A bit error rate（BER） analysis is presented for the symbol-by-symbol decoding shortwave differential frequency hopping（DFH） system over an additive white Gaussian noise（AWGN） channel and a frequency-nonselective slowly Rayleigh fading channel.The noncoherent square-law energy detector is used in the DFH receiver.Numerical and simulation results show that the inherent dependence of adjacent transmitted frequencies provides missed-hop-correction capability for DFH system.For a system with 4 available frequencies and 1 bit per hop

the BER is 10-5 when the signal-to-noise（SNR） is approximately 13.6 dB over AWGN channels

while it is 10-3 when SNR is approximately 33 dB over Rayleigh fading channels.Symbol-by-symbol decoding is a practical decoding algorithm for DFH systems.