Abstract
In this paper, the relationship between the energy efficiency in terms of the total consumed power per bit and the spectral efficiency is studied for dual-hop cooperative relaying systems consisting of multiple single-antenna amplify-and-forward relays. Considering the source and relay transmit antenna gains, the path-loss fading and the power consumption model as a whole, a new metric to measure the energy to spectral-efficiency trade-off (ESET) is formulated. Based on the convexity analysis of the new cost function, an analytical expression of the minimum per-bit power consumed by the whole relay system is derived as a general framework of the best ESET for given number of relays and relay-to-source power allocation. The relay-to-source power ratio is then further optimized, leading to a closed-form solution to relay design and power allocation. Numerical simulation results validating the theoretical analysis and the derived optimal ESET are provided.
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