Closed-Form Design of Fractional Uplink Power Control Over Hata-Class and 3GPP Macrocell Channels
Year: 2026
Type: article
Abstract: Fractional power control governs the uplink energy budget of every Long-Term Evolution and Fifth-Generation New Radio terminal, yet its two parameters, the nominal received power and the compensation factor, are still chosen by simulation sweep or closed box optimization. This paper replaces the search with closed-form design rules. Wherever path loss is affine in the logarithm of distance—the whole Hata family, and each branch and segment of the 3GPP urban-macrocell and urban-microcell models—the transmit power is affine too, and the design problem admits exact solutions: a power-limited radius, the mean transmit power in the logarithmic and in the battery-relevant linear domain, a crossover radius stating where fractional compensation stops saving battery power, and an identity fixing the exchange rate between terminal energy and cell-edge quality. Under log-normal shadowing the battery-relevant mean acquires an exact inflation factor growing with the square of the compensation factor, so a shadowing-free treatment understates the case for partial compensation. The two parameters must moreover be coupled, sweeping one at the other fixed being confounded. Every closed form is verified against quadrature and Monte-Carlo integration to 0.03 dB and 0.4 percent. A system-level study at 2 GHz, run on both COST-231 and the 3GPP urban-macrocell channel, selects 0.6 under a five-percent outage constraint—roughly fifty percent more bits per Joule and up to 18.5 percent longer uplink-limited battery life than full compensation—and the selected value moves as the closed forms predict when the outage target, the load, the link-adaptation curve or the anchor is changed.
Source: IEEE Access
Institutions: Walailak University, National University of Laos
Language: English
Subfield: Electrical and Electronic Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,075
OpenAlex ID: W7214734773