Widely Linear Versus Linear Blind Multiuser Detection With Subspace-Based Channel Estimation: Finite Sample-Size Effects

In a recent paper [A. S. Cacciapuoti et al., ldquoFinite-Sample Performance Analysis of Widely Linear Multiuser Receivers in DS-CDMA Systems, IEEE Transactions on Signal Processing, vol. 56, no. 4, pp. 1572-1588, Apr. 2008], we presented the finite-sample theoretical performance comparison between linear (L) and widely linear (WL) minimum output-energy (MOE) receivers for direct-sequence code-division multiple-access (DS-CDMA) systems, worked out under the assumption that the channel impulse response of the desired user is exactly known. The main scope of this paper is to extend such an analysis, taking into account not only autocorrelation matrix (ACM) estimation effects, but also the accuracy of subspace-based blind channel estimation (CE). We aim to answer the two following questions: Which of the two estimation processes (ACM or CE) is the main source of degradation when implementing the receivers on the basis of a finite sample-size? Compared with the L-MOE one, is the finite-sample WL-MOE receiver with blind CE capable of achieving the performance gains predicted by the theory? To this goal, simple and easily interpretable formulas are developed for the signal-to-interference-plus-noise ratio (SINR) at the output of the L- and WL-MOE receivers with blind CE, when they are implemented using either the sample ACM or its eigendecomposition. In addition, the derived formulas, which are validated by simulations, allow one to recognize and discuss interesting tradeoffs between the main parameters of the DS-CDMA system.