The quantile function [or inverse cumulative distribution function (CDF)] is a probabilistic measure that is widely employed in both statistical applications and Monte Carlo methods. In addition, this function is important to determine performances of the communication systems, especially for wireless communication systems. However, numerical computing of the Nakagami-m inverse CDF is quite difficult because of the fact that a closed-form expression of the Nakagami-m inverse CDF is not available. In this paper, an improved expression for the Nakagami-m inverse CDF is presented by using curve-fitting methods. Furthermore, parameters of the proposed mathematical model are optimized by the help of artificial bee colony algorithm that is a population based meta-heuristic optimization method motivated by the foraging behavior of honey bee swarms. The results acquired by the proposed approximation are also compared with other existing approaches in the literature in terms of complexity and performance. It is shown that the presented approximation is more accurate, simple and effective against to the previously reported approximations.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Nakagami, M. (1960). The m-distribution, a general formula of intensity distribution of rapid fading. In W. G. Hoffman (Ed.), Statistical methods in radio wave propagation. Oxford: Pergamon.
Lopez-Martinez, F. J., Morales-Jimenez, D., Martos-Naya, E., & Paris, J. F. (2013). On the bivariate Nakagami-m cumulative distribution function: closed-form expression and applications. IEEE Transactions on Communications, 61(4), 1404–1414.
Dharmawansa, P., Rajatheva, N., & Tellambura, C. (2007). Infinite series representations of the trivariate and quadrivariate Nakagami-m distributions. IEEE Transactions on Wireless Communications, 6(12), 4320–4328.
Beaulieu, N. C., & Abu-Dayya, A. A. (1991). Analysis of equal gain diversity on Nakagami-m fading channels. IEEE Transactions on Communications, 39(2), 225–234.
Abdi, A., & Kaveh, M. (2000). Performance comparison of three different estimators for the Nakagami-m parameter using Monte Carlo simulation. IEEE Communications Letters, 4(4), 119–121.
Beaulieu, N. C., & Cheng, C. (2005). Efficient Nakagami-m fading channel Simulation. IEEE Transactions on Vehicular Technology, 54(2), 413–424.
Cheng, C. (2000). A Nakagami-m fading channel simulator. M.Sc. thesis, Dept. Elect. Comp. Eng., Queen’s Univ., Kingston, ON, Canada.
Bilim, M., & Develi, I. (2015). A new Nakagami-m inverse CDF approximation based on the use of genetic algorithm. Wireless Personal Communications, 83(3), 2279–2287.
Suraweera, H. A., Smith, P. J., & Armstrong, J. (2006). Outage probability of cooperative relay networks in Nakagami-m fading channels. IEEE Communications Letters, 10(12), 834–836.
Nan, Y., Elkashlan, M., & Jinhong, Y. (2010). Outage probability of multiuser relay networks in Nakagami-m fading channels. IEEE Transactions on Vehicular Technology, 59(5), 2120–2132.
Mehemed, A., & Hamouda, W. (2012). Outage analysis of cooperative CDMA systems in Nakagami-m fading channels. IEEE Transactions on Vehicular Technology, 61(2), 618–623.
Xianfu, L., Lisheng, F., Michalopoulos, D. S., Pingzhi, F., & Hu, R. Q. (2013). Outage probability of TDBC protocol in multiuser two-way relay systems with Nakagami-m fading. IEEE Communications Letters, 17(3), 487–490.
Mathur, A., Bhatnagar, M. R., & Panigrahi, B. K. (2014). PLC performance analysis over Rayleigh fading channel under Nakagami-m additive noise. IEEE Communications Letters, 18(12), 2101–2104.
Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization. Tech. Report No. TR06, Erciyes University.
Basturk, A., & Akay, R. (2013). Performance analysis of the coarse-grained parallel model of the artificial bee colony algorithm. Information Sciences, 253, 34–55.
Basturk, A., & Akay, R. (2012). Parallel implementation of synchronous type artificial bee colony algorithm for global optimization. Journal of Optimization Theory and Applications, 155, 1095–1104.
Karaboga, D., & Ozturk, C. (2009). Neural networks training by artificial bee colony algorithm on pattern classification. Neural Network World, 19(3), 279–292.
Karaboga, D., & Ozturk, C. (2011). A novel clustering approach: artificial bee colony (ABC) algorithm. Applied Soft Computing, 11(1), 652–657.
Karaboga, N. (2009). A new design method based on artificial bee colony algorithm for digital IIR filters. Journal of the Franklin Institute, 346(4), 328–348.
Apalak, M. K., Karaboga, D., & Akay, B. (2014). The artificial bee colony algorithm in layer optimization for the maximum fundamental frequency of symmetrical laminated composite plates. Engineering Optimization, 46(3), 420–437.
Kisi, O., Ozkan, C., & Akay, B. (2012). Modelling discharge-sediment relationship using neural networks with artificial bee colony algorithm. Journal of Hydrology, 428–429, 94–103.
Haktanir, T., Karaboga, D., & Akay, B. (2012). Mix proportioning of aggregates for concrete by three different approaches. Journal of Materials in Civil Engineering, 24(5), 529–537.
Ozkan, C., Kisi, O., & Akay, B. (2011). Neural networks with artificial bee colony algorithm for modeling daily reference evapotranspiration. Irrigation Science, 29(6), 431–441.
About this article
Cite this article
Kabalci, Y. An improved approximation for the Nakagami-m inverse CDF using artificial bee colony optimization. Wireless Netw 24, 663–669 (2018). https://doi.org/10.1007/s11276-016-1396-7
- Inverse CDF
- Nakagami-m fading
- Artificial bee colony algorithm