Orthogonal sequences can be developed and used for use training and synchronizing in CDMA and TDMA systems. In particular, once a sequence is developed that has the length of the product of the channel length and the number of transmit antennas, the sequence is offset by a different amount for each transmit antenna. For example, each sequence could be offset by a multiple of the channel length for each transmit antenna, where the multiple ranges from 0 to N-1, where N is the number of transmit antennas. Furthermore, by not using exactly the same amount of offset shifting for each transmit antenna, e.g., not having each signal offset by the channel length, but keeping the overall total shifting the same, e.g., the average of each shift is the channel length, it is possible to determine at a receiver from which transmit antenna a particular signal originated.