# A Low Complexity Channel Estimation and Detection for Massive MIMO Using SC-FDE

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## Abstract

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## 1. Introduction

- Channel Estimation using superimposed pilots;
- Data Detection;
- Interference Mitigation generated in the data detection process, using an Iterative Block—Decision Feedback Equalization technique (IB-DFE) [20].

## 2. System and Signal Characterization

- For the ZF receiver, as:$${B}_{k}={\left({H}_{k}^{H}{H}_{k}\right)}^{-1}{H}_{k}^{H},$$
- Using the MRC receiver, as:$${B}_{k}={H}_{k}^{H},$$
- Using the EGC receiver, as:$${{\rm B}}_{k}=\mathrm{exp}\left\{j\mathrm{arg}\left({H}_{k}^{H}\right)\right\},$$

- For MRC: ${\left[A\right]}_{i,i\prime}={\left[H\right]}_{{}_{i,i\prime}}^{H}$.
- For EGC: ${\left[A\right]}_{i,i\prime}=\mathrm{exp}\left(j\mathrm{arg}\left({\left[H\right]}_{i,i\prime}\right)\right)$, that is, they have absolute value 1 and phase identical to the corresponding element of the matrix $H$.

## 3. Channel Estimation

_{G}, with T and T

_{G}denoting the duration of the useful part of the block and the cyclic prefix, respectively.

- Obtain the channel estimates from the pilots (remove the data from the received signal, estimated from the previous iteration, if not the first iteration);
- Obtain the channel estimates from the data, after removing the pilots from the received signal (which represents interference);
- Combine the channel estimates obtained from 1. and 2., to improve the estimate of the channel, and repeat the process.

## 4. Performance Results

#### 4.1. Channel Estimation with Conventional Pilots

_{b}/N

_{0}values required for a certain BER, but the relative positions of curves do not change significantly.

#### 4.2. Channel Estimation with Superimposed Pilots

- Perform an initial channel estimation using the pilots (added to the data).
- Remove the pilots (that represent interference), detect the data, and perform an initial channel estimate using the data.
- Combine the channel estimate obtained from step 1. with that of step 2.
- Repeat steps 1 to 3 iteratively, with the new improved channel estimates, and removing the estimated data from the pilots of step 1.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Block diagram of massive Multiple Input–Multiple Output (m-MIMO) with Single-Carrier with Frequency-Domain Equalization (SC-FDE) signals.

**Figure 4.**Bit Error Rate (BER) results for 4 × 32 MIMO with conventional pilots versus ideal channel estimation.

**Figure 5.**BER results for 4 × 32 MIMO with conventional pilots and different iteration of interference cancellation.

**Figure 8.**BER results for 4 × 32 MIMO with superimposed pilots, with two versus four iterations of the iterative channel estimator.

**Figure 9.**BER results for 4 × 32 MIMO with superimposed pilots, with pilot power of 0 dB versus −3 dB.

**Figure 10.**BER results for 4 × 32 MIMO with superimposed pilots, with a block of 5 versus 10 data symbols.

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**MDPI and ACS Style**

Marques da Silva, M.; Dinis, R.; Guerreiro, J. A Low Complexity Channel Estimation and Detection for Massive MIMO Using SC-FDE. *Telecom* **2020**, *1*, 3-17.
https://doi.org/10.3390/telecom1010002

**AMA Style**

Marques da Silva M, Dinis R, Guerreiro J. A Low Complexity Channel Estimation and Detection for Massive MIMO Using SC-FDE. *Telecom*. 2020; 1(1):3-17.
https://doi.org/10.3390/telecom1010002

**Chicago/Turabian Style**

Marques da Silva, Mário, Rui Dinis, and João Guerreiro. 2020. "A Low Complexity Channel Estimation and Detection for Massive MIMO Using SC-FDE" *Telecom* 1, no. 1: 3-17.
https://doi.org/10.3390/telecom1010002