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This paper provides a theoretical performance evaluation of the downlink of asynchronous orthogonal frequency division multiplexing (OFDM) and filter bank based multicarrier (FBMC) cellular radio communication systems. An accurate derivation, for the interference caused by the timing synchronization errors in the neighboring cells, is developed. The multipath effects on the interfering and desired signal are also considered. Based on computing the moment generating functions of the interference power, exact expressions are derived for average error rates of OFDM and FBMC systems considering the frequency correlation fading in the case of block subcarrier assignment scheme.