Noise analysis of QAM signal transmission in the AWGN channel using Haar transform

We propose a new structure for a quadrature amplitude modulated transmission using the Haar transform to reduce the noise in the channel. The corresponding points of the symbols in a rectangular signal constellation are Haar-transformed and sent to the channel, and the received signals are inverse Haar transformed to retrieve the original signals. By varying the gain of the Haar transform, we can receive the noise-reduced signals from the channel which is assumed to corrupt the signal by an additive white Gaussian noise (AWGN). We analyze the probability of bit error and simulate the model to show the validity.