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Elias Nemer

AN ITERATIVE FEEDBACK ALGORITHM FOR CORRECTING . THE I/Q IMBALANCE IN DVB-S RECEIVERS . Elias Nemer. enemer@ieee.org. COMMUNICATION SYSTEMS AND NETWORKS - CSN 2004. Outline . Context and Motivation Problem statement Blind I/Q Correction Exact Solution Iterative approximation

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Elias Nemer

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  1. AN ITERATIVE FEEDBACK ALGORITHM FOR CORRECTING THE I/Q IMBALANCE IN DVB-S RECEIVERS Elias Nemer enemer@ieee.org COMMUNICATION SYSTEMS AND NETWORKS - CSN 2004

  2. Outline • Context and Motivation • Problem statement • Blind I/Q Correction • Exact Solution • Iterative approximation • Algorithm Implementation • Simulation Data • Conclusion

  3. A/D LPF I’ LO Q’ A/D LPF Problem Context RF IF To Baseband Processing BPF amp LO LNA Imperfect Analog Demod • I and Q are non-orthogonal and un-equal in magnitude. • Increased cluster variance. • Affect the convergence behaviour of other loops (e.g. equalizer)

  4. Problem Context 8 PSK 16 QAM 16 APSK 32 APSK

  5. Problem Context Input with IQ imbalance & reflections Equalizer output Input at the receiver with IQ imbalance Equalizer output

  6. Blind Estimation Exact Solution The corrupted quadratures are expressed in terms of the originals and the imbalance It may be shown that the exact solution is : with with

  7. Blind Estimation For the un-corrupted quadratures of a square M-QAM signal, the following three conditions hold: Proof The cross correlation between the 2 impaired quadratures is: thus: The cross terms cancel, since

  8. Now consider the individual energies of the corrupted quadratures, The energy simplifies to Since Using the above equations, The phase imbalance can be determined from the ratio : The magnitude imbalance is derived from the ratio :

  9. Blind Estimation Proposed Approximation • Avoid division • Magnitude and phase : 2 independent problems • Use iterative approach (avoid explicit summations) • Make use of the fact that the total signal energy is known apriori Magnitude Imbalance : Phase Imbalance : Is known apriori from the AGC

  10. DVB-S Block Diagram

  11. Iterative Algorithm Implementation Magnitude Correction I’’ I’ H(z) G(z) 1 1st-order Integrator H(z) Q’’ Q’

  12. Iterative Algorithm Implementation Phase Correction I’’ I Vector matrix Multiply [2x2] [1x2] S1.14 x S2.7 10 bits 10 bits I[n].Q[n] 20 bits Integrator LUT H(z) S4.14 16 bits 16 bits S0.15 S1.14 16 bits Q’’ Q S0.15 S2.7 S2.7

  13. Simulation Results Nyquist Filter random QAM Symbols I / Q Mapping Baseband Symbols Transmitter (I + j Q) Baseband Channel I-Q Imbalance Reflections AWGN Avg difference Cluster SNR AGC Carrier PLL I / Q balancing Soft Symbols Slicer F F E Nyquist Filter F B E Receiver

  14. Epsilon Estimate 0.2 0.15 0.1 0.05 0 0 0.5 1 1.5 2 2.5 3 x 105 Phi estimate (rad) 0.1 0.08 0.06 0.04 0.02 0 0 0.5 1 1.5 2 2.5 3 x 105 Impairments : AWGN + reflections + IQ imbalance Time (samples) Simulation Results

  15. without IQ balancing Equalizer output Input at the receiver with IQ imbalance Equalizer output with IQ balancing

  16. Output after equalization without I-Q balancing Cluster SNR = 15.8 dB Input at the receiver with I-Q imbalance and multi-paths (2 echoes) Cluster SNR = 36 dB Output after I-Q balancing and equalization

  17. Output after equalization without I-Q balancing Cluster SNR = 14.5 dB Cluster SNR = 19.7 dB Input at the receiver with I-Q imbalance , AWGN (Eb/No=15dB), and multi-paths (4 echoes) Output after I-Q balancing and equalization

  18. Output after equalization without I-Q balancing Cluster SNR = 12.5 dB Input at the receiver with I-Q imbalance, AWGN (Eb/No=12) and multi-paths (4 echoes) Cluster SNR = 15 dB Output after I-Q balancing and equalization

  19. Output after equalization without I-Q balancing Cluster SNR = 15.8 dB Input at the receiver with I-Q imbalance and multi-paths (2 echoes) Output after I-Q balancing and equalization Cluster SNR > 45 dB

  20. Output after equalization without I-Q balancing Cluster SNR = 13.8 dB Input at the receiver with I-Q imbalance and multi-paths (2 echoes), AWGN (12 dB Eb/No) Output after I-Q balancing and equalization Cluster SNR 17.8 dB

  21. Output after equalization without I-Q balancing Input at the receiver with I-Q imbalance and multi-paths Output after I-Q balancing and equalization

  22. Conclusion • A new iterative algorithm was shown effective for correcting the I/Q imbalance for all the constellations used in DVB-S receivers. • If not corrected the I/Q imbalance increases the cluster variance (significantly sometimes) and prevents the equalizer to properly converge. • The proposed scheme has no divisions and a minimum number of multiplications. It makes use of the apriori known signal energy derived from the AGC. • It is proven robust in all the extreme channel impairments specified in the DVB-S systems and yields a significant improvement in cluster SNR.

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