This work analyzes combined effects of major synchronization errors, including the symbol time offset (STO), carrier frequency offset (CFO) and sampling clock frequency offset (SCFO) of orthogonal frequency-division multiplexing (OFDM) systems. Such errors degrade the performance of an OFDM receiver by introducing inter-carrier interference (ICI) and inter-symbol interference (ISI) into the systems. Traditionally, designing an OFDM receiver needs plenty of Monte Carlo simulations because the synchronization errors are simultaneously inevitable in practical environments. Therefore, we formulate the theoretical signal-to-interference-and-noise ratio (SINR) to assist the design of OFDM receivers. By knowing the required SINR of specific application, all combinations of allowable errors can be derived. Then, cost-effective algorithms could be easily designed.