Secure Degrees of Freedom of MIMO X-Channels with Output Feedback and Delayed CSIT

We investigate the problem of secure transmission over a two-user multi-input multi-output (MIMO) X-channel in which channel state information is provided with one-unit delay to both transmitters (CSIT), and each receiver feeds back its channel output to a different transmitter. We refer to this model as MIMO X-channel with asymmetric output feedback and delayed CSIT. The transmitters are equipped with M-antennas each, and the receivers are equipped with N-antennas each. For this model, accounting for both messages at each receiver, we characterize the optimal sum secure degrees of freedom (SDoF) region. We show that, in presence of asymmetric output feedback and delayed CSIT, the sum SDoF region of the MIMO X-channel is same as the SDoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver and delayed CSIT. This result shows that, upon availability of asymmetric output feedback and delayed CSIT, there is no performance loss in terms of sum SDoF due to the distributed nature of the transmitters. Next, we show that this result also holds if only output feedback is conveyed to the transmitters, but in a symmetric manner, i.e., each receiver feeds back its output to both transmitters and no CSIT. We also study the case in which only asymmetric output feedback is provided to the transmitters, i.e., without CSIT, and derive a lower bound on the sum SDoF for this model. Furthermore, we specialize our results to the case in which there are no security constraints. In particular, similar to the setting with security constraints, we show that the optimal sum DoF region of the (M,M,N,N)--MIMO X-channel with asymmetric output feedback and delayed CSIT is same as the DoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver, and delayed CSIT. We illustrate our results with some numerical examples.Comment: To Appear in IEEE Transactions on Information Forensics and Securit

Secure GDoF of the Z-channel with Finite Precision CSIT: How Robust are Structured Codes?

Under the assumption of perfect channel state information at the transmitters (CSIT), it is known that structured codes offer significant advantages for secure communication in an interference network, e.g., structured jamming signals based on lattice codes may allow a receiver to decode the sum of the jamming signal and the signal being jammed, even though they cannot be separately resolved due to secrecy constraints, subtract the aggregate jammed signal, and then proceed to decode desired codewords at lower power levels. To what extent are such benefits of structured codes fundamentally limited by uncertainty in CSIT? To answer this question, we explore what is perhaps the simplest setting where the question presents itself -- a Z interference channel with secure communication. Using sum-set inequalities based on Aligned Images bounds we prove that the GDoF benefits of structured codes are lost completely under finite precision CSIT. The secure GDoF region of the Z interference channel is obtained as a byproduct of the analysis.Comment: 34 pages, 10 figure

Network Convergence in Multicarrier Hybrid Cellular Network

In a multicarrier communication system with known channel state information at transmitter (CSIT), it is well-known that the water-filling power allocation scheme is optimal in achieving the Shannon capacity. However, in a multicarrier broadcast network (e.g. over-the-air TV network) without CSIT, the optimal power allocation among subcarriers is still unknown, largely due to the heterogeneity of the channel conditions associated with different receivers. In the first part of the thesis, the performance of a generic multicarrier broadcast network is thoroughly studied by exploiting the frequency diversity over subcarriers. In particular, the performance metric is first defined based on the relationship among broadcast transmission rate, coverage area and outage probability. In order to maximize the network performance, closed form expressions of the instantaneous mutual information (IMI) and the optimal power allocation schemes are derived for both low SNR and high SNR cases; upper and lower bounds are also provided to estimate broadcast coverage area in general SNR regime. Also we extend our discussion to the broadcast network with multiple collaborative transmitters. Extensive simulation results are provided to validate our analysis. In the second part of the thesis, we discuss the optimal performance of a generic broadcast cellular hybrid network. It is well known that the Dirty Paper Coding (DPC) achieves the channel capacity for multiuser degraded channels. However, the optimality of DPC remains unknown for non-degraded channel. Specifically, we derive the optimal interference pre-cancellation order for a DPC based broadcast and unicast hybrid network. Different DPC cancellation schemes are studied to maximize the hybrid capacity region. The conditions for each scheme being optimal are analytically derived. Both ergodic and outage capacity are considered as our performance metric. Our results show that the optimal interference pre-cancellation order varies with SNR and broadcast and unicast channel conditions. Moreover, in low SNR condition, the optimal power allocation scheme is derived to reach the maximal sum rate