or elements in a column format,matrices Bn for n=1, . . . , T are orthogonal matrices with the property Bn′
•
Bn=NIN,matrix element “
L”
is the new complex-conjugate operator defined by the operation “
L(w)=w*=complex-conjugate of the element w” and
L(L(w))=w,space-time TN×
N code matrix C0 satisfies the orthogonality equation C0′
•
C0=NIN for the column vectors of C0 wherein “
(o)′
”
is the complex-conjugate transpose of (o),current space-time TN×
1 codes C combine the space-time codes and the transmitted data symbols,current space-time codes C cannot be factored into the product of a code matrix with the transmitted data symbol vector except for a few codes, space-time code matrix C0 architecture enables all known space-time codes C to be represented by the C0•
X architecture wherein X is the N×
1 transmitted signal column vector and which means there exists a C0 that satisfies the identity C=C0•
X for all existing space-time codes C and for all future space-time codes C, andfactorization of the code matrix and the transmitted data symbol vector is a requirement for a ML solution; using an alternate construction of the new space-time TN×
N code matrix C0 as the matrix C0=[A1•
B1;
. . . ;
AN•
BN] whose elements are the N×
N matrix products An•
Bn for n=1 , , , , , T wherein the matrices An, Bn and the operator “
;
”
are defined in the previous;constructing the new linear MIMO matrix transmission equation for the TM×
1 output received data symbol vector Y
Y=H0•
C0•
X+Nowhich factors out the input transmitted N×
1 data symbol vector X and replaces the current MIMO matrix equation Y=HC+No whereincurrent MIMO practice does not factor the H and C into a matrix product since it is difficult to separate the elements of H and C and which means HC is the current MIMO TM×
1 encoded data vector input whose elements are the space-time encoded data symbol elements multiplied by the appropriate transmission elements,receive TM×
1 data symbol vector Y=[y(1,1);
. . . ;
y(M,1);
y(M,2);
. . . ;
y(M,T)] elements are the detected data symbol values y(m,i) indexed on the receive antenna m=1, . . . , M and the time epoch i−
1, . . . , T for the MIMO signal set being addressed,transmitted N×
1 data symbol column vector X=[X1;
. . . ;
XN] elements are the set of N data signals Xn being transmitted over T time epochs, andNo is the TM×
1 receive noise vector;implementing a new ML solution to Y=H0•
C0•
X+No to derive the estimate {circumflex over (X)} of X by solving the ML equation when L is absent
{circumflex over (X)}=[(H0C0)′
Q−
1(H0C0)]−
1(H0C0)′
Q−
1Ywherein Q=E{N0N0′
} is the noise covariance, E{o} is the mathematical expectation of “
o”
, assuming the determinant det(H0′
•
H0)≠
0 and det(C0′
•
C0)≠
0, and when the TM×
1 receive noise vector No is zero-mean additive white Gaussian noise (AWGN) with no cross-correlation this estimate reduces to
{circumflex over (X)}=[(H0C0)′
(H0C0)]−
1(H0C0)′
Yand for the applications where (H0C0) is a square matrix and assuming the determinant det(H0C0)≠
0 reduces the solution to
{circumflex over (X)}=(H0C0)−
1Y; andimplementing a new ML solution to Y=H0•
C0•
X+No to derive the estimate {circumflex over (X)} of X by solving the ML equation with L present
{circumflex over (X)}=[H2−
1•
H1−
H1*−
1•
H2*]−
1•
[H2−
1−
H1*−
1•
L]•
Ywherein by definition
H0•
C0=H1+H2•
Lassuming the determinant det((H0•
C0)′
(H0•
C0))≠
0, the TM×
1 receive noise vector No is AWGN with no cross-correlation, and the determinant det(H1′
•
H1)≠
0 and det(H2′
•
H2)≠
0.- View Dependent Claims (2, 3, 4, 5)
which factors out the input transmitted N×
1 data symbol vector X and replaces the current MIMO matrix equation Y=HC+No;implementing a new ML solution to Y=H0•
C0•
X+No to derive the estimate {circumflex over (X)} of the input data symbol vector X by solving the ML equation when L is absent
{circumflex over (X)}=[(H0C0)′
Q−
1(H0C0)]−
1(H0C0)′
Q−
1Yassuming det((H0C0)′
•
(H0C0))≠
0 which is a requirement for the ML solution to exist, and when the TM×
1 receive noise vector No is AWGN with no cross-correlation this estimate reduces to
{circumflex over (X)}=N−
1C0′
(H0′
H0)]−
1H0′
Y;
implementing a new ML solution to Y=H0•
C0•
X+No to derive the estimate {circumflex over (X)} of X by solving the ML equation when L is absent and M=N
{circumflex over (X)}=N−
1C0′
[H0′
Q−
1H0]−
1H0′
Q−
1Y;
assuming det(H0)≠
0 which is a requirement for the ML solution to exist, and when the TM×
1 receive noise vector No is AWGN with no cross-correlation this estimate reduces to
{circumflex over (X)}=N−
1C0H0−
1Y;
implementing a new ML solution to Y=H0•
C0•
X+No to derive the estimate {circumflex over (X)} of X by solving the ML equation with L present
{circumflex over (X)}=[H2−
1•
H1−
H1*−
1•
H2*]−
1•
[H2−
1−
H1*−
1•
L]•
Ywherein by definition
H0•
C0=H1+H2•
Lassuming the determinant det((H0C0)′
(H0C0))≠
0 which is a requirement for the ML solution to exist, the M×
1 receive noise vector No is AWGN with no cross-correlation, and det(H1′
•
H1)≠
0 and det(H2′
•
H2)≠
0.
- 1, comprising the steps;
-
3. The method of claim 1 or 2 for the design and implementation of the new ML architecture for MIMO systems, with the following properties:
-
orthogonal space-time codes Cs are a larger class of space-time codes than the class of current space-time code C which include the code and the input data symbol elements of the input vector X; orthogonal space-time codes C0 do not have a data rate loss with diversity; linear complex conjugate operator L is included in the selection of elements for the construction of C0; space-time transmission matrix H0 is a generalization of the transmission matrix H which enables the current MIMO encoded data vector HC to be written HC=H0•
C0•
X to factor out the input transmitted data symbol vector X which format supports a ML solution for the estimate {circumflex over (X)} of X when the determinant det(H0′
H0)≠
0;MIMO matrix equation Y=H0•
C0•
X+No factors out X and allows a direct ML calculation of the estimate {circumflex over (X)} of X wherein Y,X,No are the received data vector, transmitted data vector, and the received noise power density vector; andmultiple access encoding combined with orthogonal space-time encoding C0 uniformly spreads the transmitted data symbols over each X to improve bit error rate (BER) communications performance.
-
-
4. The method of claim 1 or 2 for the design and implementation of the new ML architecture for MIMO systems using multiple access code division multiple access (CDMA) or equalizer variations including multi-carrier CDMA (MC-CDMA), orthogonal frequency division multiple access (OFDMA), orthogonal Wavelet division multiple access (OWDMA) and using waveforms that include multi-resolution Wavelets and with Walsh, Hybrid Walsh, generalized Hybrid Walsh orthogonal and quasi-orthogonal codes for CDMA and with the following properties:
-
new orthogonal space-time codes C0 do not have a data rate loss with diversity and are a larger class of space-time codes than the class of current space-time codes C; new linear complex conjugate operator is included in the selection of elements for the construction of the space-time codes; new generalization H0 of the transmission matrix H enables the determinant det(H0′
H0)≠
0 to exist when this information exists in the transmission coefficients hi,j of the transmission matrix H;new formulation of the MIMO transmission equation Y=H0•
C0•
X+No factors out the input transmitted data symbol vector X and supports a direct ML calculation of the estimate of {circumflex over (X)} of X; andmultiple access combined with the orthogonal space-time encoding uniformly spread the user data over the input signal to improve BER (bit error rate) communications performance.
-
-
5. The method of claim 1 or 2 for the design and implementation of the new ML architecture for MIMO systems supports the implementation of ML solutions for all combinations of N transmit antennas, M receive antennas, and time epoch T, with the following properties:
-
ML architecture supports the implementation of all combinations of M,N,T parameters, transmission matrix H, and the input transmitted data symbol vector X which are solvable with acceptable communications performance; ML architecture supports an implementation which can accommodate M,N,T parameters, transmission matrix H, and input transmitted data symbol vector X that can change with the transmission elements and their solvability; ML architecture is transparent to the equalizer signal processing required to mitigate the effects of scintillation, dispersion, fading, and multipath; ML architecture supports communications using multiple access CDMA and equalizer variations including MC-CDMA, OFDMA, and OWDMA using waveforms that include multi-resolution Wavelets and with Walsh, Hybrid Walsh, generalized Hybrid Walsh orthogonal and quasi-orthogonal codes for CDMA and MC-CDMA; ML architecture supports communications using all current waveforms and multi-resolution Wavelet waveforms which optimize communication efficiency measured in units of symbols/second/H; ML architecture uses orthogonal space-time codes that do not have a data rate loss with diversity and are a larger class of space-time codes than the class of current space-time codes; ML architecture uses linear complex conjugate operator in the selection of elements for the construction of the space-time codes; ML architecture uses a generalization H0 of the transmission matrix H that enables the transmission matrix or the matrix product with the space-time code to be square and invertible when this information exists in the transmission coefficients of the transmission matrix; ML architecture uses a novel formulation of the MIMO transmission equation Y=H0•
C0•
X+No that factors out the input transmitted data symbol vector X and supports a direct ML calculation of the estimate of {circumflex over (X)} of X; andML architecture uniformly spreads the transmitted data symbols over the input signal to improve BER communications performance.
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Current AssigneeUrbain A. Von Der Embse
-
Original AssigneeUrbain A. Von Der Embse
-
Inventorsvon der Embse, Urbain Alfred
-
Primary Examiner(s)Bayard; Emmanuel
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Application NumberUS11/131,464Time in Patent Office1,763 DaysField of Search375/130, 375/260, 375/144, 375/267, 375/299, 375/347, 375/349US Class Current375/299CPC Class CodesH04B 7/0413 MIMO systemsH04B 7/0669 using different channel cod...H04L 1/0071 Use of interleaving interle...H04L 1/0625 Transmitter arrangementsH04L 1/0668 Orthogonal systems, e.g. us...H04L 2025/03426 transmission using multiple...H04L 25/03159 operating in the frequency ...H04L 27/2647 Arrangements specific to th...
