2. 1 STATISTICAL PROPERTIES OF COMPOSITE DISTORTIONS IN HFC SYSTEMS AND THEIR EFFECTS ON DIGITAL CHANNELS By Dr. Ron D. Katznelson, CTO Broadband Innovations, Inc., San Diego CA Presented at NCTA’s Cable 2002 May 7, 2002. New Orleans, LA Author ContactRon Katznelson Broadband Innovations, Inc. San Diego CA, 92121 ron@broadbandinnovations.comron@broadbandinnovations.com Tel: (858) 395-1440

3. 2 Synopsis n CSO and CTB distortions due to analog carriers u Amplitude statistics u Temporal statistics u Peak envelope (amplitude) excursion values n Are observed degradations really due to “clipping”? n The effects on digital QAM channels u Published measurement results u Comparison of 256 QAM and 64 QAM u Why 256 QAM is not always a ‘Cake Walk’. n Mitigation measures for improved reliability n Conclusions

4. 3 Composite Distortion Terms n The Multicarrier signal: u where are the amplitude, the angular frequency and phase of the n th carrier signal. n The nonlinearity: n Distortions components: u Second Order: u Third Order

5. 4 Typical time record of composite distortion in HFC (CSO at 572.5 MHz)

6. 5 Probability density function of composite distortion Levels 10 -4 10 -3 10 -2 10 -1 -80-70-60-50 Distortion Level (dBc) Pr ( dB ) Nonlinear Model:  2 =7*10 -5,  3 =2*10 -5 -2  CTB, Ch index 9 -  CSO, Ch index 9 CTB, Ch index 17 CTB, Ch index 92  CSO, Ch index 105 Based on Simulation of 75 channel system with random phases.

7. 6 Probability Density Function of CTB Distortion Levels -60-50-40-30-20-1001020 Distortion Level relative to average distortion (dB) Pr ( dB ) Simulation  = 5.69 dB Log-Rayleigh Distribution  = 5.57 dB 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1

8. 7 Probability Density of Composite Distortion Level Distortion Level (dB) Probability Density ( dB ) 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1

9. 8 Typical time record of composite distortion in HFC (CSO at 572.5 MHz)

10. 9 Composite distortion BER impairments vs. interleaver depth BER Source: S. Ovadia, NCTA Technical Papers, (1998).

11. 10 Close-in spectra of composite distortion components in HFC system. Standard Multicarrier Source Effective spectral occupancy of the order of 10 kHz Thousands of components for CTB and hundreds of components for CSO Accurate or Coherent Multicarrier Source Very narrow effective bandwidth. Same number of additive components as above.

12. 11 How Large can CSO/CTB Envelope Fluctuations be? n Relevant Observation Period: Quasi-Error-Free interval of 15 minutes n Assume correlation time is < 100  s and that at 300-  s apart, the processes are practically “independent” n Over a period of 15 minutes we have 15  60/(300  10 -6 ) = 3  10 6 “independent” experiments to draw new random envelope values. If only one of these experiments on average reaches excessive value, it has a probability of 1/ 3  10 6, which is the probability that the envelope exceeds the level that is 16 dB above average.

13. 12 Composite distortions require non-intuitive high noise margins n CTB and CSO component’s peak envelope power levels can reach up to 16 dB above their measured average levels. n Envelope power is nearly Rayleigh distributed (having a Standard Deviation of 5.7 dB). n Clipping is not the most likely cause of onset of degradations

14. 13 Source: D. Stoneback et al., NCTA Technical Papers. (1999)

15. 14 Effect of Composite Distortion on 256 QAM BER Estimated Coded BER Source: S. Ovadia, J. of Lightwave Tech., Vol. 16, N0.7, pp. 1171-1186. (July 1998).

16. 15 Why is this Noise+Interference margin level Insufficient for 256 QAM? See below:

17. 16 256 QAM – 64 QAM Comparison

18. 17 Mitigation n Reduce and control CSO and CTB n Implement 1.25 MHz frequency offsets for digital channels n Improve Head-End noise margin u Better Phase Noise u Better QAM Transmitter Aggregate Noise Specifications n Increase (if possible) interleaver depth n Establish better tuner CSO/CTB specifications

19. 18 1.25 MHz Offset Minimize Distortion Effects by Frequency Offsetting Digital Channels Frequency Analog NTSC ChannelsDigital Channels CTB Distortion Components Source: R. D. Katznelson, Presented to NCTA/EIA Joint Engineering Committee, Fall, 1992.

20. 19 Frequency CSO Levels CTB Levels Additional 1.25 MHz Offset Additional Offset at CSO Crossover in Standard Channel Frequency Plan Frequency Analog NTSC Channels Digital Channels CTB Distortion Components CSO Distortion Components

21. 20 Head-End Noise Degradations from Multiple QAM Channels

22. 21 CONCLUSION n CSO and CTB reach levels that can be much higher than expected n The aggregation of noise and distortion from an ever growing number of QAM channels results in further degradation upon the addition of services and channels. These levels may work well for 64 QAM but provide very little or no margin for 256 QAM. n Use all tools available for mitigation