Polynomial cancellation coded orthogonal frequency division multiplexing (PCC-OFDM) with overlapping symbol periods is a modulation scheme with properties that make it well suited to high speed data transmission including mobile applications. PCC-OFDM is much less sensitive to frequency offset and Doppler spread than ordinary OFDM. Equalizers to counteract multipath transmission are much simpler for PCC-OFDM than for single carrier systems or for OFDM systems without a cyclic prefix. In this paper PCC-OFDM in combination with code division multiple access (CDMA) for a downlink is considered. It is shown that the proposed system gives lower bit error rate (BER) than OFDM for channels where the frequency offset or Doppler spread is significant, and for channels where the delay spread is more than a fraction of a symbol period. Increasing the delay spread has little effect on the performance of the PCC-OFDM system. The upper limit on the delay spread, which can be tolerated, is set by the span of the equalizer which can be a number of symbol periods long without excessive complexity. It is shown that in this application the two-dimensional equalizer can be simplified to a number of one-dimensional equalizers operating in parallel without significant loss in performance.