Communication networks are often designed and analyzed assuming tight synchronization among nodes. However, in applications that require communication in the energy-efficient regime of low signal-to-noise ratios, establishing tight synchronization among nodes in the network can result in a significant energy overhead. Motivated by a recent result showing that near-optimal energy efficiency can be achieved over the AWGN channel without requiring tight synchronization, we consider the question of whether the potential gains of cooperative communication can be achieved in the absence of synchronization. We focus on the symmetric Gaussian diamond network and establish that cooperative-communication gains are indeed feasible even with unsynchronized nodes. More precisely, we show that the capacity per unit energy of the unsynchronized symmetric Gaussian diamond network is within a constant factor of the capacity per unit energy of the corresponding synchronized network. To this end, we propose a distributed relaying scheme that does not require tight synchronization but nevertheless achieves most of the energy gains of coherent combining.
The constant multiplicative approximation guarantee provided in @cite_15 implies that bursty amplify-and-forward also achieves the capacity of the synchronized symmetric Gaussian diamond per unit energy up to the same multiplicative gap. For the symmetric diamond networks with only two relays, it was shown in @cite_7 that bursty amplify-forward and superposition-partial-decode-forward achieve the capacity per unit energy up to a factor of at most @math and at most @math , respectively. The capacity per unit energy of the canonical synchronized single-relay channel was approximated to within a factor @math in @cite_0 . A bursty amplify-and-forward scheme was also shown to achieve the optimal outage capacity per unit energy for the frequency-division relay channel at low SNR and at low outage probability @cite_16 . It is worth pointing out that the bursty constructions mentioned here do not generalize to the unsynchronized diamond network considered in this paper, since, due to the synchronization errors, the bursty codewords cannot be made to combine constructively at the destination.
@cite_0 @cite_15 @cite_16 @cite_7
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We consider the Gaussian “diamond” or parallel relay network, in which a source node transmits a message to a destination node with the help of N relays. Even for the symmetric setting, in which the channel gains to the relays are identical and the channel gains from the relays are identical, the capacity of this channel is unknown in general. The best known capacity approximation is up to an additive gap of order N bits and up to a multiplicative gap of order N2, with both gaps independent of the channel gains. In this paper, we approximate the capacity of the symmetric Gaussian N-relay diamond network up to an additive gap of 1.8 bits and up to a multiplicative gap of a factor 14. Both gaps are independent of the channel gains and, unlike the best previously known result, are also independent of the number of relays N in the network. Achievability is based on bursty amplify-and-forward, showing that this simple scheme is uniformly approximately optimal, both in the low-rate as well as in the high-rate regimes. The upper bound on capacity is based on a careful evaluation of the cut-set bound. We also present approximation results for the asymmetric Gaussian N-relay diamond network. In particular, we show that bursty amplify-and-forward combined with optimal relay selection achieves a rate within a factor O(log4(N)) of capacity with preconstant in the order notation independent of the channel gains. In slow-fading scenarios, cooperation between nodes can increase the amount of diversity for communication. We study the performance limit in such scenarios by analyzing the outage capacity of slow fading relay channels. Our focus is on the low signal-to-noise ratio (SNR) and low outage probability regime, where the adverse impact of fading is greatest but so are the potential gains from cooperation. We showed that while the standard Amplify-Forward protocol performs very poorly in this regime, a modified version we called the Bursty Amplify-Forward protocol is optimal and achieves the outage capacity of the network. Moreover, this performance can be achieved without a priori channel knowledge at the receivers. In contrast, the Decode-Forward protocol is strictly suboptimal in this regime. Our results directly yield the outage capacity per unit energy of fading relay channels The performance analysis of optimal decode-and-forward (DF) relay selection for the full-duplex (FD) mode in underlay cognitive radio (CR) networks is studied, with the impact of critical parameters such as the residual self-interference, the distributions of the received signal-to-noise ratio (SNR), and the outage probability, being analyzed. Different from the conventional relay selection schemes with half-duplex (HD) mode, the FD relay suffers from the impact of residual self-interference due to its simultaneous transmission and reception using the same channel. Furthermore, the exact closed-form expressions for the outage probabilities of the proposed FD relay-selection scheme over both independent Nakagami- @math and Rayleigh fading channels are derived, with the validity of the proposed analysis being proven by using simulation. Numerical results show that, in the presence of multiple candidate relays, an optimum relay-selection solution in terms of outage probability can always be achievable within the SNR range of (10 dB, 15 dB). Upper and lower bounds on the capacity and minimum energy-per-bit for general additive white Gaussian noise (AWGN) and frequency-division AWGN (FD-AWGN) relay channel models are established. First, the max-flow min-cut bound and the generalized block-Markov coding scheme are used to derive upper and lower bounds on capacity. These bounds are never tight for the general AWGN model and are tight only under certain conditions for the FD-AWGN model. Two coding schemes that do not require the relay to decode any part of the message are then investigated. First, it is shown that the "side-information coding scheme" can outperform the block-Markov coding scheme. It is also shown that the achievable rate of the side-information coding scheme can be improved via time sharing. In the second scheme, the relaying functions are restricted to be linear. The problem is reduced to a "single-letter" nonconvex optimization problem for the FD-AWGN model. The paper also establishes a relationship between the minimum energy-per-bit and capacity of the AWGN relay channel. This relationship together with the lower and upper bounds on capacity are used to establish corresponding lower and upper bounds on the minimum energy-per-bit that do not differ by more than a factor of 1.45 for the FD-AWGN relay channel model and 1.7 for the general AWGN model.