System and method for blind equalization and carrier phase recovery in a quadrature amplitude modulated system
View Patent ↗A system and method for blind equalization of a QAM signal. Equalization is achieved using an algorithm characterized by cost function that is a function the Euclidian distance, e.g. the minimum Euclidian distance, between points of the constellation associated with the QAM signal, i.e. the distance between symbols.
1. An optical receiver system comprising:
a digital signal processor (DSP) comprising an equalizer configured to equalize a signal representative of a quadrature amplitude modulated (QAM) optical signal transmitted over an optical transmission path,
said equalizer being configured to equalize said signal by application of an equalization algorithm to said signal, said equalization algorithm being characterized by a cost function,
said cost function being a function of a Euclidian distance between detected symbols of said QAM optical signal at an output of said equalizer, wherein said cost function is:
J=E [( D 2 −|R 2 −|Re ( u ( n ))| 2 |) 2 ]+ E [( D 2 −|R 2 |Im ( u ( n ))| 2 |) 2 ]
where J represents the cost function value E[.] denotes expectation, D is said Euclidian distance and is a minimum Euclidian distance between said symbols, R 2 is equal to ½ of the average symbol power at said output of said equalizer, Re(u(n)) is a real portion of said output of said equalizer for a current update cycle, and Im(u(n)) is an imaginary portion of said output of said equalizer for said current update cycle.
2. An optical receiver system according to claim 1 , wherein said Euclidean distance is a minimum Euclidian distance between said detected symbols.
3. An optical receiver system according to claim 1 , wherein said DSP does not include a carrier phase estimation function for estimating a carrier phase of said QAM signal.
4. An optical receiver system according to claim 1 , said system further comprising a coherent receiver for receiving said QAM optical signal, and wherein said signal representative of said QAM signal is provided as an output of said coherent receiver coupled to said equalizer through at least one DSP function.
5. An optical receiver system according to claim 1 , wherein QAM optical signal is a polarization multiplexed QAM optical signal.
6. An optical receiver system according to claim 1 , wherein said equalizer comprises at least one sub-equalizer filter, said at least one sub-equalizer filter comprising a plurality of delays for producing successively delayed versions of said signal and a plurality of multipliers, each of said multipliers multiplying said signal or an associated one of said delayed versions of said signal with an associated filter coefficient to produce an associated tap weight product, said tap weight products being summed to provide said output of said equalizer.
7. An optical receiver system according to claim 1 , wherein said equalizer comprises at least one sub-equalizer filter, said at least one sub-equalizer filter comprising a plurality of delays for producing successively delayed versions of said signal and a plurality of multipliers, each of said multipliers multiplying said signal or an associated one of said delayed versions of said signal with an associated filter coefficient to produce an associated tap weight product, said tap weight products being summed to provide said output of said equalizer.
8. An optical receiver system according to claim 7 , wherein said filter coefficients for said at least one sub-equalizer are calculated according to the following equation:
h xx ( n+ 1)= h xx ( n )+με SMA ( u ( n )) u ( n ) x *( n )
where n is said current update cycle, n+1 is a next update cycle, μ is a step size, x(n) is said signal for said current update cycle, the superscript * means complex conjugation, and εsma(u(n)) is calculated as:
ε SMA ( u ( n ))=( D 2 −|R 2 −|Re ( u ( n ))| 2 |)+ j ( D 2 −|R 2 −|Im ( u ( n ))| 2 |).
9. An optical receiver system comprising:
a coherent receiver for receiving a polarization multiplexed quadrature amplitude modulated (QAM) optical signal and providing a first plurality of outputs in response to a first polarization of said optical signal and a second plurality of outputs in response to a second polarization of said optical signal; and
a digital signal processor (DSP) comprising an equalizer configured apply an equalization algorithm to a first digital signal established in response to said first plurality of outputs and a second digital signal established in response to said second plurality of outputs to provide first and second digital outputs representative of a first polarization state of said QAM optical signal at which data is modulated and a second polarization state of said QAM optical signal at which data is modulated,
said equalization algorithm being characterized by a cost function that is a function of a Euclidian distance between detected symbols of said QAM optical signal in said first digital output of said equalizer, wherein said at least one cost function is:
J=E [( D 2 −|R 2 −|Re ( u ( n ))| 2 |) 2 ]+ E [( D 2 −|R 2 |Im ( u ( n ))| 2 |) 2 ]
where J represents the cost function value E[.] denotes expectation, D is said Euclidian distance and is a minimum Euclidian distance between said symbols, R 2 is equal to ½ of the average symbol power in said first digital output of said equalizer, Re(u(n)) is a real portion of said first digital output of said equalizer for a current update cycle, and Im(u(n)) is an imaginary portion of said first digital output of said equalizer for said current update cycle.
10. An optical receiver system according to claim 9 , wherein said Euclidean distance is a minimum Euclidian distance between said detected symbols.
11. An optical receiver system according to claim 9 , wherein said DSP does not include a carrier phase estimation function for estimating a carrier phase of said QAM signal.
12. An optical receiver system according to claim 9 , wherein said equalizer comprises at least one sub-equalizer filter, said at least one sub-equalizer filter comprising a plurality of delays for producing successively delayed versions of said first digital signal and a plurality of multipliers, each of said multipliers multiplying said first digital signal or an associated one of said delayed versions of said first digital signal with an associated filter coefficient to produce an associated tap weight product, said tap weight products being summed to provide said first digital output.
13. An optical receiver system according to claim 12 , wherein said filter coefficients for said at least one sub-equalizer are calculated according to the following equation:
h xx ( n+ 1)= h xx ( n )+με SMA ( u ( n )) u ( n ) x *( n )
where n is said current update cycle, n+1 is a next update cycle, μ is a step size, x(n) is said first digital signal for said current update cycle, the superscript * means complex conjugation, and ε sma (u(n)) is calculated as:
ε SMA ( u ( n ))=( D 2 −|R 2 −|Re ( u ( n ))| 2 |)+ j ( D 2 −|R 2 −|Im ( u ( n ))| 2 |).
14. A method of demodulating a quadrature amplitude modulated (QAM) optical signal using a digital signal processor (DSP) without a carrier phase estimation function for estimating a carrier phase of said QAM signal, said method comprising:
equalizing a signal representative of said (QAM) optical signal transmitted over an optical transmission path using an equalizer configured to apply equalization algorithm to said signal, said equalization algorithm being characterized by a cost function that is a function of a Euclidian distance between detected symbols of said QAM optical signal at an output of said equalizer, wherein said cost function is:
J=E [( D 2 −|R 2 −|Re ( u ( n ))| 2 |) 2 ]+ E [( D 2 −|R 2 |Im ( u ( n ))| 2 |) 2 ]
where J represents the cost function value E[.] denotes expectation, D is said Euclidian distance and is a minimum Euclidian distance between said symbols, R 2 is equal to ½ of the average symbol power at said output of said equalizer, Re(u(n)) is a real portion of said output of said equalizer for a current update cycle, and Im(u(n)) is an imaginary portion of said output of said equalizer for said current update cycle.
15. A method according to claim 14 , wherein QAM optical signal is a polarization multiplexed QAM optical signal.
16. A method according to claim 14 , wherein said equalizer comprises at least one sub-equalizer filter, said at least one sub-equalizer filter comprising a plurality of delays for producing successively delayed versions of said signal and a plurality of multipliers, each of said multipliers multiplying said signal or an associated one of said delayed versions of said signal with an associated filter coefficient to produce an associated tap weight product, said tap weight products being summed to provide said output of said equalizer.
17. A method according to claim 16 , wherein said filter coefficients for said at least one sub-equalizer are calculated according to the following equation:
h xx ( n+ 1)= h xx ( n )+με SMA ( u ( n )) u ( n ) x *( n )
where n is said current update cycle, n+1 is a next update cycle, μ is a step size, x(n) is said signal for said current update cycle, the superscript * means complex conjugation, and εsma(u(n)) is calculated as:
ε SMA ( u ( n ))=( D 2 −|R 2 −|Re ( u ( n ))| 2 |)+ j ( D 2 −|R 2 −|Im ( u ( n ))| 2 |).