Tobias J. Oechtering

Broadcast Capacity Region of Two-Phase Bidirectional Relaying

In a three-node network bidirectional communication between two nodes can be enabled by a half-duplex relay node with a decode-and-forward protocol. In the first phase, the messages of two nodes are transmitted to the relay node. In the second phase a re-encoded composition is broadcasted by the relay node. In this work the capacity region of the broadcast phase in terms of the maximal probability of error is determined. It is characterized by the mutual informations of the separate channels coupled by the common input.

Bidirectional regenerative half-duplex relaying using relay selection

We consider the problem of relay selection in a network with N relay nodes. A half-duplex relay node enables bidirectional communication between two nodes with a spectrally efficient two-phase protocol. In the first phase both nodes transmit their messages to a relay node, which decodes the messages and broadcasts a composition using superposition encoding in the succeeding phase. The probability that the achievable rate region of one relay node contains all other rate regions decreases with the number of relay nodes N. Therefore, we propose a relay selection criterion that decides according to the weighted rate sum for any bidirectional rate pair on the boundary of the achievable rate region individually. If we allow time-sharing between the usage of different relay nodes, we can enlarge the achievable rate region. In an iid Rayleigh fading scenario relay selection realizes multi-user diversity so that the sum-rate of any rate pair on the boundary of the ergodic rate region asymptotically grows with Theta(log(log(/V))).

A new cooperative transmission scheme using the space-time delay code

We propose a new resource efficient transmission scheme to achieve cooperative diversity of a distributed smart antenna system consisting of an information source, destination, and two alternating supportive relay stations. Each station is equipped with one antenna element. Furthermore we assume perfect synchronization and channel knowledge at the receivers. The proposed linear encoding functions with interference cancellation at one relay station result in an equivalent space-time delay coded system, but with additionally colored noise from the relay stations. Based on the maximum likelihood sequence estimator we derive criteria to evaluate the performance compared to the direct S1SO transmission. Finally the numerical simulation results of an suboptimal sequence estimator show significant performance gains if the power gain from the hopping is gainful exploited. If not, the additional noise from the relay stations will degrade the performance at reasonable transmit powers.

Achievable Rates for the Restricted Half-Duplex Two-Way Relay Channel

The main result of the paper is a new achievable rate region for the two-phase two-way relay channel with half duplex nodes. The new region is obtained using a compress- and-forward like protocol. Even though all information passes the relay, there are channels where decoding at the relay is suboptimal. The proposed protocol establishes a virtual two-way channel by forwarding a good enough version of the MAC output at the relay to both the receivers. In effect, the side information at the receivers can be used for the decoding of the transmission in the first phase.

Capacity of Gaussian MIMO bidirectional broadcast channels

We consider the broadcast phase of a three-node network, where a relay node establishes a bidirectional communication between two nodes using a spectrally efficient two-phase decode-and-forward protocol. In the first phase the two nodes transmit their messages to the relay node. Then the relay node decodes the messages and broadcasts a re-encoded composition of them in the second phase. We consider Gaussian MIMO channels and determine the capacity region for the second phase which we call the Gaussian MIMO bidirectional broadcast channel.

Multiantenna Bidirectional Broadcast Channels— Optimal Transmit Strategies

We consider a three-node network where a relay node establishes a bidirectional communication between the two other nodes using a spectrally efficient decode-and-forward protocol. In the first phase we have the classical multiple-access channel where both nodes transmit a message to the relay node, which then decodes the messages. In the second phase the relay broadcasts a re-encoded composition of them based on the network coding idea. This means that each receiving node uses the same data stream to infer on its intended message. We characterize the optimal transmit strategy for the broadcast phase where either the relay node or the two other nodes are equipped with multiple antennas. Our main result shows that beamforming into the subspace spanned by the channels is always an optimal transmit strategy for the multiple-input single-output bidirectional broadcast channel. Thereby, it shows that correlation between the channels is advantageous. Moreover, this leads to a parametrization of the optimal transmit strategy which specifies the whole capacity region. In retrospect the results are intuitively clear since the single-beam transmit strategy reflects the single stream processing due to the network coding approach.

On the optimal transmit strategy for the MIMO bidirectional broadcast channel

In this work the transmit covariance matrix optimization problem for the discrete memoryless MIMO Gaussian bidirectional broadcast channel is studied. A half-duplex relay node establishes bidirectional communication between two nodes using a decode-and-forward protocol. In the initial multiple access phase both nodes transmit their messages to the relay node. In the succeeding phase the relay broadcasts an optimal re-encoded message so that both nodes can decode the others message using their own message as side information. The capacity region of the bidirectional broadcast channel is completely characterized by a weighted rate sum maximization problem, which can be solved by a simple iterative fixed point algorithm. If an efficient transmit covariance matrix is invariant with respect to the joint subspace spanned by the channels, then different combinations of the part transmitted on the orthogonal subspaces result in equivalent transmit strategies with different ranks. A closed-form procedure to obtain the optimal transmit covariance is derived for the case where the rank of the channels is equal to the number of antennas at the relay node and a full-rank transmission is optimal. It shows the complicated structure of the optimal eigenspace, which depends on the weights and the mean transmit power constraint. For parallel channels the optimal solution is completely characterized and discussed, which also solves the optimal power allocation problem for a single-antenna OFDM system.

Achievable Rate Region of a Two Phase Bidirectional Relay Channel

In this work, the capacity region of the broadcast channel in a two phase bidirectional relay communication scenario is proved. Thereby, each receiving node has perfect knowledge about the message intended for the other node. The capacity region can be achieved using an auxiliary random variable taking two values, i.e., by the principle of time-sharing. The resulting achievable rate region of the two-phase bidirectional relaying includes the region which can be achieved by network coding applying XOR on the decoded messages at the relay node.

Achievable rates for the restricted half-duplex two-way relay channel under a partial-decode-and-forward protocol

In this paper, we state a new achievable rate region for the two-phase two-way relay channel with a half-duplex relay node. The new region is obtained using a partial-decode-and-forward protocol, which is a superposition of both, decode-and-forward and compress-and-forward. It contains the achievable rate regions according to Oechtering et al. (2008) and Schmurr et al. (2007) as special cases.

Complete Characterization of the Equivalent MIMO Channel for Quasi-Orthogonal Space–Time Codes

Recently, a quasi-orthogonal space-time block code (QSTBC) capable of achieving a significant fraction of the outage mutual information of a multiple-input-multiple-output (MIMO) wireless communication system for the case of nT = 4 transmit and nR = 1 receive antennas was proposed. We generalize these results to nT = 2n transmit and an arbitrary number of receive antennas. Furthermore, we completely characterize the structure of the equivalent channel for the general case and show that for all nT = 2n and nR the eigenvectors of the equivalent channel are fixed and independent from the channel realization. Furthermore, the eigenvalues of the equivalent channel are independent identically distributed random variables each following a noncentral chi-square distribution with 4nR degrees of freedom. Based on these important insights into the structure of the QSTBC, we derive tight lower and upper bounds for the outage probability achieved with QSTBC. Finally, by utilizing the special structure of the QSTBC, we propose a new transmit strategy, which decouples the signals transmitted from different antennas in order to detect the symbols separately with a linear ML-detector rather than joint detection, an up to now only known advantage of orthogonal space-time block codes (OSTBC).