This paper deals with the design of receivers for uplink quasi-synchronous MC-DS-CDMA systems. Our purpose is twofold. Firstly, we aim at designing a reduced-rank MMSE receiver based on a matrix polynomial expansion of the inverse of the received signal autocorrelation matrix. This receiver makes it possible to get a compromise between computational cost and performances in term of Bit Error Rate (BER). Secondly, we propose to derive its asymptotic, i.e. when the spreading sequence length N and the number of active users K tend to infinity with a ratio fixed, version by using random matrix theory. The resulting asymptotic reduced-rank MMSE receiver has a computational cost per symbol which is reduced. We also investigate the relevance of both receivers in various simulation protocols.