MMSE multiuser detectors
14.1 MINIMUM MEAN-SQUARE ERROR (MMSE) LINEAR MULTIUSER DETECTION
If the amplitude of the user’s k signal in equation (13.7) is Ak , then the vector of matched ﬁlter outputs y in equation (13.10) can be represented as y = RAb + n where A is a diagonal matrix with elements Ak A = diag||Ak || (14.2) (14.1)
If the multiuser detector transfer function is denoted as M, then the minimum mean-square error (MMSE) detector is deﬁned as
M ∈ R K×K
E ||b − My||2
One can show that the MMSE linear detector outputs the following decisions [1–3]: ˆ bk = sgn 1...