Low-complexity soft-input soft-output demodulation of orthogonal modulation

This letter is concerned with the soft-input soft-output (SISO) demodulation of M-ary (M = 2^r) orthogonal modulation. We prove that the SISO orthogonal demodulation (SISO-OD) is equivalent to the SISO decoding of orthogonal Hadamard codes, for which we deduct a posteriori probability fast Hadamard transform (APP-FHT) algorithm. With FHT and the proposed APP-FHT, the demodulation complexity can be reduced from O(r2^r) to O(2^r) exponential/logarithm operations and O(r²2^r) to O(2^r) additions, respectively.