Optimal linear multistage receivers for synchronous CDMA

We analyse the optimal linear multistage receiver based on a weighted matrix polynomial expansion. We prove that the optimal linear multistage receiver which minimises the mean squared error for a particular stage also maximises the signal-to-interference-plus-noise ratio for a particular stage. We present an alternative derivation of the large system signal-to-interference-plus-noise ratio. We observe an important link between the optimal linear multistage receiver and the multistage reduced rank Wiener filter receiver.