Abstract
In low power wide area networks, packets transmitted by a device are not addressed to a specific base station: any surrounding station can receive them. This opens the way to several macro diversity schemes. As opposed to independent decoding of packets received by each base station, we propose using maximum ratio combining (MRC) to improve system performance. We use stochastic geometry to analyze the packet loss probability when MRC is implemented for both pure and slotted Aloha and obtain a closed formula when the path loss exponent \(\gamma \) is 4. However, the formula is valid when all base stations on an infinite plane participate in the MRC procedure, which gives the most optimistic evaluation. We developed simulations to get the performance when a finite number of receivers in the MRC is considered and focus on the case with only 2 receivers. We use a curve-fitting approach based on the simulation results to get a closed-form formula of the packet loss probability with 2 receivers. This curve-fitting approach is also applicable to other cases in which more receivers are leveraged by MRC. The formula is easy to use and accurate when \(\gamma \in \left[ 3.3, 4.5\right] \) and the loss probability is greater than \(0.5\%\). For pure Aloha when advanced transmission techniques (e.g., interleaving, robust channel coding, etc.) are applied and when the capture ratio is 3 dB, the system capacity for a \(10\%\) packet loss probability is increased by a factor greater than 1.26 compared to a simple scheme in which each base station independently decodes packets.
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Raza, U., Kulkarni, P., & Sooriyabandara, M. (2017). Low power wide area networks: An overview. IEEE Communications Surveys & Tutorials, 19(2), 855–873.
Song, Q., Lagrange, X., & Nuaymi, L. (2017). Evaluation of macro diversity gain in long range ALOHA networks. IEEE Communications Letters, 21(11), 2472–2475.
Sarker, J. H., & Mouftah, H. T. (2013). Self-stability of slotted aloha by limiting the number of retransmission trials in infrastructure-less wireless networks. Telecommunication Systems, 52(2), 435–444.
Ghanbarinejad, M., & Schlegel, C. (2014). Distributed probabilistic medium access with multipacket reception and markovian traffic. Telecommunication Systems, 56(2), 311–321.
Meloni, A., & Murroni, M. (2016). Interference calculation in asynchronous random access protocols using diversity. Telecommunication Systems, 63(1), 45–53.
Jung, P., Steiner, B., & Stilling, B. (1996). Exploitation of intracell macrodiversity in mobile radio systems by deployment of remote antennas. In: Proceedings of IEEE 4th International Symposium on Spread Spectrum Techniques and Applications, (vol. 1, pp. 302–307). IEEE.
Di Renzo, M., Graziosi, F., & Santucci, F. (2009). A unified framework for performance analysis of CSI-assisted cooperative communications over fading channels. IEEE Transactions on Communications, 57(9), 2551–2557.
ElSawy, H., Hossain, E., & Haenggi, M. (2013). Stochastic geometry for modeling, analysis, and design of multi-tier and cognitive cellular wireless networks: A survey. IEEE Communications Surveys & Tutorials, 15(3), 996–1019.
Sousa, E. S., & Silvester, J. A. (1990). Optimum transmission ranges in a direct-sequence spread-spectrum multihop packet radio network. IEEE Journal on Selected Areas in Communications, 8(5), 762–771.
Haenggi, M. (2017). User point processes in cellular networks. IEEE Wireless Communications Letters, 6(2), 258–261.
Haenggi, M. (2012). Diversity loss due to interference correlation. IEEE Communications Letters, 16(10), 1600–1603.
Tanbourgi, R., Dhillon, H. S., Andrews, J. G., & Jondral, F. K. (2014). Effect of spatial interference correlation on the performance of maximum ratio combining. IEEE Transactions on Wireless Communications, 13(6), 3307–3316.
Błaszczyszyn, B., & Mühlethaler, P. (2015). Interference and SINR coverage in spatial non-slotted Aloha networks. Annals of Telecommunications, 70(7–8), 345–358.
Dhillon, H. S., & Andrews, J. G. (2014). Downlink rate distribution in heterogeneous cellular networks under generalized cell selection. IEEE Wireless Communications Letters, 3(1), 42–45.
Haenggi, M., & Ganti, R. K. (2009). Interference in large wireless networks. Breda: Now Publishers Inc.
Proakis, J. G. (2007). Digital Communications (5th ed.). New York: McGraw Hill.
Wolfe, SJ. (1975). On moments of probability distribution functions. In B. Ross (Ed.), Fractional calculus and its applications: Proceedings of the international conference held at the University of New Haven, June 1974 (pp. 306–316). Berlin, Heidelberg: Springer. https://doi.org/10.1007/BFb0067116.
Hirsa, A. (2012). Computational methods in finance. Boca Raton: CRC Press.
Song, Q., Lagrange, X., & Nuaymi, L. (2017). An analytical model for S-ALOHA performance evaluation in M2M networks. In: 2017 IEEE International Conference on Communications (ICC), (pp. 1–7). IEEE.
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Song, Q., Nuaymi, L. & Lagrange, X. Analysis of macro diversity based on maximum ratio combining in long range ALOHA networks. Telecommun Syst 72, 471–482 (2019). https://doi.org/10.1007/s11235-019-00579-3
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DOI: https://doi.org/10.1007/s11235-019-00579-3