A method for transmission by a transmitting node in a communication network using a plurality of non-orthogonal carriers, including obtaining, by a processor in the transmitting node, an information element data set comprised of a first number of elements, applying, by the processor, a transform matrix to the information element data set to obtain an output samples data set comprised of a second number of elements, the transform matrix being based on a non-linear function applied to a non-orthogonal frequency division matrix comprised of a plurality of columns wherein each column is associated one of the plurality of non-orthogonal carriers, and transmitting the output samples data set from a transmitter in the transmitting node.