# K/Ka-Band Very High Data-Rate Receivers: A Viable Solution for Future Moon Exploration Missions
## 4 Receiver Architecture
### Phase Noise Impairments  
One of the main impairments in low-cost receivers is due to the phase-noise of the adopted PLL synthesizers. Although an accurate modeling of the phase noise is commonly available in modern electronic computer aided design (CAD) tools, it is not present in STK [9], the multi-physics software used for both the orbits and the link budget computations. In order to deal with this problem, a co-simulation between a CAD tool like Advanced Design System (ADS) and STK can be performed [18]. This paper uses a novel approach that, although approximated, is very light, easily integrable within STK and accurate at the same time. As shown in ([19], p. 447), the Error Vector Magnitude (EVM) of modulated signals in the presence of phase-noise can be evaluated according to:  
\[\text{EVM}_{rms}\simeq\sqrt{\frac{1}{\text{SNR}}+\Phi_{rms}^{2}} \tag{8}\]  
where SNR is the signal to noise ratio due to the additive (thermal) noise. This relation, which is an approximation for small phase errors \(\Phi\), has a very important consequence: in receivers, the EVM degradation due to phase-noise is similar to that produced by an equivalent increase of the SNR. As a result, an effective signal to noise ratio \(\text{SNR}_{eff}\) can be introduced as a cumulative parameter accounting for both the thermal noise and the oscillator phase-noise:  
Figure 4: Signal levels. Comparison between transmitted effective isotropic radiated power (EIRP) of the ground station and received power levels at 22.85 GHz. For a link distance of \(384.4\times 10^{3}\) km the path loss is \(-231\) dB, corresponding to Zenith and clear sky conditions. The RX axis also reports the noise floor (for 50 MHz IF bandwidth), the 1 dB compression point and the \(SFDR\) limit. \[\frac{1}{\text{SNR}_{eff}}=\frac{1}{\text{SNR}}+\Phi_{rms}^{2} \tag{9}\]  
Equation (9) means that, in receivers, the phase-noise sets the upper SNR limit: indeed one has \(\text{SNR}_{eff}\leq 1/\Phi_{rms}^{2}\). From the above theory it is apparent that the phase error \(\Phi_{rms}^{2}\) has to be determined. This can be done quite simply as shown in ([20], p. 8) by integrating the phase-noise spectrum \(S_{\phi}(f)\):  
\[\Phi_{rms}^{2}=n^{2}\,\int_{f_{min}}^{f_{max}}\,S_{\phi}(f)\,df \tag{10}\]  
where \(n\) is the multiplication factor of a frequency multiplier (if present), and the integration frequency range is limited by \(f_{min}\) and \(f_{max}\). The importance of (9) is that it establishes an equivalence between the phase error and the SNR. In particular, it shows that it is possible to determine an equivalent level of input additive noise which causes the same rms angular error of the given phase-noise in the I/Q scatter plot. On this basis it is possible to define an effective receiver noise figure that accounts for the local oscillator phase-noise too. At the receiver output the signal to noise ratio obeys to (9):  
\[\frac{1}{\text{SNR}_{eff}}\simeq\frac{N_{o}}{S_{o}}+\Phi_{rms}^{2} \tag{11}\]  
being \(S_{o}\) and \(N_{o}\) the output signal and noise power respectively. Equivalently we can assume an ideal receiver (with no thermal noise and no phase-noise) and refer all the quantities to the input:  
\[\frac{1}{\text{SNR}_{eff}}\simeq\frac{N_{i}+S_{i}\,\Phi_{rms}^{2}}{S_{i}} \tag{12}\]  
where \(S_{i}\) and \(N_{i}\) are the input signal and noise power levels.