We describe analog and mixed-signal primitives for implementing adaptive signal-processing algorithms in VLSI based on anti-Hebbian learning. Both on-chip calibration techniques and the adaptive nature of the algorithms allow us to compensate for the effects of device mismatch. We use our primitives to implement a linear filter trained with the Least-Mean Squares (LMS) algorithm and an adaptive decorrelation network that improves the convergence of LMS. When applied to an adaptive Code-Division Multiple- Access (CDMA) despreading application, our system, without the need for power control, achieves more than 100x improvement in the bit-error ratio in the presence of high interference between users. Our 64-tap linear filter uses 0.25mm^2 of die area and dissipates 200?W in a 0.35?m CMOS process.