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Table 1 SNR estimates under generalized fading

From: Signal-to-noise ratio estimation for M-QAM signals in ημand κμfading channels

fading Estimate of SNR γ
Nakagami-m \(\begin {array}{l} \hat {\gamma }=\frac {2(1-2\hat {\mathrm {f}})+ 2\sqrt {2\hat {\mathrm {f}}(1-2\hat {\mathrm {f}})(\epsilon -1)}} {C_{2}(2\epsilon \hat {\mathrm {f}}-1)}\\ \epsilon =2\varrho \frac {C_{4}}{C_{2}^{2}}\\ \varrho =\frac {(m+1)}{4m} \end {array}\)
\(\begin {array}{c} \text {Format I}\\ \eta -\mu \end {array}\) \(\begin {array}{l} \hat {\gamma }=\frac {2(1-2\hat {\mathrm {f}})+2\sqrt {2\hat {\mathrm {f}}(1-2\hat {\mathrm {f}})(\epsilon -1)}} {C_{2}(2\epsilon \hat {\mathrm {f}}-1)}\\ \epsilon =2\varrho \frac {C_{4}}{C_{2}^{2}}\\ \varrho =\frac {\mu (1+\eta)^{2}+\left (1+\eta ^{2}\right)}{4\mu (1+\eta)^{2}} \end {array}\)
\(\begin {array}{c} \text {Format II}\\ \eta -\mu \end {array}\) \(\begin {array}{l} \hat {\gamma }=\frac {2(1-2\hat {\mathrm {f}})+2\sqrt {2\hat {\mathrm {f}}(1-2\hat {\mathrm {f}})(\epsilon -1)}}{C_{2}(2\epsilon \hat {\mathrm {f}}-1)}\\ \epsilon =2\varrho \frac {C_{4}}{C_{2}^{2}}\\ \varrho =\frac {1+2\mu +\eta ^{2}}{8\mu }\end {array}\)
κμ \(\begin {array}{l} \hat {\gamma }=\frac {2(1-2\hat {\mathrm {f}})+2\sqrt {2\hat {\mathrm {f}}(1-2\hat {\mathrm {f}})(\epsilon -1)}}{C_{2}(2\epsilon \hat {\mathrm {f}}-1)}\\ \epsilon =2\varrho \frac {C_{4}}{C_{2}^{2}}\\ \varrho =\frac {\left (\kappa \mu (\kappa \mu +2\mu +2)+\mu ^{2}+\mu \right)}{4\mu ^{2}(1+\kappa)^{2}}\end {array}\)