## 2 System Overview  
### Multimode Digitally Reconfigurable Radar System  
To introduce digital modulation schemes to the transmitted waveform and to create the multimode radar, a CW radar system is modified by introducing a wideband BPS in the transmitter chain. The block diagram for the radar system is shown in Figure 1.  
The reconfigurable system consists of an external field programmable gate array (FPGA) board to provide the binary phase shifting schemes to the BPS, external voltage-controlled oscillator (VCO), RF front-end board, baseband board, and four-channel oscilloscope acting as the data acquisition device (DAQ). Three of the channels are used to sample the radar system, two for the in-phase (\(I\)) and quadrature (\(Q\)) signals from the RF front end,  
Figure 1: Block diagram of the digitally reconfigurable multimode radar system. VCO: voltage-controlled oscillator; BPS: binary phase shifter; LNA: low noise amplifier. The Binary Code block is implemented through an FPGA that controls the two complimentary BPS inputs and allows for easy switching between phase-modulated operating modes. and the third for the digital reference signal from the FPGA. The fourth channel is used to measure a ground truth signal from a respiration belt when measuring vital signs. To realize this system, a planar K-Band RF front-end was designed on 10 mil (0.25 mm) Rogers 3003 substrate. This substrate choice is mainly influenced by the material properties between 8 and 40 GHz, such as the low loss tangent of 0.001 and low dielectric constant of 3.00. These properties combined with the 10 mil thickness allow for a small microwave passive component form factor while designing for modern PCB manufacturing tolerances. The RF front-end, shown in Figure 2, consists of three MACOM MAAL-011111 low-noise amplifiers (LNA), two 4 \(\times\) 4 linearly polarized patch antenna arrays, Wilkinson power dividers, a wideband binary phase shifter, and a passive balanced quadrature mixer. All the RF components were designed and simulated using Ansys HFSS and AWR Microwave Office. For the BPS, the design follows [39], which takes advantage of the wideband nature and 180\({}^{\circ}\) output phase paths of a rat-race coupler to control the phase delay of the carrier frequency. Rat-race couplers are commonly used to split a signal into two paths with inverted phases while utilizing an isolation port. If instead the two outputs are loaded, as shown in Figure 3a and implemented in Figure 3b, the isolation port becomes a through port with the amplitude and phase of the output controlled by these loads. The scattering parameters of the BPS can be defined as functions of the reflective loads \(\Gamma_{b}\) and \(\Gamma_{d}\) as  
\[S_{BPS}= \begin{bmatrix}S^{\prime}{}_{11}&S^{\prime}{}_{12}\\ S^{\prime}{}_{21}&S^{\prime}{}_{22}\end{bmatrix} =\frac{-1}{2} \begin{bmatrix} \Gamma_{b}+\Gamma_{d}&-\Gamma_{b}+\Gamma_{d}\\ -\Gamma_{b}+\Gamma_{d}&\Gamma_{b}+\Gamma_{d}\end{bmatrix} . \tag{1}\]  
Figure 3: Rat-race coupler-based BPS schematic showing the two possible signal paths from port \(a\) to port \(d\) along with the reflective loads (**a**) and the fabricated BPS test circuit (**b**) [39]. Figure 2: \(K\)-Band multimode radar RF front-end consisting of TX/RX antennas, the BPS, quadrature mixer, VCO input, and TX/RX LNAs. The 10 mil Rogers 3003 board is mounted to a 63 mil baseband PCB for structural stability. To generate the two possible phase states, the \(b\) and \(d\) inputs to the phase shifter need to have two states they can switch between, and the input loads need to be nearly identical. For best performance, the states need to have high reflection coefficient magnitudes and be 180\({}^{\circ}\) out of phase, such as a pair of loads consisting of an RF open and an RF short. By controlling the bias levels of two high-speed PIN diodes with RF short stubs at their anodes, one such state pair is achieved when one diode has a 0-volt bias and the other diode has a forward voltage bias.