Code division multiple access (CDMA) is based on the spread-spectrum technology and is a dominant air interface for 2.5G, 3G, and future wireless networks. For the CDMA downlink, the transmitted CDMA signals from the base station (BS) propagate through a noisy multipath fading communication channel before arriving at the receiver of the user equipment/mobile station (UE/MS). Classical CDMA single-user detection (SUD) algorithms implemented in the UE/MS receiver do not provide the required performance for modern high data-rate applications. In contrast, multi-user detection (MUD) approaches require a lot of a priori information not available to the UE/MS. In this paper, three promising adaptive Riemannian contra-variant (or natural) gradient based user detection approaches, capable of handling the highly dynamic wireless environments, are proposed. The first approach, blind multiuser detection (BMUD), is the process of simultaneously estimating multiple symbol sequences associated with all the users in the downlink of a CDMA communication system using only the received wireless data and without any knowledge of the user spreading codes. This approach is applicable to CDMA systems with relatively short spreading codes but becomes impractical for systems using long spreading codes. We also propose two other adaptive approaches, namely, RAKE-blind source recovery (RAKE-BSR) and RAKE-principal component analysis (RAKE-PCA) that fuse an adaptive stage into a standard RAKE receiver. This adaptation results in robust user detection algorithms with performance exceeding the linear minimum mean squared error (LMMSE) detectors for both Direct Sequence CDMA (DS-CDMA) and wide-band CDMA (WCDMA) systems under conditions of congestion, imprecise channel estimation and unmodeled multiple access interference (MAI).