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Recent work has shown that repetition coding followed by interleaving induces signal structure that can be exploited to separate multiple co-channel user transmissions, without need for pilots or coordination/synchronization between the users. This is accomplished via a statistical learning technique known as canonical correlation analysis (CCA), which works even when the channels are time-varying. Previous analysis has established that it is possible to identify the user signals up to complex scaling in the noiseless case. This letter goes one important step further to show that CCA in fact yields the linear MMSE estimate of the user signals up to complex scaling, without using any explicit training. Instead, CCA relies only on the repetition and interleaving structure. This is particularly appealing in asynchronous ad-hoc and unlicensed setups, where tight user coordination is not practical. 

In this paper, we present a method for decoding uplink messages in Internet of Things (IoT) networks that employ packet repetition. We focus on the Sigfox protocol, but our approach is applicable to other IoT protocols that employ message repetition. Our approach endeavors to enhance the reliability of message capture as well as the error rate performance at the base station. To achieve this goal, we propose a novel technique that capitalizes on the unique features of the IoT network’s uplink transmission structure. Through simulations, we demonstrate the effectiveness of our method in various scenarios, including single-user and multi-user setups. We establish the resilience of our approach under higher system loads and interference conditions, showcasing its potential to improve IoT network performance and reliability even when a large number of devices operates over limited spectrum. Our findings reveal the potential of the proposed method as a promising solution for enabling more dependable and energy-efficient communication in IoT Low Power Wide Area Networks. 

Canonical correlation analysis (CCA) is a classic statistical method for discovering latent co-variation that underpins two or more observed random vectors. Several extensions and variations of CCA have been proposed that have strengthened our capabilities in terms of revealing common random factors from multiview datasets. In this work, we first revisit the most recent deterministic extensions of deep CCA and highlight the strengths and limitations of these state-of-the-art methods. Some methods allow trivial solutions, while others can miss weak common factors. Others overload the problem by also seeking to reveal what is {\em not common} among the views -- i.e., the private components that are needed to fully reconstruct each view. The latter tends to overload the problem and its computational and sample complexities. Aiming to improve upon these limitations, we design a novel and efficient formulation that alleviates some of the current restrictions. The main idea is to model the private components as {\em conditionally} independent given the common ones, which enables the proposed compact formulation. In addition, we also provide a sufficient condition for identifying the common random factors. Judicious experiments with synthetic and real datasets showcase the validity of our claims and the effectiveness of the proposed approach.