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In previous studies on the capacity of orthogonal frequency division multiple access (OFDMA) systems, it is usually assumed that co-channel interference (CCI) from adjacent cells is a Gaussian-distributed random variable. However, very-little work shows that the Gaussian assumption does not hold true in OFDMA systems. In this study, the statistical property of CCI in downlink OFDMA systems is studied, and spectral efficiency of downlink OFDMA system is analysed based on the derived statistical model. First, the probability density function (PDF) of CCI in downlink OFDMA cellular systems is studied with the considerations of path loss, multipath fading and Gaussian-like transmit signals. Moreover, some closed-form expressions of the PDF are obtained for special cases. The derived results show that the PDFs of CCI are with a heavy tail, and significantly deviate from the Gaussian distribution. Then, based on the derived statistical properties of CCI, the downlink spectral efficiency is derived. Numerical and simulation results justify the derived statistical CCI model and spectral efficiency.