To analyze the performance of space-frequency codes

the Chernoff bound was used in the existing literatures

but it was too loose to conclude the diversity order and coding gain simultaneously.Therefore

a new view of the transmission of space-frequency codes was addressed

which transformed the transmission in frequency selective channels into flat fading channels.Based on this transformation

the performance analysis of space-time coding in flat fading channels was used to present an asymptotic analysis for the performance of space-frequency coding.Then

the design criterion of the full diver-sity-achieving space-frequency code was concluded and the coding gain was also optimized.The analysis was more univer-sal and owned an intelligible comprehension.It integrated the existing analysis of the space-frequency codes.A fast detection algorithm for the code was also proposed.It exploited the trellis decoding method and had a reduced complexity compared with the ML detection.The simulation results confirm the validity of the design criterion.