A communication device's processor generates an OFDMA packet that includes different information for different recipient devices. The processor transmits, via a communication interface, different portions of the OFDMA packet via different channels. Initially, the processor transmits a first at least one field of the OFDMA packet intended for a first recipient device via the first channel. Then, the processor transmits a second at least one field of the OFDMA packet intended for the first recipient device via the first channel while simultaneously transmitting at least one other field of the OFDMA packet intended for a second recipient device via a second channel. This staggered transmission of different portions of the OFDMA packet via different channels allows a recipient device to classify different portions of the OFDMA packet and to determine which portions are intended for that recipient device.