# A Computationally Efficient Joint Cell Search and Frequency Synchronization Scheme for LTE Machine-Type Communications

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## Abstract

**:**

## 1. Introduction

## 2. System Description

#### 2.1. Frame Structure

#### 2.2. Cell Search Procedure

#### 2.3. Synchronization Signal

#### 2.4. Signal Model

## 3. Conventional Detection Scheme

#### 3.1. Half-Complexity Joint Detection (HCJD) Scheme

#### 3.2. Reduced-Complexity Sequential Detection (RCSD) Scheme

## 4. Proposed Detection Scheme

#### 4.1. Algorithm Description

- Step 1.
- For $\left|m\right|\le M$ and $n=0,1$, obtain the reduced search space based metric, ${\mathsf{\Phi}}_{d}(m,n)$, by formula (15).
- Step 2.
- The IFO estimate $\widehat{\upsilon}$ is firstly obtained by finding the peak of ${\mathsf{\Phi}}_{d}(m,n)$ over $(m,n)$, by formula (20).
- Step 3.
- If $\widehat{n}=0$ in step 2, decide that the transmitted PSS is ${P}_{0}\left(k\right)$, and complete the joint detection of IFO and SID. Otherwise, go to the next step to determine that the transmitted PSS is either ${P}_{1}\left(k\right)$ or ${P}_{2}\left(k\right)$.
- Step 4.
- Using the IFO estimate $\widehat{\upsilon}$ obtained in step 2, calculate ${\mathsf{\Phi}}_{a}^{I}(\widehat{\upsilon},1)$ and ${\mathsf{\Phi}}_{a}^{I}(\widehat{\upsilon},2)$, by formula (14).
- Step 5.
- If ${\mathsf{\Phi}}_{a}^{I}(\widehat{\upsilon},1)>{\mathsf{\Phi}}_{a}^{I}(\widehat{\upsilon},2)$, decide that the transmitted PSS is ${P}_{1}\left(k\right)$. Otherwise, decide that the transmitted PSS is ${P}_{2}\left(k\right)$.

#### 4.2. Performance Analysis

#### 4.3. Complexity Analysis

## 5. Simulation Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**Performance of the joint detection methods versus signal-to-noise ratio in the additive white Gaussian noise channel: (

**a**) $M=1$; (

**b**) $M=2$; and $M=3$.

**Figure 4.**Performance of integer carrier frequency offset and sector identity detectors in the Pedestrian A channel when ${\tau}_{max}=0$: (

**a**) integer carrier frequency offset detector (

**b**) sector identity detector.

**Figure 5.**Performance of the joint detection methods in the Pedestrian A channel: (

**a**) ${\tau}_{max}=0$; (

**b**) ${\tau}_{max}=5$.

**Figure 6.**Performance of the joint detection methods in the Vehicular A channel: (

**a**) ${\tau}_{max}=0$; (

**b**) ${\tau}_{max}=5$.

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**MDPI and ACS Style**

Jung, Y.-A.; Shin, D.; You, Y.-H.
A Computationally Efficient Joint Cell Search and Frequency Synchronization Scheme for LTE Machine-Type Communications. *Symmetry* **2019**, *11*, 1394.
https://doi.org/10.3390/sym11111394

**AMA Style**

Jung Y-A, Shin D, You Y-H.
A Computationally Efficient Joint Cell Search and Frequency Synchronization Scheme for LTE Machine-Type Communications. *Symmetry*. 2019; 11(11):1394.
https://doi.org/10.3390/sym11111394

**Chicago/Turabian Style**

Jung, Yong-An, Dongkyoo Shin, and Young-Hwan You.
2019. "A Computationally Efficient Joint Cell Search and Frequency Synchronization Scheme for LTE Machine-Type Communications" *Symmetry* 11, no. 11: 1394.
https://doi.org/10.3390/sym11111394