An apparatus is disclosed for a cellular mobile communication system utilizing a spread spectrum. A plurality of fixed base stations is connected with a central processor so that calls originating in any cell can terminate in any other cell. The available frequency spectrum is divided such that one-half is used for mobile-to-base station transmission and the other one-half is used for base station-to-mobile unit transmission. A power control/mobile locator system and method is utilized in all mobile units to compensate for changes in signal level and to maintain the average received signal level at the base station constant regardless of the location of the mobile unit within the cell. In addition, each mobile unit has a unique set of time-frequency coded waveforms that are used for both transmission and reception. The waveforms have large time-bandwidth products so that interfering signals are well suppressed, and which provide a large set of signals so that each user can be assigned a unique set of waveforms. Message modulation is accomplished by digitizing the speech and encoding the resulting binary sequences into the set of waveforms available to the user, while detection is accomplished by a demodulation system and method in which the phases of each received waveform are compared with those of the preceding waveform.