Iterative two dimensional equalization of orthogonal time frequency space modulated signals
An iterative two dimension equalizer usable in a receiver of orthogonal time frequency space (OTFS) modulated signals is described. In one configuration of the equalizer, a forward path generates, from received time-frequency domain samples and a channel estimate, estimates of data bits and likelihood numbers associated with the estimates of data bits, generated by delay-Doppler domain processing. In the feedback direction, the estimates of data bits are used to generate symbol estimates and autocorrelation matrix estimate in the time domain. In another configuration, a soft symbol mapper is used in the feedback direction for directly generating the feedback input symbol estimate without having to generate estimates of data bits.
1. A wireless communication method for recovering information bits from a received signal, by performing iterative two dimensional equalization, comprising:
receiving, at an iterative equalizer, iteration inputs including a two dimensional estimate of a wireless channel over which the received signal is received, a stream of received symbols, a symbol estimate from a previous iteration, and an input autocorrelation matrix estimate from the previous iteration, and
computing, from the iteration inputs, a Wiener estimate of the stream of received symbols;
transforming the Wiener estimate to symbol estimates in a two dimensional delay-Doppler grid using a two-dimensional symplectic Fourier transform;
estimating likelihoods of the symbol estimates in the two dimensional delay-Doppler grid; and
generating estimates of information bits from the likelihoods.
2. The method of claim 1 , wherein the generating the estimates includes:
deinterleaving the likelihoods of the symbols; and
performing error correction on an output of the deinterleaving.
3. The method of claim 1 , further including, processing in a feedback direction, by generating a symbol estimate and an input autocorrelation matrix estimate for a next iteration.
4. The method of claim 3 , wherein the processing in the feedback direction includes:
performing soft symbol mapping using the likelihoods resulting in intermediate symbol estimates and an intermediate autocorrelation estimate; and
generating the symbol estimate and the input autocorrelation matrix estimate by transforming, using an inverse of the two-dimensional symplectic Fourier transform, the intermediate symbol estimates and the intermediate autocorrelation estimate.
5. The method of claim 1 , wherein the two-dimensional symplectic Fourier transform is a symplectic fast Fourier transform (SFFT).
6. The method of claim 1 , wherein the computing the Wiener estimate comprises:
receiving information about erased time-frequency resource elements from the received signal; and
using prior symbol estimates from a feedback direction as outputs of the computing the Wiener estimates.
7. A wireless communication method for recovering information bits from a received signal, by performing iterative two dimensional equalization, comprising:
receiving, at an iterative equalizer, iteration inputs including a two dimensional estimate of a wireless channel over which the received signal is received, a stream of received symbols, a symbol estimate from a previous iteration, an input autocorrelation matrix estimate from the previous iteration, and
computing, from the iteration inputs, a Wiener estimate of the stream of received symbols;
transforming the Wiener estimate to symbol estimates a two dimensional delay-Doppler grid using a two-dimensional symplectic Fourier transform; and
processing in a feedback direction, by generating a symbol estimate and an input autocorrelation matrix estimate for a next iteration.
8. The method of claim 7 , further including:
estimating likelihoods of the symbol estimates in the two dimensional delay-Doppler grid and
generating estimates of data from the likelihoods.
9. The method of claim 7 , wherein the generating the estimates includes
deinterleaving the likelihoods of the symbols; and
performing error correction on an output of the deinterleaving.
10. The method of claim 9 , wherein the processing in the feedback direction includes:
performing soft symbol mapping using the likelihoods resulting in intermediate symbol estimates and an intermediate autocorrelation estimate; and
generating the symbol estimate and the input autocorrelation matrix estimate by transforming, using an inverse of the two-dimensional symplectic Fourier transform, the intermediate symbol estimates and the intermediate autocorrelation estimate.
11. The method of claim 7 , wherein the two-dimensional symplectic Fourier transform is a symplectic fast Fourier transform (SFFT).
12. The method of claim 7 , wherein the computing the Wiener estimates comprises:
receiving information about erased time-frequency resource elements from the received signal; and
using prior symbol estimates from a feedback direction as outputs of the computing the Wiener estimates.
13. A wireless transceiver apparatus comprising a processor, transmission and reception circuitry and a memory, the apparatus configured to perform a method for recovering information bits from a received signal, the method comprising:
receiving, at an iterative equalizer, iteration inputs including a two dimensional estimate of a wireless channel over which the received signal is received, a stream of received symbols, a symbol estimate from a previous iteration, and an input autocorrelation matrix estimate from the previous iteration, and
computing, from the iteration inputs, a Wiener estimate of the stream of received symbols;
transforming the Wiener estimate to symbol estimates in a two dimensional delay-Doppler grid using a two-dimensional symplectic Fourier transform;
estimating likelihoods of the symbol estimates in the two dimensional delay-Doppler grid; and
generating estimates of information bits from the likelihoods.
14. The apparatus of claim 13 , further configured to:
deinterleave the likelihoods of the symbols; and
perform error correction on an output of the deinterleaving.
15. The apparatus of claim 13 , further configured to process in a feedback direction, by generating a symbol estimate and an input autocorrelation matrix estimate for a next iteration.
16. The apparatus of claim 15 , wherein the processing in the feedback direction includes:
performing soft symbol mapping using the likelihoods resulting in intermediate symbol estimates and an intermediate autocorrelation estimate; and
generating the symbol estimate and the input autocorrelation matrix estimate by transforming, using an inverse of the two-dimensional symplectic Fourier transform, the intermediate symbol estimates and the intermediate autocorrelation estimate.
17. The apparatus of claim 13 , wherein the processing in the feedback direction includes:
performing soft symbol mapping using the likelihoods resulting in intermediate symbol estimates and an intermediate autocorrelation estimate; and
generating the symbol estimate and the input autocorrelation matrix estimate by transforming, using an inverse of the two-dimensional symplectic Fourier transform, the intermediate symbol estimates and the intermediate autocorrelation estimate.
18. A non-transitory computer readable storage medium having code stored thereupon, the code, when executed, causing a processor to implement a method recovering information bits from a received signal by performing iterative two dimensional equalization, comprising:
receiving, at an iterative equalizer, iteration inputs including a two dimensional estimate of a wireless channel over which the received signal is received, a stream of received symbols, a symbol estimate from a previous iteration, an input autocorrelation matrix estimate from the previous iteration, and
computing, from the iteration inputs, a Wiener estimate of the stream of received symbols;
transforming the Wiener estimate to symbol estimates a two dimensional delay-Doppler grid using a two-dimensional symplectic Fourier transform; and
processing in a feedback direction, by generating a symbol estimate and an input autocorrelation matrix estimate for a next iteration.
19. The non-transitory computer readable storage medium of claim 17 , wherein the method further includes:
estimating likelihoods of the symbol estimates in the two dimensional delay-Doppler grid and
generating estimates of data from the likelihoods.
20. The non-transitory computer readable storage medium of claim 19 , wherein the generating the estimates includes
deinterleaving the likelihoods of the symbols; and
performing error correction on an output of the deinterleaving.
21. The non-transitory computer readable storage medium of claim 18 , wherein the processing in the feedback direction includes:
performing soft symbol mapping using the likelihoods resulting in intermediate symbol estimates and an intermediate autocorrelation estimate; and
generating the symbol estimate and the input autocorrelation matrix estimate by transforming, using an inverse of the two-dimensional symplectic Fourier transform, the intermediate symbol estimates and the intermediate autocorrelation estimate.
22. The non-transitory computer readable storage medium of claim 18 , wherein the two-dimensional symplectic Fourier transform is a symplectic fast Fourier transform (SFFT).
23. The non-transitory computer readable storage medium of claim 18 , wherein the computing the Wiener estimates comprises:
receiving information about erased time-frequency resource elements from the received signal; and
using prior symbol estimates from a feedback direction as outputs of the computing the Wiener estimates.