1. A method for processing a received spread spectrum signal containing two or more simultaneously transmitted symbols of interest with known spreading codes and one or more interfering signals with known spreading codes, said method comprising: for a given despread symbol interval, forming a sample vector from samples of the received spread spectrum signal, wherein said samples span the despread symbol interval; using one or more matrix multiplication operations, performing a linear transformation of the sample vector to an interference-reduced decision statistic vector for the given symbol time, based on covariance statistics for the received signal, wherein said linear transformation depends on the known spreading codes and wherein the interference-reduced decision statistic vector comprises a single complex value for at least each of the symbols of interest; and estimating a symbol value for at least one of the symbols of interest from the interference-reduced decision statistic vector, for the given symbol time, using a non-linear detection process that accounts for code-specific leakage between the known spreading codes for the symbols of interest.