Bounds on signature coding for fast frequency hopping with asynchronous access

Signature coding for fast frequency hopped channel is studied, where the bandwidth is partitioned into frequency subbands. A frequency hopping pattern is assigned to each user that specifies the sequence of frequency subbands in which the user can transmit a sinus waveform during a time slot. Partial activity is considered where only a small fraction of the potential users may be active simultaneously. We prove that in frame asynchronous case the upper bound on the minimum code length via random coding is asymptotically the same as in the case of synchronous access.