Maximizing diversity in coded slow frequency-hopped communications

This paper examines the performance of radio systems employing error-control coding in conjunction with frequency-hopping to combat the effects of multipath fading. We show for Rayleigh fading that the achievable diversity is bounded by a maximum value which depends on the number of available frequencies, the code rate and the size of the modulation. Two keys results are that the maximum diversity can be reached with fairly simple convolutional codes, and that constellation expansion can increase diversity. With the aid of computer simulations we show that added complexity yields non-negligible coding gain in the frame error-rate performance but may have less of an effect on the bit error-rate performance.