A multi-mode transmission system supporting OFDM and single-carrier signals is configured to perform interpolation and decimation such that the ratio of the interpolation factor to the decimation factor equals the ratio between the OFDM sampling rate and the single-carrier chip rate. A constant-envelope modulator comprises a π/4 fixed rotator, a π/2 continuous rotator, and in-phase and quadrature-phase analog Bessel filters. Frame formats and signaling protocols are provided for signal acquisition, synchronization, and tracking between wireless devices that employ different antenna configurations. Spreading gains are selected to compensate for different antenna gains such that the total gain (antenna gain plus spreading gain) is substantially equal for transmissions employing different beam patterns.