Open loop residual carrier arraying with baseband combining

In deep space communications, different antenna aperture arraying techniques are used to enhance the received signal-to-noise ratio (SNR). A residual-carrier arraying scheme, which is able to jointly (two or more antennas) track the carrier when the signal is too weak to be tracked by a single antenna, is proposed in this paper. Starting with the maximum likelihood estimator (MLE) of the carrier phase of a sinusoid in white Gaussian noise, an open-loop MLE for estimating the carrier phase difference between several antennas and a reference antenna is proposed. The performance of this estimator is derived and is shown to be unbiased, and asymptotically efficient (the variance of the estimate error is given by the CRLB). Next, this residual carrier technique is illustrated in conjunction with baseband combining for PCM/BPSK/PM signal. The degradation in terms of symbol SNR and symbol error rate loss is derived based on imperfect synchronization assumptions. The results are verified by simulation for a given example.