— We examine both differentially coherent and non-coherent code acquisition schemes designed for the multiple transmit/receive antenna assisted Multi-Carrier (MC)-DS-CDMA downlink, when communicating over uncorrelated Rayleigh channels. It is demonstrated that in contrast to our expectations, when the number of transmit antennas and/or that of the subcarriers is increased in both the differentially coherent and the non-coherent code acquisition scenarios, the achievable Mean Acquisition Time (MAT) usually deteriorates over the entire Signal-to-Interference plus Noise Ratio (SINR) per chip (Ec/I0) range considered.