# Energy Efficiency and User Capacity Optimization of Cognitive MIMO Systems Via the SCMA-Based Nonorthogonal Time Slot Allocation

^{*}

## Abstract

**:**

## 1. Introduction

^{T}, A* and A

^{H}denote its trace, rank, transpose, conjugate and conjugate transpose, respectively. ${\u2102}^{N\times M}$ denotes the space of $N\times M$ complex matrices. $|\xb7|$ denotes the absolute value of a scalar, and $A\succcurlyeq 0$ means A is a Hermitian positive semidefinite matrix. $E\{\xb7\}$ represents the statistical expectation and ${I}_{m}$ stands for the $m\times m$ identity. $x\sim cN(u,{\sigma}^{2})$ indicates that the variable $x$ follows the complex normal distribution with mean $u$ and variance ${\sigma}^{2}$. $\lceil x\rceil $ denotes the ceiling of $x$. $Fix\left(x\right)$ and $\mathrm{mod}\left(x\right)$ represent the integer part and remainder part of $x$, respectively.

## 2. Related Works

## 3. System Model

_{k}and P

_{j}denote the kth secondary user and jth pair of primary transmitter–receiver links, respectively. In the underlay model, the primary links are potentially active and always protected. The primary network consists of J transmitter–receiver pairs, while the secondary one is a single cellular network, in which all SUs have the uplinks via TDMA to the secondary base station (BS), and the SCMA-based non-orthogonal strategy is used for slot allocation. The secondary BS is located at the center of the secondary system, and can evaluate the channel matrix ${H}_{BS,{S}_{k}}$ of ${S}_{k}$, and feed it back to ${S}_{k}$ through an independent control channel. Therefore, the information on both ${S}_{k}$ and the secondary BS is fed into the channel matrix of ${S}_{k}$. The uplink transmission of SUs is synchronized by the secondary BS, which allows SUs to make transmissions in orthogonal slots without interference. The coexistence of PUs and SUs in the CR networks implies their mutual interference. When the bandwidth exceeds the bandwidth of the transmitted signal, the gain of the frequency flat fading channel is constant and has a linear phase response, which is applied so that the channel matrix within the prescribed bandwidth is unchanged. Moreover, in the case of a block fading channel application, the channel matrix will not change within a TDMA frame and, thus, needs no correlation between frames. For example, consider two pairs of PUs links with a distance of 10 meters between transceivers. The SUs are randomly distributed in a 200*200m area, and the minimum separation distance from the PUs link is set to 35 m. The case of 35 SUs in the MIMO-CR network is depicted in Figure 1.

_{k}connects to the function node (FN) F

_{n}only if ${F}_{n,k}=1$, otherwise, ${F}_{n,k}=0$. When the VNs represent the SUs, and the FNs represent the time slot, the corresponding relation between the SCMA factor graph and matrix

**F**is shown in Figure 3. $F=\left\{{F}_{{T}_{n},{S}_{k}}\right\}$, where ${F}_{{T}_{n},{S}_{k}}=1$ if secondary user ${s}_{k}$ occupies time slot ${T}_{n}$, otherwise ${F}_{{T}_{n},{S}_{k}}=0$. As seen in Figure 2and Figure 3, using the SCMA principle, we can share the TDMA orthogonal slot by the packet sharing to access more SUs. Therefore, in the same SUs conditions, when a frame is ended, the slot allocation strategy of SCMA-based non-orthogonal slot sharing provides more time being eventually assigned to each SU.

## 4. Problem Formulation and Optimization

#### 4.1. Problem Formulation

#### 4.2. Problem Optimization

## 5. SCMA-Based Non-Orthogonal Slot Allocation

#### 5.1. Time Slot Grouping

#### 5.2. A Method of Virtually Adding Users

## 6. Numerical Results

#### 6.1. Energy Consumption

#### 6.2. User Capacity

#### 6.3. Interference

## 7. Discussion and Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Thompson, J.; Ge, X.H.; Wu, H.C.; Irmer, R.; Jiang, H.; Fettweis, G.; Alamouti, S. 5g Wireless Communication Systems: Prospects and Challenges Part 2. IEEE Commun. Mag.
**2014**, 52, 24–25. [Google Scholar] [CrossRef] - Liu, J.Q.; Ding, H.C.; Cai, Y.; Yue, H.; Fang, Y.G.; Chen, S.G. An Energy-Efficient Strategy for Secondary Users in Cooperative Cognitive Radio Networks for Green Communications. IEEE J. Sel. Areas Commun.
**2016**, 34, 3195–3207. [Google Scholar] [CrossRef] - Kumar, N. A Study on Green Energy Powered Cognitive Radio Network for Communication Network Architecture of Smart Grid. In Proceedings of the 2018 3rd International Innovative Applications of Computational Intelligence on Power, Energy and Controls with Their Impact on Humanity (CIPECH), Ghaziabad, India, 1–2 November 2018; pp. 3–7. [Google Scholar]
- Gandotra, P.; Jha, R.K.; Jain, S. Prolonging User Battery Lifetime using Green Communication in Spectrum Sharing Networks. IEEE Commun. Lett.
**2018**, 22, 1490–1493. [Google Scholar] [CrossRef] - Yu, H.; Afzal, M.K.; Zikria, Y.B.; Rachedi, A.; Fitzek, F.H.P. Tactile Internet: Technologies, test platforms, trials, and applications. Future Gener. Comput. Syst.
**2020**, 106, 685–688. [Google Scholar] [CrossRef] - Zikria, Y.B.; Afzal, M.K.; Kim, S.W. Internet of Multimedia Things (IoMT): Opportunities, Challenges and Solutions. Sensors
**2020**, 20, 2334. [Google Scholar] [CrossRef] [PubMed] - Liang, Y.C.; Chen, K.C.; Li, G.Y.; Mahonen, P. Cognitive Radio Networking and Communications: An Overview. IEEE Trans. Veh. Technol.
**2011**, 60, 3386–3407. [Google Scholar] [CrossRef] - Mamiya, T.; Fujimoto, M. MIMO Cognitive Radio Considering Interference. In Proceedings of the 2018 IEEE International Workshop on Electromagnetics: Applications and Student Innovation Competition (iWEM), Vancouver, BC, Canada, 29–31 August 2018; pp. 1–2. [Google Scholar]
- Nikopour, H.; Baligh, H. Sparse code multiple access. In Proceedings of the 2013 IEEE 24th Annual International Symposium on Personal, Indoor, and Mobile Radio Communications (PIMRC), London, UK, 8–11 September 2013. [Google Scholar]
- Abebe, A.T.; Kang, C.G. Grant-Free Uplink Transmission With Multi-Codebook-Based Sparse Code Multiple Access (MC-SCMA). IEEE Access
**2019**, 7, 169853–169864. [Google Scholar] [CrossRef] - Van De Beek, J.; Popovic, B.M. Multiple Access with Low-Density Signatures. In Proceedings of the GLOBECOM 2009-2009 IEEE Global Telecommunications Conference, Honolulu, HI, USA, 30 Novemver–4 December 2009; pp. 1–6. [Google Scholar]
- Razavi, R.; Hoshyar, R.; Imran, M.A.; Wang, Y. Information Theoretic Analysis of LDS Scheme. IEEE Commun. Lett.
**2011**, 15, 798–800. [Google Scholar] [CrossRef] [Green Version] - Hoshyar, R.; Wathan, F.P.; Tafazolli, R. Novel Low-Density Signature for Synchronous CDMA Systems Over AWGN Channel. IEEE Trans. Signal Process.
**2008**, 56, 1616–1626. [Google Scholar] [CrossRef] [Green Version] - Yang, D.; Dong, B.; Zhi, C.; Gao, P.; Fang, J. Joint Sparse Graph-Detector Design for Downlink MIMO-SCMA Systems. IEEE Wirel. Commun. Lett.
**2017**, 6, 14–17. [Google Scholar] - Kurniawan, D.; Arifianto, M.S.; Kurniawan, A. Low Complexity MIMO-SCMA Detector. In Proceedings of the 2019 IEEE 5th International Conference on Wireless and Telematics (ICWT), Yogyakarta, Indonesia, 25–26 July 2019; pp. 1–5. [Google Scholar]
- Sun, W.; Su, Y.; Ueng, Y.; Yang, C. An LDPC-Coded SCMA Receiver With Multi-User Iterative Detection and Decoding. IEEE Trans. Circuits Syst. I Regul. Pap.
**2019**, 66, 3571–3584. [Google Scholar] [CrossRef] - Taherzadeh, M.; Nikopour, H.; Bayesteh, A.; Baligh, H. SCMA Codebook Design. In Proceedings of the 2014 IEEE 80th Vehicular Technology Conference (VTC2014-Fall), Vancouver, BC, Canada, 14–17 September 2014. [Google Scholar]
- Dai, J.; Niu, K.; Lin, J. Iterative Gaussian-Approximated Message Passing Receiver for MIMO-SCMA System. IEEE J. Sel. Top. Signal Process.
**2019**, 13, 753–765. [Google Scholar] [CrossRef] - Wang, Y.; Wu, Y.; Zhou, F.; Chu, Z.; Wu, Y.; Yuan, F. Multi-Objective Resource Allocation in a NOMA Cognitive Radio Network With a Practical Non-Linear Energy Harvesting Model. IEEE Access
**2018**, 6, 12973–12982. [Google Scholar] [CrossRef] - Sun, H.; Zhou, F.; Hu, R.Q.; Hanzo, L. Robust Beamforming Design in a NOMA Cognitive Radio Network Relying on SWIPT. IEEE J. Sel. Areas Commun.
**2019**, 37, 142–155. [Google Scholar] [CrossRef] [Green Version] - Wang, X.; Na, Z.; Lam, K.; Liu, X.; Gao, Z.; Li, F.; Wang, L. Energy Efficiency Optimization for NOMA-Based Cognitive Radio With Energy Harvesting. IEEE Access
**2019**, 7, 139172–139180. [Google Scholar] [CrossRef] - Xiang, Z.; Yang, W.; Pan, G.; Cai, Y.; Song, Y. Physical Layer Security in Cognitive Radio Inspired NOMA Network. IEEE J. Sel. Top. Signal Process.
**2019**, 13, 700–714. [Google Scholar] [CrossRef] - Xu, L.; Xing, H.; Deng, Y.; Nallanathan, A.; Zhuansun, C. Fairness-Aware Throughput Maximization for Underlaying Cognitive NOMA Networks. IEEE Syst. J.
**2020**, in press. [Google Scholar] [CrossRef] - Xu, Y.; Hu, R.Q.; Li, G. Robust Energy-efficient Maximization for Cognitive NOMA Networks under Channel Uncertainties. IEEE Internet Things J.
**2020**, 1, in press. [Google Scholar] [CrossRef] - Fu, L.; Zhang, Y.J.A.; Huang, J. Energy Efficient Transmissions in MIMO Cognitive Radio Networks. IEEE J. Sel. Areas Commun.
**2013**, 31, 2420–2431. [Google Scholar] - Fu, L.; Johansson, M.; Bengtsson, M. Energy Efficient Transmissions in Cognitive MIMO Systems With Multiple Data Streams. IEEE Trans. Wirel. Commun.
**2015**, 14, 5171–5184. [Google Scholar] [CrossRef] - Zhang, X.; Li, H. Energy efficiency optimization for MIMO cognitive radio network. In Proceedings of the 2015 IEEE International Conference on Communications (ICC), London, UK, 8–12 June 2015; pp. 7713–7718. [Google Scholar]
- Sboui, L.; Rezki, Z.; Sultan, A.; Alouini, M. Energy-Efficient Power Allocation for Cognitive MIMO Channels. In Proceedings of the 2016 IEEE 84th Vehicular Technology Conference (VTC-Fall), Montréal, QC, Canada, 18–21 September 2016; pp. 1–6. [Google Scholar]
- Okumu, E.M.; Dlodlo, M.E. Optimal and sub-optimal iterative cross-layer energy efficient schemes for CR MIMO systems with antenna selection. In Proceedings of the IEEE EUROCON 2017-17th International Conference on Smart Technologies, Ohrid, Macedonia, 6–8 July 2017; pp. 62–67. [Google Scholar]
- Miridakis, N.I.; Tsiftsis, T.A.; Alexandropoulos, G.C. MIMO Underlay Cognitive Radio: Optimized Power Allocation, Effective Number of Transmit Antennas and Harvest-Transmit Tradeoff. IEEE Trans. Green Commun. Netw.
**2018**, 2, 1101–1114. [Google Scholar] [CrossRef] - Wu, F.; Xiao, L.; Yang, D.; Cuthbert, L.; Liu, X. Transceiver design and power allocation for SWIPT in MIMO cognitive radio systems. Symmetry
**2018**, 10, 647. [Google Scholar] [CrossRef] [Green Version] - Yuan, Y.; Ding, Z. Outage Constrained Secrecy Rate Maximization Design With SWIPT in MIMO-CR Systems. IEEE Trans. Veh. Technol.
**2018**, 67, 5475–5480. [Google Scholar] [CrossRef] [Green Version] - Maurya, S.; Bansal, M.; Trivedi, A. Joint source and relay precoder design for energy-efficient MIMO-cognitive relay networks. IET Commun.
**2019**, 13, 2226–2234. [Google Scholar] [CrossRef] - Patil, V.; Singhal, C. Throughput Improvement in Hybrid MIMO Cognitive Radio Using Simultaneous Narrowband and Wideband System. In Proceedings of the 2019 11th International Conference on Communication Systems & Networks (COMSNETS), Bangalore, India, 7–11 January 2019; pp. 285–290. [Google Scholar]
- Song, C.; Lee, H.; Lee, K. Optimal Precoder Designs for Sum-Utility Maximization in SWIPT-Enabled Multi-User MIMO Cognitive Radio Networks. IEEE Syst. J.
**2019**, 13, 2332–2343. [Google Scholar] [CrossRef] [Green Version] - Yu, Y.; Chen, H.; Li, Y.; Ding, Z.; Zhuo, L. Antenna Selection in MIMO Cognitive Radio-Inspired NOMA Systems. IEEE Commun. Lett.
**2017**, 21, 2658–2661. [Google Scholar] [CrossRef] [Green Version] - Nandan, N.; Majhi, S.; Wu, H. Secure Beamforming for MIMO-NOMA-Based Cognitive Radio Network. IEEE Commun. Lett.
**2018**, 22, 1708–1711. [Google Scholar] [CrossRef] - Yu, Y.; Chen, H.; Li, Y.; Ding, Z.; Song, L.; Vucetic, B. Antenna Selection for MIMO Nonorthogonal Multiple Access Systems. IEEE Trans. Veh. Technol.
**2018**, 67, 3158–3171. [Google Scholar] [CrossRef] [Green Version] - Thakur, P.; Singh, G. Sum-Rate Analysis of MIMO Based CR-NOMA Communication System. In Proceedings of the 2019 Fifth International Conference on Image Information Processing (ICIIP), Shimla, India, 15–17 November 2019; pp. 414–419. [Google Scholar]
- Xiao, Y.S.; Tsang, D.H.K. Interference Alignment Beamforming and Power Allocation for Cognitive MIMO-NOMA Downlink Networks. In Proceedings of the 2019 IEEE Wireless Communications and Networking Conference (WCNC), Marrakesh, Morocco, 15–18 April 2019; pp. 1–6. [Google Scholar]
- Yasrab, T.; Gurugopinath, S. Spectral Efficiency of MIMO-NOMA Cognitive Radios with Energy-Based Spectrum Sensing. In Proceedings of the 2019 IEEE International Conference on Distributed Computing, VLSI, Electrical Circuits and Robotics (DISCOVER), Manipal, India, 11–12 August 2019; pp. 1–6. [Google Scholar]
- Wang, B.; Wang, K.; Lu, Z.; Xie, T.; Quan, J. Comparison study of non-orthogonal multiple access schemes for 5G. In Proceedings of the 2015 IEEE International Symposium on Broadband Multimedia Systems and Broadcasting, Ghent, Belgium, 17–19 June 2015; pp. 1–5. [Google Scholar]
- Rappaport, T.S. Wireless Communications–Principles and Practice; Prentice Hall PTR: Upper Saddle River, NJ, USA, 1996; Volume 2. [Google Scholar]
- Telatar, E. Capacity of Multi-antenna Gaussian Channels. Eur. Trans. Telecommun.
**1999**, 10, 585–595. [Google Scholar] [CrossRef] - Gesbert, D.; Shafi, M.; Da-shan, S.; Smith, P.J.; Naguib, A. From theory to practice: An overview of MIMO space-time coded wireless systems. IEEE J. Sel. Areas Commun.
**2003**, 21, 281–302. [Google Scholar] [CrossRef] [Green Version] - Ibaraki, T.; Katoh, N. Resource Allocation Problems: Algorithmic Approaches; MIT Press: Cambridge, MA, USA, 1988. [Google Scholar]
- Baghani, M.; Parsaeefard, S.; Derakhshani, M.; Saad, W. Dynamic Non-Orthogonal Multiple Access and Orthogonal Multiple Access in 5G Wireless Networks. IEEE Trans. Commun.
**2019**, 67, 6360–6373. [Google Scholar] [CrossRef] [Green Version]

**Figure 8.**The average energy consumption per bit versus the minimum distance between the SUs and secondary BS.

**Figure 13.**Average interference power at PUs links versus the number of SUs, if and only if the min-time slot requirement is satisfied.

**Table 1.**Summary of related work. Energy efficient (EE); User capacity (UC); Energy harvesting (EH); Spectrum efficiency (SE); Cognitive radio (CR); Multiple input multiple output (MIMO); Nonorthogonal multiple access (NOMA).

Reference | Objective | Method | Advantages | Limitations | |
---|---|---|---|---|---|

CR - NOMA | [19] | EE; SE | weighted Tchebycheff | The efficiency of EH is higher than that of the linear model. | The decoding rate of users is affected. |

[20] | Power; EH | one-dimensional search | The system performance is improved. | The interference generated by multiple cells is not considered. | |

[21] | EE | Dinkelbach method | The tradeoff between EE and sub-slot is realized. | The UC has not been improved. | |

[22] | Power; security | power allocation and transmit rate control | Reduce interference and improve security. | The increase of the number of secondary users will reduce the security performance. | |

[23] | UC | successive convex approximation | Total throughput increased. | Energy consumption increased | |

[24] | EE | successive convex approximation | The algorithm has good robustness and EE. | System complexity and interference is not considered. | |

CR - MIMO | [25] | EE | matrix eigenvalue-eigenvector computation | It reduces energy consumption and interference. | The optimization problem under imperfect channel state information (CSI) is not considered. |

[26] | EE | water-filling and greedy algorithm | Both perfect CSI and imperfect CSI optimization are considered. | Secondary users will not only interfere with the primary users, but also interfere with each other. | |

[27] | EE | Dinkelbach’s method. | Network energy consumption is reduced. | Fairness may be lost. | |

[28] | EE | singular value decomposition; water-filling | Optimal power allocation improves performance. | The interference threshold has a significant effect on EE. | |

[29] | EE | iterative cross-layer algorithm | Cross-layer scheme improves UC and EE. | High computational complexity. | |

CR - MIMO - NOMA | [36] | EE | subset-based joint antenna selection | Improve the signal-to-noise ratio of secondary users. | The impact of interference was not considered. |

[37] | UC | zero-forcing-beamforming | Improve the overall security level of the system and access users. | There are certain restrictions on the number of base station antennas. | |

[38] | UC | maximum-channel- gain-based antenna selection | Near optimal performance can be achieved while reducing complexity. | Only when one user is closer to the base station than another user can a better complexity saving be achieved. | |

[39] | UC | Shannon channel capacity formula | The proposed scheme is superior to CR-NOMA in terms of data rate. | General channel is not considered. | |

[40] | UC | Interference alignment -based coordinated beamforming | Eliminate interference and increase system sum-rate. | The number of user antennas affects the system and rate. | |

[41] | SE; UC | Bblindly combined energy detection | It provides better SE. | EE is not considered. | |

proposed scheme | EE; UC | water-filling and greedy algorithm | Improve EE, reduce interference and increase the number of user access. | Interference between secondary users is not considered. |

Symbol | Definition |
---|---|

S_{k} | The kth secondary user |

P_{j} | The jth pair of primary transmitter–receiver links |

${M}_{{S}_{k}}$ | The number of transmitting antennas of ${S}_{k}$ |

${M}_{{P}_{j}}$ | The number of transmitting antennas of ${P}_{j}$ |

${N}_{{P}_{j}}$ | The number of receiver antennas of ${P}_{j}$ |

${N}_{BS}$ | The number of receiver antennas of secondary base station (BS) |

${H}_{BS,{S}_{k}}\in {\u2102}^{{N}_{BS}\times {M}_{{S}_{k}}}$ | The channel matrix from ${S}_{k}$ to the secondary BS |

${H}_{{P}_{j},{S}_{k}}\in {\u2102}^{{N}_{{P}_{j}}\times {M}_{{S}_{k}}}$ | The channel matrix from ${S}_{k}$ to the receiver of ${P}_{j}$ |

${H}_{BS,{P}_{j}}\in {\u2102}^{{N}_{BS}\times {M}_{{P}_{j}}}$ | The channel matrix from the transmitter of ${P}_{j}$ to the secondary BS |

${D}_{{S}_{k}}$ | The number of data streams of ${S}_{k}$ |

${D}_{{P}_{j}}$ | the number of data streams of ${P}_{j}$ |

${x}_{{S}_{k}}$ | The data flow matrix transmitted by ${S}_{k}$ |

${x}_{{P}_{j}}$ | The data flow matrix transmitted by ${P}_{j}$ |

${Q}_{{S}_{k}}$ | The Hermitian positive semidefinite covariance matrix of ${x}_{{S}_{k}}$, whose eigenvalues are non-negative |

${Q}_{{P}_{j}}$ | The Hermitian positive semidefinite covariance matrix of ${x}_{{P}_{j}}$, whose eigenvalues are non-negative |

Parameter | Value |
---|---|

Frame length | 20 ms |

Each frame | 200 time slots |

Carrier frequency | 1 GHz |

Bandwidth | 20 MHZ |

Cell | 200*200 m |

Noise power density (N_{0}) | −178 dBm/Hz |

Interference power threshold (${\varphi}_{{P}_{j}}/\left(N0\ast w\right)$) | 25 dB |

Outage probability (${\delta}_{{P}_{j}}$) | 0.01 |

Maximum transmitting power of PUs | 20 dBm |

Maximum transmitting power of SUs | 27.5 dBm |

Rate requirement of SU | 32 kbps |

Channel model | Rayleigh fading channel |

SCMA overload factor | 1.5\2.0\2.5 |

Number of transceiver antennas | 4 |

Minimum distance between BS and SUs | 10 m |

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## Share and Cite

**MDPI and ACS Style**

Zhang, P.; Ge, W.; Zhang, Y.; Gao, M.; Zhang, G.
Energy Efficiency and User Capacity Optimization of Cognitive MIMO Systems Via the SCMA-Based Nonorthogonal Time Slot Allocation. *Symmetry* **2020**, *12*, 1136.
https://doi.org/10.3390/sym12071136

**AMA Style**

Zhang P, Ge W, Zhang Y, Gao M, Zhang G.
Energy Efficiency and User Capacity Optimization of Cognitive MIMO Systems Via the SCMA-Based Nonorthogonal Time Slot Allocation. *Symmetry*. 2020; 12(7):1136.
https://doi.org/10.3390/sym12071136

**Chicago/Turabian Style**

Zhang, Pengju, Wenping Ge, Yongxing Zhang, Mengyao Gao, and Gecheng Zhang.
2020. "Energy Efficiency and User Capacity Optimization of Cognitive MIMO Systems Via the SCMA-Based Nonorthogonal Time Slot Allocation" *Symmetry* 12, no. 7: 1136.
https://doi.org/10.3390/sym12071136