Chapter 6 OFDM/DMT for Wireline Communications

1. Chapter 6 OFDM/DMT for Wireline Communications School of Info. Sci. & Eng. Shandong Univ.

2. CONTENT • 6.1 Discrete MultiTone (DMT) and Wireline Channel Properties • 6.2 Optical OFDM Transmission and Optical Channel Properties • 6.3 Impulse-Noise Cancellation • 6.4 Dual Polarization Optical OFDM Transmission • 6.5 Forward Error Correction • 6.6 Summary

3. Properties of the Twisted-Pair Channel • Transfer Characteristic：

4. Near-end Crosstalk (NEXT) and Far-end Crosstalk (FEXT) • NEXT results from coupling from other loops in the same cable from transmitters located at the same side as the own receiver. NEXT (as a power contribution) is modeled as: where N is the number of identical disturbers and the power of 0.6 is to halfways model the distribution of disturbers in cable.

5. Near-end Crosstalk (NEXT) and Far-end Crosstalk (FEXT) • FEXT results from coupling from other lo ops in the same cable from transmitters located at the opposite side of the own receiver. FEXT (as a power contribution) is modeled as: where N is the number of identical disturbers, l is the length of the coupling length, and the power of 0.6 is to halfways model the distribution of disturbers in the cable

6. Near-end Crosstalk (NEXT) and Far-end Crosstalk (FEXT) NEXT and FEXT

7. Near-end Crosstalk (NEXT) and Far-end Crosstalk (FEXT) • The so-called Equal-Level FEXT (EL-FEXT) is defined by eliminating the length dependency and the transfer function:

8. Near-end Crosstalk (NEXT) and Far-end Crosstalk (FEXT) Measured NEXT of an 0.4-mm layered cable

9. Near-end Crosstalk (NEXT) and Far-end Crosstalk (FEXT) • Measured NEXT of an 0.4-mm layered cable

10. Radio-frequency Interference (RFI) and Impulse Noise • Non-symmetries are characterized by unbalance parameters like Longitudinal Conversion Loss (LCL), Transverse Conversion Loss (TCL), Longitudinal Conversion Transfer Loss (LCTL),and Transverse Conversion Transfer Loss (TCTL). • The duration of an impulse follows roughly follows a combination of two log-normal densities in the form：

11. Radio-frequency Interference (RFI) and Impulse Noise Impulses resulting from welding and fluorescent tubes, measured at a telephone socket

12. Discrete MultiTone (DMT) Components of DMT transmission

13. Two-Sided Processing for MIMO Based on SVD • The singular-value decomposition rephrases the channel matrix in DFT domain H ( n) at carrier number n as： Λ(n) is a diagonal matrix. P (n ) and Q (n) are unitary matrices.

14. Two-Sided Processing for MIMO Based on SVD • Let t (n) and r(n ) be input and output vectors, respectively. At the transmitter side, we multiply the signal t(n ) by P (n ). Whereas, the signal at the receiver is multiplied by QH( n) to obtain the output r(n )：

15. Two-Sided Processing for MIMO Based on SVD • Using the SVD，we obtain： x (n) is the product of P ( n) and t (n )

16. Two-Sided Processing for MIMO Based on SVD • OFDM and SVD as Reed-Solomon or RS-like codes RS codes are commonly defined as follows • the structures of OFDM and SVD：

17. QR decomposition for upstream processing • For upstream processing we write the L × L channel matrix as (In the following, we omit the carrier index n): H=QR • With a unitary matrix Q and an upper triangular matrix R .Working with column vectors for information and received values, a post-processing with QH leads to:

18. QR decomposition for upstream processing Spatial DFE structure resulting from QR decomposition

19. QR decomposition for downstream processing • For downstream processing, the idea is to apply a QR decomposition to the transpose of the channel matrix. This enables us to do a pre-processing instead of the post-processing of the previous paragraph. We hence obtain: • The diagonal matrix is added to obtain a similar structure in the following formula . Equation can equivalently be rephrased as:

20. QR decomposition for downstream processing QR decomposition for downstream processing

21. Optical OFDM Transmission and Optical Channel Properties • Commercially available systems for high bit-rate optical data transmission utilize on-off-keying or differential phase shift keying (DPSK) and reach bit-rates up to 40 Gbit/s. • A straightforward approach is bit-interleaved coded modulation with iterative decoding (BICM-ID) , which can be considered as the most simple approach to achieve high spectral efficiency while providing a low decoding complexity.

22. Common Mode and Differential Mode • Differential-Mode (DM) signals have been the conventional approach of transmission over copper cables. • Common-Mode (CM) signals are taken as the arithmetic mean of the two signals measured with respect to ground, which makes them prone to interference. • Both DM and CM signals are readily available on the receiver side:

23. Coupling and Transfer Functions • Transfer functions for DM and CM obtained from measurements of a 0.4 mm Swiss cable of length 100 m

24. Coupling and Transfer Functions • NEXT coupling functions, obtained from measurements of different TPs in the bundle. The outlier is due to measuring the other TP in the same star quad

25. Coupling and Transfer Functions • FEXT coupling functions, obtained from measurements of different TPs in the bundle. The outliers are due to measuring adjacent TPs

26. Common-Mode Reference-Based Canceler • Impulse noise generated from light switching, both in DM and CM

27. Impulse Noise Detection and Cancellation—Detection • For the first method , in order to obtain the envelope, the CM is split into non overlapping frames of size M .Out of every frame, the maxim value is chosen and interpolation is performed among all local maxima. Envelope of CM signal (green)

28. Impulse Noise Detection and Cancellation—Detection • A second method which can be easily implemented in the analog domain uses a rectifier and a low pass filter to detect the envelope of the CM signal ： Second method for CM envelope detection

29. Simulation Results • The green line depicts the overall received DM signal, which is corrupted by impulsive noise, while the black waveform illustrates the same DM signal, impulse noise free. • The red line presents the ideal transmitted signal, with no interference, only attenuated by the loop.

30. Dual Polarization Optical OFDMTransmission Investigated system: Dual polarization OFDM transmission, coherent detection.

31. Noise Variance Estimation • The transmission of symbol vectors[X1(d) X2(d)]T on sub-carrier d can be written as: • Then the relative noise variance for both receive branches can be determined:

32. Noise Variance Estimation Estimated relative noise power

33. Achievable Spectral Efficiency • According to Shannon the maximum information-rate which can be transmitted over a band-limited additive white Gaussian noise channel is: • The contributions of the orthogonal polarizations are added up. Furthermore we average over the OFDM sub-carriers:

34. Achievable Spectral Efficiency • The investigated transmission system is assumed to consist of equally spaced, identical optical amplifiers. The optical SNR (OSNR) after Nspans amplifiers is given by: Here h and c denote Planck’s constant and the speed of light, respectively. G is the amplifiers’ gain which shall equal the loss of one fiber span. The noise figure is given by FN

35. Achievable Spectral Efficiency • Achievable spectral efficiency versus distance and launch power

36. Achievable Spectral Efficiency • Achievable spectral efficiency vs. distance

37. ADC/DAC Resolution • Achievable spectral efficiency versus distance considering quantization noise.

38. Forward Error Correction Iterative demapping and decoding, BICM-ID system configuration

39. Forward Error Correction • The function btst (i, h ) takes the value ‘1’if bit number h is set in the binary decomposition of i, otherwise it is ‘0’ where: • When the channel symbols z are corrupted by complex Gaussian noise, the conditional PDF calculates to:

40. Forward Error Correction • The soft-demapping algorithm of for the complex AWGN channel as:

41. Influence of the Applied Mapping • For anti-Gray mapping a quite high SNR is required to reach the so called “turbo cliff”, which is the required SNR at which the decoding process starts to deliver an iteration gain. • The symbols within a CW are mapped to a ratio of α according to Gray and to a ratio 1 − α according to anti-Gray:

42. Simulations on the Performance of Coded OFDM Complete optical COFDM system

43. Simulations on the Performance of Coded OFDM Simulations on systems performance; BER at BICM-ID output

44. Simulations on the Performance of Coded OFDM EXIT functions of decoder and soft-demapper for different mappings at optical input power of -9 dBm

45. Summary • This chapter gave an impression of some of the research issues related to the wireline use of multicarrier modulation. Many aspects are similar as in wireless, but the channels offer different possibilities or have other challenges, such as, e.g., more stationary behavior, an additional common mode in twisted-pair, or non-linearities in optical communication. • We adapted the principle of an iterative decoding scheme, namely BICM-ID, to our system. The obtained results for the investigated optical OFDM system promise to reach a spectral efficiency of 8 bit/s/Hz for a 960 km fiber link.