Table 4 ADC angle quantization range for complex signal with maximum signal amplitude in a 3-bit ADC
From: Quantization error for weak RF simultaneous signal estimation
N-bit | \(\varvec{a}_{{\varvec{p},\varvec{p} + {\mathbf{1}}}}\) | \(\varvec{b}_{{\varvec{p},\varvec{p} + {\mathbf{1}}}}\) | \(\varvec{c}_{{{\mathbf{max}}}} = \varvec{s}_{{{\mathbf{max}}}}\) | angle \(\varvec{\theta }_{{\varvec{p},\varvec{p} + {\mathbf{1}}}}\) | ADC angle quantization range in pth bit |
|---|---|---|---|---|---|
ADC | Â | Â | Â | Â | Â |
\(\varvec{N} = {\mathbf{3}}\) | \(\varvec{a}_{{\varvec{p},\varvec{p} + {\mathbf{1}}}}\) | \(\varvec{b}_{{\varvec{p},\varvec{p} + {\mathbf{1}}}}\) | \({\mathbf{2}}^{{\varvec{N} - {\mathbf{1}}}}\) | \(\varvec{\theta }_{{\varvec{p},\varvec{p} + {\mathbf{1}}}}\) | \(\Delta \theta _{p}\) |
| Â | \(a_{1,2}\) | \(b_{1,2}=1\) | \(s_{\text {max}} = 4\) | \(\tan {\theta _{1,2}} = \frac{1}{\sqrt{(\frac{2^3}{2})^2 - 1^2}}\) |
 |
| Â | \(a_{2,3}\) | \(b_{2,3}=2\) | \(s_{\text {max}} = 4\) | \(\tan {\theta _{2,3}} = \frac{2}{\sqrt{(\frac{2^3}{2})^2 - 2^2}}\) |
 |
| Â | \(a_{3,4}=3\) | \(b_{3,4}\) | \(s_{\text {max}} = 4\) | \(\tan {\theta _{3,4}} = \frac{\sqrt{(\frac{2^3}{2})^2 - 3^2}}{3}\) |
 |
| Â | \(a_{4,5}\) | \(b_{4,5}=3\) | \(s_{\text {max}} = 4\) | \(\tan {\theta _{4,5}} = \frac{3}{\sqrt{(\frac{2^3}{2})^2 - 3^2}}\) |
 |
| Â | \(a_{5,6}=2\) | \(b_{5,6}\) | \(s_{\text {max}}= 4\) | \(\tan {\theta _{5,6}} = \frac{\sqrt{(\frac{2^3}{2})^2 - 2^2}}{2}\) |
 |
| Â | \(a_{6,7}=1\) | \(b_{6,7}\) | \(s_{\text {max}} = 4\) | \(\tan {\theta _{6,7}} = \frac{\sqrt{(\frac{2^3}{2})^2 - 1^2}}{1}\) |
 |
| Â | Â | Â | Â | Â |
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