## 5 Results
### Validation of Theory, Simulations and Flatsat Results  
The test signals described in Section 4.1 are used to validate the measurement algorithm. The results analysed are: _average power_ (\(m_{2k}\)); the variation of \(m_{2k}\) from the smallest time window to the largest normalised, referred to as _normalised LME second moment_; and the difference of \(m_{2k}\) between consecutive windows normalised (\(m_{2k}^{T_{i}}-m_{2k}^{T_{i+1}}\)), named _bin difference_. The results obtained when measuring different input signals: AWGN; a CW; a pulsed signal with pulses 5 s long and repetition period of 16.67 ms; and a chirp signal with pulses 5 s long, repetition period of 16.67 ms, and 300 kHz bandwidth are shown in Figures 3-5, respectively. All results are measured with the configuration in Table 1. The average power spectrum (\(m_{2k}\)) is plotted for AWGN (Figure 3a), a CW (Figure 3b), a pulsed signal (Figure 3c), and a chirp signal (Figure 3d). The signals generated are the same both for simulations and measurements with the flatsat. \begin{table}
\begin{tabular}{l l l l} \hline  & **(A) Our Software** & **(B) 10 min Waterfall** & **(C) 5 s Waterfall** \\ \hline Sampling frequency (\&Spps) & 600 & 600 & 600 \\ \hline Number of frequency bins & 128 & 128 & 128 \\ \hline Freq. resolution (kHz/bin) & 4.7 & 4.7 & 4.7 \\ \hline Number of bits & 32 & 32 & 32 \\ \hline Number of parameters & 10 & - & - \\ \hline kBytes per measurement & 51.2 & 11,520,000 & 96,000 \\ \hline MBytes per measurement & **0.05** & 11,520 & 96 \\ \hline \end{tabular}
\end{table} 
Table 2: Data budget to show how the on-board processing software dramatically reduces the data size to be downlinked compared to standard waterfalls. \begin{table}
\begin{tabular}{l l l l} \hline  & **(A) Our Software** & **(B) 10 min Waterfall** & **(C) 5 s Waterfall** \\ \hline Net time (h) & 0.11 & 3200 & 26.6 \\ \hline Effective days & **1.4** & 38,400 & 320 \\ \hline \end{tabular}
\end{table} 
Table 3: Downlink time for the data output of the on-board processing software compared to standard waterfalls. The main differences between the simulation results (blue lines) and the flatast results (red lines) are the filter, whose frequency response can be seen in Figure 3a, when transmitting AWGN, and the measured noise. In the simulation, the spectrum is flat because the noise transmitted is white (all frequencies are affected in the same way). When the noise is transmitted in the flatsat setup, the spectrum measured is not completely flat because of the receive filter. The filter is configured to have a bandwidth of 200 kHz for the AD9364 transceiver chip. Nevertheless, the measured 3 dB bandwidth is larger (from 434.75 to 435.25 MHz), so this is the band analysed in the remainder of the paper (indicated by vertical black dotted lines). The TOTEM in the lab setup was calibrated for the spectral power density, but, for the TOTEM on LUME-1, there is no power calibration available. Measured power on LUME-1 is a relative measure and is displayed in dB. In both the CW simulations and flatsat results (Figure 3b), there is one peak at 435.1 MHz. This peak is expected since a complex tone is transmitted at 100 kHz and modulated onto the 435 MHz carrier. In the pulsed case (Figure 3c), there is one peak at around 435.1 MHz since the transmitted signal was also shifted 100 kHz from the centre frequency. For a 5 s long pulse, the sidelobes appear at multiples of 0.2 kHz, but there is not enough frequency resolution (4.7 kHz) to distinguish them. The spectrum of a chirp signal with 300 kHz bandwidth can be seen in Figure 3d. The chirp was directly modulated  
Figure 3: Test signal comparison of spectrum of average power in simulations (blue curves) and the median of 10 measurements with the flatsat (red curves). Black dotted lines indicate the 3 dB bandwidth of the receive filter. (**a**) AWGN (Additive White Gaussian Noise). (**b**) Complex CW (Continuous Wave) transmitted. (**c**) Complex pulse (5 s long and period 16.67 ms) transmitted.