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It is well known that a frequency-nonselective multipath fading channel can be modeled by a sum of complex sinusoids, also called sum-of-cisoids (SOC). By using the SOC, we can efficiently model the scattered component of the received signal in non-isotropic scattering environments. Such SOC-based multipath channel models provide the flexibility of having correlated in-phase and quadrature phase components of the received signal. This paper presents the derivation and analysis of the statistical properties of the capacity of multipath fading channels under LOS conditions. As an appropriate stochastic model for the multipath fading channel, we have adopted the SOC model. We have derived the exact analytical expressions for the probability density function (PDF), cumulative distribution function (CDF), level-crossing rate (LCR), and average duration of fades (ADF) of the channel capacity. The statistical behavior of the channel capacity is studied for different values of the number of multipaths (cisoids) in the SOC model and the results are compared with the reference model which can be obtained by using an infinite number of cisoids. It is shown that the SOC model with ten cisoids produces results very close to the reference model. The validity of all the theoretical expressions is tested with the help of simulations.