# Efficient Estimation of CFO-Affected OFDM BER Floor in Small Cells with Resource-Limited IoT End-Points

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Efficient Estimation of Residual OFDM BER for Small Cells

#### 2.1. General Error Floor Due to Time Dispersion

_{S}each. On the other hand, the multipath channel is represented by the sum of complex delta functions, each with a Rayleigh-weighted amplitude ${A}_{i}$, uniformly distributed phase, and certain delay ${\tau}_{i}$, $i\in \left[1,2,\dots ,N\right]$.

_{m}in Equation (1) is the only distinguishing BER factor of higher modulation schemes with respect to binary phase-shift keying (BPSK), this implies that we can substitute the value 1/M for BPSK variances in Equation (5) into Equation (1), which transforms the latter to:

#### 2.2. Computationally Efficient BER Floor for Small Cells

#### 2.3. Optimal Sample Delay for Least BER Floor

## 3. Efficient OFDM BER Floor with Joint Near-Optimal Time Sampling and CFO

#### 3.1. CFO Abstraction by AWGN

#### 3.2. CFO Abstraction by Time Dispersion

## 4. Experimental Analysis

^{2}” (measure, compute and communicate) overall mission activities of cellular IoT networks, our model has to do with “c

^{2}” focusing on the second “c” (i.e., communicate), while taking care of the first one (compute) efficiently; meaning that the model applicability is not limited by any specific “m” scenario (i.e., use case) of OFDM-based wireless networks.

#### 4.1. Simulation Setup

#### 4.2. Verification of Efficient BER for Small Cells with Optimal and Near-Optimal Sampling

^{−8}s and 1.2141 × 10

^{−7}s, respectively.

^{−8}s and 1.2095 × 10

^{−7}s, respectively, which is an excellent match to the figures obtained by the simulator.

#### 4.3. Verification of CFO Abstraction by Time Dispersion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Carrier lock angle error [16].

**Figure 2.**Bit error rate (BER) vs. maximal carrier frequency offset (CFO)-made phase deviation; 16 quadrature amplitude modulation (QAM), 10 dB high-power amplifier (HPA) back-off.

**Figure 5.**Exponential profile; rms delay spread ${\sigma}_{\tau}=2{T}_{S};$ ${T}_{\mathrm{S}}=76\begin{array}{c}\mathrm{ns}\end{array}$.

**Figure 7.**Estimated and simulated BER vs. (optimal) sample time for the exponential LTE FDD downlink.

**Table 1.**EPA delay profile [8]; mean= 0.2555, variance = 0.0613.

Tap | Delay (ns) | Power (dB) |
---|---|---|

1 | 0 | 0.0 |

2 | 30 | −1.0 |

3 | 70 | −2.0 |

4 | 90 | −3.0 |

5 | 110 | −8.0 |

6 | 190 | −17.2 |

7 | 410 | −20.8 |

Tap | Delay (ns) | Power (dB) |
---|---|---|

1 | 0 | 0.0 |

2 | 30.01 | −1.0 |

3 | 70.02 | −2.0 |

4 | 90.03 | −3.0 |

5 | 110.04 | −8.0 |

6 | 190.06 | −17.2 |

7 | 410.14 | −20.8 |

Tap | Delay (ns) | Power (dB) |
---|---|---|

1 | 0 | 0.0 |

2 | 30.14 | −1.0 |

3 | 70.33 | −2.0 |

4 | 90.42 | −3.0 |

5 | 110.51 | −8.0 |

6 | 190.91 | −17.2 |

7 | 411.91 | −20.8 |

Tap | Delay (ns) | Power (dB) |
---|---|---|

1 | 0 | 0.0 |

2 | 30.61 | −1.0 |

3 | 71.41 | −2.0 |

4 | 91.82 | −3.0 |

5 | 112.23 | −8.0 |

6 | 193.81 | −17.2 |

7 | 418.22 | −20.8 |

Tap | Delay (ns) | Power (dB) |
---|---|---|

1 | 0 | 0.0 |

2 | 32.01 | −1.0 |

3 | 74.67 | −2.0 |

4 | 96.11 | −3.0 |

5 | 117.33 | −8.0 |

6 | 202.67 | −17.2 |

7 | 437.33 | −20.8 |

Tap | Delay (ns) | Power (dB) |
---|---|---|

1 | 0 | 0.0 |

2 | 40.01 | −1.0 |

3 | 93.33 | −2.0 |

4 | 120.01 | −3.0 |

5 | 146.67 | −8.0 |

6 | 253.33 | −17.2 |

7 | 546.67 | −20.8 |

**Table 7.**Inter-symbol interference (ISI) and (time-dispersion-abstracted) CFO-based BER floor; 16 QAM, EPA profile.

CFO | BER Estimated (21) | BER Estimated (18) | BER Simulated |
---|---|---|---|

0 Hz (EPA) | 1.2969 × 10^{−2} | 1.3141 × 10^{−2} | 1.2827 × 10^{−2} |

5 Hz | 1.2990 × 10^{−2} | 1.3182 × 10^{−2} | 1.2901 × 10^{−2} |

70 Hz | 1.3096 × 10^{−2} | 1.3244 × 10^{−2} | 1.2978 × 10^{−2} |

300 Hz | 1.3498 × 10^{−2} | 1.3711 × 10^{−2} | 1.3415 × 10^{−2} |

1 kHz | 1.4767 × 10^{−2} | 1.5013 × 10^{−2} | 1.4681 × 10^{−2} |

5 kHz | 2.3081 × 10^{−2} | 2.3454 × 10^{−2} | 2.2901 × 10^{−2} |

CFO | BER Estimated (21) | BER Estimated (18) | BER Simulated |
---|---|---|---|

0 Hz (EPA) | 1.2969 × 10^{−2} | 1.3141 × 10^{−2} | 1.2827 × 10^{−2} |

5 Hz | 0.0021 × 10^{−2} | 0.0041 × 10^{−2} | 0.0074 × 10^{−2} |

70 Hz | 0.0127 × 10^{−2} | 0.0103 × 10^{−2} | 0.0151 × 10^{−2} |

300 Hz | 0.0498 × 10^{−2} | 0.0570 × 10^{−2} | 0.0588 × 10^{−2} |

1 kHz | 0.1798 × 10^{−2} | 0.1872 × 10^{−2} | 0.1854 × 10^{−2} |

5 kHz | 1.0112 × 10^{−2} | 1.0313 × 10^{−2} | 1.0074 × 10^{−2} |

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**MDPI and ACS Style**

Lipovac, A.; Lipovac, V.; Modlic, B.
Efficient Estimation of CFO-Affected OFDM BER Floor in Small Cells with Resource-Limited IoT End-Points. *Sensors* **2020**, *20*, 3747.
https://doi.org/10.3390/s20133747

**AMA Style**

Lipovac A, Lipovac V, Modlic B.
Efficient Estimation of CFO-Affected OFDM BER Floor in Small Cells with Resource-Limited IoT End-Points. *Sensors*. 2020; 20(13):3747.
https://doi.org/10.3390/s20133747

**Chicago/Turabian Style**

Lipovac, Adriana, Vlatko Lipovac, and Borivoj Modlic.
2020. "Efficient Estimation of CFO-Affected OFDM BER Floor in Small Cells with Resource-Limited IoT End-Points" *Sensors* 20, no. 13: 3747.
https://doi.org/10.3390/s20133747