This paper investigates covert multi-hop communication in wireless networks where an adversary employs a cyclostationary (cycle) detector to reveal hidden transmissions. The covert route employs direct sequence spread spectrum (DSSS) signaling to ensure either maximum end-to-end covertness maximization or minimum latency minimization-under quality-of-service (QoS) and link budget constraints. Optimal bandwidth, transmit power, and spreading gain for each hop jointly satisfy reliability and either rate or covertness requirements. We show the equivalence between the covertness and the detection SNR gain-based widest-path formulations, and, hence, enabling efficient route computation. Numerical simulations in a realistic 3D environment illustrate that (i) end-to-end latency increases exponentially with the covertness requirement, (ii) the end-to-end latency increase is super-linear with the packet size M, and (iii) cycle and energy detectors impose different latency behavior as a function of the message length and the covertness requirement. The proposed framework provides important insights into resource allocation and routing design for covert networks against advanced detection adversaries.
Low probability of detection (LPD) or covert communications [1] refers to a communication system that aims to hide its transmissions from a watchful adversary. Intuitively, reducing a wireless signal's transmission power and data rate lowers the likelihood of transmissions being detected by unintended observers. Multi-hop routing improves covertness by enabling reduced-power hop-by-hop transmission. In addition, Direct Sequence Spread Spectrum (DSSS) modulation is an effective technique for achieving covert communication, as it spreads the message signal across a wider bandwidth, thereby modulating the signal to a level comparable to or exceeding the noise level and providing inherent covertness. Nevertheless, the statistical characteristics of the spreading codes typically exhibit characteristic features/patterns that an adversary can exploit to infer the presence of a transmitted signal [2]- [4]. Beyond security considerations, practical communication systems must also satisfy the Quality of Service (QoS) requirements [5], [6], such as low latency, high throughput, and reliability.
In [7], authors take an information-theoretic approach to study communication covertness, an approach that does not consider the limitations of a practical detector. Authors in [7]- [10] study the covertness against an adversary employing an energy detector. Adversary that exploits the signal’s cyclostationary properties (i.e., spectral correlations) has been studied extensively [5], [11]. We refer to such an adversary as a cycle detector. The authors [2]- [4] identify different strategies that enhance covertness against cycle detectors. In [5], we compare the covertness of single link communication systems against energy and cycle detectors under common communication QoS requirements. Motivated by the multi-hop routing covertness advantage, several works optimize per-hop resource allocation and routing jointly [9], [12]- [14] against energy detectors. On the other hand, to the best of our knowledge, no prior research has studied the covertness of multi-hop routing schemes against adversaries employing cycle detectors.
In this paper, we examine a wireless covert routing problem comprising Alice, Bob, multiple friendly relaying nodes, and a passive adversary, Willie (Fig. 1), employing a cycle detector. Alice transmits a confidential message with M bits, modulated by DSSS, to Bob. Alice prefers a lower probability of detection by Willie, with the help of relay nodes whose transmissions satisfy QoS constraints. The message generated by Alice is transmitted hop-by-hop to Bob. Direct communication between Alice and Bob may require high transmitted power due to channel fading and QoS requirements, thereby revealing her communication to Willie. Conversely, multihop communications may provide more opportunities for the adversary to detect transmissions and/or increase end-to-end message-routing latency. Key contributions are:
• We propose two novel routing algorithms for covert multi-hop communication under a cycle detector with QoS guarantees: a covertness-maximization and a latency-minimization approach. • We validated the proposed approach in a realistic (3D) environment, revealing that the end-to-end latency ex-hibits a sub-linear, linear, and and exponential with an increase in the covertness requirement. Additionally, with an increase in the message size M , the route latency exhibits super-linear and exponential growth under relaxed and stringent covertness requirements, respectively. • We also illustrate that, for latency maximization, the adversary may favor the cycle detector at low covert requirements and the energy detector under stringent covert requirements. Section II gives the legitimate network and signaling model. Section III introduces the per-hop cycle detector. Section IV formulates the optimization problems. Section V describes our proposed method. Section VI gives the numerical results.
As shown in Fig. 1, Alice can select multiple possible routes to transmit a message to Bob. We define Ψ as the set of all possible routes. Let us denote ψ = (v 1 , . . . , v N ψ ) ∈ Ψ as a route from Alice to Bob, where v i = (T vi , R vi ) is the singlehop communication link between transmitter T vi and receiver R vi , and N ψ is the number of hops of the route ψ. Here, T v1 and R v N ψ are Alice and Bob, respectively. Alice generates a message of M bits, which is transmitted sequentially, hop by hop, along the selected route ψ until it reaches Bob. As the analysis of each hop communication is identical, we will drop the hop index i and use v to denote a single-hop communication link. In the network, each of the transmitters {T v } along the path ψ adaptively selects bandwidth Ω v and transmitted power P v based on the dynamic wireless environment, QoS requirements, and covert requirements. There are multiple time slots between any transmitter T v and R v . Transmitter T v chooses one of the time slots randomly (discussed i
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