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For a given set of power strategies,, the single-user maximization problem (4) is a convex optimization problem [18].
For a given power allocation and a given set of power partitions the region bounded by the constraints in (1a)–(1c) is the region of rates achievable by superposition coding and Gaussian signalling (SPCGS).
Let us define Γ ~ as the matrix of achievable SINR targets under a given set of power constraints p ̂ (8) as follows: Γ ~ = [ diag ( V p ̂ + z ) ] ( - 1 ) diag ( p ̂ ).
The user-removal techniques [11] exploit the Perron-Frobenius theory to identify the infeasibility of a set of links in scenarios where, for a given set of power constraints and rate (SINR) requirements, the classical power control algorithms (e.g., [17]) do not converge.
Assuming that power is evenly distributed over the sub-bands in every cell[7 10], we consider the power assignment scheme where each cell can select, among a given set of power levels, the power to be used per sub-band.
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Here, the reconstruction points ĝ n, m work the same as the thresholds, because for a given set of powers, the transmission rate is set to log ( 1 + ĝ n, m T n, m ) if the quantization index m is received for the n th user.
You can play this game forever, with any given set of magical powers.
In contrast, the PM problem guarantees per-UT rate targets to be satisfied while minimizing total transmit power for a given set of per-antenna power constraints.
Initially, we perform a detailed simulation study using Matlab tool to find the R eff of a vehicular node for a given set of parameters such as transmit power, path loss exponent etc.
For any given set of cell dimensions and characteristics, power density was maximized at an optimal cell length – the power decreased at larger cell lengths due to electrode lateral resistance loss and decreased at smaller cell lengths due to a decreasing fraction of cell active area.
For a given set of operating conditions the defined power loss model allows to optimize the design parameters for the power stage, including the gate-driver tapering factor and the width of the power MOSFETs.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com