Phase-Noise in TDM-Switched MIMO Channel Sounding and Its Impact on Channel Capacity Estimation

Time-division multiplexing (TDM) is commonly used to switch between the elements of the transmit and receive antenna arrays in multiple-input multiple-output (MIMO) radio channel sounding. However, phase noise of the local phase- locked oscillators at the transmitter (TX) and the receiver (RX) causes measurement errors that can lead to significant impairment of the performance of traditional estimators of the radio channel parameters, like the path parameters (direction of departure, direction of arrival) and the channel capacity. In this paper, we derive a signal model for phase noise on short- term and long-term observation window scales. The short-term and long-term behaviours of phase noise are modelled as an autoregressive moving average (ARMA) and an autoregressive integrated moving average (ARIMA) model respectively. We focus the investigations on the characterization of the short-term component of phase noise, as this component predominates on the scale of the duration of the measurement cycles in MIMO channel sounding. All pair of TX and RX array elements are switched once in a measurement cycle. The ARMA model for the short-term phase noise component is validated by contrasting the sample autocorrelation function, the periodogram, and the sample Allan variance obtained from phase-noise measurement data with those computed from the estimated ARMA model. Finally, the impact of phase noise on the traditional estimate of MIMO channel capacity is analyzed. We show that the performance impairment is less than that shown in [5] under the hypothesis of uncorrelated phase-noise samples. The difference is due to the non-vanishing correlation between temporally nearby phase-noise samples. In addition, we show that the length of the period of the sounding signal affects the channel capacity estimate as well. This can be explained by the fact that the correlation between phase noise samples corresponding to different sounding periods decreases as the period length increases.