Lattice reduction in orthogonal time frequency space modulation
Methods, systems and devices for lattice reduction in decision feedback equalizers for orthogonal time frequency space (OTFS) modulation are described. An exemplary wireless communication method, implementable by a wireless communication receiver apparatus, includes receiving a signal comprising information bits modulated using OTFS modulation scheme. Each delay-Doppler bin in the signal is modulated using a quadrature amplitude modulation (QAM) mapping. The method also includes estimating the information bits based on an inverse of a single error covariance matrix of the signal, with the single error covariance matrix being representative of an estimation error for all delay-Doppler bins in the signal.
1. A wireless communication method, implementable by a wireless communication receiver apparatus, comprising:
receiving a signal comprising information bits modulated using an orthogonal time frequency space (OTFS) modulation scheme, wherein each delay-Doppler bin in the signal is modulated using a quadrature amplitude modulation (QAM) mapping; and
estimating the information bits based on an inverse of a single error covariance matrix of the signal, wherein the single error covariance matrix is representative of an estimation error for all delay-Doppler bins in the signal.
2. The method of claim 1 , further including:
computing a unimodular matrix comprising integer entries and having a unity determinant; and
decreasing a condition number of the inverse of the single covariance matrix based on multiplication with the unimodular matrix.
3. The method of claim 1 , further including:
performing, upon determining that the inverse of the single error covariance matrix is numerically well-conditioned, a slicing operation on QAM symbols in all the delay-Doppler bins.
4. The method of claim 2 , wherein the computing the unimodular matrix includes applying a lattice reduction algorithm to obtain the unimodular matrix.
5. The method of claim 4 , wherein the applying the lattice reduction algorithm includes:
applying a Lenstra Lenstra Lovasz (LLL) lattice reduction algorithm.
6. The method of claim 4 , further including, for each delay-Doppler bin, performing Babai detection on an output of the lattice reduction algorithm.
7. The method of claim 4 , further including, for each delay-Doppler bin, performing sphere detection on an output of the lattice reduction algorithm.
8. The method of claim 4 , further including, for each delay-Doppler bin, performing a closest lattice point (CLP) detection on an output of the lattice reduction algorithm.
9. The method of claim 4 , wherein the lattice reduction algorithm includes a size reduction transformation followed by a flipping transformation.
10. The method of claim 9 , wherein the size reduction transformation is based on the unimodular matrix, and wherein the flipping transformation is based on another unimodular matrix different from the unimodular matrix.
11. The method of claim 4 , wherein the lattice reduction algorithm comprises a Lenstra Lenstra Lovasz (LLL) algorithm, a Block Korkine Zolotarev (BKZ) algorithm, a random sampling reduction (RSR) algorithm or a primal dual reduction (PDR) algorithm.
12. The method of claim 1 , further including, for each delay Doppler bin, converting an output of detected symbols to a standard lattice.
13. The method of claim 1 , wherein the estimating the information bits includes performing a symbol to bits de-mapping of the QAM symbols.
14. A wireless communication device comprising a processor and transceiver circuitry wherein the transceiver circuitry is configured for receiving a signal comprising information bits modulated using an orthogonal time frequency space (OTFS) modulation scheme, wherein each delay-Doppler bin in the signal is modulated using a quadrature amplitude modulation (QAM) mapping; and
wherein the processor is configured for estimating the information bits based on an inverse of a single error covariance matrix of the signal, wherein the single error covariance matrix is representative of an estimation error for all delay-Doppler bins in the signal.
15. The wireless communication device of claim 14 , wherein the processor is further configured for:
computing a unimodular matrix comprising integer entries and having a unity determinant; and
decreasing a condition number of the inverse of the single covariance matrix based on multiplication with the unimodular matrix.
16. The wireless communication device of claim 14 , wherein the processor is further configured for:
performing, upon determining that the inverse of the single error covariance matrix is numerically well-conditioned, a slicing operation on QAM symbols in all the delay-Doppler bins.
17. The wireless communication device of claim 15 , wherein the computing the unimodular matrix includes applying a lattice reduction algorithm to obtain the unimodular matrix.
18. The wireless communication device of claim 17 , wherein the applying the lattice reduction algorithm includes:
applying a Lenstra Lenstra Lovasz (LLL) lattice reduction algorithm.
19. The wireless communication device of claim 17 , wherein the processor is further configured for, for each delay-Doppler bin, performing Babai detection on an output of the lattice reduction algorithm.
20. The wireless communication device of claim 17 , wherein the processor is further configure for, for each delay-Doppler bin, performing sphere detection on an output of the lattice reduction algorithm.