Table 1 SNR estimates under generalized fading
From: Signal-to-noise ratio estimation for M-QAM signals in η−μand κ−μfading channels
fading | Estimate of SNR γ |
|---|---|
Nakagami-m | \(\begin {array}{l} \hat {\gamma }=\frac {2(1-2\hat {\mathrm {f}})+ 2\sqrt {2\hat {\mathrm {f}}(1-2\hat {\mathrm {f}})(\epsilon -1)}} {C_{2}(2\epsilon \hat {\mathrm {f}}-1)}\\ \epsilon =2\varrho \frac {C_{4}}{C_{2}^{2}}\\ \varrho =\frac {(m+1)}{4m} \end {array}\) |
\(\begin {array}{c} \text {Format I}\\ \eta -\mu \end {array}\) | \(\begin {array}{l} \hat {\gamma }=\frac {2(1-2\hat {\mathrm {f}})+2\sqrt {2\hat {\mathrm {f}}(1-2\hat {\mathrm {f}})(\epsilon -1)}} {C_{2}(2\epsilon \hat {\mathrm {f}}-1)}\\ \epsilon =2\varrho \frac {C_{4}}{C_{2}^{2}}\\ \varrho =\frac {\mu (1+\eta)^{2}+\left (1+\eta ^{2}\right)}{4\mu (1+\eta)^{2}} \end {array}\) |
\(\begin {array}{c} \text {Format II}\\ \eta -\mu \end {array}\) | \(\begin {array}{l} \hat {\gamma }=\frac {2(1-2\hat {\mathrm {f}})+2\sqrt {2\hat {\mathrm {f}}(1-2\hat {\mathrm {f}})(\epsilon -1)}}{C_{2}(2\epsilon \hat {\mathrm {f}}-1)}\\ \epsilon =2\varrho \frac {C_{4}}{C_{2}^{2}}\\ \varrho =\frac {1+2\mu +\eta ^{2}}{8\mu }\end {array}\) |
κ−μ | \(\begin {array}{l} \hat {\gamma }=\frac {2(1-2\hat {\mathrm {f}})+2\sqrt {2\hat {\mathrm {f}}(1-2\hat {\mathrm {f}})(\epsilon -1)}}{C_{2}(2\epsilon \hat {\mathrm {f}}-1)}\\ \epsilon =2\varrho \frac {C_{4}}{C_{2}^{2}}\\ \varrho =\frac {\left (\kappa \mu (\kappa \mu +2\mu +2)+\mu ^{2}+\mu \right)}{4\mu ^{2}(1+\kappa)^{2}}\end {array}\) |