The present invention is directed to a method for canceling the Doppler shift, multi-path propagation, delays, and long time selective
fading influences of phase and / or amplitude modulated signals carried by RF sub-carriers, without requiring
pilot signals. The number of m=2n, over which individual datum is transmitted in each
communication channel, is determined. Pairs of Walsh functions are selected from a Walsh-
Hadamard matrix such that each function is not selected more than once. Each
signal is partitioned to its I factor and
Q factor and coding each I and Q factors of the signals by the pair functions. A corresponding phase and amplitude is allocated for each sub-carrier wherein the amplitude and phase values are determined by the data that is transmitted, the digital modulation scheme or inverse
spectral transformation, and signs of both corresponding elements taken from the pair Walsh functions. Data is transmitted over the sub-carriers and received and the corresponding phases and amplitudes of all the received signals are obtained using
spectral transformation. The received signals are decoded by changing signs of I and Q factors of the received signals in accordance with corresponding elements from the pair functions, used to decode said signals. The I and Q factors of received signals are summed separately, after changing signs of said I and Q factors of received signals, and each of the summations of I and Q factors is divided by m. The
signal is reconstructed using said divided I and Q factors, by calculating its phase.