A method for transmit beamforming in a MIMO antenna for a radar system having N transmit antennas includes acquiring a coding matrix defining a desired field-of-view, generating a transmit signal matrix based on a singular value decomposition (SVD) of the coding matrix, wherein the columns of the transmit signal matrix are transmit signal vectors formed from the singular vectors corresponding to the maximal singular values of the coding matrix based on the SVD, the transmit signal vectors defining spatial codewords, and transmitting signals in sequences over the N transmit antennas according to the transmit signal matrix, the sequences correspond to the spatial codewords from the transmit signal vectors, wherein each sequence is defined by a number of spatial codewords transmitted in a single repetition sequence interval, and wherein transmitting the spatial codewords according to the transmit signal matrix enables beamforming of the transmitted signals to the desired field-of-view.
1. A method for transmit beamforming in a multiple input multiple output (MIMO) antenna for a radar system having N transmit antennas, the method comprising:
acquiring a coding matrix defining a desired field-of-view;
generating a transmit signal matrix based on a singular value decomposition (SVD) of the coding matrix, wherein the columns of the transmit signal matrix are transmit signal vectors formed from the singular vectors corresponding to the maximal singular values of the coding matrix based on the SVD, the transmit signal vectors defining spatial codewords; and
transmitting signals in sequences over the N transmit antennas according to the transmit signal matrix, the sequences correspond to the spatial codewords from the transmit signal vectors, wherein N is an integer greater than one, wherein each sequence is defined by a number of spatial codewords transmitted in a single repetition sequence interval, and wherein transmitting the spatial codewords according to the transmit signal matrix enables beamforming of the transmitting signals to the desired field-of-view.
2. The method of claim 1 , wherein transmission of the spatial codewords spans the desired field-of-view.
3. The method of claim 1 , wherein the number of columns in the transmit signal matrix is less than the N transmit antennas.
4. The method of claim 1 , wherein the number of columns in the transmit signal matrix corresponds to the number of spatial codewords transmitted in the single repetition sequence interval.
5. The method of claim 1 , wherein the number of spatial codewords transmitted in a single repetition sequence interval is less than the N transmit antennas.
6. The method of claim 1 , wherein each spatial codeword in the transmit signal vectors has N symbols.
7. The method of claim 1 , wherein the sequence of codewords transmitted over the N antennas are orthogonal enabling separation of the transmit channels in the desired field-of-view.
8. The method of claim 1 , wherein the transmit signal vectors are eigenvectors corresponding to the maximum eigen values of the coding matrix enabling maximal energy from the transmitting signals to be directed to the desired field-of-view.
9. The method of claim 1 , wherein the transmit signal vectors have a dimension of N×1.
10. The method of claim 1 , wherein the coding matrix includes a diagonal masking matrix configured to mask an angular field-of-view of the radar to exclude spatial regions outside of the desired field-of-view.
11. The method of claim 10 , wherein the diagonal masking matrix is an N×N matrix with diagonal elements corresponding to N equally spaced regions in the radar field-of-view, wherein diagonal elements having a value of 1 indicate spatial regions in the desired field-of-view and diagonal elements having a value of 0 indicate spatial regions outside of the desired field-of-view.
12. The method of claim 1 , wherein the SVD of the coding matrix is the product of an orthogonal matrix, a diagonal matrix, and a transpose matrix of the orthogonal matrix, wherein the orthogonal matrix is an N×N matrix with columns that represent left singular vectors of the coding matrix, and diagonal elements in the diagonal matrix represent the singular values of the coding matrix.
13. The method of claim 12 , wherein the columns of the transmit signal matrix formed from singular vectors of the coding matrix are the singular vectors in the orthogonal matrix that correspond to maximal singular values in the diagonal matrix.
14. A method for transmit beamforming in a multiple input multiple output (MIMO) antenna for a radar system having N transmit antennas, the method comprising:
calculating a coding matrix as a function of a desired field-of-view;
decomposing the coding matrix to determine the eigenvectors of the coding matrix that correspond to the maximum eigen values of the coding matrix;
generating a transmit signal matrix based on the decomposition of the coding matrix, the transmit signal matrix having a dimension of N×Q, wherein N is an integer greater than one, wherein Q is an integer greater than zero, wherein the Q columns of the transmit signal matrix are the eigenvectors of the coding matrix, and wherein each column defines a spatial codeword having N symbols; and
transmitting signals in sequences over the N transmit antennas according to the transmit signal matrix, the sequences correspond to the spatial codewords from the columns of the transmit signal matrix, wherein Q spatial codewords are transmitted for each sequence, and wherein transmitting the Q spatial codewords according to the transmit signal matrix enables beamforming of the transmitting signals to the desired field-of-view.
15. The method of claim 14 , wherein the eigenvectors of the coding matrix correspond to the maximum eigen values of the coding matrix enabling maximal energy from the transmitting signals to be directed to the desired field-of-view.
16. The method of claim 14 , wherein the Q spatial codewords in each sequence are less than the N transmit antennas.
17. The method of claim 14 , wherein the coding matrix includes a diagonal masking matrix configured to mask an angular field-of-view of the radar to exclude spatial regions outside of the desired field-of-view.
18. A multiple input multiple output (MIMO) antenna for a radar system, the antenna comprising:
an antenna array having N transmit antennas, wherein N is an integer greater than one; and
a transmitter configured to:
acquire a coding matrix defining a desired field-of-view;
generate a transmit signal matrix based on a singular value decomposition (SVD) of the coding matrix, wherein the columns of the transmit signal matrix are transmit signal vectors formed from the singular vectors corresponding to the maximal singular values of the coding matrix based on the SVD, the transmit signal vectors defining spatial codewords; and
transmit signals over the N transmit antennas according to the transmit signal matrix, wherein the signals represent sequences of the spatial codewords from the transmit signal vectors, wherein each sequence corresponds to a number of spatial codewords transmitted in a single repetition sequence interval, and wherein transmitting the spatial codewords according to the transmit signal matrix achieves beamforming of the transmit signals to the desired field-of-view.
19. The MIMO antenna of claim 18 , wherein the number of spatial codewords transmitted in a single repetition sequence interval is less than the N transmit antennas.
20. The MIMO antenna of claim 18 , wherein the coding matrix includes a diagonal masking matrix configured to mask an angular field-of-view of the radar to exclude spatial regions outside of the desired field-of-view.