The role of frequency hopping in today´s digital communications

We investigate the capacity of an OOK FH CDMA channel. We assume random FH codes and that the i-th receiver is only interested in the message transmitted by the i-th transmitter. The degradation of the AWGN and non-selective Rayleigh fading environments on the FH system are also investigated. We then give an algebraic construction of a new family of FH codes. The construction is based on the property of cyclic groups in finite fields; it is shown that for each field GF(p^m) there exists a large number of codes of length p^m. The codes are also shown to possess the best possible two-dimensional auto- and cross-correlation properties