Packet error probabilities for FHMA radio networks with radio-threshold test and unequal, power levels

The authors investigate the multiple-access capability of spatially distributed packet radio networks which employ frequency-hopping spread-spectrum signaling, random hopping patterns, and Reed-Solomon (RS) coding with errors-and-erasures decoding via the radio-threshold test. In addition to multiple access interference, thermal noise is present in the channel. Using Laguerre-series expansions for the statistics of the envelope of a sum of randomly phased sinusoids in Gaussian noise, analytic expressions for the probabilities of symbol events are obtained. These expressions can be accurately and rapidly evaluated compared to direct numerical integration. The general setup is applicable to the important case of varying and random amplitudes, which is related to the near-far problem in terrestrial radio networks