A method for constructing architectures for multiple input transmit and multiple output receive (MIMO) systems with generalized orthogonal space-time codes (C0) and generalizations (H0) of the transmission matrix (H) that enable the MIMO equation to be written Y=H0∘C0∘X+No which factors out the input signal symbol vector X and allows a direct maximum-likelihood calculation of the estimate {circumflex over (X)} of X, and where Y is the received symbol vector and No is the received noise vector. The architectures spread the users uniformly over the transmission paths to provide improved bit error rate performance and are developed to support code division multiple access (CDMA) and variations including multi-carrier CDMA (MC-CDMA) for equalization, orthogonal frequency division multiple access (OFDMA), and orthogonal Wavelet division multiple access (OWDMA) using waveforms that include multi-resolution Wavelets and with Walsh, Hybrid Walsh, generalized Hybrid Walsh orthogonal and quasi-orthogonal codes for CDMA and MC-CDMA and variations.