Estimation of the Impulse Response of the AWGN Channel with ISI within an Iterative Equalization and Decoding System That Uses LDPC Codes
Abstract
:1. Introduction
- Creating a new scheme for estimating involving a training sequence and re-estimating it only once using the estimated sequence produced by the decoder. This estimated sequence from the output of the decoder is then used to re-estimate twice more. This approach helps to improve the accuracy of the estimation.
- Performing the performance analysis regarding the BER against SNR of the new schemes contrasted with the ideal situation where we assumed a perfect estimate of . The simulations carried out in Section 4 demonstrated that BER performance approaches the case where we have a perfect estimate of impulse response when it was estimated based on the training sequence and re-estimated twice using the estimated sequence produced by the min-sum LDPC decoder.
2. Related Work
3. Materials and Methods
3.1. The Least Squares Estimator
3.2. The System Model
- Log MAP Equalizer: removes or reduces the effect of intersymbol interference (ISI) introduced by the multipath channel. The role of the equalizer placed in front of the decoder will be to compensate for this ISI, by trying to filter the output so that it finds the shape of the input pulse or, in any case, to reduce the ISI by identifying the channel parameters and taking this information into account in the decision-making process.
- Data interleaving/de-interleaving: whose role here consists essentially in separating the error at the equalizer’s output (to prevent the spread of errors) and decoupling the LLRs transferred among the decoder and the equalizer. Then, the iterative receiver can completely counteract the damage owing to the intersymbol interference, as long as the channel interleaver is large enough and judiciously built.
- Min-sum LDPC decoder: the achievement of the iterative decoding in the reception creates an LLR transfer among the decoder and the equalizer in a certain number of iterations.
4. Results and Discussion
- The case where we have the perfect estimate of (It5).
- estimated using the training sequence (It5-LS0).
- estimated using the training sequence and re-estimated only once using the sequence from the exit of the decoder (It5-LS1).
- estimated using the training sequence and re-estimated twice using the sequence from the exit of the decoder (It5-LS2).
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
References
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Perfect impulse response estimation, when | ||
Figure | h | BER (Range) |
Figure 4 | hl = [0.18 0.85 0.32] | 1/9 × 10−2 |
Estimation of based on the training sequence | ||
Figure | h | BER (Range) |
Figure 4 | hl = [0.18 0.85 0.32] | 1/7 × 10−2–1/8 × 10−2 |
is re-estimated based on the sequence from the min-sum LDPC decoder output after one cycle. | ||
Figure | h | BER (Range) |
Figure 6 | hl = [0.18 0.85 0.32] | 1/8 × 10−2–1/9 × 10−2 |
is re-estimated based on the sequence from the min-sum LDPC decoder output after two cycles. | ||
Figure | h | BER (Range) |
Figure 7 | hl = [0.18 0.85 0.32] | 1/9 × 10−2 |
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Cuc, A.-M.; Morgoș, F.L.; Grava, A.-M.; Grava, C. Estimation of the Impulse Response of the AWGN Channel with ISI within an Iterative Equalization and Decoding System That Uses LDPC Codes. Entropy 2024, 26, 720. https://doi.org/10.3390/e26090720
Cuc A-M, Morgoș FL, Grava A-M, Grava C. Estimation of the Impulse Response of the AWGN Channel with ISI within an Iterative Equalization and Decoding System That Uses LDPC Codes. Entropy. 2024; 26(9):720. https://doi.org/10.3390/e26090720
Chicago/Turabian StyleCuc, Adriana-Maria, Florin Lucian Morgoș, Adriana-Marcela Grava, and Cristian Grava. 2024. "Estimation of the Impulse Response of the AWGN Channel with ISI within an Iterative Equalization and Decoding System That Uses LDPC Codes" Entropy 26, no. 9: 720. https://doi.org/10.3390/e26090720