Table 3 ADC angle quantization range for complex signal with maximum signal amplitude in 1-bit and 2-bit ADCs
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 |
\(N=1\) | \(a_{p,p+1}\) | \(b_{p, p+1}\) | \(2^{N-1}\) | \(\theta _{p,p+1}\) | \(\Delta \theta _{p}\) |
\(a_{0,1}=0\) | \(b_{0,1}=0\) | \(s_{\text {max}} = 1\) | \(\tan {\theta _{0,1}} = 0\) |
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\(N=2\) | \(a_{p,p+1}\) | \(b_{p,p+1}\) | \(2^{N-1}\) | \(\theta _{p,p+1}\) | \(\Delta \theta _{p}\) |
\(a_{1,2}\) | \(b_{1,2}=1\) | \(s_{\text {max}} = 2\) | \(\tan {\theta _{1,2}} = \frac{1}{\sqrt{(\frac{2^2}{2})^2 - 1^2}}\) |
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\(a_{2,3} = 1\) | \(b_{2,3}\) | \(s_{\text {max}} = 2\) | \(\tan {\theta _{2,3}} = \frac{\sqrt{(\frac{2^2}{2})^2 - 1^2}}{1}\) |
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| Â | Â | Â | Â |
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