A CDMA multi-code joint demodulation solution in which impairment suppression and channel matching operations are performed prior to despreading. Embodiments include a linear front end that performs chip-level suppression of signal components that are not included in a subsequent joint demodulation process. The pre-processing stage also carries out metric preparation and provides a vector decision statistic that is processed by a joint demodulation stage to extract per-code soft values for the symbols of interest in the received signal. Both code-specific and code-averaged versions of the linear processing are disclosed, as are several front-end configurations with equivalent performance, but different complexity trade-offs. These new approaches use a block formulation, requiring a set of input chip samples as an input, and perform all operations as matrix-vector multiplications, which is an approach amenable to efficient DSP or hardware implementation.