Fast square root algorithm for MIMO equalization
Systems and methodologies are described that facilitate equalization of received signals in a wireless communication environment. Using multiple transmit and/or receive antennas and MIMO technology, multiple data streams can be transmitted within a single tone. During equalization, receivers can separate data received within a tone into individual data streams. The equalization process generally is computationally expensive. Equalizer functions include the inverse operation, which can be computed using the fast square root method; however, the fast square root method involves large numbers of computations for a set of matrices, where the size of a matrix in the set of matrices increases with the number of transmit or receive antennas. Utilizing a modification of the fast square root method, a subset of the elements of the matrices can be selected and updated to reduce the number and/or complexity of computations.
1. A method for facilitating equalization in a receiver chain in a wireless communication system, the method comprising:
generating, with a processor, an equalizer matrix for a tone of a received signal, wherein the equalizer matrix is a function of an inverse matrix computed based at least in part upon a partial update of a subset of elements of a fast square root matrix, wherein the fast square root matrix is specified as a function of an interference variance; and
equalizing, with the processor the tone as a function of the equalizer matrix;
wherein performing the partial update of the subset of elements of the fast square root matrix comprises determining a rotation matrix in accordance with a Householder reflection approach.
2. The method of claim 1 , wherein the fast square root matrix is a pre-array matrix.
3. The method of claim 1 , wherein the fast square root matrix is a post-array matrix.
4. The method of claim 1 , further comprising modifying, with the processor, the fast square root matrix so as to reduce the dynamic range requirements.
5. The method of claim 1 , further comprising performing, with the processor, maximum ratio combining equalization when a single data stream is contained within the received signal.
6. The method of claim 1 , further comprising generating, with the processor, a logging packet that includes symbols derived from the equalized tone.
7. An apparatus that facilitates equalization in a wireless communication environment, the apparatus comprising:
a processor configured to compute an inverse matrix based at least in part upon an iterative partial update of a fast square root matrix, to compute an equalizer matrix as a function of the inverse matrix, and to obtain at least one data stream from a received signal utilizing the equalizer matrix, wherein the fast square root matrix is specified as a function of an interference variance; and
a memory coupled to the processor;
wherein performing the iterative partial update of the fast square root matrix comprises determining a rotation matrix in accordance with a Householder reflection approach.
8. The apparatus of claim 7 , wherein the fast square root matrix is at least one of a pre-array matrix or a post array matrix.
9. The apparatus of claim 7 , wherein the processor is further configured to reduce a dynamic range requirement of the fast square root matrix.
10. The apparatus of claim 7 , wherein the processor is further configured to perform a maximum ratio combining equalization when the received signal includes a single data stream.
11. A device that that facilitates equalization of a signal in a wireless environment, the device comprising:
means for generating an equalizer matrix utilizing a modified fast square root method that updates a subset of the fast square root matrix during iterative processing, wherein the fast square root matrix is specified as a function of an interference variance; and
means for separating at least one data stream in a received signal utilizing the equalizer matrix;
wherein updating the subset of the fast square root matrix during iterative processing comprises determining a rotation matrix in accordance with a Householder reflection approach.
12. The device of claim 11 , wherein the fast square root matrix is at least one of a pre-array matrix or a post-array matrix.
13. The device of claim 11 , further comprising:
means for modifying the fast square root matrix so as to reduce the dynamic range requirements.
14. The device of claim 11 , further comprising means for equalizing the received signal utilizing a maximum ratio combining equalization when the signal contains a single data stream.
15. A computer program product including a non-transitory computer-readable medium comprising:
code for causing a computer to calculate an equalizer matrix for a tone of a received signal, wherein calculation of the equalizer matrix is based upon iterative partial update of a fast square root matrix, wherein the fast square root matrix is specified as a function of an interference variance; and
code for causing a computer to equalize the received signal as a function of the equalizer matrix;
wherein performing the partial update of the subset of elements of the fast square root matrix comprises determining a rotation matrix in accordance with a Householder reflection approach.
16. The computer program product of claim 15 , wherein the fast square root matrix is at least one of a pre-array matrix or a post-array matrix.
17. The computer program product of claim 15 , the non-transitory computer-readable medium further comprising:
code for causing a computer to modify the fast square root matrix so as to reduce the dynamic range requirements.
18. The computer program product of claim 15 , the non-transitory computer-readable medium further comprising:
code for causing a computer to equalize the received signal utilizing maximum ratio combining equalization when the signal contains a single data stream.