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Filter-based fading channel simulators universally use White Gaussian Noise (WGN) to generate complex tap coefficients. In this work, we will show that replacing WGN source by Uniform Random Number Generator (URNG) results in improved simulation speed in case of software simulator; and reduced area/power in case of hardware simulator. We will verify, both analytically and through extensive simulations, that use of URNG does not cause any degradation in important simulator performance parameters like statistical properties, spectral shape, level crossing rate and bit error rate. To validate our analysis, we have designed fading channel simulators both in software and hardware. We will show that use of URNG causes 6 percent improvement in simulation time in case of software simulator. Similarly, we will demonstrate that for a hardware simulator, we obtain an improvement of 30 and 40 percent in area and power consumption respectively.