Joint Spatio-Temporal Precoding for Practical Non-Stationary Wireless Channels

The high mobility, density and multi-path evident in modern wireless systems makes the channel highly non-stationary. This causes temporal variation in the channel distribution that leads to the existence of time-varying joint interference across multiple degrees of freedom (DoF, e.g., users, antennas, frequency and symbols), which renders conventional precoding sub-optimal in practice. In this work, we derive a High-Order Generalization of Mercer's Theorem (HOGMT), which decomposes the multi-user non-stationary channel into two (dual) sets of jointly orthogonal subchannels (eigenfunctions), that result in the other set when one set is transmitted through the channel. This duality and joint orthogonality of eigenfuntions ensure transmission over independently flat-fading subchannels. Consequently, transmitting these eigenfunctions with optimally derived coefficients eventually mitigates any interference across its degrees of freedoms and forms the foundation of the proposed joint spatio-temporal precoding. The transferred dual eigenfuntions and coefficients directly reconstruct the data symbols at the receiver upon demodulation, thereby significantly reducing its computational burden, by alleviating the need for any complementary post-coding. Additionally, the eigenfunctions decomposed from the time-frequency delay-Doppler channel kernel are paramount to extracting the second-order channel statistics, and therefore completely characterize the underlying channel. We evaluate this using a realistic non-stationary channel framework built in Matlab and show that our precoding achieves ${\geqslant}$4 orders of reduction in BER at SNR${\geqslant}15$dB in OFDM systems for higher-order modulations and less complexity compared to the state-of-the-art precoding.

Collaboration with Cellular Networks for RFI Cancellation at Radio Telescope

The growing need for electromagnetic spectrum to support the next generation (xG) communication networks increasingly generate unwanted radio frequency interference (RFI) in protected bands for radio astronomy. RFI is commonly mitigated at the Radio Telescope without any active collaboration with the interfering sources. In this work, we provide a method of signal characterization and its use in subsequent cancellation, that uses Eigenspaces derived from the telescope and the transmitter signals. This is different from conventional time-frequency domain analysis, which is limited to fixed characterizations (e.g., complex exponential in Fourier methods) that cannot adapt to the changing statistics (e.g., autocorrelation) of the RFI, typically observed in communication systems. We have presented effectiveness of this collaborative method using real-world astronomical signals and practical simulated LTE signals (downlink and uplink) as source of RFI along with propagation conditions based on preset benchmarks and standards. Through our analysis and simulation using these signals, we are able to remove 89.04% of the RFI from cellular networks, which reduces excision at the Telescope and capable of significantly improving throughput as corrupted time frequency bins data becomes usable.

Unified Characterization and Precoding for Non-Stationary Channels

Modern wireless channels are increasingly dense and mobile making the channel highly non-stationary. The time-varying distribution and the existence of joint interference across multiple degrees of freedom (e.g., users, antennas, frequency and symbols) in such channels render conventional precoding sub-optimal in practice, and have led to historically poor characterization of their statistics. The core of our work is the derivation of a high-order generalization of Mercer's Theorem to decompose the non-stationary channel into constituent fading sub-channels (2-D eigenfunctions) that are jointly orthogonal across its degrees of freedom. Consequently, transmitting these eigenfunctions with optimally derived coefficients eventually mitigates any interference across these dimensions and forms the foundation of the proposed joint spatio-temporal precoding. The precoded symbols directly reconstruct the data symbols at the receiver upon demodulation, thereby significantly reducing its computational burden, by alleviating the need for any complementary decoding. These eigenfunctions are paramount to extracting the second-order channel statistics, and therefore completely characterize the underlying channel. Theory and simulations show that such precoding leads to ${>}10^4{\times}$ BER improvement (at 20dB) over existing methods for non-stationary channels.

Proofs and Supplementary Material: Unified Characterization and Precoding for Non-Stationary Channels

This document provides the supplementary material including a comprehensive related work, the complete proofs and extended evaluation results that support the manuscript, "Unified Characterization and Precoding for Non-Stationary Channels", that was accepted for publication at IEEE International Conference on Communications (ICC) 2022. Equations (1)--(34) refer to the equations from the main manuscript, and the Theorem, Lemma and Corollaries correspond to those from the manuscript.