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Several time-division multiple-access (TDMA) cooperative wireless relay protocols and their performances have recently been developed by Nabar, Bolcskei, and Kneubuhler. Their work, however, is limited to an upper bound-based performance analysis for Rayleigh fading. We thus provide an exact analysis of two of their protocols in single-relay and multiple-relay networks over independent identically distributed (i.i.d.) Nakagami-m fading channels. Our analysis is focused on an Alamouti-coded system with two-stage protocols, fixed-gain amplify-and-forward (AF) relays, and maximal ratio combiner (MRC) reception. The performance metrics are the capacity, the diversity order, and the symbol error rate (SER). The closed-form moment-generating function (MGF) of the total end-to-end signal-to-noise ratio (SNR) is derived. The MGF is then used to derive the diversity order and the SER of M-ary phase-shift keying (M-PSK) and M-ary quadrature amplitude modulation (M -QAM). It is found that the end-to-end SNR for relaying with orthogonal channels is higher than that of nonorthogonal relay channels. The diversity order of a multiple-relay network (n relays) in a Nakagami-m environment is shown to be (n + 1)m. The closed-form SER expressions for relay-destination links with high SNRs and static relay-destination links are derived. Numerical and simulation results are provided to verify the analysis.