## 3 Measurement Results  
### Transmitted Phase Modulated Power Spectrums  
While the output of CW radar has a constant average and instantaneous power, once modulation is added the carrier power spreads out over the frequency spectrum. For FMCW radar systems, the carrier frequency is constantly moving across the operating spectrum. This is commonly implemented by applying a periodic sawtooth ramp to the tuning voltage of the VCO, which ideally results in a constant change in the carrier frequency until resetting from the highest frequency to the lowest. As the frequency sweeps across the operation bandwidth, the output power should be constant. For PMCW radar systems, the instantaneous power across phase states should also not change, while the average power follows the equation  
\[PS(f)=F_{\mathrm{C}}(f)*F_{M}(f) \tag{16}\]  
where \(F_{\mathrm{C}}(f)\) and \(F_{M}(f)\) are the frequency components of the carrier and the modulated phase, respectively. To ensure the RF front-end of the multimode radar is properly modulating the carrier signal, a test board with the block diagram in Figure 5a was developed. The fabricated test board is shown in Figure 5b. Three possible output modes of the RF front-end were tested using the binary input schemes in Table 2 and a logical timing diagram for the phase states of each waveform is shown in Figure 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Radar Mode** & \(\mathbf{Vbias_{b}}\) & \(\mathbf{Vbias_{d}}\) \\ \hline CW & \{0\} & \{1\} \\ PSK & \{01\} & \{10\} \\ PMCW & \{MLS\} & \{\sim MLS\} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: BPS Bias Logic Input Sequences. Each pair of inputs corresponds to the repeating normalized magnitude of the bias voltages supplied by the FPGA. Figure 5: RF front-end test circuit **(a)** block diagram and (**b**) corresponding test board. For spectral analysis, the VCO is connected to a variable frequency generator, the output of the BPS is measured with a spectrum analyzer, and the RF input to the mixer is loaded with 50 \(\Omega\). Figure 6: Logical timing diagram for the BPS bias voltages corresponding to the radar modes in Table 2. The PSK signal repeats at the frequency \(F_{Clk}\) and the PMCW symbol updates on every rising clock edge. When applying PSK and PMCW modulation schemes to the BPS, the power of the output wave is spread across the spectrum, resulting in lower average power compared to the unmodulated carrier at \(F_{C}\). To compare the average output power to an FMCW radar, the VCO frequency is swept while the BPS states in the front-end test board are in CW mode. The average power spectrum of the FMCW wave is also spread out over time depending on the chirp rate \(F_{Chirp}\). Since both MLS-based PMCW and FMCW carriers are periodic, the average power spectrum per cycle is compared. Figure 7 shows the output spectrum of phase shifting schemes. The \(F_{Clk}\) used for the comparisons in Figure 7 is 10 MHz for both the PSK square wave modulation and the 15-bit MLS encoding, which repeats every 1.5 usec. Figure 8 shows the normalized output power spectrum per cycle of CW, FMCW, and PMCW signals. As the main lobe of PMCW waveforms occupies \(2\times F_{Clk}\), the available bandwidth is half of that which is accessible by FMCW waveforms. Figure 8 demonstrates this concept with a 50 MHz bandwidth FMCW spectrum that uses a 1 kHz sawtooth wave to sweep the carrier frequency and a 15-bit MLS-PMCW spectrum with a 25 MHz clock frequency, repeating every 0.6 usec. The FMCW signal will have twice the range resolution of the PMCW signal because of this drawback but will also suffer from high radar-radar noise when operating in the same band as another FMCW radar. Figure 8: Comparison of average output power per cycle for CW, FMCW, and PMCW waveforms measured with the RF front-end test circuit. The bandwidth occupied by the FMCW waveform is similar to that of the PMCW waveform’s main lobe when the carrier’s phase is modulated with a clock speed that is half of the swept PMCW bandwidth.