Memoryless Relay Strategies for Two-Way Relay Channels: Performance Analysis and Optimization

We consider relaying strategies for two-way relay channels, where two terminals transmits simultaneously to each other with the help of relays. A memoryless system is considered, where the signal transmitted by a relay depends only on its last received signal. For binary antipodal signaling, we analyze and optimize the performance of existing amplify and forward (AF) and absolute (abs) decode and forward (ADF) for two- way AWGN relay channels. A new abs-based AF (AAF) scheme is proposed, which has better performance than AF. In low SNR, AAF performs even better than ADF. Furthermore, a novel estimate and forward (EF) strategy is proposed which performs better than ADF. More importantly, we optimize the relay strategy within the class of abs-based strategies via functional analysis, which minimizes the average probability of error over all possible relay functions. The optimized function is shown to be a Lambert's W function parameterized on the noise power and the transmission energy. The optimized function behaves like AAF in low SNR and like ADF in high SNR, resp., where EF behaves like the optimized function over the whole SNR range

Amplify-and-Forward in Wireless Relay Networks

A general class of wireless relay networks with a single source-destination pair is considered. Intermediate nodes in the network employ an amplify-and-forward scheme to relay their input signals. In this case the overall input-output channel from the source via the relays to the destination effectively behaves as an intersymbol interference channel with colored noise. Unlike previous work we formulate the problem of the maximum achievable rate in this setting as an optimization problem with no assumption on the network size, topology, and received signal-to-noise ratio. Previous work considered only scenarios wherein relays use all their power to amplify their received signals. We demonstrate that this may not always maximize the maximal achievable rate in amplify-and-forward relay networks. The proposed formulation allows us to not only recover known results on the performance of the amplify-and-forward schemes for some simple relay networks but also characterize the performance of more complex amplify-and-forward relay networks which cannot be addressed in a straightforward manner using existing approaches. Using cut-set arguments, we derive simple upper bounds on the capacity of general wireless relay networks. Through various examples, we show that a large class of amplify-and-forward relay networks can achieve rates within a constant factor of these upper bounds asymptotically in network parameters.Comment: Minor revision: fixed a typo in eqn. reference, changed the formatting. 30 pages, 8 figure

Memoryless relay strategies for two-way relay channels

We propose relaying strategies for uncoded two-way relay channels, where two terminals transmit simultaneously to each other with the help of a relay. In particular, we consider a memoryless system, where the signal transmitted by the relay is obtained by applying an instantaneous relay function to the previously received signal. For binary antipodal signaling, a class of so called absolute (abs)-based schemes is proposed in which the processing at the relay is solely based on the absolute value of the received signal. We analyze and optimize the symbol-error performance of existing and new abs-based and non-abs-based strategies under an average power constraint, including abs-based and non-abs-based versions of amplify and forward (AF), detect and forward (DF), and estimate and forward (EF). Additionally, we optimize the relay function via functional analysis such that the average probability of error is minimized at the high signal-to-noise ratio (SNR) regime. The optimized relay function is shown to be a Lambert W function parameterized on the noise power and the transmission energy. The optimized function behaves like abs-AF at low SNR and like abs-DF at high SNR, respectively; EF behaves similarly to the optimized function over the whole SNR range. We find the conditions under which each class of strategies is preferred. Finally, we show that all these results can also be generalized to higher order constellations

Network Code Design for Orthogonal Two-hop Network with Broadcasting Relay: A Joint Source-Channel-Network Coding Approach

This paper addresses network code design for robust transmission of sources over an orthogonal two-hop wireless network with a broadcasting relay. The network consists of multiple sources and destinations in which each destination, benefiting the relay signal, intends to decode a subset of the sources. Two special instances of this network are orthogonal broadcast relay channel and the orthogonal multiple access relay channel. The focus is on complexity constrained scenarios, e.g., for wireless sensor networks, where channel coding is practically imperfect. Taking a source-channel and network coding approach, we design the network code (mapping) at the relay such that the average reconstruction distortion at the destinations is minimized. To this end, by decomposing the distortion into its components, an efficient design algorithm is proposed. The resulting network code is nonlinear and substantially outperforms the best performing linear network code. A motivating formulation of a family of structured nonlinear network codes is also presented. Numerical results and comparison with linear network coding at the relay and the corresponding distortion-power bound demonstrate the effectiveness of the proposed schemes and a promising research direction.Comment: 27 pages, 9 figures, Submited to IEEE Transaction on Communicatio

Bayesian Symbol Detection in Wireless Relay Networks via Likelihood-Free Inference

This paper presents a general stochastic model developed for a class of cooperative wireless relay networks, in which imperfect knowledge of the channel state information at the destination node is assumed. The framework incorporates multiple relay nodes operating under general known non-linear processing functions. When a non-linear relay function is considered, the likelihood function is generally intractable resulting in the maximum likelihood and the maximum a posteriori detectors not admitting closed form solutions. We illustrate our methodology to overcome this intractability under the example of a popular optimal non-linear relay function choice and demonstrate how our algorithms are capable of solving the previously intractable detection problem. Overcoming this intractability involves development of specialised Bayesian models. We develop three novel algorithms to perform detection for this Bayesian model, these include a Markov chain Monte Carlo Approximate Bayesian Computation (MCMC-ABC) approach; an Auxiliary Variable MCMC (MCMC-AV) approach; and a Suboptimal Exhaustive Search Zero Forcing (SES-ZF) approach. Finally, numerical examples comparing the symbol error rate (SER) performance versus signal to noise ratio (SNR) of the three detection algorithms are studied in simulated examples

Analog network coding in general SNR regime: Performance of a greedy scheme

The problem of maximum rate achievable with analog network coding for a unicast communication over a layered relay network with directed links is considered. A relay node performing analog network coding scales and forwards the signals received at its input. Recently this problem has been considered under certain assumptions on per node scaling factor and received SNR. Previously, we established a result that allows us to characterize the optimal performance of analog network coding in network scenarios beyond those that can be analyzed using the approaches based on such assumptions. The key contribution of this work is a scheme to greedily compute a lower bound to the optimal rate achievable with analog network coding in the general layered networks. This scheme allows for exact computation of the optimal achievable rates in a wider class of layered networks than those that can be addressed using existing approaches. For the specific case of Gaussian N-relay diamond network, to the best of our knowledge, the proposed scheme provides the first exact characterization of the optimal rate achievable with analog network coding. Further, for general layered networks, our scheme allows us to compute optimal rates within a constant gap from the cut-set upper bound asymptotically in the source power.Comment: 11 pages, 5 figures. Fixed an issue with the notation in the statement and proof of Lemma 1. arXiv admin note: substantial text overlap with arXiv:1204.2150 and arXiv:1202.037