Stability of CDMA data networks with fixed and adaptive MMSE receivers

The stability of a direct-sequence code-division multiple-access (DS-CDMA) packet data network employing minimum-mean squared-error (MMSE) receivers is investigated. It is observed that, in contrast to prior work, conditions exist under which the MMSE receiver system exhibits bistable behavior. However, for a sufficiently large user population, it can be shown that the stochastic MMSE receiver system has a high probability in any given neighborhood of a single operating point, which can be shown to be a globally stable equilibrium point of an associated deterministic system. In addition, adaptive versions of the MMSE receiver based on least-mean squares and recursive least squares are considered. Again, if the adaptation parameters are properly chosen to ensure a limited amount of excess mean-squared error, the DS-CDMA packet data network with adaptive MMSE receivers is also stable in the sense defined herein.