Kalman Smoothing for Irregular Pilot Patterns; A Case Study for Predictor Antennas in TDD Systems

For future large-scale multi-antenna systems, channel orthogonal downlink pilots are not feasible due to extensive overhead requirements. Instead, channel reciprocity can be utilized in time division duplex (TDD) systems so that the downlink channel estimates can be based on pilots transmitted during the uplink. User mobility affects the reciprocity and makes the channel state information outdated for high velocities and/or long downlink subframe durations. Channel extrapolation, e.g. through Kalman prediction, can reduce the problem but is also limited by high velocities and long downlink subframes. An alternative solution has been proposed where channel predictions are made with the help of an extra antenna, e.g. on the roof of a car, so called predictor antenna, with the primary objective to measure the channel at a position that is later encountered by the rearward antenna(s). The predictor antenna is not directly limited by high velocities and allows the channel in the downlinks to be interpolated rather than extrapolated. One remaining challenge here is to obtain a good interpolation of the uplink channel estimate, since a sequence of uplink reference signals (pilots) will be interrupted by downlink subframes. We here evaluate a Kalman smoothing estimate of the downlink channels and compare it to a cubic spline interpolation. These results are also compared to results where uplink channels are estimated through Kalman filters and predictors. Results are based on measured channels and show that with Kalman smoothing, predictor antennas can enable accurate channel estimates for a longer downlink period at vehicular velocities. The gaps in the uplink pilot stream, due to downlink subframes, can have durations that correspond to a vehicle movement of up to 0.75 carrier wavelengths in space, for Rayleigh-like non-line-of-sight fading.