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Feedback Reliability Calculation for an Iterative Block Decision Feedback Equalizer (IB-DFE) Gillian Huang, Andrew Nix and Simon Armour Centre for Communications Research

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Outline Introduction to linear equalizer (LE), hybrid decision feedback equalizer (H-DFE) and iterative block decision feedback equalizer (IB-DFE) Feedback Reliability (FBR) Calculation Techniques Performance comparison of IB-DFE with the proposed feedback reliability calculation and the training sequence (TS) method Conclusions

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SC-FDE with Linear Equalizer (LE) Single-carrier (SC) systems have low PAPR at the TX. MMSE-FDE is equivalent to LE. The LE filtered noise results in a large performance gap to the matched filter bound (MFB). DFE can be used to reduce the filtered noise by cancelling the ISI in the FB process. Note: frequency-selective channel does not introduce ISI to OFDM systems since the baseband symbols are directly mapped onto the subcarriers in the FD.

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Hybrid Decision Feedback Equalizer (H-DFE) While the TD-FB filter aims to cancel all the postcursor-ISI, FD-FF filter minimizes the sum of the precursor-ISI and FF filtered noise. Since the FF filtered noise is smaller than the LE filtered noise, better performance can be achieved with H-DFE. However, the H-DFE is liable to error propagation, especially in the coded systems. This is because the hard-limited equalized symbols can be very unreliable before decoding.

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Iterative Block Decision Feedback Equalizer (IB-DFE) All the detected symbols from the previous iteration are used as the FB symbols. Hence both precursor and postcursor ISI can be cancelled. The operation of IB-DFE is optimized at each iteration according to the reliability of the FB symbols. Hence IB-DFE is robust against error propagation. Both FF and FB filters are implemented in the FD efficiently.

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Iterative Block DFE (cont.) At the first iteration, p=0. The FF filter coincides with MMSE-LE. The FB filter is turned off. When p=1, the FF filter coincides with the matched filter. The FB filter aims to cancel all the ISI. As the FBR increases, the FB filter tends to cancel more and more ISI. How do we calculate the FBR? FF filter: FB filter: FB reliability is defined as:

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Feedback Reliability (FBR) Calculation One solution is the training sequence (TS) method. However, this lowers the bandwidth efficiency. Since the TS must have the same modulation and coding scheme as the data sequence, it cannot be shared with the existing reference signals. We propose to calculate the FBR from the SNR at the equalizer output. The SNR at the equalizer output can be estimated as

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Feedback Reliability Calculation – 4QAM We can use the probability integration method to derive the expression of as a function of SNR. Hence the FBR for 4QAM can be calculated as The FBR: (where is the hard-decision error)

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Feedback Reliability Calculation – 16QAM The linear regression method is used to obtain the best-fit reliability curve. For 16QAM, and. We propose to use a Gaussian CDF model to approximate the reliability curve for 16QAM, i.e. where is the SNR value in dB. The parameters a and b can adjust the Gaussian CDF curve. The derivation of the FBR for 16QAM is very tedious.

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Feedback Reliability Calculation – Channel Coding Case When operating the IB-DFE with channel coding, it is recommended to decode the equalized symbols and use the re-encoded symbols to form the FB symbols with higher reliability. There is no explicit method to derive the reliability of the re-encoded FB symbols. We propose to use a pre-define lookup table for FBR mapping in the channel coding case.

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Simulation Parameters SC-FDE with 512 subcarriers is used. The urban macro scenario of the Spatial Channel Model Extended (SCME) is used. The subframe structure in the LTE uplink is adopted to calculate the bandwidth efficiency. Each subframe has six data blocks and one pilot blocks. The bandwidth efficiency for the proposed FBR calculation is 6/7. Assuming one data block is used as the TS in the TS method, the bandwidth efficiencies for the TS method is 5/7.

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Simulation Results – 4QAM Large performance gap between LE and MFB. The proposed FBR gives similar BER performance as the TS method. The second iteration gives a large gain over the first iteration (since the filtered noise is significantly reduced). The second iteration gives similar performance as the H-DFE. However, IB-DFE (2) gives a lower complexity due to the efficient FD-FB filter.

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Simulation Results – 16QAM Similar results as the 4QAM case. The FBR calculation method outperforms the TS method in the 16QAM. This is because 16QAM symbols do not have uniform reliability. The TS composed of random 16QAM symbols can result in more FBR mismatch, while the proposed Gaussian CDF model is based on the average FBR.

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Simulation Results – 16QAM with Channel Coding The proposed FBR method has similar BLER performance as the TS method. The second iteration gives a 2.5dB gain over the first iteration (i.e. LE). The fourth iteration performs within 1dB to the MFB. The H-DFE gives worse performance than the LE due to error propagation. Higher throughput is achieved with the proposed FBR method due to better bandwidth efficiency.

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Conclusions For broadband single-carrier systems, LE gives a large performance gain to the MFB due to large LE filtered noise. DFE can be used to improve the equalization performance. While the H-DFE is liable to error propagation (especially in the channel coding case), the IB-DFE is robust against error propagation. Moreover, the IB-DFE provides a low complexity iteration solution due to the efficient FD-FB filters. The proposed FBR method shows a similar or better error rate performance as the TS method without lowering the bandwidth efficiency.

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Centre for Communications Research Thank You Gillian Huang, Andrew Nix and Simon Armour

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