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The accurate simulation of wireless channels is important since it permits the realistic and repeatable performance measurement of wireless systems. A new technique is proposed for simulating Rayleigh fading channels with isotropic or non-isotropic scattering and with arbitrary temporal correlation. Fading samples are generated by passing Gaussian samples through a spectrum shaping filter. A new iterative algorithm is then presented for designing stable complex infinite impulse response (IIR) filters with quantised coefficients. The algorithm utilises a least-squares cost function augmented with a barrier function to ensure filter stability and to reduce quantisation noise. The performance of the proposed filter design algorithm is verified with 18-bit fixed-point simulations of different fading channel scenarios including isotropic and non-isotropic scattering and the IEEE 802.11n model F fading spectrum.