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In this paper, we present a unified asymptotic symbol error rate (SER) analysis of linearly modulated signals impaired by fading and (possibly) non-Gaussian noise, which in our definition also includes interference. The derived asymptotic closed-form results are valid for a large class of fading and noise processes. Our analysis also encompasses diversity reception with equal gain and selection combining and is extended to binary orthogonal modulation. We show that for high signal-to-noise ratios (SNRs) the SER of linearly modulated signals depends on the Mellin transform of the probability density function (pdf) of the noise. Since the Mellin transform can be readily obtained for all commonly encountered noise pdfs, the provided SER expressions are easy and fast to evaluate. Furthermore, we show that the diversity gain only depends on the fading statistic and the number of diversity branches, whereas the combining gain depends on the modulation format, the type of fading, the number of diversity branches, and the type of noise. An exception are systems with a diversity gain of one, since their combining gain and asymptotic SER are independent of the type of noise. However, in general, in a log-log scale for high SNR the SER curves for different types of noise are parallel but not identical and their relative shift depends on the Mellin transforms of the noise pdfs.