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Statistical Characterization of Hardware Impairments

Statistical Characterization of Hardware Impairments. Thomas Eriksson. Trends. MillimeterWave communication Hardware effects more serious (phase noise, amplifier nonlinearity) HetNet, dense deployment of small basestations Small size, cheaper hardware Low-complex algorithms Massive MIMO

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Statistical Characterization of Hardware Impairments

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  1. StatisticalCharacterizationof Hardware Impairments Thomas Eriksson

  2. Trends • MillimeterWave communication • Hardware effects more serious (phase noise, amplifier nonlinearity) • HetNet, dense deployment of small basestations • Small size, cheaper hardware • Low-complexalgorithms • Massive MIMO • Low cost absolutely necessary • Low-complex or no compensation algorithms • .... Effects due to imperfect hardware increases in importance, and may start to dominate the additive noise

  3. Traditional approach For some upcoming scenarios, we may not be able to fix the problems with high enough accuracy.

  4. Statistical approach General idea: model all the hardware imperfections as additive noise. Previous work by Schenk, Suzuki, Studer, Björnson, etc typically consider the distortion due to hardware impairments to be additive Gaussian where the variance of is approximated to scale with the variance of . We wish to improve upon this simple and, as we show, not very accurate model.

  5. Amplifiers

  6. Amplifiers • Three key parameters indicate nonlinearity: • Saturation power (Pout@3dB) • 3rd order intercept point (IP3) • 1 dB compression point (Pout@1dB) • From these, a 3rd order polynomial can be directly computed. Mini-Circuits ZHL-16W-43+

  7. AmplifiersDerivation of the distortion

  8. AmplifiersTaylor expansion of the distortion

  9. Amplifiers

  10. Oscillators This fits well with the previously developed model, with no constant part and no signal-independent addition to the AWGN.

  11. I/Q modulators I/Q phase mismatch I/Q gain mismatch I/Q imbalance is often constant over time, so that the mean of is dominating.

  12. Gain AGC tracking mismatch

  13. Symbol timing The variance of the distortion is proportional to the variance of the communication signal.

  14. Statistical effects of hardware • , can be approximated as complex Gaussian • As a 1st approximation, , are iid between Re and Im • Otherwise, estimate covariances from measurements • Subtract the constant distortion at the transmitter if possible, otherwise at the receiver using decision feedback. Further, the constant should be modeled with a complex polynomial higher than 1st order. • Useful model also if the distortion is tracked/compensated

  15. Example In this example, we have used the RF impairment blockset in Simulink/MATLAB and simulated the effect of a nonlinear amplifier and phase noise.

  16. MIMO Transmitters With a MIMO transmitter, we get crosstalk between antennas, leading to distortion in one branch whose variance is proportional to the signal in other branches. This effects depends on the antenna configuration and isolation. Further, MIMO transmitters will give correlated noise cross the antennas at the receiver.

  17. What to do now? • Estimation of noise means, covariances, constants etc. for a more extensive set of hardware impairments • Optimal detector, new codes • New constellations • Capacity • Development of MIMO models • What to do with OFDM?

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