# Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

#### 2.1. System Overview

#### 2.2. Channel Model

#### 2.3. Noncoherent Detection

#### 2.4. Digital Beamspace Preprocessing

#### 2.4.1. Full-Array

#### 2.4.2. Sub-Array

## 3. Numerical Results

#### 3.1. Full-Array vs. Sub-Array Architecture

#### 3.2. Influence of Propagation Channel

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Gupta, A.; Jha, R.K. A Survey of 5G Network: Architecture and Emerging Technologies. IEEE Access
**2015**, 3, 1206–1232. [Google Scholar] [CrossRef] - Marzetta, T.L. Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas. IEEE Trans. Wirel. Commun.
**2010**, 9, 3590–3600. [Google Scholar] [CrossRef] - Larsson, E.G.; Edfors, O.; Tufvesson, F.; Marzetta, T.L. Massive MIMO for Next Generation Wireless Systems. IEEE Commun. Mag.
**2014**, 52, 186–195. [Google Scholar] [CrossRef][Green Version] - Rusek, F.; Persson, D.; Lau, B.K.; Larsson, E.G.; Marzetta, T.L.; Edfors, O.; Tufvesson, F. Scaling Up MIMO: Opportunities and Challenges with Very Large Arrays. IEEE Signal Process. Mag.
**2013**, 30, 40–60. [Google Scholar] [CrossRef][Green Version] - Andrews, J.G.; Buzzi, S.; Choi, W.; Hanly, S.V.; Lozano, A.; Soong, A.C.K.; Zhang, J.C. What Will 5G Be? IEEE J. Sel. Areas Commun.
**2014**, 32, 1065–1082. [Google Scholar] [CrossRef] - Lu, L.; Li, G.Y.; Swindlehurst, A.L.; Ashikhmin, A.; Zhang, R. An Overview of Massive MIMO: Benefits and Challenges. IEEE J. Sel. Top. Signal Process.
**2014**, 8, 742–758. [Google Scholar] [CrossRef] - Elijah, O.; Leow, C.Y.; Rahman, T.A.; Nunoo, S.; Iliya, S.Z. A Comprehensive Survey of Pilot Contamination in Massive MIMO—5G System. IEEE Commun. Surv. Tutor.
**2016**, 18, 905–923. [Google Scholar] [CrossRef] - Stojanovic, M.; Proakis, J.; Catipovic, J. Analysis of the Impact of Channel Estimation Errors on the Performance of a Decision-Feedback Equalizer in Fading Multipath Channels. IEEE Trans. Commun.
**1995**, 43, 877–886. [Google Scholar] [CrossRef] - Peng, W.; Adachi, F.; Ma, S.; Wang, J.; Ng, T.S. Effects of Channel Estimation Errors on V-BLAST Detection. In Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM), New Orleans, LA, USA, 30 November–4 December 2008. [Google Scholar] [CrossRef][Green Version]
- Marzetta, T.L.; Larsson, E.G.; Yang, H. Fundamentals of Massive MIMO; Cambridge University Press: Cambridge, UK, 2016. [Google Scholar]
- Schenk, A.; Fischer, R.F.H. Noncoherent Detection in Massive MIMO Systems. In Proceedings of the 17th International ITG Workshop on Smart Antennas (WSA), Stuttgart, Germany, 13–14 March 2013; pp. 1–8. [Google Scholar]
- Fischer, R.F.H.; Bense, M. Noncoherent Decision-Feedback Equalization in Massive MIMO Systems. In Proceedings of the International Zurich Seminar on Communications (IZS), Zurich, Switzerland, 26–28 February 2014; pp. 112–115. [Google Scholar] [CrossRef]
- Fischer, R.F.H.; Bense, M.; Stierstorfer, C. Noncoherent Joint Decision-Feedback Detection in Multi-User Massive MIMO Systems. In Proceedings of the 18th International ITG Workshop on Smart Antennas (WSA), Erlangen, Germany, 12–13 March 2014; pp. 1–8. [Google Scholar]
- Yammine, G.; Fischer, R.F.H. Feedback-Aware Noncoherent Receivers for Massive MIMO Systems. In Proceedings of the 24th International ITG Workshop on Smart Antennas (WSA), Hamburg, Germany, 18–20 February 2020; pp. 1–6. [Google Scholar]
- Bucher, S.; Yammine, G.; Fischer, R.F.H.; Waldschmidt, C. Influence of Channel Parameters on Noncoherent Massive MIMO Systems. In Proceedings of the 22nd International ITG Workshop on Smart Antennas (WSA), Bochum, Germany, 14–16 March 2018. [Google Scholar]
- Bucher, S.; Ragab, A.N.; Yammine, G.; Fischer, R.F.H.; Waldschmidt, C. Antenna Design for Noncoherent Massive MIMO Systems. In Proceedings of the 15th International Symposium on Wireless Communication Systems (ISWCS), Lisbon, Portugal, 28–31 August 2018. [Google Scholar] [CrossRef][Green Version]
- Bucher, S.; Yammine, G.; Fischer, R.F.H.; Waldschmidt, C. On the Impact of Hardware Impairments in Noncoherent Massive MIMO Systems. In Proceedings of the 24th International ITG Workshop on Smart Antennas (WSA), Hamburg, Germany, 18–20 February 2020. [Google Scholar]
- Bense, M.; Weigel, R. Channel Measurements for the Evaluation of Noncoherent Massive MIMO Systems. In Proceedings of the 47th European Microwave Conference (EuMC), Nuremberg, Germany, 10–12 October 2017. [Google Scholar] [CrossRef]
- Yammine, G.; Bucher, S.; Fischer, R.F.H. Noncoherent Detection for an EM-Lens-Enabled Massive MIMO System. In Proceedings of the International ITG Conference on Systems, Communication and Coding (SCC), Rostock, Germany, 11–14 February 2019. [Google Scholar]
- Bucher, S.; Yammine, G.; Fischer, R.F.H.; Waldschmidt, C. A Noncoherent Massive MIMO System Employing Beamspace Techniques. IEEE Trans. Veh. Technol.
**2019**, 68, 11052–11063. [Google Scholar] [CrossRef][Green Version] - Zeng, Y.; Zhang, R.; Chen, Z.N. Electromagnetic Lens-Focusing Antenna Enabled Massive MIMO: Performance Improvement and Cost Reduction. IEEE J. Sel. Areas Commun.
**2014**, 32, 1194–1206. [Google Scholar] [CrossRef][Green Version] - Zeng, Y.; Zhang, R. Millimeter Wave MIMO With Lens Antenna Array: A New Path Division Multiplexing Paradigm. IEEE Trans. Commun.
**2016**, 64, 1557–1571. [Google Scholar] [CrossRef] - Zeng, Y.; Yang, L.; Zhang, R. Multi-User Millimeter Wave MIMO With Full-Dimensional Lens Antenna Array. IEEE Trans. Wirel. Commun.
**2018**, 17, 2800–2814. [Google Scholar] [CrossRef][Green Version] - Zeng, Y.; Zhang, R. Cost-Effective Millimeter-Wave Communications with Lens Antenna Array. IEEE Wirel. Commun.
**2017**, 24, 81–87. [Google Scholar] [CrossRef] - Kwon, T.; Lim, Y.; Chae, C. Limited Channel Feedback for RF Lens Antenna Based Massive MIMO Systems. In Proceedings of the International Conference on Computing, Networking and Communications (ICNC), Kauai, HI, USA, 15–18 February 2015; pp. 6–10. [Google Scholar] [CrossRef]
- Kwon, T.; Lim, Y.G.; Min, B.W.; Chae, C.B. RF Lens-Embedded Massive MIMO Systems: Fabrication Issues and Codebook Design. IEEE Trans. Microw. Theory Tech.
**2016**, 64, 2256–2271. [Google Scholar] [CrossRef][Green Version] - Sayeed, A.; Behdad, N. Continuous Aperture Phased MIMO: Basic Theory and Applications. In Proceedings of the 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, IL, USA, 29 Septembet–1 October 2010; pp. 1196–1203. [Google Scholar] [CrossRef]
- Brady, J.; Behdad, N.; Sayeed, A.M. Beamspace MIMO for Millimeter-Wave Communications: System Architecture, Modeling, Analysis, and Measurements. IEEE Trans. Antennas Propag.
**2013**, 61, 3814–3827. [Google Scholar] [CrossRef] - Amadori, P.V.; Masouros, C. Low RF-Complexity Millimeter-Wave Beamspace-MIMO Systems by Beam Selection. IEEE Trans. Commun.
**2015**, 63, 2212–2223. [Google Scholar] [CrossRef] - Huang, W.; Huang, Y.; Zeng, Y.; Yang, L. Wideband Millimeter Wave Communication With Lens Antenna Array: Joint Beamforming and Antenna Selection With Group Sparse Optimization. IEEE Trans. Wirel. Commun.
**2018**, 17, 6575–6589. [Google Scholar] [CrossRef] - Shen, W.; Bu, X.; Gao, X.; Xing, C.; Hanzo, L. Beamspace Precoding and Beam Selection for Wideband Millimeter-Wave MIMO Relying on Lens Antenna Arrays. IEEE Trans. Signal Process.
**2019**, 67, 6301–6313. [Google Scholar] [CrossRef] - Balanis, C.A. Antenna Theory: Analysis and Design, 3rd ed.; John Wiley & Sons: Hoboken, NJ, USA, 2005. [Google Scholar]
- Liu, L.; Oestges, C.; Poutanen, J.; Haneda, K.; Vainikainen, P.; Quitin, F.; Tufvesson, F.; Doncker, P.D. The COST 2100 MIMO Channel Model. IEEE Wirel. Commun.
**2012**, 19, 92–99. [Google Scholar] [CrossRef][Green Version] - Verdone, R.; Zanella, A. Pervasive Mobile and Ambient Wireless Communications; Springer: London, UK, 2012. [Google Scholar] [CrossRef]
- Yammine, G.; Fischer, R.F.H.; Waldschmidt, C. On the Influence of the Antenna Pattern in Noncoherent Massive MIMO Systems. In Proceedings of the International Symposium on Wireless Communication Systems (ISWCS), Brussels, Belgium, 25–28 August 2015; pp. 391–395. [Google Scholar] [CrossRef]
- Krim, H.; Viberg, M. Two Decades of Array Signal Processing Research: The Parametric Approach. IEEE Signal Process. Mag.
**1996**, 13, 67–94. [Google Scholar] [CrossRef] - Veen, B.V.; Buckley, K. Beamforming: A Versatile Approach to Spatial Filtering. IEEE ASSP Mag.
**1988**, 5, 4–24. [Google Scholar] [CrossRef] - Manolakis, D.G.; Ingle, V.K.; Kogon, S.M. Statistical and Adaptive Signal Processing: Spectral Estimation, Signal Modeling, Adaptive Filtering and Array Processing; Artech House: Norwood, MA, USA, 2005. [Google Scholar]
- Van Trees, H.L. Optimum Array Processing; Wiley-Blackwell: Hoboken, NJ, USA, 2002. [Google Scholar]
- Li, J.; Stoica, P. Robust Adaptive Beamforming; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2005. [Google Scholar] [CrossRef]
- Capon, J. High-Resolution Frequency-Wavenumber Spectrum Analysis. Proc. IEEE
**1969**, 57, 1408–1418. [Google Scholar] [CrossRef][Green Version] - Schmidt, R. Multiple Emitter Location and Signal Parameter Estimation. IEEE Trans. Antennas Propag.
**1986**, 34, 276–280. [Google Scholar] [CrossRef][Green Version] - Roy, R.; Kailath, T. ESPRIT-Estimation of Signal Parameters via Rotational Invariance Techniques. IEEE Trans. Acoust. Speech Signal Process.
**1989**, 37, 984–995. [Google Scholar] [CrossRef][Green Version] - Yu, J.L.; Yeh, C.C. Generalized Eigenspace-Based Beamformers. IEEE Trans. Signal Process.
**1995**, 43, 2453–2461. [Google Scholar] [CrossRef] - Foschini, G.J.; Chizhik, D.; Gans, M.J.; Papadias, C.; Valenzuela, R.A. Analysis and Performance of Some Basic Space-Time Architectures. IEEE J. Sel. Areas Commun.
**2003**, 21, 303–320. [Google Scholar] [CrossRef] - Del Re, E.; Morosi, S.; Marabissi, D.; Mucchi, L.; Pierucci, L.; Ronga, L.S. Reconfigurable Antenna for Future Wireless Communication Systems. Wirel. Pers. Commun.
**2007**, 42, 405–430. [Google Scholar] [CrossRef]

**Figure 1.**Digital beamspace preprocessing in noncoherent massive multiple-input/multiple-output (MIMO) systems: (

**a**) Full-array and (

**b**) sub-array architecture.

**Figure 2.**Spatial power distribution at ${N}_{\mathrm{rx}}$ = 12 receive branches (×) in case of Bartlett beamforming ( ) and in case of a combination with eigenspace-based post-processing ( ) considering two incident waves ( / ) and a field of view (FoV) of $\Phi $ = $\pi /2$.

**Figure 3.**User and base station (BS) arrangement to evaluate the noncoherent massive MIMO system with digital beamspace preprocessing.

**Figure 4.**Full-array architecture: Power-space profile and symbol error rate performance. Colors correspond to users: user 1 ( ), user 2 ( ), user 3 ( ). Gray plots ( ) represent results without digital beamspace preprocessing for each user.

**Figure 5.**Sub-array architecture of ${N}_{\mathrm{sub}}$ = 8 and ${N}_{\mathrm{rx},\mathrm{sub}}$ = 16: Power-space profile and symbol error rate performance. Colors correspond to users: user 1 ( ), user 2 ( ), user 3 ( ). Gray plots ( ) represent results without digital beamspace preprocessing for each user.

**Figure 6.**Symbol error rate vs. angle ${\varphi}_{2}$ of user 2 for the full-array system ( ) and for different sub-array configurations (${N}_{\mathrm{sub}}$ = 4 and ${N}_{\mathrm{rx},\mathrm{sub}}$ = 32 ( ), ${N}_{\mathrm{sub}}$ = 8 and ${N}_{\mathrm{rx},\mathrm{sub}}$ = 16 ( ), ${N}_{\mathrm{sub}}$ = 16 and ${N}_{\mathrm{rx},\mathrm{sub}}$ = 8 ( )).

**Figure 7.**Symbol error rate vs. angle ${\varphi}_{2}$ of user 2 at different LMR considering the full-array architecture: $\mathrm{LMR}$ = $0\mathrm{dB}$ ( ), $\mathrm{LMR}$ = $10\mathrm{dB}$ ( ), $\mathrm{LMR}$ = $20\mathrm{dB}$ ( ).

**Figure 8.**Symbol error rate vs. angle ${\varphi}_{2}$ of user 2 at different spatial spread ${\sigma}_{\mathrm{s}}$ considering the full-array architecture: ${\sigma}_{\mathrm{s}}$ = ${2}^{\xb0}$ ( ), ${\sigma}_{\mathrm{s}}$ = ${4}^{\xb0}$ ( ), ${\sigma}_{\mathrm{s}}$ = ${8}^{\xb0}$ ( ).

**Table 1.**System configuration and parameterization of propagation channel and noncoherent detection.

System Configuration | |

number of users ${N}_{\mathrm{u}}$ | 3 |

number of BS antennas ${N}_{\mathrm{rx}}$ | 128 |

BS antenna spacing ${d}_{\mathrm{a}}$ | $\lambda /2$ |

FoV $\Phi $ | $\pi /2$ |

user antenna type | omni-directional |

BS antenna type | patch [15] |

angle ${\varphi}_{u}$ of user | ${\varphi}_{1}$ = $-{30}^{\xb0}$, ${\varphi}_{2}$, ${\varphi}_{3}$ = ${30}^{\xb0}$ |

Noncoherent Detection | |

modulation alphabet | 4-ary DPSK |

block length ${N}_{\mathrm{bl}}$ | 201 |

Propagation Channel | |

cluster types | local |

number of multi-path components ${N}_{p}$ | 3 |

angular spread ${\sigma}_{\mathrm{s}}$ at BS | variable |

LOS-to-MPC ratio (LMR) | variable |

number of different channel realizations ${N}_{\mathrm{ch}}$ | $50,000$ |

channel normalization (power control) | ${\left|\right|H\left|\right|}_{\mathrm{F}}^{2}$ = ${N}_{\mathrm{u}}$ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bucher, S.; Waldschmidt, C. Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing. *Telecom* **2020**, *1*, 211-227.
https://doi.org/10.3390/telecom1030015

**AMA Style**

Bucher S, Waldschmidt C. Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing. *Telecom*. 2020; 1(3):211-227.
https://doi.org/10.3390/telecom1030015

**Chicago/Turabian Style**

Bucher, Stephan, and Christian Waldschmidt. 2020. "Advanced Noncoherent Detection in Massive MIMO Systems via Digital Beamspace Preprocessing" *Telecom* 1, no. 3: 211-227.
https://doi.org/10.3390/telecom1030015