Optimal linear multistage receivers and the recursive large system SIR

In this paper, we analyse the output signal to interference-plus-noise ratio (SIR) of the optimal linear multistage receiver based on a weighted matrix polynomial expansion. By "optimal" we mean the linear multistage receiver which minimises the mean squared error between the data symbol and the data estimate for user k with respect to the polynomial coefficients at stage m. For an overview of linear multistage receivers and large system analysis see [1-4] and references therein. Our main contribution is the direct derivation of the recursive large system SIR of the optimal linear multistage receiver.