A method for receiving an Orthogonal Frequency Division Multiplexing (OFDM) signal transmitted by a user device in a wireless network comprises determining which subcarrier frequencies are allocated to the user device; converting the OFDM signal to a frequency-domain values corresponding to the subcarrier frequencies; and decoding the frequency-domain values to recover data symbols encoded by the user device on the subcarrier frequencies. The decoding employs codes that are inverse to, complex-conjugate of, or complementary to a set of complex-valued codes employed by the user device to shape the OFDM signal into a superposition of cyclic-shifted pulse waveforms, wherein each of the pulse waveforms has one of the data symbols modulated thereon.