We develop a parametric receiver for packet data systems based on the generalized Rake (G-Rake) formulation. The focus here is on multi-antenna receivers to exploit both the spatial and temporal dimensions in suppressing interference. We extend previous G-Rake formulations to multi-antenna reception and propose an adaptive, parametric form to handle the (potentially) rapid interference variation in packet data systems. This parametric form estimates an impairment covariance matrix using a model, and calculates the model parameters based solely on short-term received data. The parameter calculation involves least-squares fitting of a short-term estimated impairment covariance matrix to the model. Simulation of a two-antenna G-Rake receiver shows that significant gains in performance are possible in both the uplink and downlink