Fast transform for multi-carrier wireless communications

The proposed fast transform is originated from the Haar wavelet. The N-point (N=2 power d) fast transform requires no multiplications in case d is even, and N real multiplications with constant in case d is odd, and it uses at least 33 percent less real additions than the Fast Fourier Transform. The proposed fast transform is developed to reduce complexity of Wavelet Packet Multiplexing (WPM). The same fast transform algorithm can be used for both multiplexing and demultiplexing of data streams. Simulations show that multi-carrier wireless communication systems can profit from use of WPM based on the proposed transform, because, in terms of complexity, WPM outperforms the most used now-a-days Orthogonal Frequency Division Multiplexing (OFDM).