Asymptotic oscillator tracking performance analysis for distributed massive MIMO 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 much be tracked and predicted to facilitate coherent transmission. This paper presents a unified state-space model in which a single node aggregates all of the observations and tracks all of the channel states in the system. To quantify the performance of this tracking system, the steady-state prediction covariance is analyzed. Since the dimension of the prediction covariance matrix grows proportionally to the product N_tN_r, the resulting discrete-time algebraic Riccati equation is difficult to solve for large systems, e.g., distributed massive MIMO systems. It is shown, however, that the structure of the dynamic model allows the steady-state prediction covariance to be efficiently calculated irrespective of the number of transmit and receive nodes. An asymptotic analysis is also presented for systems with a large number of transmit and receive nodes with closed-from 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.