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The authors propose a new multi-tone (MT) code division multiple access (CDMA) design which has a superior bit error rate (BER) performance than conventional MT CDMA in the presence of frequency offset. The design involves multiplexing of Walsh codes onto the sub-carriers in conjunction with double differential modulation. To exploit the full potential of the design a partial correlation receiver has been proposed. Depending on the signal-to-noise ratio (SNR) and frequency offset it is possible to tune this receiver for the best possible performance. The simulated BER performance of the proposed system has been found to be better than MT CDMA for small as well as large frequency offsets for both single and multi-user systems in additive white Gaussian noise (AWGN) and Rayleigh fading channels.