Approximation of recursive least squares equalization
A receiver is configured to detect, at a communication interface, a received signal that suffers from degradations incurred over a communication channel. The receiver applies an adaptive filter to a series of received blocks of a digital representation of the received signal, thereby generating respective filtered blocks, where each received block represents 2N frequency bins, and where N is a positive integer. The receiver calculates coefficients for use by the adaptive filter on a j th received block as a function of (i) error estimates associated with an (j−D−1) th filtered block, where D is a positive integer representing a number of blocks, and where j is a positive integer greater than (D−1); and (ii) an inverse of an approximate covariance matrix associated with the (j−D−1) th received block, where the approximate covariance matrix is a diagonal matrix of size L×L, and where L is a positive integer lower than 2N.
1. A receiver device comprising:
a communication interface configured to detect a received signal comprising a degraded version of a transmitted signal, the received signal suffering from degradations incurred over a communication channel; and
circuitry configured to
apply an adaptive filter to a series of received blocks of a digital representation of the received signal, thereby generating respective filtered blocks, wherein each received block represents 2N frequency bins, and wherein N is a positive integer; and
calculate coefficients for use by the adaptive filter on a j th received block using (i) error estimates associated with a (j−D−1) th filtered block, wherein D is a positive integer representing a number of blocks, and wherein j is a positive integer greater than (D−1); and (ii) an inverse of an approximate covariance matrix associated with the (j−D−1) th received block, wherein the approximate covariance matrix is a diagonal matrix of size L×L, and wherein L is a positive integer lower than 2N.
2. The receiver device as claimed in claim 1 , wherein the circuitry is further configured to calculate the coefficients for use by the adaptive filter on the j th received block using (iii) delay compensation terms dependent on a difference between coefficients used by the adaptive filter on a (j−D−1) th received block and coefficients used by the adaptive filter on a (j−1) th received block.
3. The receiver device as claimed in claim 1 , wherein the approximate covariance matrix is expressed in a frequency domain, and wherein each one of L diagonal terms of the approximate covariance matrix corresponds to a different frequency.
4. The receiver device as claimed in claim 1 , wherein the approximate covariance matrix is one of a plurality of sub-matrices comprised in a composite matrix, and wherein the circuitry is further configured to calculate the coefficients using an inverse of each sub-matrix in the composite matrix.
5. The receiver device as claimed in claim 4 , wherein the composite matrix consists of four diagonal L×L sub-matrices, each sub-matrix approximating a covariance matrix associated with a different polarization of the received signal.
6. The receiver device as claimed in claim 1 , wherein the circuitry is further configured to calculate the approximate covariance matrix for the (j−D−1) th received block as a recursive function of a preceding approximate covariance matrix associated with a preceding received block of the series.
7. The receiver device as claimed in claim 1 , wherein each received block comprises a respective digital representation of a plurality of samples of the received signal detected at the communication interface over a period of time.
8. The receiver device as claimed in claim 1 , wherein the received signal is representative of symbols, and wherein the circuitry is further configured to
decode estimates of the symbols represented by the (j−D−1) th filtered block; and
calculate the error estimates associated with the (j−D−1) th filtered block using the decoded estimates of the symbols.
9. The receiver device as claimed in claim 8 , wherein the symbols include one or more predetermined symbols.
10. The receiver device as claimed in claim 1 , wherein the communication channel comprises an optical communication channel.
11. A method comprising:
at a communication interface of a receiver device, detecting a received signal comprising a degraded version of a transmitted signal, the received signal suffering from degradations incurred over a communication channel;
applying an adaptive filter to a series of received blocks of a digital representation of the received signal, thereby generating respective filtered blocks, wherein each received block represents 2N frequency bins, and wherein N is a positive integer; and
calculating coefficients for use by the adaptive filter on a j th received block using (i) error estimates associated with a (j−D−1) th filtered block, wherein D is a positive integer representing a number of blocks, and wherein j is a positive integer greater than (D−1); and (ii) an inverse of an approximate covariance matrix associated with the (j−D−1) th received block, wherein the approximate covariance matrix is a diagonal matrix of size L×L, and wherein L is a positive integer lower than 2N.
12. The method as claimed in claim 11 , further comprising
calculating the coefficients for use by the adaptive filter on the j th received block using (iii) delay compensation terms dependent on a difference between coefficients used by the adaptive filter on a (j−D−1) th received block and coefficients used by the adaptive filter on a (j−1) th received block.
13. The method as claimed in claim 11 , wherein the approximate covariance matrix is expressed in a frequency domain and wherein each one of L diagonal terms of the approximate covariance matrix corresponds to a different frequency.
14. The method as claimed in claim 11 , wherein the approximate covariance matrix is one of a plurality of sub-matrices comprised in a composite matrix, the method further comprising calculating the coefficients using an inverse of each sub-matrix in the composite matrix.
15. The method as claimed in claim 14 , wherein the composite matrix consists of four diagonal L×L sub-matrices, each sub-matrix approximating a covariance matrix associated with a different polarization of the received signal.
16. The method as claimed in claim 11 , further comprising calculating the approximate covariance matrix for the (j−D−1) th received block as a recursive function of a preceding approximate covariance matrix associated with a preceding received block of the series.
17. The method as claimed in claim 11 , wherein each received block comprises a respective digital representation of a plurality of samples of the received signal detected at the communication interface over a period of time.
18. The method as claimed in claim 11 , wherein the received signal is representative of symbols, the method further comprising
decoding estimates of the symbols represented by the (j−D−1) th filtered block; and
calculating the error estimates associated with the (j−D−1) th filtered block using the decoded estimates of the symbols.
19. The method as claimed in claim 18 , wherein the symbols include one or more predetermined symbols.
20. The method as claimed in claim 11 , wherein the communication channel comprises an optical communication channel.