# Channel Estimation Based on Statistical Frames and Confidence Level in OFDM Systems

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## Abstract

**:**

## Featured Application

**This channel estimation method can be utilized to improve the communication quality of OFDM receiver.**

## Abstract

## 1. Introduction

## 2. Related Work

## 3. System Model

## 4. Block-Type Pilot-Based LS, IMMSE, Threshold Value and Chi-square Distribution Channel Estimation Methods

#### 4.1. Block-Type Pilot-Based LS Channel Estimation Method

#### 4.2. IMMSE Channel Estimation Method

#### 4.3. Threshold Value Channel Estimation Method

#### 4.4. Chi-Square Distribution Channel Estimation Method

## 5. Channel Estimation Based on Statistical Frames and the Confidence Level

## 6. Simulation Results

#### 6.1. The Performance in Static Multipath Channels

^{−2}, respectively.

^{−2}, respectively. Therefore, the SER curves of ${T}_{1}=5$ have the best SER gain under the CDT1 and Brazil A multipath fading channels.

^{–2}. The proposed confidence level method outperforms the conventional LS method by about a 1.6 dB SNR gap at the target SER of 10

^{−3}. It could be seen that AWGN is the main factor that impacts the accuracy of channel estimation [16].

#### 6.2. The Performance in Dynamic Multipath Channels

^{−2}, respectively. In Figure 7, the gap of the SNR gain among ${T}_{1}=5$, ${T}_{2}=7$, ${T}_{3}=9$ and ${T}_{4}=11$ is about 4 dB, 1.8 dB and 0.5 dB at the SER of 8 × 10

^{−2}, respectively. Therefore, ${T}_{1}=5$ is a suitable value, which can be chosen for the dynamic multipath channels.

^{−2}, respectively. The IMMSE method has bad SER performance when the SNR is higher than 19 dB. The confidence level method has the best SER performance except the ideal estimation and threshold value methods. As shown in Figure 8, the proposed confidence level method and threshold value method have almost the same SER performance in the lower SNR range. Compared with the ideal channel estimation method, the proposed confidence level method has 2.2 dB SNR degradation at the target SER of 2 × 10

^{−2}.

^{−2}compared with the LS, IMMSE and Chi-square distribution methods, respectively. The IMMSE method has bad SER performance when the SNR is higher than 19 dB. The confidence level method has the best SER performance except the ideal estimation and threshold value methods. Compared with the threshold value method, the proposed confidence level method has 0.4 dB SNR degradation at SER of 2 × 10

^{−2}. Compared with the ideal channel estimation, the proposed confidence level method has 1.9 dB SNR degradation at the target SER of 2 × 10

^{−2}. Furthermore, the SNR gap between the SER performance curves of ideal channel estimation and the proposed confidence level methods is about 1.8 dB at the SER of 2 × 10

^{−2}.

^{−2}when the maximum Doppler spread equals 80 Hz. The confidence level method has the best SER performance except the ideal estimation. The IMMSE estimation method has worse SER performance in the high SNR region, and the Chi-square distribution method has the worst SER performance. Compared with the ideal channel estimation, the proposed confidence level method has 2.3 dB SNR degradation at the target SER of 3 × 10

^{−2}. Moreover, compared with the threshold value method, the proposed confidence level method provides the SNR gains of 0.05 dB at the SER of 10

^{−2}with the maximum Doppler spread equal to 80 Hz.

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**System model of cyclic prefix (CP)-OFDM. OFDM: orthogonal frequency division multiplexing; QAM: quadrature amplitude modulation; IFFT: inverse fast Fourier transform; FFT: fast Fourier transform.

**Figure 2.**The probability distribution function of the Gaussian distribution of noise under different statistical frames.

**Figure 3.**Symbol error rate (SER) performance of the 16 QAM-modulated CP-OFDM system over static China digital television (DTV) Test 1st (CDT1). SNR: signal-to-noise ratio.

**Figure 5.**SER performance of the 16 QAM-modulated CP-OFDM system over static CDT1. LS: least square; IMMSE: improved minimum mean square error.

**Figure 6.**SER performance of the 16 QAM-modulated CP-OFDM system over Brazil B with a Doppler spread of 20 Hz.

**Figure 7.**SER performances of the 16 QAM-modulated CP-OFDM system over Brazil D with a Doppler spread of 20 Hz.

**Table 1.**Profiles for the China digital television (DTV) Test 1st (CDT1) and Brazil A multipath fading channels.

Tap | CDT1 | Brazil A | ||
---|---|---|---|---|

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

1 | 0 | 0 | 0 | 0 |

2 | −1.8 | −20 | 0.15 | −13.8 |

3 | 0.15 | −20 | 2.22 | −16.2 |

4 | 1.8 | −10 | 3.05 | −14.9 |

5 | 5.7 | −14 | 5.86 | −13.6 |

6 | 18 | −18 | 5.93 | −16.4 |

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

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

1 | 0 | 0 | 0 | −0.1 |

2 | 0.3 | −12 | 0.48 | −3.9 |

3 | 3.5 | −4 | 2.07 | −2.6 |

4 | 4.4 | −7 | 2.90 | −1.3 |

5 | 9.5 | −15 | 5.71 | 0.0 |

6 | 12.7 | −22 | 5.78 | −2.8 |

**Table 3.**Simulation parameters of CP-OFDM systems. SPS: symbols per second; CP: cyclic prefix; OFDM: orthogonal frequency division multiplexing; QAM: quadrature amplitude modulation; IMMSE: improved minimum mean square error.

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

Baseband signal rate | 7.56 × 10^{6} SPS |

System model | CP-OFDM |

Modulation mode | 16 QAM |

Guard interval length | 180 |

Subcarrier number | 300 |

Doppler spread | 20/60/80 Hz |

Pilots insertion types | Block-type pilots |

α in IMMSE method | 0.995 |

λ in threshold value method | 0.05 |

**Table 4.**Computational complexity comparison of channel estimation methods. LS: least square; IFFT: inverse fast Fourier transform; FFT: fast Fourier transform.

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**MDPI and ACS Style**

Zhou, X.; Wang, C.; Tang, R.; Zhang, M.
Channel Estimation Based on Statistical Frames and Confidence Level in OFDM Systems. *Appl. Sci.* **2018**, *8*, 1607.
https://doi.org/10.3390/app8091607

**AMA Style**

Zhou X, Wang C, Tang R, Zhang M.
Channel Estimation Based on Statistical Frames and Confidence Level in OFDM Systems. *Applied Sciences*. 2018; 8(9):1607.
https://doi.org/10.3390/app8091607

**Chicago/Turabian Style**

Zhou, Xiao, Chengyou Wang, Ruiguang Tang, and Mingtong Zhang.
2018. "Channel Estimation Based on Statistical Frames and Confidence Level in OFDM Systems" *Applied Sciences* 8, no. 9: 1607.
https://doi.org/10.3390/app8091607