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 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, and at least one symbol estimate from a previous iteration;
performing, based on the iteration inputs, an affine minimum mean-squared error (MMSE) equalization operation on the stream of received symbols to generate a first stream of estimated symbols;
transforming, using a two-dimensional symplectic Fourier transform, the first stream of estimated symbols from a two-dimensional time-frequency grid to a second stream of estimated symbols in a two-dimensional delay-Doppler grid; and
generating, based on the second stream of estimated symbols in the two-dimensional delay-Doppler grid, estimates of the information bits.
2. The method of claim 1 , wherein the iteration inputs further include an input autocorrelation matrix estimate from the previous iteration.
3. The method of claim 1 , further comprising:
generating a plurality of likelihoods for the second stream of estimated symbols.
4. The method of claim 3 , wherein the plurality of likelihoods is based on a variance of an estimation error for the second stream of estimated symbols.
5. The method of claim 3 , wherein generating the estimates of the information bits comprises:
deinterleaving the plurality of likelihoods; and
performing a forward error correction (FEC) operation on an output of the deinterleaving.
6. The method of claim 5 , wherein the FEC operation is based on a convolutional code, a turbo code or a low-density parity-check (LDPC) code.
7. The method of claim 1 , wherein the two-dimensional symplectic Fourier transform is a symplectic fast Fourier transform (SFFT).
8. 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, and at least one symbol estimate from a previous iteration;
performing, based on the iteration inputs, an affine minimum mean-squared error (MMSE) equalization operation on the stream of received symbols to generate a first stream of estimated symbols;
transforming, using a two-dimensional symplectic Fourier transform, the first stream of estimated symbols from a two-dimensional time-frequency grid to a second stream of estimated symbols in a two-dimensional delay-Doppler grid; and
generating, based on the second stream of estimated symbols in the two-dimensional delay-Doppler grid, estimates of the information bits.
9. The apparatus of claim 8 , wherein the iteration inputs further include an input autocorrelation matrix estimate from the previous iteration.
10. The apparatus of claim 8 , further comprising:
generating a plurality of likelihoods for the second stream of estimated symbols.
11. The apparatus of claim 10 , wherein the plurality of likelihoods is based on a variance of an estimation error for the second stream of estimated symbols.
12. The apparatus of claim 10 , wherein generating the estimates of the information bits comprises:
deinterleaving the plurality of likelihoods; and
performing a forward error correction (FEC) operation on an output of the deinterleaving, wherein the FEC operation is based on a convolutional code, a turbo code or a low-density parity-check (LDPC) code.
13. The apparatus of claim 8 , wherein the two-dimensional symplectic Fourier transform is a symplectic fast Fourier transform (SFFT).
14. The apparatus of claim 8 , wherein a number of iterations performed by the iterative equalizer is based on a total number of iterations, a time budget for recovering the information bits from the received signal, or a comparison of an improvement in successive iterations to a threshold.
15. A non-transitory computer readable storage medium having instructions stored thereupon, the instructions, when executed by a processor, causing the processor to implement a method for recovering information bits from a received signal by performing iterative equalization, comprising:
instructions for 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, and at least one symbol estimate from a previous iteration;
instructions for performing, based on the iteration inputs, an affine minimum mean-squared error (MMSE) equalization operation on the stream of received symbols to generate a first stream of estimated symbols;
instructions for transforming, using a two-dimensional symplectic Fourier transform, the first stream of estimated symbols from a two-dimensional time-frequency grid to a second stream of estimated symbols in a two-dimensional delay-Doppler grid; and
instructions for generating, based on the second stream of estimated symbols in the two-dimensional delay-Doppler grid, estimates of the information bits.
16. The non-transitory computer readable storage medium of claim 15 , wherein the iteration inputs further include an input autocorrelation matrix estimate from the previous iteration.
17. The non-transitory computer readable storage medium of claim 15 , further comprising:
generating a plurality of likelihoods for the second stream of estimated symbols.
18. The non-transitory computer readable storage medium of claim 17 , wherein the plurality of likelihoods is based on a variance of an estimation error for the second stream of estimated symbols.
19. The non-transitory computer readable storage medium of claim 17 , wherein generating the estimates of the information bits comprises:
deinterleaving the plurality of likelihoods; and
performing an forward error correction (FEC) operation on an output of the deinterleaving, wherein the FEC operation is based on a convolutional code, a turbo code or a low-density parity-check (LDPC) code.
20. The non-transitory computer readable storage medium of claim 15 , wherein the two-dimensional symplectic Fourier transform is a symplectic fast Fourier transform (SFFT).