On blind multiuser forward link channel estimation by the subspace method: identifiability results

Blind channel estimation for periodic sequence DS-CDMA systems can be cast into the framework of “structured” blind estimation of multi-input/multi-output (MIMO) FIR systems, where the structure is imposed by the userʹs signatures. A possible approach to tackle this problem consists in looking for a structured solution to one of the blind MIMO-FIR systems, proposed previously. This is the approach undertaken by several authors. However, most of them did not address identifiability issues. In this paper, we first recall and reformulate some general MIMO FIR identification results of Meraim, Loubaton and Moulines (see IEEE Trans. Inform. Theory, vol.43, p.499-511, 1997), and point out some difficulties posed by the subspace approach. Next, we use the above material in order to analyze the behavior of the subspace forward link channel estimate of CDMA systems. We derive new results showing that the subspace method is not robust to an over-determination of the channel order greater than the spreading factor. If however the over-determination error is less than the spreading factor, we show that the subspace estimate is consistent if the codes of the users are properly designed