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The availability of an accurate and systematic channel simulation technique is critical for the verification of the performance of digital radio transceivers designed for use on wireless channels. Despite the abundant results on channel simulation techniques available in the literature, an accurate technique for simulating Nakagami- m fading signals that have nonuniform phase distributions and any prespecified temporal autocorrelation function is not yet available. Such a technique is reported for the first time in this paper. We develop new cumulative distribution function (cdf) mapping methods to generate complex Nakagami sequences from complex Gaussian sequences, based on the independent transformation of their real and imaginary parts. Additionally, we analyze the relationships between the autocorrelation functions of Rayleigh and Nakagami fading signals to determine the autocorrelation function of Rayleigh input that is required to produce a specified autocorrelation function for the Nakagami output. Then, we implement the mapping algorithm to transform Rayleigh sequences with the so-determined autocorrelation functions into Nakagami sequences with the desired prespecified autocorrelation functions. Simulation results verify that our approaches can lead to the accurate simulation of Nakagami fading signals with prespecified autocorrelation functions and nonuniform phase distributions.