In this paper, we study the secrecy capacity of Gaussian multiple-input multiple-output (MIMO) wiretap channels (WTCs) with a finite memory, subject to a per-symbol average power constraint on the MIMO channel input. MIMO channels with finite memory are very common in wireless communications as well as in wireline communications (e.g., in communications over power lines). To derive the secrecy capacity of the Gaussian MIMO WTC with finite memory, we first construct an asymptotically equivalent block-memoryless MIMO WTC, which is then transformed into a set of parallel, independent, memoryless MIMO WTCs in the frequency domain. The secrecy capacity of the Gaussian MIMO WTC with finite memory is obtained as the secrecy capacity of the set of parallel, independent, memoryless MIMO WTCs, and is expressed as maximization over the input covariance matrices in the frequency domain. Finally, we detail two applications of our result: First, we show that the secrecy capacity of the Gaussian scalar WTC with finite memory can be achieved by waterfilling, and obtain a closed-form expression for this secrecy capacity. Then, we use our result to characterize the secrecy capacity of narrowband powerline channels, thereby resolving one of the major open issues for this channel model.

Handling interference is one of the main challenges in the design of wireless networks. In this paper, we study the application of cooperation for interference management in the weak interference (WI) regime, focusing on the Z-interference channel with a causal relay (Z-ICR), in which the channel coefficients are subject to ergodic phase fading, all transmission powers are finite, and the relay is full-duplex. The phase fading model represents many practical communications systems in which the transmission path impairments mainly affect the phase of the signal, such as non-coherent wireless communications and fiber optic channels. In order to provide a comprehensive understanding of the benefits of cooperation in the WI regime, we characterize, for the first time, two major performance measures for the ergodic phase fading Z-ICR in the WI regime: the sum-rate capacity and the maximal generalized degrees-of-freedom (GDoF). In the capacity analysis, we obtain conditions on the channel coefficients, subject to which the sum-rate capacity of the ergodic phase fading Z-ICR is achieved by treating interference as noise at each receiver, and explicitly state the corresponding sum-rate capacity. In the GDoF analysis, we derive conditions on the exponents of the magnitudes of the channel coefficients, under which treating interference as noise achieves the maximal GDoF, which is explicitly characterized as well. It is shown that under certain conditions on the channel coefficients, relaying strictly increases both the sum-rate capacity and the maximal GDoF of the ergodic phase fading Z-interference channel in the WI regime. Our results demonstrate for the first time the gains from relaying in the presence of interference, when interference is weak and the relay power is finite, both in increasing the sum-rate capacity and in increasing the maximal GDoF, compared with the channel without a relay.

Privacy is a critical issue when communicating over shared mediums. A fundamental model for the information-theoretic analysis of secure communications is the wiretap channel (WTC), which consists of a communicating pair and an eavesdropper. In this work we study the secrecy capacity of Gaussian multiple-input multiple-output (MIMO) WTCs with finite memory. These channels are very common in wireless communications as well as in wireline communications (e.g., in power line communications). We derive a closed-form expression for the secrecy capacity of the MIMO Gaussian WTC with finite memory via the analysis of an equivalent block-memoryless model, which is transformed into a set of parallel independent memoryless MIMO WTCs. The secrecy capacity is expressed as the maximization over the input covariance matrices in the frequency domain. Finally, we show that for the Gaussian scalar WTC with finite memory, the secrecy capacity can be obtained by waterfilling.

We study the diversity-multiplexing tradeoff (DMT) for the slow fading interference channel with a relay (ICR). We derive four inner bounds on the DMT region: the first is based on the compress-and-forward (CF) relaying scheme, the second is based on the decode-and-forward (DF) relaying scheme, and the last two bounds are based on the half-duplex (HD) and full-duplex (FD) amplify-and-forward (AF) schemes. For the CF and DF schemes, we find conditions on the channel parameters and the multiplexing gains, under which the corresponding inner bound achieves the optimal DMT region. We also identify the cases in which the DMT region of the ICR corresponds to that of two parallel slow fading relay channels, implying that interference does not decrease the DMT for each pair, and that a single relay can be DMT-optimal for two pairs simultaneously. For the HD-AF scheme, we derive conditions on the channel coefficients under which the proposed scheme achieves the optimal DMT for the AF-based relay channel. Finally, we identify the conditions under which adding a relay strictly enlarges the DMT region relative to the interference channel without a relay.

We study the generalized degrees of freedom (GDoF) of the phase fading Z-interference channel with a relay in the weak interference regime. We consider the scenario in which the relay node receives transmissions only from one of the sources but its transmissions are received at both destinations. We first derive two upper bounds on the achievable GDoF: the first bound is based on the genie-aided approach, and the second bound is based on the cut-set theorem. We then derive an achievable GDoF by employing the decode-and-forward strategy at the relay and by treating interference as noise at each receiver. Lastly, we derive conditions on the gains of the links, under which this simple scheme is GDoF-optimal. Our results support the application of relaying in scenarios in which the interference is weak.

We study the sum-rate capacity of the Z-interference channel with a relay (Z-ICR) in the weak interference regime, when the channel coefficients are subject to phase fading. This fading model represents many practical communication systems in which phase noise is a major concern, such as OFDM communications and line-of-sight microwave communications. We consider the case in which the relay receives transmissions from only one of the two transmitters, but the transmission of the relay is received at both destinations. We present conditions on the channel coefficients under which the sum-rate capacity of the phase fading Z-ICR is achieved by treating interference as noise at each receiver, and derive the corresponding sum-rate capacity. Our results show the benefits of relaying in the presence of interference when interference is weak and relay power is finite.

We study the diversity-multiplexing tradeoff (DMT) for the slow fading interference channel with a relay (ICR). We first derive an outer bound on the DMT based on the cut-set bound. We then derive two inner bounds on the DMT: One is based on the compress-and-forward relaying scheme and the other is based on the decode-and-forward relaying scheme. We find conditions on the channel parameters and the multiplexing gains under which the proposed inner bounds achieve the optimal DMT. We also identify cases in which the DMT of the ICR is the same as two parallel fading relay channels, implying that interference does not decrease the DMT for each pair, and that a single relay can be DMT-optimal for two pairs simultaneously. Lastly, we identify conditions under which adding a relay strictly improves the DMT relative to the interference channel without a relay.

Handling interference is one of the main challenges in the design of wireless networks. One of the key approaches to interference management is node cooperation, which can be classified into two main types: relaying and feedback. In this paper, we consider simultaneous application of both cooperation types in the presence of interference. We obtain exact characterization of the capacity regions for Rayleigh fading and phase fading interference channels with a relay and with feedback links, in the strong and very strong interference regimes. Four feedback configurations are considered: 1) feedback from both receivers to the relay, 2) feedback from each receiver to the relay and to one of the transmitters (either corresponding or opposite), 3) feedback from one of the receivers to the relay, and 4) feedback from one of the receivers to the relay and to one of the transmitters. Our results show that there is a strong motivation for incorporating relaying and feedback into wireless networks.

Handling interference is one of the main challenges in the design of wireless networks. One of the key approaches to interference management is node cooperation, which can be classified into two main types: relaying and feedback. In this work we consider simultaneous application of both cooperation types in the presence of interference. We obtain exact characterization of the capacity regions for Rayleigh fading and phase fading interference channels with a relay and with feedback links, in the strong and very strong interference regimes. Two feedback configurations are considered. In the first configuration there are feedback links from both receivers to the relay, and in the second configuration there are feedback links from both receivers to the relay and to their opposite transmitters.