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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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**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 • Algorithm Implementation • Simulation Data • Conclusion**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)**Problem Context**8 PSK 16 QAM 16 APSK 32 APSK**Problem Context**Input with IQ imbalance & reflections Equalizer output Input at the receiver with IQ imbalance Equalizer output**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**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**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 :**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**Iterative Algorithm Implementation**Magnitude Correction I’’ I’ H(z) G(z) 1 1st-order Integrator H(z) Q’’ Q’**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**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**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**without IQ balancing**Equalizer output Input at the receiver with IQ imbalance Equalizer output with IQ balancing**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**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**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**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**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**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**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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