## 1 Introduction  
Wireless bio-signal sensing has received significant attention in recent years due to its possible applications in healthcare, fitness, and security. In particular, radar-based vital-sign sensing has received a great deal of attention [1; 2; 3; 4; 5; 6]. However, these methods have limitations, such as signal interferences caused by human movements and surrounding clutter objects, which can lead to inaccuracy and performance degradation. To overcome these limitations, researchers have developed non-linear tags based on harmonic responses that incorporate components exhibiting non-linear behavior, such as diodes, transistors, and mixers [7; 8]. These tags are attached to the human body and generate harmonic responses upon excitation by the radar-transmit pulses, which are then retransmitted back to the radar, carrying the vital signal information. By receiving and processing the harmonic responses returned from the non-linear tags only, unwanted signals and clutter at the fundamental frequency due to the movements from other parts of the body and surrounding clutter objects can be suppressed, thereby increasing the fidelity of the extracted vital signal information. On the other hand, using harmonic frequencies for receiving has its own constraints. Having to use the harmonic bands on the receiving end increases system complexity due to the large difference between transmit and receive frequencies, as well as higher path loss at the harmonic frequencies. To overcome the constraints of using harmonic tags, researchers have turned to the use of non-linear tags based on the third-order intermodulation (IM3) responses [9; 10; 11; 12]. By transmitting two closely spaced frequencies, IM3 responses can be generated in the vicinity of the two fundamental bands, thereby allowing for the transmitter and receiver to use similar bands. In general, the amplitude of non-linear responses is much smaller than that of fundamental signals. For example, a frequency tripler specifically designed to maximize third-order harmonics, such as the HMC-XTB110 in the K and Ka-band, exhibits a conversion loss of 18.3-21.2 dB [13]. Therefore, to efficiently detect the non-linear responses from non-linear tags, the antenna is a critical component to ensure good reception and re-radiation of the fundamental incident signals and non-linear responses, respectively [7,8]. However, using an antenna in the tag may increase the size of the tag, which may not be practical for attaching to the body if microwave frequencies are used. By utilizing the millimeter wave (mmWave) frequency bands, it is possible to minimize the size of the antenna and tag to be more compact [14], which can reduce discomfort when attached to the body. Therefore, using a mmWave frequency band can be a promising approach to wireless bio-signal sensing as it can achieve efficient sensing while minimizing the size of the tag and reducing the burden of attachment. For a reliable detection performance, the polarization alignment between the radar and the tag is important. However, when the tag is attached to the body, its orientation may vary, which causes the polarization to fluctuate. In this regard, using circular polarization inherently allows for polarization diversity, thereby improving the sensing performance. In recent years, there has been an increasing interest in using circularly polarized antennas for wireless bio-signal sensing due to their ability to provide more reliable signal reception in complex and dynamic environments compared to linearly polarized antennas [15, 16, 17, 18]. Circular polarizations are known to effectively mitigate the effects of multipath propagation, fading, and polarization mismatch. Due to these advantages, circularly polarized antennas are widely used in various applications [19], including wireless communication systems and bio-signal sensing. Additionally, microstrip patch antennas provide benefits such as low-profile and low-cost fabrication, making them suitable for a wide range of applications, including healthcare.