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In this study, the effects of timing and frequency offsets on bit-error rate (BER) performance of fast frequency-hopped M-ary frequency-shift keying communication systems over Rician-fading channels with both multitone jamming (MTJ) and partial-band noise jamming (PBNJ) are investigated. Analytical BER expressions are derived for both linear-combining and product-combining receivers. Numerical results show that under both MTJ and PBNJ conditions, the BER performance falls between the two extreme cases, in which either MTJ or PBNJ presents. It is found that the BER performance is severely degraded as the timing or frequency offset increases. The product-combining receiver is found to be more sensitive to the timing and frequency offsets than the linear-combining receiver. It is also observed that for the linear-combining receiver, the optimum diversity order increases as the timing and frequency offset increases over both Rician-fading and Rayleigh-fading channels; however, the reverse is true for the product-combining receiver.