In full duplex amplify-and-forward (FD-AF) relays, self-interference from the transmit side causes a major problem hindering its commercial spread. To alleviate the front-end saturation problem, we propose a spatial self-interference nullification method employing extra transmit antennas in FD-AF multiple-input-multiple-output (MIMO) relay systems, and analyze characteristics of the proposed system when there exist channel estimation errors. In particular, the probability of relay stability is derived, and the capacity of the relay is analyzed with zero delay assumption. The results indicate that excessive channel estimation errors drive FD-AF relay into unstable modes and cause capacity reduction.

We propose a DPLL (digital phase-locked loop) with time-varying loop gains which are derived from the RLS method. This method, in contrast to the one based on the standard Kalman filtering algorithm, is appropriate for the situation where no statistics are known. If the forgetting factor in the RLS method is constant, the acquisition performance only improves in the initial stage. However, with the variable forgetting factor adaptive to the measurements, the DPLL shows excellent acquisition and tracking performance under a non-stationary environment which are comparable to that based on the adaptive Kalman filter with lock detection algorithm.

An approach to the derivation of variable loop gain sequences of dual-loop digital phase-locked loop (DPLL) is developed based on some modifications of the Kalman filtering formulation. It is shown that optimal loop gain sequences which are independent of measurement noise statistics can be obtained under a deterministic source model. Computer simulation results demonstrate that the adaptive dual-loop DPLL designed by using the proposed method is more robust to noise variations than the adaptive DPLL of Driessen (see ibid., vol.47, p.673-75, 1994).

A salient adaptive carrier recovery with a multi-order Digital Phase-Locked Loop (DPLL) based on Kalman filtering is presented in this paper. Using optimal loop gain sequence, that is Kalman gain sequence, for various optimization criteria, the proposed DPLL achieves fast phase acquisition and low phase jitter. The loop gain sequence optimized under the Least Squares (LS) criterion shows enough phase tracking capability under severe fading and can be used for mobile communication applications. Finally, the multi-order DPLL allows robust stability and bandwidth control and achieves zero phase offset.