Robust Blind Multiuser Detection in Multipath Channels

Robust Blind Multiuser Detection in Multipath Channels

Suppose that user 1 is the user of interest. Then we can rewrite (4.150) as

Equation 4.153

Equation 4.154

where denotes the (K_I + 1)th column of H (corresponding to the bit b₁[i]), H₀ denotes the submatrix of H obtained by striking out the (K_I+1)th column, and b₀[i] denotes the subvector of b[i] obtained by striking out the (K_I+1)th element. As before, the basic idea behind robust blind multiuser detection is first to obtain a robust estimate of z[i] using the identified signal subspace U_s. On the other hand, as discussed in Section 2.7.3, given the spreading waveform s₁ of the desired user, by exploiting the orthogonality between the signal subspace and noise subspace, the composite signature waveform of this user can be estimated (up to a complex scaling factor). Once an estimate of is available, the robust estimate of z[i] can then be translated into a robust estimate of b₁[i] (upto a complex scaling factor) by Proposition 4.2, as

Equation 4.155

Finally, differential detection is performed according to

Equation 4.156

The algorithm is summarized as follows.

Algorithm 4.6: [Robust blind multiuser detector—multipath CDMA]

• Compute the sample autocorrelation matrix of the received augmented signal r[i] and its eigendecomposition.

• Compute the robust estimate of z[i] following a procedure similar to (4.128)-(4.132).

• Compute an blind estimate of according to (2.202)-(2.203).

• Compute the output of the robust blind detector according to (4.155).

• Perform differential detection according to (4.156).