Page 117 - ITU Journal Future and evolving technologies Volume 2 (2021), Issue 1

ITU Journal on Future and Evolving Technologies, Volume 2 (2021), Issue 1

A MULTI‑LINK COMMUNICATION CONNECTIVITY GAME UNDER HOSTILE INTERFERENCE

2
1
1
Andrey Garnaev , Wade Trappe , Narayan B. Mandayam , H.Vincent Poor 3
1 WINLAB, Rutgers University, North Brunswick, NJ, USA (e‑mail: andrey.garmaev@gmail.com,
2
trappe@winlab.rutgers.edu), Department of Electrical and Computer Engineering, Rutgers University, Piscataway, NJ,
3
USA, (e‑mail: narayan@winlab.rutgers.edu), Department of Electrical Engineering, Princeton University, Princeton, NJ
USA (e‑mail: poor@princeton.edu)
NOTE: Corresponding author: A. Garnaev, e‑mail: andrey.garmaev@gmail.com

Abstract – In this paper, we consider a communication connectivity problem involving a primary user (transmitter, for
example, a Ground Control Station (GCS)) servicing a group of secondary users (receivers, for example, drones) under hostile
interference. We formulate this multi‑link communication connectivity problem, where the channels are affected by Rayleigh
fading, as a zero‑sum power resource allocation game between a transmitter and an adversary (jammer). The transmitter’s
objective is to maximize the probability of communication connectivity with all the receivers. It is proven that the problem
has unique equilibrium in power allocation strategies, and the equilibrium is derived in closed form. Moreover, we reduce
the problem of designing the equilibrium in power resource allocation strategies to the problem of inding a ixed point of a
real‑valued function. An algorithm based on the bisection method to ind the ixed point (and so equilibrium strategies) is
developed, and its convergence is proven.

Keywords – communication connectivity, interference, jamming, Nash equilibrium, resource allocation

1. INTRODUCTION of the transmitted signal at the receiver greater or equal
to a threshold value, which we refer to as the Threshold of
Communication between a transmitter and a receiver un‑ Communication Connectivity (TCC). This leads generally
der hostile interference is a well‑studied problem in the to to the non‑existence of equilibria in power‑level assign‑
wireless literature (see, for example, the survey in [1]). ment strategies, i.e., pure strategies, even in a Single‑Link
Such problems are multi‑objective problems since they Communication Connectivity (SLCC) problem [14, 17], and
deal with different agents (say, a transmitter and an ad‑ it may cause destabilization of communication. One of
versary (jammer)), and each of these agents has its own the ways to stabilize such systems, i.e., to make them
objective. Game theory supplies concepts for analyzing have equilibrium, is to extend the set of feasible strategies
and solving such multi‑objective problems [2], and, thus,
to mixed strategies (in other words, to assign the equi‑
game theory has been widely used to model jamming
librium strategy via randomization (lottery) over pure
problems. Typically, jamming problems can be catego‑
strategies). Although using a lottery introduces a factor of
rized according to two frameworks: (i) maintaining com‑
uncertainty for the decision maker it allows it to ind an
munication reliability and (ii) maintaining communica‑ equilibrium in such mixed strategies for the MLCC prob‑
tion connectivity. In communication reliability problems, lem via the Colonel Blotto game approach [12, 13, 16, 18,
the transmitter’s payoff is a function of throughput or 19, 17] and for the SLCC problem via a war of attrition
Signal‑to‑Interference‑plus‑Noise Ratio (SINR) at the re‑ game approach [17].
ceiver, and the transmitter intends to maximize such pay‑
off [3, 4, 5, 6, 7, 8, 9, 10, 11]. Meanwhile, in communi‑ To avoid introducing a random factor in decision making,
cation connectivity problems the transmitter must keep in [14, 15], another approach was suggested to stabilize
its SINR greater than or equal to a threshold value to en‑ such communication. In [14, 15], it was proven that if
sure a connection can be sustained [12, 13, 14, 15, 16, 17, channels are affected by Rayleigh fading and background
18, 19]. In this paper, we consider the communication noise at the receiver is negligible, then an equilibrium in
connectivity problem under hostile interference involv‑ power‑level assignment strategies (i.e., pure strategies)
ing a transmitter servicing a group of secondary users (re‑ exists and is unique for an SLCC problem.
ceivers) with the channels affected by Rayleigh fading. We The goal of this paper is to prove that if channels are af‑
formulate and solve this Multi‑Link Communication Con‑ fected by Rayleigh fading and any background noise, a
nectivity (MLCC) problem as a zero‑sum power allocation random factor can be eliminated in decision making for
problem between the transmitter and the jammer, where communication stabilization even in MLCC systems. To
the transmitter wants to maximize the Probability of Com‑ the best of the authors’ knowledge this problem has not
munication Connectivity (PCC) with all the receivers. been considered before.
One of the core dif iculties in communication connectiv‑ The main contributions of this paper are as follows:
ity problems is that the transmitter has to keep its SINR (1) A problem of multi‑link communication connectivity

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