We present a novel relationship between the distribution of circular and non-circular complex Gaussian random variables. Specifically, we show that the distribution of the squared norm of a non-circular complex Gaussian random variable, usually referred to as squared Hoyt distribution, can be constructed from a conditional exponential distribution. From this fundamental connection we introduce a new approach, the Hoyt transform method, that allows to analyze the performance of a wireless link under Hoyt (Nakagami-q) fading in a very simple way. We illustrate that many performance metrics for Hoyt fading can be calculated by leveraging well-known results for Rayleigh fading and only performing a finite-range integral. We use this technique to obtain novel results for some information and communication-theoretic metrics in Hoyt fading channels.
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