Channel State Tracking for Large-Scale Distributed MIMO Communication Systems

This paper considers the problem of estimating and tracking channels in a distributed transmission system with N_t transmit nodes and N_r receive nodes. Since each node in the distributed transmission system has an independent local oscillator, the effective channel between each transmit node and each receive node has time-varying phase and frequency offsets which must be tracked and predicted to facilitate coherent transmission. A linear time-invariant state-space model is developed and is shown to be observable but nonstabilizable. To quantify the steady-state performance of a Kalman filter channel tracker, two methods are developed to efficiently compute the steady-state prediction covariance. The first method requires the solution of a 2(N_t + N_r-1)-dimensional discrete-time algebraic Riccati equation, but allows for nonhomogenous oscillator parameters. The second method requires the solution of four two-dimensional discrete-time algebraic Riccati equations but requires homogenous oscillator parameters for all nodes in the system. An asymptotic analysis is also presented for the homogenous oscillator case for systems with a large number of transmit and receive nodes with closed-form results for all of the elements in the asymptotic prediction covariance as a function of the carrier frequency, oscillator parameters, and channel measurement period. Numeric results confirm the analysis and demonstrate the effect of the oscillator parameters on the ability of the distributed transmission system to achieve coherent transmission.