Mobility-Assisted Covert Communication over Wireless Ad Hoc Networks - - PowerPoint PPT Presentation

Mobility-Assisted Covert Communication over Wireless Ad Hoc Networks

Hyeon-seong Im1 and Si-Hyeon Lee2

1Department of Electrical Engineering, POSTECH 2School of Electrical Engineering, KAIST

ISIT 2020

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Overview

1

Introduction

2

Problem Statement

3

Result

4

Proof Idea

5

Extension

6

Conclusion

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Covert Communication

Communication should be not detected from a warden. Hypothesis test: communicating (H1) or non-communicating (H0) P(H0|H1) + P(H1|H0) > 1 −

• D(QZ lQl

0)

(1) Covertness constraint: D(QZ lQl

0) ≤ δ

AWGN channel: Sufficiently small transmission power compared with noise level is required. [Bash et al. 2013, Wang et al. 2016].

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Covert Communication over a Wireless Ad Hoc Network

Unit area network: n nodes and nw wardens are randomly distributed. n source-destination pairs are randomly determined. n nodes should communicate while satisfying the covertness constraint from each warden. Focus: Proving the capacity scaling law

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Capacity Scaling with Fixed Node Location [Cho, Lee, and Tan 2019]

Fixed node location :

nw = Θ(ns) (s > 0): The number of wardens Covertness constraint: Warden’s received power should not be large.

Preservation region: Transmission of nodes is not permitted.

Throughput scaling

SNRs1 = n(1/2−s/2)(α−2)

√ l

: Short range SNR (length of Θ(n−1/2))

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Capacity Scaling with Mobile Node Location

Our model: Nodes have mobility.

Mobility is essential in some cases. ex) military communication

No covertness constraint: Capacity is linearly scaled over n regardless

• f the mobility of the nodes [Tse et al. 2002, Ozgur et al. 2007].

Q) If covertness constraint exists, then does mobility improves throughput scaling?

A) Mobility improves throughput scaling! (Why?)

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Problem Statement: Network Model

Unit disk network n nodes: uniformly and independently distributed in each time t

Location of nodes: SSS and ergodic across time t Each node is a source and a destination simultaneously. n source-destination pairs are randomly determined.

nw = Θ(ns) (0 < s < 1) non-colluding wardens: Same distribution with nodes (or fixed location)

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Problem Statement: Network Model

Received signal at node j: Yj[t] = n

k=1 Hjk[t]Xk[t] + Nj[t]

Xk[t]: Transmitted signal by node k Nj[t] ∼ CN(0, N0): Gaussian random noise Hjk[t] =

√ G (djk[t])α/2 exp(jθjk[t]): Large scale path loss

α > 2, θjk[t]: uniformly and independently distributed phase

Received signal at warden w: Zw[t] = n

k=1 H′ wk[t]Xk[t] + N′ w[t]

CSI is available only at the receivers.

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Problem Statement: Covertness Constraint

Each warden observes l channel outputs.

Test hypothesis whether nodes are communicating or not.

Covertness constraint for all wardens with threshold δ > 0: D(QZ l

w Q×l

N′

w ) ≤ δ for w = 1, 2, ..., nw

D(··): Relative entropy QZ l

w : Distribution of the received signal at warden w over l channel

uses (communicating). Q×l

N′

w : Distribution of the received signal at warden w over l channel

uses (non-communicating).

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Problem Statement: Long-Term Throughput

Long-term throughput λ(n, s) is feasible if lim

T→∞

1 T

T

• t=1

Rjk(n, s, t) ≥ λ(n, s) (2) for all source-destination pairs (j, k).

Rjk(n, s, t): Throughput of a source-destination pair

Goal: Characterize the scaling of the maximally achievable aggregate throughput T(n, s) = nλ(n, s).

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Result: Achievable Aggregate Throughput

Throughput scaling

SNRs1 := n(1/2−s/2)(α−2)

√ l

: Short range (n−1/2) SNR for 0 < s < 1 Non-covertness constraint: SNRs1 = 1

Red box: p(Rpair(n, s) = Θ(1))

Rpair(n, s) : Throughput of a sender-receiver pair

Throughput is linearly scaled in n if l is sufficiently small.

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Result: Mobility Improves Throughput Scaling

Throughput scaling for 2 < α ≤ 3

HC scheme: Long range communication and several hops Our scheme: Short range communications and two hops Covertness constraint: Transmission power is limited.

Long range communication has throughput loss!

For 2 < α ≤ 3, our scheme has throughput gain.

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Result: Mobility Improves Throughput Scaling

Throughput scaling for α > 3

MH scheme: Short range communications and multi (Θ(n1/2)) hops Our scheme: Short range communications and two hops Fewer hops have throughput gain.

For α > 3, our scheme has throughput gain. Mobility improves throughput scaling!

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Result: Upper bound on Aggregate Throughput

Proving a non-trivial upper bound is not easy.

Distances between senders and wardens → upper bound on the transmit power Distances between senders and receivers → transmission rate These two things are independently vary over time.

Assumption: Nodes distant from every warden to a certain extent use the same power. Throughput scaling

Tight under the assumption!

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Mobility-Assisted Two-Hop Scheme

Inspired by the Two-Hop scheme [Tse et al. 2002]

Scheme for mobile nodes without any covertness constraint

Nodes are partitioned by senders and receivers in each time t. Each sender communicates with the nearest receiver (sender-receiver pair). Preservation region [S.-W.Jeon et al. 2011]: Transmission of nodes is not permitted. Overall communication is divided into two phases:

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Mobility-Assisted Two-Hop Scheme

Phase 1: Active in odd time (t = 1, 3, 5, ...)

Sender → source, receiver → relay Each sender transmits its own source data to its paired receiver.

Senders in a preservation region: No transmission

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Mobility-Assisted Two-Hop Scheme

Phase 2: Active in even time (t = 2, 4, 6, ...)

Sender → relay, receiver → destination Each sender selects and transmits destined data to its paired receiver.

Senders in a preservation region: No transmission

Sender might not have destined data → steady state is assumed

Data transmission in each period: source → relay → destination

Only using two hops

Mobile nodes: Short range communications are sufficient.

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Mobility-Assisted Two-Hop Scheme

Mobility-assisted two-hop scheme ensures us T(n, s) = θn(1 − ǫ(n)) 2 · λpair(n, s) = Θ(n) · λpair(n, s).

T(n, s): Achievable aggregate throughput θ: Proportion of senders ǫ(n): Region of total preservation region. λpair(n, s): Feasible throughput of a sender-receiver pair

Proof of λpair(n, s): Different proof technique is required. (Why?)

Allowable transmit power is precisely evaluated by covertness constraint. Distance between sender-receiver pair affects the order of λpair(n, s).

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Extension to s ≥ 1

Extension to s ≥ 1

SNRs2 := nα(1/2−s/2)

√ l

: Short range (n−1/2) SNR for s ≥ 1

Not tight (Why?)

Distance between a warden and the nearest sender without a preservation region is different between the pessimistic and optimistic derivations.

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Conclusion

Consider covert communications over a wireless ad hoc network with mobility. Propose mobility-assisted two-hop scheme. Capacity is linearly scaled in n for 0 < s < 1 if testing channel length is sufficiently small. Mobility improves throughput scaling. Tight for 0 < s < 1 under some mild assumption. Detailed proofs can be found on arXiv [2004.08852].

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