Achievable Rate With 1-Bit Quantization and Oversampling Using Continuous Phase Modulation-Based Sequences

Analog-to-digital conversion with high resolution in amplitude has a relatively high energy consumption in communication systems. A promising alternative to reduce the energy consumption is 1-bit quantization. Considering such a receiver, we design and analyze continuous phase modulation (CPM) schemes, which are favorable because of their bandwidth efficiency and their constant envelope. In this context, oversampling with respect to the symbol duration is promising because CPM signals are not strictly bandlimited and because it reduces the loss in achievable rate caused by the quantization. The additional degrees of freedom brought by oversampling can be exploited by higher order modulation schemes. A lower bound on the achievable rate is computed based on an auxiliary channel law. In a further step, we optimize the input distribution with an optimization strategy based on a Markov source model. For a specific example, we give upper bounds on the achievable rate and present a state-machine representation for sequences which are reconstructible at the receiver. Finally, the proposed approach has the advantage of a constant envelope enabling an energy efficient transmitter design while achieving only a slightly lower 90% power containment bandwidth efficiency than existing methods with 1-bit quantization and oversampling.