This paper introduces a multi-dimensional quadrature phase shift keying (MD-QPSK) structure for a direct sequence spread spectrum (DSSS) modem that employs constant envelope linear root-of-unity (CE-LRU) filtered generalized chirp-like (GCL) complex spreading sequences (CSS's) and codeposition-modulation (CPM). The resulting MD-QPSK CPM modem exhibits a spectrally efficient minimum (Nyquist) bandwidth output power spectral density (PSD). In addition, the transmitter output signal power is virtually constant. It is shown that the MD-QPSK CPM modem's data transmission rate is larger than other proposed WCDMA systems that use these unique CSS's, with a negligible difference in spectral occupancy.