CAPACITY OF MULTIPLE ACCESS CHANNELS WITH CORRELATED JAMMING ∗ Shabnam Shafiee and Sennur Ulukus Department of Electrical and Computer Engineering University of Maryland College Park, MD ABSTRACT We investigate the behavior of two users and one jammer in an AWGN channel with and without fading when they participate in a non-cooperative zero-sum game, with the channel’s input/output mutual information as the objec- tive function. We assume that the jammer can eaves- drop the channel and can use the information obtained to perform correlated jamming. Under various assump- tions on the channel characteristics, and the extent of information available at the users and the jammer, we show the existence, or otherwise nonexistence of a simul- taneously optimal set of strategies for the users and the jammer. Whenever the game has a solution, we find the corresponding user and jammer strategies, and whenever the game does not admit a solution, we find the max-min user strategies and the corresponding jammer strategy. INTRODUCTION Correlated jamming, the situation where the jammer has full or partial knowledge about the user signals has been studied in the information-theoretic context un- der various assumptions [1–3]. In [1] the best transmit- ter/jammer strategies are found for a single user AWGN channel with a jammer who has full or partial knowledge of the transmitted signal. In [2], the problem is extended to a single user MIMO fading channel. This model has been further extended in [3], to consider fading in the channel between the jammer and the receiver. In [3] various assumptions are made on the availability of the user channel state at the user, and the jammer channel state at the jammer. In this paper, we study a multi-user system under correlated jamming. Partial results of this study have been reported in [4]. We consider a system of two users * This work was supported by NSF Grants ANI 02-05330 and CCR 03-11311; and ARL/CTA Grant DAAD 19-01-2-0011. and one jammer who has full or partial knowledge of the user signals through eavesdropping. In the non- fading two user channel, we show that the game has a solution which is Gaussian signalling for the users, and linear jamming for the jammer. Here we define linear jamming as employing a linear combination of the avail- able information about the user signals plus Gaussian noise. We then consider fading in the user channels. As opposed to [3], where the user channel states could only be known at the users, we assume the possibility of the jammer gaining information about the user channel states by eavesdropping the feedback channel from the receiver to the users and show that if the jammer is not aware of the user channel states, it would disregard its eavesdropping information and only transmit Gaussian noise. If the jammer knows the user channel states but not the user signals, the game has a solution which is composed of the optimal user and jammer power allo- cation strategies over the channel states, together with Gaussian signalling and linear jamming at each channel state. If the jammer knows the user channel states and the user signals, the game does not always have a Nash equilibrium solution, in which case, we characterize the max-min user strategies, and the corresponding jammer best response. The term capacity will hereafter always refer to the channel’s information capacity, defined as the channel’s maximum input/output mutual information [5]. SYSTEM MODEL Figure 1 shows a communication system with two users and one jammer. In the absence of fading, the attenu- ations of the user channels are known to everyone. The AWGN channel with two users and one jammer is Y =  h 1 X 1 +  h 2 X 2 + √ γJ + N (1) 1 of 7