Blind Multiuser Detection: Subspace Methods
Blind Multiuser Detection: Subspace Methods
In this section we discuss another approach to blind multiuser
detection, which was first developed in [549] and is based on estimating the
signal subspace spanned by the user signature waveforms. This approach leads to
blind implementation of both the linear decorrelating detector and the linear
MMSE detector. It also offers a number of advantages over the direct methods
discussed in Section 2.3.
Assume that the spreading waveforms  of K users are linearly independent. Note that Cr of
(2.27) is the
sum of the rank-K matrix S|A|2SH and
the identity matrix s2 IN.
This matrix then has K eigenvalues that are
strictly larger than s2 and (N -
K) eigenvalues that equal s2. Its
eigendecomposition can be written as
Equation 2.72
where Ls =
diag(l1, ..., lK) contains the
largest K eigenvalues of Cr,
Us = [u1, ..., uK]
contains the K orthogonal eigenvectors
corresponding to the largest K eigenvalues in
Ls; and Un =
[uK +
1, ..., uN] contains the (N
- K) orthogonal eigenvectors corresponding to the
smallest eigenvalue s2 of Cr. It
is easy to see that range(S) =
range(Us). The column space of Us is
called the signal subspace and its orthogonal
complement, the noise subspace, is spanned by the
columns of Un. We next derive expressions for the linear
decorrelating detector and the linear MMSE detector in terms of the signal
subspace parameters Us, Ls, and
s2.
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