Erratum to: Cooperative Communication Protocols in Wireless Networks: Performance Analysis and Optimum Power Allocation

Abstract In this paper, symbol-error-rate (SER) performance analysis and optimum power 1 allocation are provided for uncoded cooperative communications in wireless networks with 2 either decode-and-forward (DF) or amplify-and-forward (AF) cooperation protocol, in which 3 source and relay send information to destination through orthogonal channels. In case of the 4 DF cooperation systems, closed-form SER formulation is provided for uncoded coopera5 tion systems with PSK and QAM signals. Moreover, an SER upper bound as well as an 6 approximation are established to show the asymptotic performance of the DF cooperation 7 systems, where the SER approximation is asymptotically tight at high signal-to-noise ratio 8 (SNR). Based on the asymptotically tight SER approximation, an optimum power allocation 9 is determined for the DF cooperation systems. In case of the AF cooperation systems, we 10 obtain at first a simple closed-form moment generating function (MGF) expression for the 11 harmonic mean to avoid the hypergeometric functions as commonly used in the literature. By 12 taking advantage of the simple MGF expression, we obtain a closed-form SER performance 13 analysis for the AF cooperation systems with PSK and QAM signals. Moreover, an SER 14 approximation is also established which is asymptotically tight at high SNR. Based on the 15 asymptotically tight SER approximation, an optimum power allocation is determined for the 16 AF cooperation systems. In both the DF and AF cooperation systems, it turns out that an 17 equal power strategy is good, but in general not optimum in cooperative communications. 18 The optimum power allocation depends on the channel link quality. An interesting result 19 is that in case that all channel links are available, the optimum power allocation does not 20