Characteristics of Short-Term Phase Noise of MIMO Channel Sounding and Its Effect on Capacity Estimation

Multi-input-multi-output (MIMO) radio channel sounders commonly employ a time-division-multiplexing (TDM) technique to switch between transmit (TX) and receive (RX) antennas. The TDM-based switching enables very cost-effective solutions. Nevertheless, it can cause measurement errors due to phase noise in the local oscillators. In typical MIMO applications with a relatively small number of TX and RX antennas, the measurement cycle for a single snapshot of a MIMO radio channel is so short that independent or white Gaussian noise samples cannot be assumed. Indeed, the characteristics of the phase noise depend on the observing-time scale and the local oscillator design in the TX and the RX. In free-running systems, in which the local oscillators of the TX and the RX employ their own clocks, the properties of the phase noise have a strong dependence on the scale of the observing time. In particular, the short-term characteristics of the phase noise have not been considered in literature regarding MIMO measurements. In this paper, the characteristics of the short-term phase noise in time-switched MIMO radio channel measurements are disclosed. We show also that the Allan deviation, which commonly characterizes the frequency stability of the local oscillators, does not apply well to the short-term scale. Instead, an autoregressive model that is well suited for modeling of correlated noise is applied to characterize the short-term behavior of the phase noise. Finally, the effect of short-term phase noise on the estimation of MIMO channel capacity is analyzed. We also derive an upper bound for the ergodic channel capacity and show that it is dependent on the distribution of the largest eigenvalue of the noise covariance matrix. The results reveal that the effect of short-term phase noise always overestimates MIMO channel capacity.