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Separation algorithm of vital sign signal in complex environments based on timefrequency filtering
EURASIP Journal on Wireless Communications and Networking volume 2016, Article number: 90 (2016)
Abstract
Life detection radar that combines radar technology with biomedical engineering detects human physiological signals (respiration, heartbeat, body movement, etc.) from a long distance with noncontact method. In this field, vital sign detection and parameter extraction are hot issues in current researches, and the acquisition of vital sign signal of human target with radar may very helpful. In this paper, a separation method for vital sign signals based on timefrequency filtering (TFF) is proposed, which mainly predicts the instantaneous frequency (IF) by combining the Viterbi algorithm (VA) with strong noise immunity and taking advantage of the highresolution timefrequency transformation method with good crossterm inhibitory effect in B distribution (BD), so as to extract the weak vital sign signals in the radar echo effectively. According to the simulation result, this algorithm has good resolution precision and antinoise performance, and it is applicable for the extraction of vital sign signals in low signaltonoise ratio, which may provide basis for the further launch of parameter extraction of the vital sign signals.
Introduction
Life detection radar that combines radar technology with biomedical engineering detects human physiological signals (respiration, heartbeat, body movement, etc.) from a long distance with noncontact method. Realtime noncontact detection is an effective approach of monitoring the human physiological features, as well as the significant development direction of future lifemonitoring equipment [1–3]. The principle is to conduct the microDoppler modulation for the electromagnetic wave with the partial weak periodic motion caused by the heartbeat and breathing and to extract the corresponding microDoppler parameters in the echo signal for realizing the extraction of physiological feature parameters [4–6]. At present, it has wide applications in throughwall target detection, searchandrescue missions at disaster sites, biomedical monitoring, and other related fields [7, 8].
Some studies show that radar has the capability of detecting human’s vital signs such as breathing, heartbeat, and other body movements [9–11]. When the human target is exposed under the incidence of electromagnetic wave source [12–14], the reflected signal is phasemodulated due to the chest movements associated with breathing and heartbeat. The frequency and phase of the incident wave are modulated according to the characteristics of the movement amplitude. We can identify and extract the life signal frequency from the change of reflected wave by applying appropriate signalprocessing techniques. However, in practical application, there contains human body echo, clutter, and noise in the radar echo, of which the energy is far greater than that of the microDoppler signal of heartbeat and breathing. The detection accuracy can be significantly influenced by this kind of interference. In order to achieve the heartbeat and breathing parameters, microDoppler signals, subject echoes, and noises shall be separated or suppressed. Zhang et al. [15] gave a method to suppress the interference by an experimental setup with a dualfrequency continuouswave radar. The authors used an adaptive filtering method to suppress the interference caused by the operator’s respiratory movements and improved detection accuracy. Li et al. [16] used curvelet transform to remove the sourcereceiver direct coupling wave and background clutters and singular value decomposition to denoise in the life signals. The results are presented based on FFT and HilbertHuang transform to separate and to extract human vital sign frequencies, as well as the microDoppler shift characteristics.
Li and Pi [17] gave a result that terahertz radar system could be very helpful to observe some slight micromotion because of its short wavelength, huge bandwidth, and obvious microDoppler shift [18]. Combining these characteristics with a highprecision timefrequency filtering method, weak human physiological features can be extracted more accurately (the heartbeat and breathing). It can realize the noncontact extraction of human physiological feature signals, so as to lay a foundation for further extracting of the physiological feature parameters. Section 2 constructs the model of human of breathing and heartbeat. Section 3 introduces the algorithm of frequency estimation and timefrequency filtering. Section 4 gives some simulation results to compare this algorithm with other methods.
Modeling of human target echo
Generally, radar echo signal can be expressed as follows [19]:
in which, A is the range and ϕ(t) = 4πR(t)/λ _{ c } is the phase function. If derivation is conducted for the time, the Doppler frequency can be obtained
The ECG signal chart can be referred to during the modeling for heartbeat, and it is in a periodic sharp pulse form. The breathing is accomplished by the expansion and contraction of the chest, and it can be expressed by the sinusoidal signal model. Suppose that the human body is in a static state relative to radar, the modeling is shown as follows:
in which R _{0} is the distance between the radar and the human body; the second term is the breathing, while the third is the heartbeat; r _{1} and r _{2} are the range of breathing and heartbeat, respectively, while ω _{1} and ω _{2} are the frequency of breathing and heartbeat, respectively. δ(t) can be expressed as follows:
in which τ is the heart rate excursion, a = 1/2−rω _{2}, and r is the radius of the heartbeat. The simulation parameters are shown in Table 1 and the results are shown in Fig. 1.
The echo signal removing the carrier frequency received by the receiver consists of S _{BODY} and S _{MD} modulated by the heartbeat and breathing.
The derivation of the S _{MD} phase that may obtain the Doppler frequency caused by the heartbeat and breathing is
The accuracy of Doppler information extraction may impact the effect of the extraction of human target physiological feature parameters. The heartbeat and breathing echo is buried in the subject echo and noise, and it may not be able to measure in the time domain or frequency domain. The timefrequency transformation may spread the noise energy to the entire time domain, while the signal energy may concentrate in limited time and frequency range [20], for realizing the separation of microDoppler information from the target and noise.
The algorithm flow of the separation of vital sign signal based on the timefrequency filtering is shown in Fig. 2.
The algorithm may conduct the timefrequency analysis for the echo signal at first, gain the timefrequency domain data of the human echo, and separate the microDoppler information of breathing and heartbeat through timefrequency filtering. The human echo may interact with the heartbeat and breath, and highresolution timefrequency transformation method and highprecision timefrequency filtering separation shall be applied in order to recognize and extract the microDoppler information accurately.
Timefrequency filtering separation algorithm
In order to separate the microDoppler signal caused by the heartbeat and breathing with timefrequency filtering, it may transfer the microDoppler signal to the timefrequency with the B distribution (BD) which has good crossterm inhibitory effect and high timefrequency resolution [21]. And then the instantaneous frequency of vital sign signal shall be estimated with the Viterbi algorithm [22], which has high estimation precision. Eventually, the coverage function shall be designed according to the instantaneous frequency curve, and the timefrequency point of vital sign signal shall be separated with the coverage function, so as to gain the microDoppler signal of vital sign signals.
Timefrequency transformation
Heartbeat and breathing are typical nonstationary signals, with evident timevarying features, and they shall be analyzed with the timefrequency analysis method. Common timefrequency analysis methods include shorttime Fourier transform (STFT), WignerVille distribution (WVD), etc. When multicomponent signal is processed, WVD has severe crossterm, and although the improved smoothed pseudo WignerVille distribution (SPWVD) can overcome the impact of the crossterm, it sacrifices the resolution. Although STFT has no crossterms, it is poor in energy aggregation and low in precision. In this paper, BD algorithm with good crossterm inhibitory effect and high timefrequency resolution is adopted, and it is a kind of Cohen timefrequency distribution [21]. The definition is
The kernel function is
in which \( \cosh (t)=\frac{e^t+{e}^{t}}{2},\;\left\tau \right/{ \cosh}^2(t) \) is obtained by expanding the 1/cosh^{2}(t) function to twodimensional plane (t, τ). When processing the multicomponent with the variable α(0 < α ≤ 1), it is a real parameter that controls the sharpness of cutoff of the twodimensional filter in the ambiguity domain, and the value α = 0.01 is suggested for most of the signals concerning the crossterm suppression and timefrequency (TF) resolution. It can adjust the passing degree of each component and attenuation degree of the crossterm to get a balance between them.
The human target echo shall be simulated with the timefrequency analysis, and the signaltonoise ratio is −3 dB. In there, signal means the energy of echo caused by breathing and heartbeat in the time range of simulation, noise is an additive white Gaussian noise, and the simulation parameter is shown in Table 2.
It can be seen from Fig. 3 that after the timefrequency analysis for the echo signal, microDoppler signal may overlap with the human body signal in the timefrequency domain, and the noise may spread in the entire timefrequency domain. It can be seen from Fig. 3a that the STFT method is poor in energy focus, which may result in the mixing of signals and low timefrequency resolution. It can be seen from Fig. 3b, c that WVD and SPWVD may be impacted by noise substantially and low in timefrequency resolution, and it may not be able to recognize the microDoppler information clearly. In Fig. 3d, it is the processing result of BD transformation, although the frequency resolution is different from the above methods, but from the outline, we still could get the conclusion that its resolution and noiseinhibiting ability are relatively ideal.
Estimation of instantaneous frequency
The concept of timefrequency filtering is proposed by Boashash B, and it mainly realizes the filtering in timefrequency domain with the timefrequency filter established [23]. It shall estimate the instantaneous frequency of signals within the timefrequency domain. If it wants to separate the microDoppler signal of vital signs in the timefrequency domain, it shall estimate the instantaneous frequency of vital sign signal at first.
The estimation of instantaneous frequency is quite significant in the analysis of nonstationary signal [24]. The simplest estimation method shall be the peak test method, namely it shall seek for the maximum timefrequency point at any moment in the timefrequency plane
in which n is the time sequence, k is the frequency sequence, and TF(n,k) is the timefrequency distribution.
This method is not applicable for estimating the instantaneous frequency of multicomponent signals in low signaltonoise ratio (SNR) environment, for the range of noise or other signal components at a certain moment may be greater than the range of a signal component that shall be estimated, and it may result in the severe deviation of estimation frequency from the real frequency. In this paper, the instantaneous frequency of signal is estimated with the Viterbi algorithm that is not sensitive to the SNR. In 2004, Igor Djurovic and L. Jubisa Stankovi proposed a method to estimate the instantaneous frequency of multicomponent signal by combining the Viterbi algorithm to WVD [22].
The estimation of instantaneous frequency based on the Viterbi algorithm is based on two basic assumptions: (1) the range of timefrequency point corresponding to the instantaneous frequency at any moment is the largest; and (2) the instantaneous frequency curve shall be a relatively smooth curve, namely the frequency changes at any adjacent moment is relatively flat. The algorithm may search a curve in the timefrequency domain to make the cost function of the curve minimum, namely
in which K is all paths from n _{1} to n _{2} in the entire timefrequency surface, k(n) is one of the paths, and g(x,y) and h(x) are the cost functions. p(k(n);n _{1},n _{2}) is the total cost of the cost functions h(x) and g(x,y) in path k(n) from moment n _{1} to n _{2}. h(x) is a nonincreasing function, corresponding to hypothesis (1). g(x,y) is the nondecreasing function about xy, corresponding to hypothesis (2).
Along a certain moment n, nonascending order is conducted for all timefrequency points at this moment.
in which j = 1, 2, ⋅ ⋅⋅, M is the serial number. The cost function
namely at the largest timefrequency point the function h(x) is 0, and at the second largest timefrequency point is 1; and in this way, the larger the range of timefrequency point is, the smaller the cost will be.
If g(x,y) is a constant, the estimation of instantaneous frequency will be the maximum estimation, and g(x,y) will be defined as
in which c is a constant and Δ is the maximum frequency change value allowed by the adjacent instantaneous frequency. The stronger the instantaneous frequency change of adjacent moment is, the higher the cost will be. In the specific realization process, Δ often relies on the frequency resolution of timefrequency transformation, and higher timefrequency transformation resolution may gain more accurate estimation of instantaneous frequency. In this paper, c = 2.5 and Δ = 1.
Estimation of instantaneous frequency shall be conducted for the timefrequency analysis result gained in BD transformation with the Viterbi algorithm, and the simulation parameters are shown in Table 2. It can be learnt from Figs. 4 and 5 that the instantaneous frequency curve gained in the peak test is severely impacted by the SNR, and low SNR may result in the curvilinear distortion, while the Viterbi algorithm may gain relatively good estimation result in two types of SNR conditions.
Timefrequency filtering
After estimating the instantaneous frequency curve of vital sign signals by the method mentioned above, the timefrequency filter can be constructed according to the estimation result to separate the microDoppler signal of vital signs. The progress is as follows.

Evaluate IF—Using the algorithm mentioned above to estimate the instantaneous frequency of multicomponent signal, it should be estimated in sequence by the signal power in the timefrequency domain.

1.
Evaluate the instantaneous frequency of all components, \( {\widehat{\omega}}_i(n), \) i = 1 corresponding to the highest signal component.

2.
Set the neighborhood region of \( {\widehat{\omega}}_i(n),\;\left[{\widehat{\omega}}_i(n)\delta, {\widehat{\omega}}_i(n)+\delta \right] \) to zerovalue, where δ is the zero region around the instantaneous frequency, forming a new timefrequency representation by B distribution method again.

3.
Repeat these two steps to estimate the instantaneous frequency corresponding to all signal components.

1.

Construct TFF—Timefrequency filter can be constructed based on the instantaneous frequency curve acquired by the steps above to separate the signal components.

1.
Choosing the suitable bandwidth based on the estimated instantaneous frequency to design the masking function C _{i}(n,ω) [24],
$$ {C}_i\left(n,\omega \right)=\left\{\begin{array}{c}\hfill 1,\hfill \\ {}\hfill 0,\hfill \end{array}\right.\begin{array}{c}\hfill k\in \left[{\widehat{\omega}}_i(n)B(n)/2,{\widehat{\omega}}_i(n)+B(n)/2\right]\hfill \\ {}\hfill \mathrm{others}\hfill \end{array}, $$(14)in which \( {\widehat{\omega}}_i(n) \) is the instantaneous frequency evaluated and B(n) is the bandwidth of the masking region which is either time varying or constant. In this paper, we choose B(n) = 8.

2.
The timefrequency data BD_{ i }(n,ω) can be obtained by multiplying the timefrequency of the original signal BD(n,w) with the masking function C _{ i }(n,ω).

3.
The mD signals can be obtained from the timefrequency data BD_{ i }(n,ω) inverse result.

1.
Simulation experiment and performance analysis
The result of separation in simulation
In this paper, the algorithm performance is verified by comparing the impact of different timefrequency transformations and instantaneous frequency estimation methods on the separation algorithm. At first, the vital sign signal separation result based on the combination of BD transformation and Viterbi algorithm is proposed. Figure 6a is the separation result when the SNR is −3 dB, while Fig. 6b is the timefrequency spectrum of the actual vital sign microDoppler signal. It can be seen from the comparison of the two figures that the algorithm proposed in this paper can restore the microDoppler signal caused by the heartbeat and breathing effectively, which may lay the foundation for further extraction of the signal parameters.
TF transformation methods influence on performance of separation
In order to discuss the algorithm performance quantitatively, the correlation coefficient of the vital sign signal X obtained from the separation and its theoretical value Y can be defined as
At first, the impact of different timefrequency analysis methods on the separation result shall be discussed. Simulation shall be conducted with the parameters in Table 2, and timefrequency analysis shall be conducted for the echo signals with STFT, WVD, SPWVD, and BD transformation, the instantaneous frequency curve shall be estimated with the Viterbi algorithm for the results, and the timefrequency filter shall be constructed. In Fig. 7 is the curve of correlation coefficient of the vital sign microDoppler signal and its theoretical value changes with SNR, by using different timefrequency transformation methods.
It can be seen from Fig. 7 that the correlation result separated based on the BD transformation is obviously better than the STFT, WVD, and SPWVD methods, and meanwhile, the separation result of the timefrequency filtering based on BD transformation is relatively ideal in all kinds of SNR conditions.
IF estimation methods influence on performance of separation
Secondly, the impact of different instantaneous frequency estimation methods on the separation result is discussed. Simulation is conducted with the parameters in Table 2, and timefrequency analysis is conducted with BD transformation. In Fig. 8 is the varying curve of the correlation coefficient of the result gained from the algorithm and its theoretical value changes with SNR, based on the Viterbi algorithm and peak estimation.
It can be seen from Fig. 8 that in low SNR, the peak estimation is impacted by noise substantially and the correlation coefficient is smaller than that of the Viterbi algorithm. With the increase of SNR, the result of peak estimation may get close or be equal to the result of the Viterbi algorithm. The simulation shows that the timefrequency filtering based on the Viterbi algorithm is slightly impacted by the noise, and it has strong antinoise capacity, being more applicable for separating the weak human vital sign signals.
Compare with empirical mode decomposition
Empirical mode decomposition (EMD) has been pioneered by N.E. Huang et al. for adaptively decomposing nonstationary signals as sums of zeromean AMFM components, called intrinsic mode functions (IMFs) [25]. Using this signal decomposition algorithm, the returns from the target body and the vibrating/rotating structures can be efficiently separated. Better target image will be obtained with the reduction of the interferences from vibrating/rotating parts. On the other hand, microDoppler signature can also be revealed much clearer after the separation [26]. Li et al. [16] show the result of vital sign extract from complex environments by EMD method. Now, we compare the separation results given by EMD and VABD combined algorithm.
Figure 9 shows the result of microDoppler separation by EMD and VABD combined algorithm. From Fig. 9b, we can see that the separation result is influenced by noise when the SNR is not high. Because after separating echo into IMF, we will choose some IMFs to reconstruct the vital signal we need. If the IMF with a higher frequency is chosen, we cannot get rid of the noise, but if the lower frequency is chosen, the real component of vital signal will lose.
From Fig. 10 we can see that, in the situation of low SNR, the result given by EMD has greater influence by noise than the VABD algorithm. When the SNR becomes lower, the correlation coefficient by EMD becomes much lower than the VABD’s. Unfortunately, the SNR of the vital sign signal obtained by the radar system is always very low because of the echo of the body and the clutters contributed by the ground, walls, and other complex environments. In this case, we can get the conclusion that VABD combined algorithm is more suitable than the EMD method in this low SNR condition.
Conclusions
In this paper, an algorithm that can separate the microDoppler signal of vital sign signals in timefrequency filtering is proposed. In this algorithm, the timefrequency of echo signal is analyzed by BD transformation, which is good in crossterm inhibitory effect and high in resolution. Secondly, the instantaneous frequency of signal is estimated by the Viterbi algorithm, which is not sensitive to noise, and may gain good effect in low SNR condition. Eventually, the timefrequency filter is constructed according to the estimated instantaneous frequency, so as to extract the microDoppler of vital sign signals.
In this paper, simulation verification is conducted for the performance of timefrequency filtering separation algorithm, and the impact of different timefrequency transformation methods and instantaneous frequency estimation methods on the separation effect is analyzed. It is concluded that the timefrequency filtering algorithm based on the combination of BD transformation and the Viterbi algorithm has good performance, and the extraction result can be further applied in the parameter extraction of vital sign signals. At last, we chose a typical method EMD used by many references for microDoppler extraction to compare with this VABD combined algorithm in this condition. We can obtain the conclusion that VABD combined algorithm is suitable for vital sign signal separation because of its low SNR in normal conditions.
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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China under Grants 61271287, 61371048, and 61301265 and in part by the Fundamental Research Funds for the Central Universities under Grants ZYGX2012Z001 and ZYGX2013J027.
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Tian, K., Li, J. & Yang, X. Separation algorithm of vital sign signal in complex environments based on timefrequency filtering. J Wireless Com Network 2016, 90 (2016). https://doi.org/10.1186/s1363801605891
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Keywords
 Vital sign signal
 Timefrequency filtering
 B distribution (BD)
 Viterbi algorithm (VA)