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Fig. 12 shows the behavior of the optimum parameter ν as a function of the SNR. The
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linear dependence at high SNR is not surprising, because, for a fixed noise power σ , an
SNR increase corresponds to an increase of the signal subspace eigenvalues. Consequently,
the correction should scale in a similar manner. On the contrary, when the SNR is low, the
parameter ν has to compensate for the channel estimation errors too, and therefore the
linear dependence is no longer satisfied.
2.4. REGULARIZED DETECTORS FOR DOWNLINK TRANSMISSIONS
As previously anticipated by the CMOE detector, regularization techniques [Hans] deal with
ill-conditioned problems by substituting the matrix R with a matrix characterized by a
smaller eigenvalue spread. Consequently, the variance of the estimation errors decreases, at
the cost of introducing some bias in the detector estimate. The goal of these techniques is to
find a good trade-off between bias and variance, constructing the regularized matrix by
judiciously modifying ˆR . Among the eigenvalue spread reduction techniques, we can
distinguish between full-rank regularization techniques, where the inverse covariance matrix
−1
R is approximated by a matrix with full rank MN , and reduced-rank approaches, where
the inverse covariance matrix is approximated by a matrix with rank r lower than MN .
Most of the techniques proposed in the DS-CDMA literature fall in this second category.
The main reason is that the projection of the received signal onto a lower-dimensional
subspace speeds up the convergence of adaptive algorithms, because the number of
parameters to be updated is smaller with respect to the full-rank case. However, since we are
dealing with short data blocks, the application of adaptive algorithms seems inopportune,
because the limited time may not be enough to guarantee the convergence of the algorithm.
Therefore, when batch approaches are employed, also the full-rank regularization
techniques should be considered, because a higher subspace dimension leads to an increased
number of degrees of freedom, which can potentially be exploited to improve the
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