Mixed anti-jamming strategies in fixed-rate wireless systems over fast fading channels

Abstract

This is the first part of a two-part paper that studies the problem of jamming in a fixed-rate transmission system with fading, under the general assumption that the jammer has no knowledge about either the codebook used by the legitimate communication terminals, or the source's output. Both transmitter and jammer are subject to power constraints which can be enforced over each codeword (short-term / peak) or over all codewords (long-term / average), hence generating different scenarios. All our jamming problems are formulated as zero-sum games, having the probability of outage as pay-off function and power control functions as strategies. The paper aims at providing a comprehensive coverage of these problems, under fast and slow fading, peak and average power constraints, pure and mixed strategies, with and without channel state information (CSI) feedback. In this first part we study the fast fading scenario. We first assume full CSI to be available to all parties. For peak power constraints, a Nash equilibrium of pure strategies is found. For average power constraints, both pure and mixed strategies are investigated. With pure strategies, we derive the optimal power control functions for both intra-frame and inter-frame power allocation. Maximin and minimax solutions are found and shown to be different, which implies the non-existence of a saddle point. In addition we provide alternative perspectives in obtaining the optimal intra-frame power control functions under the long-term power constraints. With mixed strategies, the Nash equilibrium is found by solving the generalized form of an older problem dating back to Bell and Cover [1]. Finally, for comparison purposes, we derive a Nash equilibrium of the game in which no CSI is fed back from the receiver. We show that full channel state information brings only a very slight improvement in the system's performance. 5 an optimal solution has already been reached and show it has to satisfy a set of properties. We first assume these properties are not satisfied, and then show that under this assumption there is room for improvement. Thus we prove that any solution not satisfying our set of properties cannot be optimal (i.e. the properties are necessary). We pick the properties in such a manner that they are sufficient for the complete characterization of the optimal solution. That is, we make sure that the system of necessary properties has a unique solution.In the maximin case (when jammer plays first), assume that the jammer has already allocated some power J M to a given frame. Depending on the value of J M , and its own power constraints, the transmitter decides whether it wants to achieve reliable communication over that frame. If it decides to transmit, it needs to spend as little power as possible (the transmitter will be able to use the saved power for achieving reliable communication over another set of frames, and thus to decrease the probability of outage). Therefore, the transmitter's objective is to minimize the power P M spent for achieving reliable c...

Jamming in Wireless Networks Under Uncertainty

“…The transmitter and the jammer have the same power budgets, namely, letT =J = 3. The jammer fading and transmitter gains are given by ((1, 5), (2, 4)), (3,3), (4, 2), (5, 1)) and ((20, 1), (4,2), (3,3), (2,4), (1,5)), respectively. For the optimization scenario we assume that the transmitter applies the uniform strategy T 0 , so T 0 = (3/5, 3/5, 3/5, 3/5, 3/5).…”

“…The recent literature covers a variety of jamming problems [1], [2], [4], [5], [6], [13], [14], [15].…”

Alpha-Fair Resource Allocation under Incomplete Information and Presence of a Jammer

“…The optimal payoffs v D , v I and the Jain's fairness indexes J D , J I for dependent and independents plots are given in Table 1 as functions on α = 0.1(0.2)0.9 and p 1 = 0.0(0.1)1.0. We assume that g = ((5, 1), (4,2), (3,3), (2,4), (1,5)) and h = ((1, 1), (1, 1), (1, 1), (1, 1), (1, 1)) and for the independent plot we assume that K = L q i = p i , i ∈ [1, K]. We consider three cases of jamming power: (a) a small total jamming powerJ = 0.1 (Table 1), (b) a comparable total jamming powerJ = 1 with the base station power (Table 2) and (c) an overwhelming jamming power over the base station oneJ = 30 (Table 3).…”

“…Namely, we develop a concept of α-fairness under uncertainty to allocate power resource in the presence of a jammer under two types of uncertainty: (a) the decision maker does not have complete knowledge about the parameters of the environment but knows only their distribution, (b) the jammer can come into the environment with some probability bringing extra background noise. These scenarios have not been considered previously in the literature (see e.g., [1][2][3][4] and references therein). The goal of the decision maker is to maximize the α-fairness utility function with respect to the SNIR (signal to noise-plus-interference ratio).…”

Jamming-aware minimum energy routing in wireless networks

“…Thus, jammers that target the physical layer of the network, because of their simplicity and effectiveness, are of interest here. For instance, in [5], [6], [7], [8], [9], [10], strategies to combat one such jammer are considered.…”