LATTICE-REDUCTION-AIDED MIMO DETECTORS
A Lenstra-Lenstra-Lovász (LLL)-based technique is utilized to reduce the complexity of a MIMO detector. Basis vectors can be pre-sorted, such as by V-BLAST ordering or sorted-QR ordering, prior to applying Gram-Schmidt Orthogonalization (GSO) to further improve performance. Alternatively, a joint sorting and LLL reduction (JSAR) technique can be utilized such that after each reduction step, a vector remaining to be reduced can be selected that will minimize the overall complexity. The JSAR technique can be applied on real or complex lattice bases. LLL reduction can be stopped after a predetermined threshold is exceeded.
1 . A computer-readable medium containing instructions that when executed perform a method comprising:
determining a channel matrix corresponding to a channel in a multiple-input multiple-output wireless network;
sorting basis vectors of the channel matrix; and
performing Lenstra-Lenstra-Lovász (LLL) lattice reduction on the sorted basis vectors to determine a reduced lattice basis.
2 . The computer-readable medium of claim 1 wherein the sorting of the basis vectors includes V-BLAST ordering.
3 . The computer-readable medium of claim 1 wherein the sorting of the basis vectors includes sorted-QR ordering.
4 . The computer-readable medium of claim 1 wherein the method further comprises symbol decoding based on the determined reduced lattice basis.
5 . The computer-readable medium of claim 1 wherein the determining of a channel matrix corresponding to a channel includes determining a complex channel matrix and the performing of the LLL lattice reduction includes performing LLL reduction on the complex channel matrix and not a real-valued equivalent matrix of the complex channel matrix.
6 . A method of determining a lattice basis in a multiple-input multiple-output (MIMO) receiver, the method comprising:
determining a channel matrix that represents at least one channel in a MIMO network including the MIMO receiver, the matrix comprised of multiple basis vectors;
performing a first Lenstra-Lenstra-Lovász (LLL) reduction step;
for each subsequent LLL reduction step,
selecting a remaining vector to be used as the next vector to be reduced so as to minimize computational complexity of determining the lattice basis; and
performing the subsequent LLL reduction step.
7 . The method of claim 6 wherein the selecting of a vector to be used as the next vector to be reduced comprises picking the vector with the shortest projection.
8 . The method of claim 6 wherein the performing of the first LLL reduction step comprises performing the first LLL reduction step on a basis vector with the smallest norm.
9 . The method of claim 6 wherein performing the first LLL reduction step comprises performing the first LLL reduction step on a complex channel matrix instead of a real-valued equivalent matrix of the complex channel matrix.
10 . The method of claim 6 wherein the performing of subsequent LLL reduction step comprises swapping.
11 . The method of claim 6 further comprising for each subsequent LLL reduction step, determining if a predetermined condition occurred and when the predetermined condition occurs, ending the determination of the lattice basis.
12 . The method of claim 11 wherein the predetermined condition is at least one of a predetermined number of iterations have occurred or a predetermined amount of time has elapsed in performing the first and subsequent LLL reduction steps.
13 . The method of claim 6 further comprising decoding the channel matrix using the determined lattice basis to determine the transmitted symbols.
14 . The method of claim 6 further comprising sorting the basis vectors prior to performing the first LLL reduction step.
15 . An electronic apparatus that decodes signals in a multiple-input multiple-output (MIMO) wireless network, the apparatus comprising:
a memory;
a plurality of receive antennas;
a channel estimation component that identifies a channel matrix corresponding to a communication channel, the channel matrix comprising multiple basis vectors to reduce; and
a lattice reduction component that analyzes the channel matrix and determines a reduced lattice basis using a Lenstra-Lenstra-Lovász (LLL) technique in which after each iteration of the LLL technique, a next vector to reduce is selected so as to minimize computational complexity of determining the reduced lattice basis.
16 . The electronic apparatus of claim 15 wherein the lattice reduction component comprises a truncation component that stops the LLL technique after a predetermined condition is met.
17 . The electronic apparatus of claim 16 wherein the predetermined condition is at least one of a predetermined number of or a predetermined amount of time has elapsed in the LLL technique.
18 . The electronic apparatus of claim 15 further comprising a decoder component that uses the reduced lattice basis to determine the transmitted symbols.
19 . The electronic apparatus of claim 18 wherein the channel estimation component identifies a complex channel matrix and the LLL technique is performed on the complex channel matrix and not a real-valued equivalent matrix of the complex channel matrix.
20 . The electronic apparatus of claim 15 wherein the selected vector is the vector with the shortest projection.