Pseudo channel reciprocity in FDD satellite channels

Channel reciprocity can significantly reduce the overhead of obtaining channel-state information at the transmitter (CSIT). However, true reciprocity only exists in time division duplex (TDD). In this paper, we propose a novel tracking method that exploits implicit reciprocity in FDD line-of-sight (LOS) channels as in low-earth-orbit (LEO) satellite communication (SatCom). This channel reciprocity, dubbed pseudo-reciprocity, is crucial for applying multiple-user multiple-input multiple-output (MU-MIMO) to SatCom, which requires CSIT. We consider an LEO SatCom system where multiple satellites communicate with a multi-antenna land terminal (LT). In this innovative method, the LT can track the downlink channel changes and use them to estimate the uplink channels. The proposed method achieves precoding performance that is comparable to precoding with full CSIT knowledge. Furthermore, the use of pseudo reciprocity typically requires only initial CSIT feedback when the satellite rises. Over very long periods of time, pseudo reciprocity can fail as a result of phase ambiguity, which is referred to as cycle slip. We thus also present a closed-form approximation for the expected time until cycle slip, which indicates that in normal operating conditions, these cycle slips are extremely rare. Our numerical results provide strong support for the derived theory.

Asymptotic Performance of TDOA Estimation using Satellites

We present novel lower bounds on the localization error using a network of satellites randomly deployed on a sphere around Earth. Our new analysis approach characterizes the localization performance by its asymptotic behavior as the number of satellites gets large while assuming a dense network. Using the law of large numbers, we derive closed-form expressions for the asymptotic Cramer Rao bound (CRB) from which we draw valuable insights. The resulting expressions depend solely on the network statistics and are not a function of a particular network configuration. We consider two types of estimators. The first uses the exact statistical model, and hence employs both timing and amplitude information. The second estimator ignores the amplitudes and hence uses only time difference of arrival (TDOA) information. The asymptotic CRB indicates that for practical system setup, a TDOA estimator approaches the performance of the ideal estimator. For both estimators, the localization accuracy improves as satellites get closer to Earth. The latter finding is essential in light of the proliferation of low-Earth-orbit (LEO) satellites and motivates a further study of localization-performance in such networks. Besides, we show that the vertical localization accuracy is lower than the horizontal accuracy and is also more sensitive to the receiver field-of-view.