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Table 1 Closed form expressions for the DL ergodic peak rate for different path-loss exponents

From: A tractable closed form approximation of the ergodic rate in Poisson cellular networks

β DL ergodic peak rate:
3 Rpeak=\(\left [2\sqrt {1-P_{\text {active}}}\left (-(-1+P_{\text {active}}){~}^{3}+\left (P_{\text {active}}\Gamma \left (\frac {1}{3}\right)\right)^{3}\right)\right ], \text {where}~b=2\sqrt {4+\frac {1}{P_{\text {active}}}},~ c=1.2528\qquad \qquad (34)\)
4 Rpeak=\(\frac {{\pi }^{1.5}P_{\text {active}}-2\sqrt {\pi }P_{\text {active}}\arctan {\sqrt {c}}-2(P_{\text {active}}-1)\log \left (1-P_{\text {active}}+\sqrt {\pi c}P_{\text {active}}\right)}{1+P_{\text {active}}(-2+P_{\text {active}}(1+\pi))}, \text {where}~b=\sqrt {9+\frac {6}{P_{\text {active}}}},~ c=1.2873\qquad \qquad (35)\)
5 Rpeak=\(\left.-(-1+\sqrt {5})\log \left (2-(1+\sqrt {5})c^{1/5}+2c^{2/5}\right)\right)+\left (-1+P_{\text {active}}\right){~}^{3}\Gamma \left (\frac {3}{5}\right)\left (\mathrm {i}\sqrt {10-2\sqrt {5}}\right.\)
5 \( \text {where}~b=2\sqrt {\frac {16}{9}+\frac {2}{P_{\text {active}}}},~ c=1.3099\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \quad \quad (36)\)