The system architecture is shown in Fig. 1. The Tx and Rx antennas are integrated on-chip and the Rx and Tx share the same Integer-N PLL with I/Q VCO. At the Rx side the Rx antenna signal is applied to the I/Q mixer. The baseband signals are obtained after demodulation by the quadrature mixer then subsequently filtered, further amplified by the variable-gain amplifier (VGA) and digitized by the ADC before being processed by a FPGA. At the Tx side the VCO is applied to a buffer and thereafter to the PA. The time domain transmitted signal, denoted by T(t) and the received signal by R(t) are:
$$\:T\left(t\right)={A}_{t}cos\left(?t+f\left(t\right)\right)$$
1
$$\:R\left(t\right)={A}_{r}cos\left[?t-\frac{4p}{?}\left({d}_{0}+f\left(t-\frac{2{d}_{0}}{c}\right)\right)\right]$$
2
where At and Ar are the amplitudes of the transmitted and received signals, respectively; ω the angular frequency of the transmitted signal; λ the carrier wavelength; c the speed of light; d0 the constant distance between the antennas and the subject; x(t) the instantaneous displacement of the chest, given by (3):
$$\:x\left(t\right)={A}_{b}cos\left({?}_{b}t+{f}_{b}\right)+{A}_{h}cos\left({?}_{h}t+{f}_{h}\right)$$
3
where Ab, Ah, ϕb and ϕh are the amplitudes and the phase shifts of the chest displacement due to breathing and heartbeat, respectively. As seen from (1) and (2), the signal sent by the radar is modulated in frequency and phase due to the displacement of the chest. This modulation is called the Doppler Effect.
For a zero-IF radar, the in-phase baseband signal BI(t) is obtained by mixing a replica of the transmitted signal in (1) with the received signal in (2):
$$\:{B}_{I}\left(t\right)=T\left(t\right)xR\left(t\right)$$
4
Similarly, the quadrature baseband signal is obtained by mixing the received signal with a replica of the transmitted signal, shifted by a phase of 90◦:
$$\:{B}_{Q}\left(t\right)=T\left(t-\frac{p}{2?}\right)xR\left(t\right)$$
5
The above I and Q baseband signals are used in signal processing to determine the vital signs. In order to realize this architecture, on chip, we propose the following system (see Fig. 1). The two antennas for the Tx and Rx are integrated on-chip. They are bow-tie antenna with an area of 0.4mm x 0.32mm and a gain of 7dB. At the Rx side the 3-stage LNA (see Fig. 2a)) has a power gain of 17dB, a NF less than 8dB. and the input reflection coefficient of S11<-12dB. At the Tx side (see Fig. 2c)), the three stage PA has a power gain of maximum 10dB and OP1dB compression of -4.2dBm and a saturated power of 10dBm. The Integer-N PLL employs feedback dividing ratio of 256. The first and the second divider are injection locked dividers from 160GHz to 80GHz and 80GHz to 40GHz (Fig. 2d)).
The following dividers are classical CML dividers (see Fig. 3a)). The 5GHz external reference is divided by 8 and used as internal reference for the PFD. LFMCW modulation at RF is achieved by injecting a sawtooth signal at the input of the VCO (see Fig. 1), generated internally from an external rectangular signal provided by a FPGA. The VCO has an output frequency of 159.5GHz to 167.5GHz and a measured phase noise of -136dBc/Hz @ 1MHz. I and Q baseband signals are applied to the FPGA (ADS9-V2EBZ). Firstly, those signals are digitized. The ADCs are AD9081 4GSPS, 12-bit RF ADC. After digitization of the I and Q baseband signals we generate the phase signal and after FFT we get respiration rate and heart rate. More details in Methods.