This paper presents a performance analysis framework for linear detection in fast-fading channels with possibly correlated channel and noise. The framework is both accurate and adaptable, making it well-suited for analyzing a wide range of channel and noise models. As such, it serves as a valuable tool for the design and evaluation of detection algorithms in next-generation wireless communication systems. By characterizing the distribution of the effective noise after zero-forcing filtering, we derive a semi-analytical and asymptotic expression for the symbol error rate under Rayleigh fading and channel-dependent additive circular complex Gaussian noise. The proposed approach demonstrates excellent agreement with integration-based benchmarks as confirmed by numerical simulations thus validating its accuracy. The framework is flexible and can be extended to various channel and noise models, offering a valuable tool for the design and analysis of detection algorithms in next-generation communication systems.