Abstract
Two methods are proposed in this paper to estimate asymptotic and exact bit error rate (BER) in two-hop amplify-and-forward (AF) relay networks . Rayleigh-fading channels are considered and selection strategy is used to select the highest end-to-end signal-to-noise ratio relay among all relays. The first presented method unifies the BER analysis performance for both one and two hop networks in one scheme and this refers to as the unified BER (U-BER) . The second method, namely the optimal BER (O-BER), is developed to measure BER for an AF relay network that is optimized with respect to its energy and spectral efficiency. Expressions for asymptotic BER performance for (U-BER) and (O-BER) are derived. An expression for the exact BER for (U-BER) is also obtained. The proposed methods provide useful and efficient tools for analyzing the BER performance in AF relay networks . Analytical and simulated results are compared to validate the BER calculation.
Similar content being viewed by others
References
Tianxi, L., Lingyang, S., Yonghui, L., Qiang, H., & Bingli, J. (2012). Performance analysis of hybrid relay selection in cooperative wireless systems. IEEE Transactions on Communications, 60(3), 779–788.
Laneman, J. N., Wornell, G. W., & Tse, D. N. C. (2001). An efficient protocol for realizing cooperative diversity in wireless networks. In IEEE International Symposium on Information Theory, Proceedings 2001, p. 294.
Nosratinia, A., Hunter, T. E., & Hedayat, A. (2004). Cooperative communication in wireless networks. IEEE Communications Magazine, 42(10), 74–80.
Laneman, J. N., Tse, D. N. C., & Wornell, G. W. (2004). Cooperative diversity in wireless networks: Efficient protocols and outage behavior. IEEE Transactions on Information Theory, 50(12), 3062–3080.
Jung-Chieh, C., & Chao-Kai, W. (2011). Near-optimal relay subset selection for two-way amplify-and-forward mimo relaying systems. IEEE Transactions on Wireless Communications, 10(1), 37–42.
Salhab, A., & Zummo, S. (2013). A low-complexity relay selection scheme based on switch-and-examine diversity combining for af relay systems. IET Communications, 7(9), 848–859.
Bullck, S. R. (2014). Basic probability and pulse theory. In Transceiver and System Design for Digital Communications (pp. 159–188). Edison, NJ: SciTech Publishing.
Brennan, D. (2003). Linear diversity combining techniques. Proceedings of the IEEE, 91(2), 331–356.
Molisch, A. (2012). Diversity. In Wireless Communications (2nd ed., pp. 249–275). New York: Wiley.
Xie, K., Cao, J., Wang, X., & Wen, J. (2013). Optimal resource allocation for reliable and energy efficient cooperative communications. IEEE Transactions on Wireless Communications, 12(10), 4994–5007.
Asaduzzaman, & Kong, H. Y. (2011). Multi-relay cooperative diversity protocol with improved spectral efficiency. Journal of Communications and Networks, 13(3), 240–249.
Zhengdao, W., & Giannakis, G. B. (2003). A simple and general parameterization quantifying performance in fading channels. IEEE Transactions on Communications, 51(8), 1389–1398.
Hasna, M. O., & Alouini, M. S. (2004). A performance study of dual-hop transmissions with fixed gain relays. IEEE Transactions on Wireless Communications, 3(6), 1963–1968.
Hasna, M. O., & Alouini, M. S. (2003). End-to-end performance of transmission systems with relays over rayleigh-fading channels. IEEE Transactions on Wireless Communications, 2(6), 1126–1131.
Ribeiro, A., Xiaodong, C., & Giannakis, G. B. (2005). Symbol error probabilities for general cooperative links. IEEE Transactions on Wireless Communications, 4(3), 1264–1273.
Farhadi, G., & Beaulieu, N. C. (2008). On the performance of amplify-and-forward cooperative systems with fixed gain relays. IEEE Transactions on Wireless Communications, 7(5), 1851–1856.
Dohler, M., & Li, Y. (2010). Transparent relaying techniques. In Cooperative communications (pp. 141–207). New York: Wiley.
Kezhi, W., Yunfei, C., Alouini, M. S., & Feng, X. (2014). Ber and optimal power allocation for amplify-and-forward relaying using pilot-aided maximum likelihood estimation. IEEE Transactions on Communications, 62(10), 3462–3475.
Anghel, P. A., & Kaveh, M. (2004). Exact symbol error probability of a cooperative network in a rayleigh-fading environment. IEEE Transactions on Wireless Communications, 3(5), 1416–1421.
Ikki, S. S., & Ahmed, M. H. (2010). On the performance of cooperative-diversity networks with the nth best-relay selection scheme. IEEE Transactions on Communications, 58(11), 3062–3069.
Soliman, S. S., & Beaulieu, N. C. (2012). Exact analysis of dual-hop af maximum end-to-end snr relay selection. IEEE Transactions on Communications, 60(8), 2135–2145.
Behnad, A., & Xianbin, W. (2014). Accuracy of harmonic mean approximation in performance analysis of multihop amplify-and-forward relaying. IEEE Wireless Communications Letters, 3(2), 125–128.
Qiang, H., Tianxi, L., Shaohui, S., Lingyang, S., & Bingli, J. (2014). Selective combining for hybrid cooperative networks. IET Communications, 8(4), 471–482.
Liu, K. J. R., Sadek, A. K., Su, W., & Kwasinski, A. (2008). Cooperative communications with single relay. In Cooperative communications and networking (pp. 152–193). Cambridge: Cambridge University Press.
Zhang, W., Duan, D., & Yang, L. (2011). Relay selection from a battery energy efficiency perspective. IEEE Transactions on Communications, 59(6), 1525–1529.
Waqar, O., Imran, M., Dianati, M., & Tafazolli, R. (2014). Energy consumption analysis and optimization of ber-constrained amplify-and-forward relay networks. IEEE Transactions on Vehicular Technology, 63(3), 1256–1269.
Elsheikh, E., Wong, K.-K., Zhang, Y., & Cui, T. (2010). Chapter 10—user cooperative communications. In A. M. W. N. T. Hou (Ed.), Cognitive radio communications and networks (pp. 261–305). Oxford: Academic Press.
Ramakrishna, J. (2001). Spatial diversity for wireless communications. In Handbook of antennas in wireless communications, ser. Electrical Engineering & Applied Signal Processing Series, Boca Raton: CRC Press.
Tripathi, N., & Reed, J. (2014). Fundamentals of cdma, wcdma, and is-95. In Cellular communications: A comprehensive and practical guide (pp. pp. 363–421). New York: Wiley,.
Yong, L., & Zhengguang, Z. (2014). Energy-efficient power allocation for two-hop relay networks. Electronics Letters, 50(2), 123–125.
Alamouti, S. (1998). A simple transmit diversity technique for wireless communications. IEEE Journal on Selected Areas in Communications, 16(8), 1451–1458.
Proakis, J., & Salehi, M. (2007). Digital communications. New York: McGraw-Hill Education.
Bullock, S. R. (2014). Transceiver design. Edison, NJ: SciTech Publishing.
Goldsmith, A. (2005). Wireless communications. Cambridge: Cambridge University Press.
Prasad, R., & Mihovska, A. (2009). Protocols and algorithms for ad hoc networks. In New Horizons in Mobile and Wireless Communications: Ad hoc networks and PANs. Artech House, pp. 25–127.
Simon, M. (2007). Probability distributions involving gaussian random variables: A handbook for engineers and scientists. Springer US. https://books.google.co.nz/books?id=zjJdP0CJUAYC.
Linear vector spaces. (2009) In Advanced Linear Algebra for Engineers with MATLAB (pp. 105–155). Boca Raton: CRC Press.
David, H., & Nagaraja, H. (2004). Order statistics. New York: Wiley.
Kaltenbach, H.-M. (2012). Basics of probability theory. In A Concise Guide to Statistics, ser. SpringerBriefs in Statistics. Springer Berlin Heidelberg, 2012/01/01 2012, ch. 1, pp. 1–27.
Salo, J., El-Sallabi, H. M., & Vainikainen, P. (2006). The distribution of the product of independent rayleigh random variables. IEEE Transactions on Antennas and Propagation, 54(2), 639–643.
Patel, C. S., Stuber, G. L., & Pratt, T. G. (2006). Statistical properties of amplify and forward relay fading channels. IEEE Transactions on Vehicular Technology, 55(1), 1–9.
Karagiannidis, G. K. (2006). Performance bounds of multihop wireless communications with blind relays over generalized fading channels. IEEE Transactions on Wireless Communications, 5(3), 498–503.
Dohler, M., & Li, Y. (2010). Wireless relay channel. In Cooperative communications (pp. 43–139). New York: Wiley.
Pahlavan, K., & Krishnamurthy, P. (2013). Physical layer alternatives for wireless networks (pp. 99–145). New York: Wiley. [Online]. https://books.google.co.nz/books?id=ZXewAAAAQBAJ.
Komo, J. (1987). Functions of random variables. In Random signal analysis in engineering systems. Philadelphia: Elsevier, ch. 3, pp. 89–123.
Chapter II classical variational methods. In Rustagi, J. S. (ed.) Variational methods in statistics, ser. Mathematics in Science and Engineering, Elsevier, 1976, vol. 121, pp. 16–45.
Ross, S. (2013). Chapter 2—elements of probability. In S. Ross (Ed.) Simulation (Fifth Edition) (pp. 5–38). Cambridge: Academic Press.
Papadogiannis, A., Alexandropoulos, G., Burr, A., & Grace, D. (2012). Bringing mobile relays for wireless access networks into practice—Learning when to relay. IET Communications, 6(6), 618–627.
Cho, W., Cao, R., & Yang, L. (2008). Optimum resource allocation for amplify-and-forward relay networks with differential modulation. IEEE Transactions on Signal Processing, 56(11), 5680–5691.
Mallick, S., Kaligineedi, P., Rashid, M. M., & Bhargava, V. K. (2011). Radio resource optimization in cooperative cellular wireless networks. In E. Hossain, D. I. Kim, & V. K. Bhargava (Eds.), Cooperative cellular wireless networks (pp. 205–232). Cambridge: Cambridge University Press.
Zaeri-Amirani, M., ShahbazPanahi, S., Mirfakhraie, T., & Ozdemir, K. (2012). Performance tradeoffs in amplify-and-forward bidirectional network beamforming. IEEE Transactions on Signal Processing, 60(8), 4196–4209.
Chen, Y., Zhang, S., Xu, S., & Li, G. (2011). Fundamental trade-offs on green wireless networks. IEEE Communications Magazine, 49(6), 30–37.
Torabi, M., & Haccoun, D. (2011). Capacity of amplify-and-forward selective relaying with adaptive transmission under outdated channel information. IEEE Transactions on Vehicular Technology, 60(5), 2416–2422.
Sun, C., Cen, Y., & Yang, C. (2013). Energy efficient ofdm relay systems. IEEE Transactions on Communications, 61(5), 1797–1809.
Xiong, C., Li, G., Zhang, S., Chen, Y., & Xu, S. (2011). Energy- and spectral-efficiency tradeoff in downlink ofdma networks. IEEE Transactions on Wireless Communications, 10(11), 3874–3886.
Cui, S., Goldsmith, A., & Bahai, A. (2005). Energy-constrained modulation optimization. IEEE Transactions on Wireless Communications, 4(5), 2349–2360.
Miao, G., Himayat, N., & Li, G. (2010). Energy-efficient link adaptation in frequency-selective channels. IEEE Transactions on Communications, 58(2), 545–554.
Li, Y., & Zheng, Z. (2014). Energy-efficient power allocation for two-hop relay networks. Electronics Letters, 50(2), 123–125, iD: 1.
McCune, E. (2010). Common issues and signal characterization. In Practical digital wireless signals (pp. 23–73). Cambridge: Cambridge University Press, cambridge Books Online.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Khalil, M.I., Berber, S.M. & Sowerby, K.W. Bit error rate performance analysis in amplify-and-forward relay networks. Wireless Netw 23, 947–957 (2017). https://doi.org/10.1007/s11276-016-1196-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11276-016-1196-0