Asymptotic design and analysis of multistage detectors with unequal powers

In this work we provide equations to precisely calculate the asymptotic weighting of multistage detectors satisfying the individually and jointly LMMSE criteria in the projection subspace for scenarios with unequal powers. Additionally, a general expression of the SINR achievable at the filter output as system size grows large is derived. Such an equation can be applied to any multistage detector. We specialize this result to both the individually and jointly LMMSE multistage detector with asymptotic weighting. We show that the individually LMMSE detector outperforms the other detector in the case of unequal received powers while both the detectors are equivalent in the case of equal received powers.