An Alternative Method to Compute the Bit Error Probability of Modulation Schemes Subject to Nakagami- Fading
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Research Article An Alternative Method to Compute the Bit Error Probability of Modulation Schemes Subject to Nakagami-m Fading Wamberto J. L. Queiroz,1 Waslon T. A. Lopes,1 Francisco Madeiro,2 and Marcelo S. Alencar1 1 Departamento 2 Escola
de Engenharia El´etrica, Universidade Federal de Campina Grande, 58.429-900, Campina Grande, PB, Brazil Polit´ecnica de Pernambuco, Universidade de Pernambuco, 50.750-470, Recife, PE, Brazil
Correspondence should be addressed to Marcelo S. Alencar, [email protected] Received 4 March 2010; Revised 23 June 2010; Accepted 24 September 2010 Academic Editor: Athanasios Rontogiannis Copyright © 2010 Wamberto J. L. Queiroz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This paper presents an alternative method for determining exact expressions for the bit error probability (BEP) of modulation schemes subject to Nakagami-m fading. In this method, the Nakagami-m fading channel is seen as an additive noise channel whose noise is modeled as the ratio between Gaussian and Nakagami-m random variables. The method consists of using the cumulative density function of the resulting noise to obtain closed-form expressions for the BEP of modulation schemes subject to Nakagamim fading. In particular, the proposed method is used to obtain closed-form expressions for the BEP of M-ary quadrature amplitude modulation (M-QAM), M-ary pulse amplitude modulation (M-PAM), and rectangular quadrature amplitude modulation (I × JQAM) under Nakagami-m fading. The main contribution of this paper is to show that this alternative method can be used to reduce the computational complexity for detecting signals in the presence of fading.
1. Introduction The growing need for improvement in capacity and performance of wireless communication systems has demanded high data transmission rates, in a scenario suitable to accommodate the ever-increasing multimedia traffic and new applications. In this context, spectrally efficient modulation schemes have attracted the attention of companies and academia. Quadrature amplitude modulation (QAM) is an attractive modulation scheme to achieve high transmission rates, without increasing the bandwidth of the wireless communication system. Traditionally, the computation of the BEP of M-QAM has been carried out by calculating the symbol error probability or simply estimating it using lower or upper bounds [1]. Good approximations for the BEP of M-QAM subject to additive white Gaussian noise (AWGN) have been presented in [2, 3] based on signal-space concepts and recursive algorithms. It is worth mentioning that although some approximate expressions give accurate error rates for high signal-to-noise ratio (SNR), the evaluation of the error
rates using those expressions tends to deviate from their corresponding exact values when the SNR is low. In spite of the attention devoted to the study of the BEP of QAM for
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