Coordinated controlling a large UAV swarm requires significant spectrum resources due to the need for bandwidth allocation per UAV, posing a challenge in resource-limited environments. Over-the-air (OTA) control has emerged as a spectrum-efficient approach, leveraging electromagnetic superposition to form control signals at a base station (BS). However, existing OTA controllers lack sufficient optimization variables to meet UAV swarm control objectives and fail to integrate control with other BS functions like sensing. This work proposes an integrated sensing and OTA control framework (ISAC-OTA) for UAV swarm. The BS performs OTA signal construction (uplink) and dispatch (downlink) while simultaneously sensing objects. Two uplink post-processing methods are developed: a control-centric approach generating closed-form control signals via a feedback-looped OTA control problem, and a sensing-centric method mitigating transmission-induced interference for accurate object sensing. For the downlink, a non-convex problem is formulated and solved to minimize control signal dispatch (transmission) error while maintaining a minimum sensing signal-to-interference-plus-noise ratio (SINR). Simulation results show that the proposed ISAC-OTA controller achieves control performance comparable to the ideal optimal control algorithm while maintaining high sensing accuracy, despite OTA transmission interference. Moreover, it eliminates the need for per-UAV bandwidth allocation, showcasing a spectrum-efficient method for cooperative control in future wireless systems.

This paper investigates the performance of adaptive LoRa networks with dynamic SF allocation accounting for Duty Cycle (DC) restrictions and quantifying the imperfect orthogonality of Spreading Factor (SF)s. The study presents a novel spatiotemporal model that combines stochastic geometry and queuing theory where LoRa devices are perceived as interacting two-dimensional DTMCs. Each chain jointly tracks the number of packets in the buffer and the node’s protocol state. Numerical simulations are carried out to validate the accuracy of the proposed model. The network performance is studied in terms of Pareto frontiers under different orthogonality assumptions and adaptation settings, showcasing the ranges of sensing applications that LoRa can accommodate without compromising the network stability. The evolution of SFs activity distribution, coverage probability and average latency is examined against different network parameters. The results show that activating SF adaptation with higher cardinality is not always advantageous and evince the existence of an adaptation cardinality that minimises the delay. The study also identifies regimes where SF adaptation is advantageous for the network scalability and reveals ‘SF-Up’ and ‘SF-Down’ rates that maximise the coverage or minimise the delay. Comparing dynamic to static SF allocations, the results highlight a tradeoff between coverage and latency yielding valuable insights into scenarios where either of the allocation strategies would be more beneficial to the network.

An analytical model joining stochastic geometry and queuing theory is devised to study the performance of adaptive LoRa networks with dynamic Spreading Factor (SF) allocation. LoRa devices are perceived as interacting two-dimensional Discrete Time Markov Chains (DTMC)s. Each chain jointly tracks the number of packets in the buffer and the node's protocol state while accounting for Duty Cycle (DC) restrictions and quantifying the imperfect orthogonality of SFs. The network performance is characterised in terms of coverage, delay and Pareto frontiers under different orthogonality assumptions and for various adaptation settings highlighting insights useful for the design of application-aware decentralised or semi-decentralised SF adaptation schemes.

In this article, we provide, for the first time, a comprehensive understanding of long-range (LoRa) waveform theory in order to quantify its orthogonality. We present LoRa waveform expressions in continuous- and discrete-time domains, and analyze measures of orthogonality between different LoRa spreading factors (SFs) through cross-correlation functions. The cross-correlation functions are analytically expressed in a general form and they account for diverse configuration parameters (bandwidth, SF, etc.) and different cases of signal displacements (time delay shift, frequency shift, etc.). We quantify their mean and maximum in all time domains. We highlight the impact of the temporal displacement and different bandwidths. The general result is that LoRa modulation is nonorthogonal. First, we observe that for same bandwidths, the largest maximum cross-correlation happens for same SF and is equal to 100% due to same symbols; whereas for different bandwidths, the largest maximum cross-correlation is no longer observed at the same SF. Second, the maximum cross-correlation is less than 26% between different SFs, is higher for closer SFs, and decreases as the difference between SFs increases. After downchirping, the maximum cross-correlation increases and the mean decreases compared to those before downchirping. Moreover, the maximum cross-correlation is insignificantly impacted by the temporal delay, which makes it valid to adopt for the performance analysis of both synchronous and asynchronous systems. Finally, we analyze by simulating the bit error probability statistics for different bandwidth ratios and highlighting their correlated behavior with the insights obtained from the maximum cross-correlation expressions.

Meticulous modelling and performance analysis of Low-Power Wide-Area (LPWA) networks are essential for large scale dense Internet-of-Things (IoT) deployments. As Long Range (LoRa) is currently one of the most prominent LPWA technologies, we propose in this paper a stochastic-geometry-based framework to analyse the uplink transmission performance of a multi-gateway LoRa network modelled by a Matern Cluster Process (MCP). The proposed model is first to consider all together the multi-cell topology, imperfect spreading factor (SF) orthogonality, random start times, and geometric data arrival rates. Accounting for all of these factors, we initially develop the SF-dependent collision overlap time function for any start time distribution. We, then analyse the Laplace transforms of intra-cluster and inter-cluster interference and formulate the uplink transmission success probability. Through simulation results, we highlight the vulnerability of each SF to interference, illustrate the impact of parameters such as the network density and the power allocation scheme on the network performance. Uniquely, our results shed light on when it is better to activate adaptive power mechanisms, as we show that an SF-based power allocation that approximates LoRa Adaptive Data Rate (ADR) negatively impacts nodes near the cluster head. Moreover, we show that the interfering SFs degrading the performance the most depend on the decoding threshold range and the power allocation scheme.