Reduced complexity Kalman filtering for phase recovery in XPIC systems

Reduced-complexity Kalman-based algorithms are proposed to recover the phase of cross-polar interference cancellation (XPIC) receivers in microwave radio relay links. In particular, two completely independent radio frequency (RF) transceiver chains are considered for the two different polarizations, in order to have the maximum flexibility to connect different single carrier transceivers to dual-polarized antennas. A one-state Kalman model is proposed, which is of low complexity and thus suitable for a modern higher data rates M-ary quadrature amplitude modulation (M-QAM) receiver. Moreover, a further reduced complexity version is developed that uses a lower amount of information to recover the phase at the receiver, as well as a downsampling procedure to speed up the Kalman algorithm, and an alternative error computation that is essential to ease the Kalman implementation. It is worth noting that the three last simplifications are general and can be applied not only to a one-state Kalman model. Simulation results compare the proposed simplified Kalman solutions to typical phase-locked loop (PLL) algorithms proving their comparable performance with the benefit of lower complexity. Finally, the relationships between the Extended Kalman and the PLL approaches are investigated. The obtained relation is essential for the cross-polar phase recovery, since, as far as the authors know, there are not closed-form solutions for the PLL parameter optimization in cross schemes.