In this paper, we investigate the application of M-ary orthogonal modulation for multicarrier spread spectrum (MC-SS) uplink transmission over a Rayleigh fading indoor channel. Different coherent detection strategies with perfectly known channel coefficients are analyzed. Furthermore, we present a decision-directed estimation receiver to apply channel phase estimation. With decision-directed estimation no redundancy like training data is required to be transmitted. Simulation results show no performance loss for low EbINo and only a moderate degradation for high Eb/No in comparison to ideal phase equalization. Moreover, the results are always contrasted with BPSK performance. Applying M-ary orthogonal modulation reveals to outperfom BPSK with respect to bit error rate and spectral efficiency, even if ideal equalization is considered for BPSK and decision-directed estimation for M-ary orthogonal modulation. The results are generally valid, whereas in this paper, they are based on the European HIPERLAN/2-~tandardization.