# Performance Analysis of Cooperative Low-Power Wide-Area Network for Energy-Efficient B5G Systems
## 5 Conclusions  
In this paper, the performance of a cooperative low-power wide-area network (LPWAN) was analyzed in terms of outage probability, bit error rate (BER), and diversity order, while there existed  
Figure 4: Diversity order of LPWAN according to the number of total received antennas when \(d_{1}=1\), \(d_{2}=3\), and \(d_{3}=5\).  
Figure 3: BER performance of LPWAN for varying the total received SNR when \(N=3\); i.e.,\(\gamma(K_{1},K_{2},K_{3})\in\{(1,3,5)(5,3,1)\}\), \(d_{1}=1\), \(d_{2}=4\), \(d_{3}=8\), and \(\alpha=3\).  
\(N\) gateways (GWs) with multiple antennas. Despite the assumption that each GW is independently located at an arbitrary position and has an arbitrary number of antennas, we attained the exact closed-form expression on both outage probability and BER by using the hyper-Erlang distribution. It was shown that the mathematical analyses provided in this paper exactly matched with Monte-Carlo computer simulations, and thus the analytical results were validated. We investigated the diversity order of the cooperative LPWAN and verified that it is equal to the total number of received antennas in cooperative LPWANs via both mathematical analysis and computer simulations. As expected, the performance of cooperative LPWAN outperforms conventional non-cooperative LPWAN. Consequently, the cooperative LPWAN architecture is very promising for reducing the costs, extending the coverage ranges, and enhancing the battery lives of IoT devices.  
Formal analysis, C.S.Y.; investigation, C.S.Y. and J.S.Y.; methodology, C.S.Y.; project administration, B.C.J.; resources, B.C.J.; software, J.S.Y.; supervision, B.C.J.; validation, J.S.Y. writing--original draft, C.S.Y.; writing--review and editing, J.S.Y. and B.C.J. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the ICT R&D program of MSIT/IITP (2019-0-00964-001, Development of Incumbent Radio Stations Protection and Frequency sharing Technology through Spectrum Challenge), and in part by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2020-2017-0-01635) supervised by the IITP (Institute for Information and communications Technology Promotion.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
LPWANLow-power wide-area network BERBit error rate MRCMaximum-ratio combining IoTInternet of Things LTELong-term evolution LTE-MTCLTE machine-type-communications NB-IoTNarrow band-IoT LoRaLong range BLEBluetooth low energy mMTCMassive machine-type-communications GWGateway RRHRemote radio head SNRSignal-to-noise ratio CDIChannel distribution information IDIoTdevice AWGNAdditive white Gaussian noise p.d.f. Probability density function c.d.f. Probability distribution function QPSKQuadrature phase-shift keying The following mathematical symbols and functions are used in manuscript:  
\(N\)The total number of GWs that participate in the cooperative communication \(K_{i}\)The total number of antennas of \(i\)-th GW \(K\)The total sum of antennas of all GWs that participate in the cooperative communication \(d_{i}\)The distance between ID and \(i\)-th GW \(\alpha\)Path loss factor \(\Gamma(\cdot)\)The gamma function \({}_{2}F_{1}(\cdot)\)The Gaussian hyper-geometry function