Multiuser Detection in a Dynamic Environment— Part II: Joint User Identification and Parameter Estimation

The problem of jointly estimating the number, the identities, and the data of active users in a time-varying multiuser environment was examined in a companion paper (IEEE Trans. Information Theory, vol. 53, no. 9, September 2007), at whose core was the use of the theory of finite random sets on countable spaces. Here we extend that theory to encompass the more general problem of estimating unknown continuous parameters of the active-user signals. This problem is solved here by applying the theory of random finite sets constructed on hybrid spaces. We do so deriving Bayesian recursions that describe the evolution with time of a posteriori densities of the unknown parameters and data. Unlike in the above cited paper, wherein one could evaluate the exact multiuser set posterior density, here the continuous-parameter Bayesian recursions do not admit closed-form expressions. To circumvent this difficulty, we develop numerical approximations for the receivers that are based on sequential Monte Carlo (SMC) methods (ldquoparticle filteringrdquo). Simulation results, referring to a code-division multiple-access (CDMA) system, are presented to illustrate the theory.