Systems and methods for circular convolution
System and method embodiments are provided for a receiver for circularly convolved signals. In an embodiment, a universal decoder for a circularly convolved signal includes a first decoder configured to decode the circularly convolved signal; a second decoder configured to decode a plurality of symbol lengths signal from a first portion of the circularly convolved signal, wherein the plurality of symbol lengths signal is time aligned with the circularly convolved signal before passing through the second decoder; and an adder component configured to sum a first decoder output coming from the first decoder and a second decoder output coming from the second decoder to produce a symbol value from which a log likelihood ratio (LLR) output is obtained.
1. A universal decoder for a circularly convolved signal, comprising:
a first decoder configured to decode the circularly convolved signal;
a second decoder configured to decode a plurality of symbol lengths signal obtained from a first portion of the circularly convolved signal, wherein the plurality of symbol lengths signal is time aligned with the circularly convolved signal before passing through the second decoder; and
an adder component configured to sum a first decoder output coming from the first decoder and a second decoder output coming from the second decoder to produce a symbol value from which a log likelihood ratio (LLR) output is obtained.
2. The decoder of claim 1 , further comprising a multiplier component configured to weight a circular part of the signal with a weighting factor in order to remove an abrupt change of a channel, wherein the weighting is determined according to a compensated channel.
3. The decoder of claim 2 , wherein the weighting factor is determined according to
h
n
h
1
*
h
1
2
,
where h 1 is a channel value at the beginning of the circularly convolved signal, h N is a channel value at the end of the circularly convolved signal, h* 1 is the complex conjugate of h 1 , and |h 1 | is the amplitude of h 1 .
4. The decoder of claim 1 , wherein the decoders comprise linear orthogonal frequency division multiplexing (OFDM)-offset quadrature amplitude modulation (OQAM) decoders.
5. The decoder of claim 1 , wherein the decoders comprise poly-phase filters.
6. The decoder of claim 1 , wherein the plurality of symbol lengths comprises a length of prototype filter minus T/2, where T is an offset quadrature amplitude modulation (OQAM) symbol duration.
7. The decoder of claim 1 , further comprising an LLR weighting component configured to weight the LLR output with a weighting factor with channel compensation taken into account.
8. The decoder of claim 7 , wherein the weighting factor is given by
2
h
1
2
h
N
2
h
1
2
+
h
N
2
where h 1 is a channel at the beginning of the circularly convolved signal, h N is a channel at the end of the circularly convolved signal, |h 1 | is the amplitude of h 1 , and |h N | is the amplitude of h N .
9. The decoder of claim 1 , further comprising:
an equalizer component to remove a channel effect from the symbol; and
a quadrature amplitude modulation (QAM) soft demapping component to generate an unweighted LLR.
10. A method for receiving a circularly convolved signal, the method comprising:
passing the circularly convolved signal through a first decoder;
passing a plurality of symbol length signal obtained from a first portion of the circularly convolved signal through a second decoder, the plurality of symbol length signal is time aligned with the circularly convolved signal before passing through the second decoder; and
summing the outputs of the first and second decoder for a log likelihood ratio (LLR) de-mapping output.
11. The method of claim 10 , further comprising weighting a circular part of the signal with a weighting factor according to a compensated channel to remove an abrupt change of the channel.
12. The method of claim 11 , wherein the weighting factor is determined according to
h
n
h
1
*
h
1
2
,
where h 1 is a channel value at the beginning of the circularly convolved signal, h N is a channel value at the end of the circularly convolved signal, h* 1 is the complex conjugate of h 1 , and |h 1 | is the amplitude of h 1 .
13. The method of claim 10 , further comprising weighting the LLR de-mapping output with a weighting factor according to channel compensation.
14. The method of claim 13 , wherein the weighting factor is given by
2
h
1
2
h
N
2
h
1
2
+
h
N
2
where h 1 is a channel at the beginning of the circularly convolved signal, h N is a channel at the end of the circularly convolved signal, |h 1 | is the amplitude of h 1 , and |h N | is the amplitude of h N .
15. The method of claim 10 , wherein the decoders comprise linear orthogonal frequency division multiplexing (OFDM)/offset quadrature amplitude modulation (OQAM) decoders.
16. The method of claim 10 , wherein a plurality of first signal lengths comprises a length of prototype filter minus T/2, where T is OQAM symbol duration.
17. A network component, comprising:
a transmitter; and
a receiver, wherein the receiver comprises:
a first decoder for decoding a circularly convolved signal;
a second decoder for decoding a plurality of symbol lengths signal obtained from a first portion of the circularly convolved signal, wherein the plurality of symbol lengths signal is time aligned with the circularly convolved signal before passing through the second decoder; and
an adder component for summing a first decoder output coming from the first decoder and a second decoder output coming from the second decoder to produce a symbol value from which a log likelihood ratio (LLR) output is obtained.
18. The network component of claim 17 , further comprising a multiplier component for weighting a circular part of the signal with weighting factor determined according to a compensated channel to remove an abrupt change of the channel.
19. The network component of claim 18 , wherein the weighting factor is determined according to
h
n
h
1
*
h
1
2
,
where h 1 is a channel value at the beginning of the circularly convolved signal, h N is a channel value at the end of the circularly convolved signal, h* 1 is the complex conjugate of h 1 , and |h 1 | is the amplitude of h 1 .
20. The network component of claim 17 , wherein the decoders comprise linear orthogonal frequency division multiplexing (OFDM)/offset quadrature amplitude modulation (OQAM) decoders.
21. The network component of claim 17 , wherein the decoders comprise poly-phase filters.
22. The network component of claim 17 , wherein the copied first plurality of symbol lengths comprises a length of prototype filter minus T/2, where T is OQAM symbol duration.
23. The network component of claim 17 , wherein the adder component is further configured to weight the LLR output with a weighting factor with channel compensation taken into account.
24. The network component of claim 23 , wherein the weighting factor is given by
2
h
1
2
h
N
2
h
1
2
+
h
N
2
where h 1 is a channel at the beginning of the circularly convolved signal, h N is a channel at the end of the circularly convolved signal, |h 1 | is the amplitude of h 1 , and |h N | is the amplitude of h N .
25. The network component of claim 17 , wherein the receiver further comprises:
an equalizer component to remove a channel effect from the symbol; and
a quadrature amplitude modulation (QAM) soft demapping component to generate an unweighted LLR.