Recently, microwave Doppler radar has been utilized to detect movements of the human body, such as respiration and heartbeat. The detection of movements is used for various applications such as life detection in earthquake events [1] and localization monitoring of enemies in military applications [2]. The microwave radar sensing system radiates a single tone continuous-wave (CW) signal [3–8]; the reflected signal is then demodulated in the receiver. The CW radar can obtain movement information from the phase change of the time-varying chest-wall position. The received signal with the demodulated phase is proportional to the chest-wall position information due to respiration and heartbeat.

While CW radar extracts only vital Doppler parameters, frequency-modulated continuous-wave (FMCW) radar can extract multiple parameters, such as distance or Doppler. In the case of FMCW radar, fast Fourier transform (FFT)-based algorithms are used in conventional FMCW radar systems to acquire multiple parameters. However, the FFT-based parameter estimator has considerably low resolution and accuracy [9]. Since the resolution of FFT is low, super-resolution algorithms such as multiple signal classification (MUSIC) and estimation of signal parameters via rotational invariance techniques (ESPRIT) have been used for vital Doppler estimation. In specific, the MUSIC algorithm utilizes the orthogonality between the signal subspace and the noise subspace. In this way, the algorithm can estimate the super-resolution frequency for the parameters; however, compared to low complexity FFT-based methods, this super-resolution method involves much higher complexity. For this reason, it is difficult to apply the super-resolution method to low-cost and real-time vital FMCW systems, and low-complexity two-dimensional (2D) high-resolution algorithms are subsequently required for compact vital radar.

To date, conventional research has been processed on super-resolution algorithms to reduce complexity. A low-complexity super-resolution algorithm without eigenvalue decomposition (EVD) was proposed [10]. The EVD is an essential function to distinguish signal eigenvectors from noise eigenvectors. In this method, the effect of signal eigenvectors is minimized by performing the inverse function as opposed to the EVD. It has similar resolution performance to super-resolution algorithms such as MUSIC. However, a 2D estimation technique is required to simultaneously estimate the respiration signal and position. It still possesses a high complexity to perform multiple parameter estimation for the purpose of obtaining multiple parameters. Therefore, the low-complexity super-resolution algorithm without EVD [10] is difficult to apply to a real-time system. A low-complexity ESPRIT algorithm using reduced-dimension (RD) transformation in a monostatic MIMO radar [11] was proposed. This research assumed that the transmit/receive module is on a radar. In [11], RD transformation was generated by rearranging the Kronecker product of the transmitted steering vector and the received steering vector. However, the low-complexity ESPRIT algorithm using RD transformation in a monostatic MIMO radar [11] has a limitation wherein it can only be operated in the monostatic MIMO radar. An efficient subspace-based algorithm technique for L-shaped array radar [12] was proposed. The azimuth and elevation direction antenna array structure is the L structure. In [12], a new matrix with information for each parameter was generated by using cross correlation between the received signal in the azimuth direction and the received signal in the elevation direction. The cost function of this matrix with the steering vector of the interested signal obtained a 2D direction-of-arrival (DOA) result using maximum value. However, the efficient subspace-based algorithm technique for L-shaped array radar [12] also has a limitation wherein it can only be operated in the 2D L-shaped antenna array structure. Since conventional research is still high complexity and may have disadvantages of operating solely under specific conditions, these research methods have limitations in their application for vital radars. For low complexity, the proposed algorithm needs a method to reduce the complexity by extracting only the interested signal. This method reduces complexity by using Doppler processing of only the interested signal in the distance 1D estimation result.

This paper proposes a low-complexity FFT-MUSIC vital Doppler estimator based on target detection for contactless vital FMCW radar. The proposed method uses FFT to estimate the distance parameter; chirp data of each range bin, with the exception of clutter with stationary phase information, are subsequently used to detect the phase variation and extract the vital signal. After range peak detection, the 1D-MUSIC algorithm is employed to obtain vital Doppler results using only human FFT results. Thus, when compared with full-search super-resolution algorithms, the proposed algorithm reduces the complexity.

The remainder of this paper is organized as follows. Section II presents the signal model of the distance and the vital Doppler for the vital FMCW radar. Section III presents the proposed low complexity MUSIC vital Doppler estimator based on target detection for contactless vital FMCW radar. The complexity of each algorithm is also analyzed in this section. Section IV details the simulations for the various environments. In Section V, experimental results are provided. Finally, conclusions are given in Section VI.

This section addresses the system models of the vital FMCW radar. The vital FMCW radar can estimate parameters such as distance and vital Doppler of humans. Particularly, vital Doppler signals, such as those for respiration and heartbeat, are estimated from the phase information of a reflected signal. An FMCW transmitted (TX) signal is reflected from multiple humans. The reflected signal is changed into a beat signal as a sinusoidal signal at the received (RX) part. The sinusoidal signal’s frequency is proportional to the time delay from the human subject. The system model of FMCW radar is considered for multiple humans. The vital FMCW TX signal in Fig. 1 is denoted by s_tx(t) and it is represented by

where L indicates the number of FMCW chirp signals, and T_F denotes the total duration of chirp symbol and idle period, i.e., T_F = T+T_i, T is the duration of the chirp symbol, and T_i represents the duration of the idle period.

The vital FMCW chirp symbol s₀(t) is composed of

where f₀ indicates the initial frequency, μ is the frequency slope of the FMCW chirp symbol according to time, i.e., μ = 2πf_BW/T, and f_BW represents the bandwidth of the FMCW signal.

For vital Doppler estimation of M targets, the definition of body movement is needed to determine the targets’ fixed distance d_0,m and the time-varying distance x_m(t) of the m-th target, such as heartbeat signal and chest displacement by respiration. The time-varying distance between the radar and the human subject is represented by

where x_m(t)=x_m,r(t)+x_m,h(t); x_m,r(t) and x_m,h(t) represent the m-th human’s body motions by respiration and heartbeat, respectively. The time-varying distance x_m(t) is composed of movements of

where a_m,r and a_m,h are the amplitude of the respiration and the heartbeat, respectively, and f_m,r and f_m,h denote the frequency of respiration and heartbeat, respectively. The RX signal from the m-th human is denoted by ỹ_l(t) and obtained with time delay τ_m in (5), at the bottom of this page, where ã_m is the m-th target’s complex amplitude, x_m,r,p(t) are the p-th respiration harmonic components for the m-th human, θ denotes the residual phase, λ is the wavelength and ω(t) is the additive white Gaussian noise (AWGN) signal. In order to reduce the complexity of the FMCW radar, a de-chirping method is utilized. The de-chirping method defines the multiplication technique of the conjugation FMCW TX signals stx*(t) and ỹ_l(t); the beat signal y_l(t) at the l-th chirp symbol is expressed as

After an analog-to-digital converter (ADC) with f_s = 1/T_s where f_s is the sampling frequency and T_s is sampling time interval and N_s is the number of samples, the converted FMCW signal is denoted by y_l[n] and it is expressed in (7), at the top of this page, where a_m = ã_mexp (ω_sτ_m − μτ_m²/2) and p is the index of respiration harmonic, i.e., the case of p = 1 means the main respiration signal and the cases of p = 2, 3,…, P denotes the respiration harmonic components. From (7), the vector form y_l[n] is denoted by y_l and expressed as:

The vector form y_l is rewritten by the range, the vital Doppler, and the DOA terms, respectively, as follows:

where α, r, and ω are vectors composed of amplitude, range, and noise terms, respectively, i.e., α = [a₀, a₁,…, a_{N −1}]^T, r = [r(τ₀, r(τ₁ ), …,r(τ_M )] and ω = [ω ₀ ω₁,…, ω_{N −1}]^T where r(τ_m) is the FMCW beat signal as shown in (7) and V_l is the diagonal matrix composed of the Doppler term, as follows:

where diag(·) denotes a matrix operator and v_l(m) is the m-th vector of the velocity term.

This section proposes a low-complexity FFT-MUSIC algorithm based on target detection for range-vital Doppler estimation. This architecture is aimed at reducing the complexity to use the super resolution algorithm with accurate vital information. While conventional algorithms estimate the vital Doppler information of all targets, the proposed algorithm estimates only the target’s vital Doppler information, as shown in Fig. 2.

In this section, performance of the proposed algorithm, estimated in various simulations, is compared with that of conventional algorithms, such as FFT and MUSIC.

Experiment results were established in an indoor experimental laboratory in South Korea. In Fig. 7, the overall experimental environment is represented. The RF parameters are provided in Table 1. With a 24 GHz center frequency, a FMCW RF module with 1 TX channel and 3 RX channels was involved. The TX consisted of a frequency synthesizer, a voltage-controlled oscillator, and an oscillator with 26 MHz. An FMCW signal was generated for the 200 MHz bandwidth in a range of 24.05–24.25 GHz with 8 dBm output power as shown in Fig. 8 [10]. This multi-patch antenna has a gain of 15.6 dBi. An RF signal is moved to the TX antenna and receiver mixer via the power divider. The power divider with an S₂₁ parameter of −6 dB, an S₃₁ parameter of −1.5 dB, and an S₁₁ parameter of −20 dB were used.

The receiver consisted of two high-pass filters (HPFs), two low-pass filters (LPFs), two low-noise amplifiers (LNAs), and two mixers. The receiver had an overall noise figure of 8 dB. The gain and the noise figure of the LNAs were 14 dB and 2.5 dB, respectively. An RF signal was down-converted to an intermediate frequency (IF) signal (beat signal) by the mixer. The measured 3 dB cutoff frequency of the HPFs and the LPFs are approximately 13 kHz and 2 MHz, respectively. The developed 24 GHz FMCW RF module is shown in Fig. 9 [10]. The reference equipment was a watch-type monitoring device, i.e., a Xiaomi Mi Band 2.

When two targets were together in an indoor room, the experimental estimation results obtained using these algorithms were compared with the corresponding reference signal. In this part, the same parameters are required as in the simulation. In addition, experiments for two cases are performed, as shown in Table 2. Two far-field targets, such as humans, were located at d_0,1 = 2.9 m and d_0,2 = 4.9 m in Case I and d_0,1 = 2.9 m and d_0,2 = 5.4 m in Case II.

In terms of Case I, when the two humans were located at a distance difference of 2.5 m, the FFT results with MTI and the proposed results with MTI were able to separate the two humans simultaneously, as shown in Fig. 10. Due to the distance resolution of 2.0 m at this bandwidth, the experimental results with distance difference over 2.5 m show that the conventional algorithms and proposed algorithm can resolve the two targets.

In Case II, the FFT results and the proposed FFT-MUSIC results simultaneously detect two persons, as shown in Fig. 11. Through an experimental comparison of the FFT and proposed algorithms, the conventional and proposed algorithms have similar performance.

This paper proposed the low-complexity FFT-MUSIC algorithm based on target detection for a range-vital Doppler estimator of contactless vital FMCW radar. To improve the accuracy of the parameters for the vital radar, a high resolution-based algorithm was proposed in the form of MUSIC. However, the high resolution-based vital radar is difficult to apply to low-cost and real-time vital FMCW systems. As only target information and vital information through distance FFT by phase variation detection is extracted, the low complexity FFT-MUSIC can be obtained. In cases of complexity, when the number of chirp signals L are 16 and 64, the complexity values of the proposed algorithm are approximately 4.6 × 10⁶ and 2.4 × 10⁷ greater than that of the 2D-MUSIC, respectively. Through simulation and experimental comparisons of the full search FFT-MUSIC and proposed algorithms, the conventional and proposed algorithms are found to have similar performance. In the future, these results will be utilized in an embedded system to enhance the parameter accuracy.