ON THE DEGREES OF FREEDOM OF THE RELAY X-CHANNEL

Interference is a principal source of capacity limitations in today's multi-access multi-user wireless systems. Despite the fact that the capacity of interference channels is still an unsolved problem, the research community has already established a substantial work towards this goal. In effort to provide alternative attainable expressions for performance limits in interference channels, the concept of the Degrees of Freedom (DoF) has been introduced. DoF describes network capacity in terms of the number of maximum possible simultaneous interference-free streams. X-channel is defined where there are two transmitters, two receivers and each transmitter has an independent message for each receiver. Interference channel, broadcast channel and the multiple access channels are special cases of the X-channel. In this thesis, we further investigate the effect of a relay on the DoF of a single input single output (SISO) X-channel with no channel state information at transmitters (CSIT). In contrast to previous work, which has focused on two antennas at the relay to achieve the optimal 4/3 DoF, we focus on the case of a single antenna half duplex relay. We show that with a single antenna relay and delayed output feedback, the upper bound of 4/3 DoF for the X-channel is achievable and we provide the achievability scheme. We revisit the previously studied case of single antenna relay in the more practical setting of alternating CSIT. We show that the optimal 4/3 DoF achievability does not mandate full CSIT availability. For the case of partial alternating CSIT availability at the relay transmitters, we propose a scheme that can achieve the optimal 4/3 DoF and we deduce the minimum CSIT availability for the proposed scheme to achieve optimality

Retrospective Interference Alignment for Two-Cell Uplink MIMO Cellular Networks with Delayed CSIT

In this paper, we propose a new retrospective interference alignment for two-cell multiple-input multiple-output (MIMO) interfering multiple access channels (IMAC) with the delayed channel state information at the transmitters (CSIT). It is shown that having delayed CSIT can strictly increase the sum-DoF compared to the case of no CSIT. The key idea is to align multiple interfering signals from adjacent cells onto a small dimensional subspace over time by fully exploiting the previously received signals as side information with outdated CSIT in a distributed manner. Remarkably, we show that the retrospective interference alignment can achieve the optimal sum-DoF in the context of two-cell two-user scenario by providing a new outer bound.Comment: 7 pages, 2 figures, to appear in IEEE ICC 201

Degrees of Freedom and Achievable Rate of Wide-Band Multi-cell Multiple Access Channels With No CSIT

This paper considers a $K$-cell multiple access channel with inter-symbol interference. The primary finding of this paper is that, without instantaneous channel state information at the transmitters (CSIT), the sum degrees-of-freedom (DoF) of the considered channel is $\frac{\beta -1}{\beta}K$ with $\beta \geq 2$ when the number of users per cell is sufficiently large, where $\beta$ is the ratio of the maximum channel-impulse-response (CIR) length of desired links to that of interfering links in each cell. Our finding implies that even without instantaneous CSIT, \textit{interference-free DoF per cell} is achievable as $\beta$ approaches infinity with a sufficiently large number of users per cell. This achievability is shown by a blind interference management method that exploits the relativity in delay spreads between desired and interfering links. In this method, all inter-cell-interference signals are aligned to the same direction by using a discrete-Fourier-transform-based precoding with cyclic prefix that only depends on the number of CIR taps. Using this method, we also characterize the achievable sum rate of the considered channel, in a closed-form expression.Comment: Submitted to IEEE Transactions on Communication

SECURITY UNDER IMPERFECT CHANNEL KNOWLEDGE IN WIRELESS NETWORKS

This dissertation studies physical layer security in wireless networks using an information theoretic framework. The central theme of this work is exploring the effect of delayed or no channel state information (CSI) on physical layer security in various wireless channel models. We begin with the fast Rayleigh fading wiretap channel, over which a legitimate transmitter wishes to have secure communication with a legitimate receiver in the presence of an eavesdropper. Subject to an average power constraint on the input, and with no CSI at any user, we show that the input distribution that achieves the secrecy capacity for this wiretap channel is discrete with a finite number of mass points. This enables us to evaluate the exact secrecy capacity of this channel numerically. Next, we consider multi-user models, specifically, the wiretap channel with M helpers, the K-user multiple access wiretap channel, and the K-user interference channel with an external eavesdropper, when no eavesdropper's CSI is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSI at the transmitter (CSIT) does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper's CSIT, the K-user multiple access wiretap channel reduces to a wiretap channel with (K-1) helpers from a sum s.d.o.f. perspective, and the optimal sum s.d.o.f. reduces from K(K-1)/(K(K-1)+1) to (K-1)/K. For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from K(K-1)/(2K-1) to (K-1)/2 in the absence of the eavesdropper's CSIT. Our results show that the lack of eavesdropper's CSIT does not have a significant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large. We, then, study multiple-input multiple-output (MIMO) multi-user channels. We begin with the case when full CSIT is available. We consider a two-user MIMO multiple access wiretap channel with N antennas at each transmitter, N antennas at the legitimate receiver, and K antennas at the eavesdropper. We determine the optimal sum s.d.o.f. for this model for all values of N and K. We subdivide our problem into several regimes based on the values of N and K, and provide achievable schemes based on real and vector space alignment techniques for fixed and fading channel gains, respectively. To prove the optimality of the achievable schemes, we provide matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel. In line with the theme of this dissertation, we next consider the MIMO wiretap channel with one helper and the two-user MIMO multiple access channel when no eavesdropper CSIT is available. In each case, the eavesdropper has K antennas while the remaining terminals have N antennas. We determine the optimal sum s.d.o.f. for each channel model for the regime K= N. Finally, we explore the effect of delayed CSIT on physical layer security. In particular, we consider the two user multiple-input single-output (MISO) broadcast channel with confidential messages, in which the nature of CSIT from each user can be of the form I_{i}, i=1,2 where I_{i} belongs to {P, D,N}, and the forms P, D and N correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can be any of nine possible states corresponding to all possible values of (I_{1},I_{2}). While the optimal sum s.d.o.f. in the homogeneous settings corresponding to I_1=I_2 are already known in the literature, we focus on the heterogeneous settings where I_1 is not equal to I_2 and establish the optimal s.d.o.f. region in each case. We further consider the case where the CSIT state varies with time. Each state (I_1,I_2) can then occur for \lambda_{I_{1}I_{2}} fraction of the total duration. We determine the s.d.o.f. region of the MISO broadcast channel with confidential messages under such an alternating CSIT setting, with a mild symmetry assumption, where \lambda_{I_{1} I_{2}}=\lambda_{I_{2}I_{1}}