# A Novel Noise Suppression Channel Estimation Method Based on Adaptive Weighted Averaging for OFDM Systems

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. System Model

## 4. Conventional Channel Estimation Methods

#### 4.1. Time-Domain LS Channel Estimation

#### 4.2. IMMSE Channel Estimation

#### 4.3. Threshold Value Channel Estimation

## 5. The Proposed Adaptive Weighted Averaging Channel Estimation Method

#### 5.1. Determination of the Average Frames

#### 5.1.1. Estimation of the SNR

#### 5.1.2. Estimation of the Doppler Spread

_{0}, the Doppler spread can be estimated as [34]:

#### 5.1.3. Determine the Average Frames Adaptively

#### 5.2. The Process of Weighted Averaging

## 6. Simulation Results and Performance Analysis

#### 6.1. The Performance in Static Channel

#### 6.2. The Performance in Dynamic Channel

^{−3}, compared with the ICE method, the proposed AWA method has about 0.8 dB SNR degradation, compared with the AUA, IMMSE, threshold value, and LS methods, the proposed AWA method has about 0.1 dB, 0.6 dB, 1.4 dB, and 2.1 dB SNR gains, respectively. In Figure 10, at the NMSE of 10

^{−1}, compared with the AUA, IMMSE, threshold value, and LS methods, the proposed AWA method has about 0.5 dB, 1.8 dB, 7.4 dB, and 9.3 dB SNR gains, respectively. Thus, the proposed adaptive averaging-based noise suppression channel estimation method works well under Brazil A channel with Doppler spread 20 Hz, and its performance can be further improved by introducing weighting factor to combat the distortion caused by Doppler spread and ICI.

^{−2}, respectively. Therefore, with the increase of Doppler spread, the AWA method has more obvious advantages over the AUA method. In Figure 12, the IMMSE method has bad NMSE performance when the SNR is higher than 18 dB. This is because the IMMSE method suffers from a loss of the partial path energy while suppressing the noise effect. At the NMSE of 10

^{−1}, the proposed AWA method has about 0.5 dB, 1.5 dB, 4.1 dB, and 5.6 dB SNR gains compared with the AUA, IMMSE, threshold value, and LS methods, respectively. It can be seen that the proposed AWA method effectively suppresses the residual noise in the threshold value channel estimation and greatly improves the accuracy of channel estimation.

^{−2}, respectively. In Figure 14, at the NMSE of 10

^{−1}, the proposed AWA method has about 0.8 dB, 0.9 dB, 3.7 dB, and 5.4 dB SNR gains compared with the AUA, IMMSE, threshold value, and LS methods, respectively. However, when the SNR is greater than 30 dB, the performance of the proposed AWA method is no longer optimal. This is because the noise effect is small in the high SNR and Doppler spread scenarios, and the channel distortion brought by the averaging becomes significant.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**System model of the cyclic prefix orthogonal frequency division multiplexing (CP-OFDM) system. Abbreviations: AWGN, additive white Gaussian noise; FFT, fast Fourier transform; IFFT, inverse fast Fourier transform; QPSK, quadrature phase shift keying.

**Figure 2.**The specific processes of the proposed adaptive weighted averaging (AWA) method. Abbreviations: LS, least squares; SNR, signal-to-noise ratio.

**Figure 3.**The optimal value of $\gamma $ corresponding to different $R$ and ${f}_{\mathrm{d}}$ selected by simulation or calculation of Equation (23) obtained from $4\times {10}^{4}$ trail runs: (

**a**) 20 and 60 Hz; (

**b**) 40 and 80 Hz.

**Figure 4.**The theoretical performance value of the AWA and adaptive unweighted averaging (AUA) methods under different $R$ and ${f}_{\mathrm{d}}$: (

**a**) average frame number $B$; (

**b**) noise suppression ratio.

**Figure 5.**Normalized mean square error (NMSE) performance of fixed and adaptive multi-frame averaging method under static China digital television (DTV) Test 1st (CDT1) channel.

**Figure 6.**Bit error rate (BER) performance under static CDT6 channel. Abbreviations: ICE, ideal channel estimation; IMMSE, improved minimum mean square error.

**Figure 8.**NMSE performance of fixed and adaptive multi-frame averaging method under Brazil A channel with Doppler spread 40 Hz.

Tap | Brazil A | Brazil B | Brazil D | |||
---|---|---|---|---|---|---|

Delay (μs) | Power (dB) | Delay (μs) | Power (dB) | Delay (μs) | Power (dB) | |

1 | 0 | 0 | 0 | 0 | 0 | −0.10 |

2 | 0.15 | −13.80 | 0.30 | −12 | 0.48 | −3.90 |

3 | 2.22 | −16.20 | 3.50 | −4 | 2.07 | −2.60 |

4 | 3.05 | −14.90 | 4.40 | −7 | 2.90 | −1.30 |

5 | 5.86 | −13.60 | 9.50 | −15 | 5.71 | 0 |

6 | 5.93 | −16.40 | 12.70 | −22 | 5.78 | −2.80 |

Tap | CDT1 | CDT6 | ||
---|---|---|---|---|

Delay (μs) | Power (dB) | Delay (μs) | Power (dB) | |

1 | 0 | 0 | 0 | 0 |

2 | −1.8 | −20 | −18 | −10 |

3 | 0.15 | −20 | −1.80 | −20 |

4 | 1.80 | −10 | 0.15 | −20 |

5 | 5.70 | −14 | 1.80 | −10 |

6 | 18 | −18 | 5.70 | −14 |

Parameters | Specifications |
---|---|

System model | CP-OFDM |

Baseband symbol rate | 7.56 × 10^{6} symbols per second (SPS) |

Modulation mode | QPSK |

The number of OFDM frame | 400 |

Subcarrier number | 1152 |

CP length (subcarriers) | 192 |

Pilot interval (subcarriers) | 3 |

Doppler spread | 20/40/60/80 Hz |

Suppression factor $\alpha $ | 0.997 (20/40 Hz)/0.999 (60/80 Hz) |

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**MDPI and ACS Style**

Zhang, M.; Zhou, X.; Wang, C. A Novel Noise Suppression Channel Estimation Method Based on Adaptive Weighted Averaging for OFDM Systems. *Symmetry* **2019**, *11*, 997.
https://doi.org/10.3390/sym11080997

**AMA Style**

Zhang M, Zhou X, Wang C. A Novel Noise Suppression Channel Estimation Method Based on Adaptive Weighted Averaging for OFDM Systems. *Symmetry*. 2019; 11(8):997.
https://doi.org/10.3390/sym11080997

**Chicago/Turabian Style**

Zhang, Mingtong, Xiao Zhou, and Chengyou Wang. 2019. "A Novel Noise Suppression Channel Estimation Method Based on Adaptive Weighted Averaging for OFDM Systems" *Symmetry* 11, no. 8: 997.
https://doi.org/10.3390/sym11080997