Methods, apparatus, and systems for alternating quadratures differential binary phase shift keying (AQDBPSK) modulation and demodulation radically increase overall energy efficiency of a communication system due to the combined effect of efficient utilization of transmitter power, high noise immunity of modulation and demodulation, fast synchronization, and simple implementation. Efficient utilization of transmitter power is achieved because radical reduction of side lobe regeneration provided by AQDBPSK allows operation of all amplifiers of the transmitter analog signal path, including power amplifiers, in energy efficient nonlinear mode (for example, they can operate as class C amplifiers) without causing interchannel interference. AQDBPSK radically reduces side lobe regeneration by limiting phase transitions between adjacent in time modulator output symbols to ±90° and smoothly executing the transitions. High noise immunity of AQDBPSK is achieved due to transmitting modulator input data by binary 0° and 180° phase differences between adjacent in time same parity modulator output symbols and optimal noncoherent demodulation of the received same parity symbols. Use of noncoherent demodulation reduces synchronization time, and fast synchronization substantially lowers energy consumption during burst transmissions. Proposed methods of modulation, noncoherent demodulation, and synchronization can easily be realized using the simplest digital signal processing operations and the simplest digital circuits. These methods can also be implemented in a universal reconfigurable digital modem. This enables significant reduction of power consumption in real world applications. In addition, entirely digital realization of the proposed methods, apparatus, and systems make them resistant to all destabilizing factors and simplifies their practical implementation; and fast and reliable synchronization increases time allocated for data transmission when transmission time is limited.