# Spectral and Energy Efficient Low-Overhead Uplink and Downlink Channel Estimation for 5G Massive MIMO Systems

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. System Model

_{t}transmitter antennas, K receiving antennas such that (N

_{t}>> K), SNR, channel length, channel sparsity, slot-interval, and various relevant parameters to obtain the required results.

#### 3.1. CS-Differential Channel Feedback

#### 3.1.1. Temporal-Correlation of Massive MIMO Channels

#### 3.1.2. Support-Vector

#### 3.1.3. Amplitude-Vector

#### 3.1.4. Differential CIR (DCIR)

#### 3.1.5. Compression CIR (CCIR)

#### 3.1.6. Feedback-Overhead

#### 3.1.7. CS-Recovery Algorithm

#### 3.1.8. Flowchart

#### 3.2. Block-ISD Pilot Feedback

#### Creating Block-ISD CIR

#### 3.3. AoD-Adaptive Subspace Codebook Algorithm

#### 3.4. S-CoSaMP Algorithm

#### 3.5. Energy Efficiency Maximization

## 4. Simulation Results

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Illustration of the previous, current and differential channel impulse responses (CIRs) in different time slots with same channel length.

**Figure 6.**Comparison of the codebooks: (

**a**) classical Grassmannian N-dimension; (

**b**) Proposed AoD based codebook.

**Figure 7.**Comparison of the: (

**a**) Conventional CS based separate DL and UL channel feedback; (

**b**) Proposed CS based joint algorithm for channel estimation.

**Figure 10.**Feedback-bits comparison for maintaining a data-rate gap between the perfect-CSI and proposed AoD-codebook.

**Figure 11.**Comparison of the required number of feedback-bits with increasing the SNR between the ideal CSI and the proposed AoD-codebook schemes.

**Figure 12.**Comparison of the per-user rate of the ideal perfect-CSI and the proposed scheme with quantized-channel feedback in terms of SNR.

**Figure 13.**Comparison of the proposed and the conventional channel feedback algorithms in terms of NMSE versus SNR.

**Figure 14.**Comparison of sum-rate between the ideal CSI; proposed S-CoSaMP and the conventional CoSaMP algorithms under two-compression ratios.

**Figure 15.**Energy Efficiency versus the BS density comparison of massive MIMO system for different SINRs ($\zeta $).

**Figure 17.**Energy Efficiency versus the level of hardware impairment of massive MIMO system for different SINRs.

S. No | Parameter | Symbol | Value |
---|---|---|---|

1 | Max. Channel Length | L | 32 |

2 | Pilot length | $p$ | 640 |

3 | OFDM symbol-length | $\mathcal{S}$ | 2048 |

4 | Signal-to-Noise-Ratio | SNR | 25 dB |

5 | Block Elements | B | 8 |

6 | Noise Variance | ${\sigma}_{n}$ | 1 |

7 | Transition-Probability | P_{01} | 0.05 (5%) |

8 | Channel-Sparsity | μ | 0.1 (10%) |

9 | Doppler-frequency | f_{d} | 10 Hz |

10 | Slot-interval | τ | 1 ms |

11 | Channel-variance | ${\sigma}_{w}$ | 1 |

12 | Correlation coefficient | $\rho $ | 0.0628 |

13 | Number of BS antennas | N_{t} | 130 |

14 | Number of User antennas | K | 10 |

15 | Number of Paths | P | 5 |

16 | AoD Feedback bits | b | 5 |

17 | Sensing-Matrix | φ | Random Gaussian |

18 | Static Power Consumption | P_{s} | 10 W |

19 | Circuit power per antenna | P_{ca} | 0.1 W |

20 | Path Loss Exponent | α | 3.76 |

21 | Coherence Block Length | S | 400 |

22 | Coherence Time | T_{c} | 2.16 ms |

23 | Bandwidth | BW | 20 MHz |

24 | Macrocell Radius | $r$ | 250 m |

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**MDPI and ACS Style**

Khan, I.; Zafar, M.H.; Jan, M.T.; Lloret, J.; Basheri, M.; Singh, D.
Spectral and Energy Efficient Low-Overhead Uplink and Downlink Channel Estimation for 5G Massive MIMO Systems. *Entropy* **2018**, *20*, 92.
https://doi.org/10.3390/e20020092

**AMA Style**

Khan I, Zafar MH, Jan MT, Lloret J, Basheri M, Singh D.
Spectral and Energy Efficient Low-Overhead Uplink and Downlink Channel Estimation for 5G Massive MIMO Systems. *Entropy*. 2018; 20(2):92.
https://doi.org/10.3390/e20020092

**Chicago/Turabian Style**

Khan, Imran, Mohammad Haseeb Zafar, Mohammad Tariq Jan, Jaime Lloret, Mohammed Basheri, and Dhananjay Singh.
2018. "Spectral and Energy Efficient Low-Overhead Uplink and Downlink Channel Estimation for 5G Massive MIMO Systems" *Entropy* 20, no. 2: 92.
https://doi.org/10.3390/e20020092