We analyze coding for energy efficiency in relay channels at a fixed source rate. We first propose a half-duplex decode-forward coding scheme for the Gaussian relay channel. We then derive three optimal sets of power allocation, which respectively minimize the network, the relay and the source energy consumption. These optimal power allocations are given in closed-form, which have so far remained implicit for maximumrate schemes. Moreover, analysis shows that minimizing the network energy consumption at a given rate is not equivalent to maximizing the rate given energy, since it only covers part of all rates achievable by decode-forward. We thus combine the optimized schemes for network and relay energy consumptions into a generalized one, which then covers all achievable rates. This generalized scheme is not only energy-optimal for the desired source rate but also rate-optimal for the consumed energy. The results also give a detailed understanding of the power consumption regimes and allow a comprehensive description of the optimal message coding and resource allocation for each desired source rate and channel realization. Finally, we simulate the proposed schemes in a realistic environment, considering path-loss and shadowing as modelled in the 3GPP standard. Significant energy gain can be obtained over both direct and two-hop transmissions, particularly when the source is far from relay and destination.

Abstract-The performance of a relay-based cellular network is greatly affected by the relay location within a cell. Existing results for optimal relay placement do not reflect how the radio propagation environment and choice of the coding scheme can impact system performance. In this paper, we analyze the impact on relaying performance of node distances, relay height and lineof-sight conditions for both uplink and downlink transmissions, using several relay coding schemes. Our first objective is to propose a geometrical model for energy-efficient relay placement that requires only a small number of characteristic distances. Our second objective is to estimate the maximum cell coverage of a relay-aided cell given power constraints, and conversely, the averaged energy consumption given a cell radius. We show that the practical full decode-forward scheme performs close to the energy-optimized partial decode-forward scheme when the relay is ideally located. However, away from this optimum relay location, performance rapidly degrades and more advanced coding scheme, such as partial decode-forward, is needed to maintain good performance and allow more freedom in the relay placement. Finally, we define a trade-off between cell coverage and energy efficiency, and show that there exists a relay location for which increasing the cell coverage has a minimal impact on the average energy consumed per unit area.

Energy harvesting brings a key solution to the increasing energy bill and environmental concerns but, at the same time, potential energy shortage may deteriorate the network availability. In this paper, we analyze the performance of offgrid small-cell base stations (scBS) with finite battery capacity and design a new power-availability-aware cell association based on periodical broadcast of the scBS battery level. Each mobile terminal (MT) targets its own set of available scBSs before association, i.e. the set of scBSs that can guarantee service provided (i) the scBS battery level, (ii) the power required to satisfy a received power constraint at each MT, given the scBS-MT distance and the shadowing attenuation, and (iii) the estimated power consumed to serve other MTs potentially associated to the same scBS, which is computed using stochastic geometry tools. Next, we develop for it a tractable performance analysis and derive closed-form expressions for the probability of power outage and the coverage probability. By dynamically adapting to the fluctuations of the base station battery and the MT received power requirement, the proposed cell association allows a more even distribution of the available energy in the network, brings robustness against harvesting impairment and thereby, significantly outperforms conventional strategies.

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By relying on a wireless backhaul link, relay stations enhance the performance of cellular networks at low infrastructure cost, but at the same time, they can aggravate the interference issue. In this paper, we analyze for several relay coding schemes the maximum energy gain provided by a relay, taking into account the additional relay-generated interference to neighboring cells. First, we define spatial areas for relaying efficiency in log-normal shadowing environments and propose three easily-computable and tractable models. These models allow the prediction of 1) the probability of energy-efficient relaying, 2) the spatial distribution of energy consumption within a cell and 3) the average interference generated by relays. Second, we define a new performance metric that jointly captures both aspects of energy and interference, and characterize the optimal number and location of relays. These results are obtainable with significantly lower complexity and execution time when applying the proposed models as compared to system simulations. We highlight that energy-efficient relay deployment does not necessarily lead to interference reduction and conversely, an interference-aware deployment is suboptimal in the energy consumption. We then propose a map showing the optimal utilization of relay coding schemes across a cell. This map combines two-hop relaying and energy-optimized partial decode-forward as a function of their respective circuitry consumption. Such a combination not only alleviates the interference issue, but also leads to a reduction in the number of relays required for the same performance.