Modulation and Demodulation Coding Scheme of Signals with Peak of Power Constraint

From the perspective of information theory, we investigate a model for modulation and demodulation coding scheme of an oversampled signal of given bandwidth and a limited peak of power with a finite code length under an additive white Gaussian noise channel. We extend Gallager's Theorem of finite length code and connect the problem with the volume of a smooth manifold in a complex space. Two modifications of the orthogonal frequency-division multiplexing systems are proposed based on transforms mapping the ball to the manifolds. Analysis shows relations between the proposed methods and existing PAPR reduction techniques. The result shows that the PAPR reduction ability of a proposed cascade of a clipping and a companding transform is supported by the information theory. Features of the proposed methods, such as spectral spreading, computational complexity, and code rate loss, are investigated and simulation results show that one of the proposed method is one of the best state-of-art peak-to-average power ratio reduction methods.