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This paper addresses a novel Walsh-Hadamard (WH)-spread multicarrier code division multiple access (MC-CDMA) system which employs carrier interferometry (CI) codes to achieve improved bit error rate (BER) performance. In frequency selective channel, phase characteristic of CI codes ensures better estimates of received WH-spread CI/MC-CDMA signal. In this paper an iterative receiver structure is used for decoding WH-spread CI/MC-CDMA signal. Estimation of multiple access interference (MAI) becomes more reliable with time and frequency diversities of CI/MC-CDMA signal with spreading gain diversity of WH code over multipath channel. It is shown by simulation that WH-spread CI/MC-CDMA provides 2 dB gain at a BER of 1e-03 after 6th iteration with soft decision subcarrier parallel interference cancellation (SDSub-PIC) at 25% overload compared to CI/MC-CDMA.