Achievable rate regions and outer bounds for a multi-pair bi-directional relay network

In a bi-directional relay channel, a pair of nodes wish to exchange independent messages over a shared wireless half-duplex channel with the help of relays. Recent work has mostly considered information theoretic limits of the bi-directional relay channel with two terminal nodes (or end users) and one relay. In this work we consider bi-directional relaying with one base station, multiple terminal nodes and one relay, all of which operate in half-duplex modes. We assume that each terminal node communicates with the base-station in a bi-directional fashion through the relay and do not place any restrictions on the channels between the users, relays and base-stations; that is, each node has a direct link with every other node. Our contributions are three-fold: 1) the introduction of four new temporal protocols which fully exploit the two-way nature of the data and outperform simple routing or multi-hop communication schemes by carefully combining network coding, random binning and user cooperation which exploit over-heard and own-message side information, 2) derivations of inner and outer bounds on the capacity region of the discrete-memoryless multi-pair two-way network, and 3) a numerical evaluation of the obtained achievable rate regions and outer bounds in Gaussian noise which illustrate the performance of the proposed protocols compared to simpler schemes, to each other, to the outer bounds, which highlight the relative gains achieved by network coding, random binning and compress-and-forward-type cooperation between terminal nodes.Comment: 61 pages, 12 figures, will be submitted to IEEE info theor

Resource Allocation and Rate Gains in Practical Full-Duplex Systems

Full-duplex communication has the potential to substantially increase the throughput in wireless networks. However, the benefits of full-duplex are still not well understood. In this paper, we characterize the full-duplex rate gains in both single-channel and multi-channel use cases. For the single-channel case, we quantify the rate gain as a function of the remaining self-interference and SNR values. We also provide a sufficient condition under which the sum of uplink and downlink rates on a full-duplex channel is concave in the transmission power levels. Building on these results, we consider the multi-channel case. For that case, we introduce a new realistic model of a small form-factor (e.g., smartphone) full-duplex receiver and demonstrate its accuracy via measurements. We study the problem of jointly allocating power levels to different channels and selecting the frequency of maximum self-interference suppression, where the objective is maximizing the sum of the rates over uplink and downlink OFDM channels. We develop a polynomial time algorithm which is nearly optimal in practice under very mild restrictions. To reduce the running time, we develop an efficient nearly-optimal algorithm under the high SINR approximation. Finally, we demonstrate via numerical evaluations the capacity gains in the different use cases and obtain insights into the impact of the remaining self-interference and wireless channel states on the performance.Comment: Partial and preliminary version appeared in ACM SIGMETRICS'15. A shorter version of v2 is to appear in IEEE/ACM Transactions on Networkin

Bi-directional half-duplex protocols with multiple relays

In a bi-directional relay channel, two nodes wish to exchange independent messages over a shared wireless half-duplex channel with the help of relays. Recent work has considered information theoretic limits of the bi-directional relay channel with a single relay. In this work we consider bi-directional relaying with multiple relays. We derive achievable rate regions and outer bounds for half-duplex protocols with multiple decode and forward relays and compare these to the same protocols with amplify and forward relays in an additive white Gaussian noise channel. We consider three novel classes of half-duplex protocols: the (m,2) 2 phase protocol with m relays, the (m,3) 3 phase protocol with m relays, and general (m, t) Multiple Hops and Multiple Relays (MHMR) protocols, where m is the total number of relays and 3<t< m+3 is the number of temporal phases in the protocol. The (m,2) and (m,3) protocols extend previous bi-directional relaying protocols for a single m=1 relay, while the new (m,t) protocol efficiently combines multi-hop routing with message-level network coding. Finally, we provide a comprehensive treatment of the MHMR protocols with decode and forward relaying and amplify and forward relaying in the Gaussian noise, obtaining their respective achievable rate regions, outer bounds and relative performance under different SNRs and relay geometries, including an analytical comparison on the protocols at low and high SNR.Comment: 44 pages, 17 figures, Submitted to IEEE Transactions on Information Theor

On the Capacity Regions of Single-Channel and Multi-Channel Full-Duplex Links

We study the achievable capacity regions of full-duplex links in the single- and multi-channel cases (in the latter case, the channels are assumed to be orthogonal -- e.g., OFDM). We present analytical results that characterize the uplink and downlink capacity region and efficient algorithms for computing rate pairs at the region's boundary. We also provide near-optimal and heuristic algorithms that "convexify" the capacity region when it is not convex. The convexified region corresponds to a combination of a few full-duplex rates (i.e., to time sharing between different operation modes). The algorithms can be used for theoretical characterization of the capacity region as well as for resource (time, power, and channel) allocation with the objective of maximizing the sum of the rates when one of them (uplink or downlink) must be guaranteed (e.g., due to QoS considerations). We numerically illustrate the capacity regions and the rate gains (compared to time division duplex) for various channel and cancellation scenarios. The analytical results provide insights into the properties of the full-duplex capacity region and are essential for future development of scheduling, channel allocation, and power control algorithms

Relay-Assisted Interference Channel: Degrees of Freedom

This paper investigates the degrees of freedom of the interference channel in the presence of a dedicated MIMO relay. The relay is used to manage the interference at the receivers. It is assumed that all nodes including the relay have channel state information only for their own links and that the relay has M (greater than or equal to K) antennas in a K-user network. We pose the question: What is the benefit of exploiting the direct links from the source to destinations compared to a simpler two-hop strategy. To answer this question, we first establish the degrees of freedom of the interference channel with a MIMO relay, showing that a K-pair network with a MIMO relay has K/2 degrees of freedom. Thus, appropriate signaling in a two-hop scenario captures the degrees of freedom without the need for the direct links. We then consider more sophisticated encoding strategies in search of other ways to exploit the direct links. Using a number of hybrid encoding strategies, we obtain non-asymptotic achievable sum-rates. We investigate the case where the relay (unlike other nodes) has access to abundant power, showing that when sources have power P and the relay is allowed power proportional to O(P^2), the full degrees of freedom K are available to the network.Comment: 7 double-column pages, 3 figures, accepted in IEEE Transactions on Information Theor

Full-Duplex Communications: Performance in Ultra-Dense Small-Cell Wireless Networks

Theoretically, full-duplex (FD) communications can double the spectral-efficiency (SE) of a wireless link if the problem of self-interference (SI) is completely eliminated. Recent developments towards SI cancellation techniques have allowed to realize the FD communications on low-power transceivers, such as small-cell (SC) base stations. Consequently, the FD technology is being considered as a key enabler of 5G and beyond networks. In the context of 5G, FD communications have been initially investigated in a single SC and then into multiple SC environments. Due to FD operations, a single SC faces residual SI and intra-cell co-channel interference (CCI), whereas multiple SCs face additional inter-cell CCI, which grows with the number of neighboring cells. The surge of interference in the multi-cell environment poses the question of the feasibility of FD communications. In this article, we first review the FD communications in single and multiple SC environments and then provide the state-of-the-art for the CCI mitigation techniques, as well as FD feasibility studies in a multi-cell environment. Further, through numerical simulations, the SE performance gain of the FD communications in ultra-dense massive multiple input multiple-output enabled millimeter wave SCs is presented. Finally, potential open research challenges of multi-cell FD communications are highlighted.Comment: Accepted for publication in IEEE Vehicular Technology Magazine, Special Issue on 5G Technologies and Application

On the Capacity of the Half-Duplex Diamond Channel

In this paper, a dual-hop communication system composed of a source S and a destination D connected through two non-interfering half-duplex relays, R1 and R2, is considered. In the literature of Information Theory, this configuration is known as the diamond channel. In this setup, four transmission modes are present, namely: 1) S transmits, and R1 and R2 listen (broadcast mode), 2) S transmits, R1 listens, and simultaneously, R2 transmits and D listens. 3) S transmits, R2 listens, and simultaneously, R1 transmits and D listens. 4) R1, R2 transmit, and D listens (multiple-access mode). Assuming a constant power constraint for all transmitters, a parameter $\Delta$ is defined, which captures some important features of the channel. It is proven that for $\Delta$=0 the capacity of the channel can be attained by successive relaying, i.e, using modes 2 and 3 defined above in a successive manner. This strategy may have an infinite gap from the capacity of the channel when $\Delta\neq$0. To achieve rates as close as 0.71 bits to the capacity, it is shown that the cases of $\Delta$>0 and $\Delta$<0 should be treated differently. Using new upper bounds based on the dual problem of the linear program associated with the cut-set bounds, it is proven that the successive relaying strategy needs to be enhanced by an additional broadcast mode (mode 1), or multiple access mode (mode 4), for the cases of $\Delta$0, respectively. Furthermore, it is established that under average power constraints the aforementioned strategies achieve rates as close as 3.6 bits to the capacity of the channel.Comment: 25 pages, 2 figures, submitted to IEEE Transactions on Information Theor

On the Capacity of the Half-Duplex MIMO Gaussian Diamond Channel

In this paper, we analyze the 2-relay multiple-input multiple-output (MIMO) Gaussian diamond channel. We show that a multihopping decode-and-forward with multiple access (MDF-MAC) protocol achieves rates within a constant gap from capacity when a channel parameter $\Delta$ is greater than zero. We also identify the transmit covariance matrices to be used by each relay in the multiple-access (MAC) state of the MDF-MAC protocol. As done for the single-antenna 2-relay Gaussian diamond channel, the channel parameter $\Delta$ is defined to be the difference between the product of the capacities of the links from the source to the two relays and the product of the capacities of the links from the two relays to the destination.Comment: Submitted to ISIT 201

The DoF of Two-way Butterfly Networks

This paper studies the two-way butterfly network, a class of two-way four-unicast networks. We first show that bidirectional links do not increase the degrees of freedom for this network thus giving the first example for networks, to the best of our knowledge, where bidirectional links do not increase the degrees of freedom. Further, we see that sufficient caching at the relays or increasing the number of antennas in the relays can double the two-way degrees of freedom for butterfly network

Decode-Forward Transmission for the Two-Way Relay Channels

We propose composite decode-forward (DF) schemes for the two-way relay channel in both the full- and half-duplex modes by combining coherent relaying, independent relaying and partial relaying strategies. For the full-duplex mode, the relay partially decodes each user's information in each block and forwards this partial information coherently with the source user to the destination user in the next block as in block Markov coding. In addition, the relay independently broadcasts a binning index of both users' decoded information parts in the next block as in independent network coding. Each technique has a different impact on the relay power usage and the rate region. We further analyze in detail the independent partial DF scheme and derive in closed-form link regimes when this scheme achieves a strictly larger rate region than just time-sharing between its constituent techniques, direct transmission and independent DF relaying, and when it reduces to a simpler scheme. For the half-duplex mode, we propose a 6-phase time-division scheme that incorporates all considered relaying techniques and uses joint decoding simultaneously over all receiving phases. Numerical results show significant rate gains over existing DF schemes, obtained by performing link adaptation of the composite scheme based on the identified link regimes.Comment: This work has been submitted to IEEE Transactions on Communications for possible publicatio