Optimal Pilot Symbols Ratio in terms of Spectrum and Energy Efficiency in Uplink CoMP Networks

In wireless networks, Spectrum Efficiency (SE) and Energy Efficiency (EE) can be affected by the channel estimation that needs to be well designed in practice. In this paper, considering channel estimation error and non-ideal backhaul links, we optimize the pilot symbols ratio in terms of SE and EE in uplink Coordinated Multi-point (CoMP) networks. Modeling the channel estimation error, we formulate the SE and EE maximization problems by analyzing the system capacity with imperfect channel estimation. The maximal system capacity in SE optimization and the minimal transmit power in EE optimization, which both have the closed-form expressions, are derived by some reasonable approximations to reduce the complexity of solving complicated equations. Simulations are carried out to validate the superiority of our scheme, verify the accuracy of our approximation, and show the effect of pilot symbols ratio.Comment: 5 pages, 3 figures, 2017 IEEE 85th Vehicular Technology Conference (VTC Spring

Measuring the degree of unitarity for any quantum process

Quantum processes can be divided into two categories: unitary and non-unitary ones. For a given quantum process, we can define a \textit{degree of the unitarity (DU)} of this process to be the fidelity between it and its closest unitary one. The DU, as an intrinsic property of a given quantum process, is able to quantify the distance between the process and the group of unitary ones, and is closely related to the noise of this quantum process. We derive analytical results of DU for qubit unital channels, and obtain the lower and upper bounds in general. The lower bound is tight for most of quantum processes, and is particularly tight when the corresponding DU is sufficiently large. The upper bound is found to be an indicator for the tightness of the lower bound. Moreover, we study the distribution of DU in random quantum processes with different environments. In particular, The relationship between the DU of any quantum process and the non-markovian behavior of it is also addressed.Comment: 7 pages, 2 figure