A fast algorithm based on a butterfly structure is presented that demultiplexes the symbols of a particular type of MC-MA (multi-carrier multiple-access) modulation previously proposed for indoor radio communications. A special transform is used to packetize the different symbols on the down-link such that the code sequences associated with the different symbols are transmitted synchronously at the base station. The input to the FFT bins is defined as a symbol-dependent combination of Walsh-Hadamard codes. We derive a fast architecture that can combine the common redundancy found in the Walsh-Hadamard and the inverse Fourier transform. In the direct implementation, the receiver would compute the IFFT (as in OFDM) before the Walsh-Hadamard transform. The proposed algorithm evaluates both transforms in a single step. A general expression for the butterfly weights is derived and the savings in computational complexity in terms of the frame length is evaluated.

Peer Reviewed