### Description of the system

The schematic diagram of the single-channel UWB radar system is illustrated in Figure1. The oscillator generates a narrow pulse signal with a center frequency of 400 MHz that is controlled by a pulse coder. The output of the oscillator is fed through an electromagnetic pulse generator to the transmitting antenna. The bowtie dipole antenna transmits vertically polarized pulses with a peak power of about 5 W. The echo is received by the receiving antenna and then sent to the sample integrator, and the signal out from the oscillator generates range gates through a delay circuit and a range gates generator. The echo signal is sampled according to the range gates and is accumulated by an integral circuit, which next leads to the extraction of the weak low-frequency signal. This signal is amplified and filtered by a signal processor and passed through a high-speed Analog/Digital (A/D) converter before reaching the Digital Signal Processor (DSP) for further processing. Finally, the distance of each human target is computed by DSP and sent to a PC terminal to display the detecting result via Bluetooth.

### Decomposition and synthesis of the signal

The basic flowchart of the signal processing is shown in Figure2. The amount of data is too large for real-time computation, so that the signal out from the A/D converter should be integrated by sliding the window first to cut down the length of the data. Great computational load is avoided by the integration, but the SNR of signal is not decreased. The echo *s*(*t*, *d*) is a function of two parameters: the delay or range (distance) and the time. The echo is then decomposed and synthesized in the time and space domain. Thus, Time Signal of echo *x*(*t*) is defined as *x*(*t*) = *s*(*t*, *d*) for a fix distance, and Distance Signal *y*(*d*) = *s*(*t*, *d*) for a fix time.

### Improving SNR by filtering and moving average subtraction

The Time Signals of echo *x*(*k*) are filtered by a 160-order low-pass Hamming window-based filter with a cut-off frequency of 0.5 Hz to restrain high-frequency noise and keep the respiration signal of human. A moving average subtraction is then applied to remove the background clutter of the echo, which can enhance the stationary human life characteristic of the signals and improve the SNR. The formula of moving average subtraction is as follows:

\phantom{\rule{1em}{0ex}}X\left(n\right)=x\left(n\right)-\frac{{\displaystyle \sum _{k=n-m}^{k=n-1}x\left(k\right)}}{m}\text{,}

(1)

where *X* is the output signal, *x* is the input signal, *m* is the width of moving window, and *n* is the sequence number of the Time Signal of echo.

### Distance identification by space–frequency analysis

The signal (time window is 60 ns: range 0–9 m) from the subtraction is divided equally into 26 segments. The number of segments is selected according to the range resolution needed. The distance denoted by each segment is about 0.36 m. The first four segments are cut out to remove the interference caused by the direct-coupling arrival (echo directly from the transmitting antenna to the receiving one). Then, every amplitude of *y*(*d*) in each segment from the 5th to 26th is summed respectively. As a result, a new Distance Signal is composed by these 22 sums.

In the light of the time resolution needed in practical detection, the data length is selected as 10 s. So in the time domain the collected data forms 22 new Time Signals of echo which last for 10s. Finally, according to the range sequence, these new Time Signals of echo are connected and regarded as the Input Signal.

STFT is performed to the Input Signal, and the window width used is equal to the length of the new Time Signal of echo. The number of Fourier Transform points is 1024, thus, the STFT can be expressed as:

\phantom{\rule{1em}{0ex}}STFT\left(t,w\right)=\int S\left(\tau \right)\gamma (\tau -t)exp\left(-jw\phantom{\rule{0.12em}{0ex}}\tau \right)d\phantom{\rule{0.12em}{0ex}}\tau \text{,}

(2)

whereS\left(\tau \right) is the Input Signal, *γ*(*t*) is the window function.

The typical STFT of stationary human signals is respectively shown in Figures3,4 and5.

Threshold of estimation: The result of space-frequency transformation denotes a three-dimensional relation. Two coordinates represent the range and the frequency respectively, and the colors of the spectrogram represent the signal power amplitude. An appropriate adaptive non-linear threshold is chosen to distinguish the multi-stationary subjects. If the power amplitude in the frequency range of human respiration at a certain distance is obviously higher than that at other distances, and exceeds the threshold simultaneously, then the result is judged such that there is a stationary human in this distance (one-dimensional distance). If more than one high-power spectral peak appears at different distances, then many stationary human targets are assumed in the corresponding distances. And these target distances are recorded; thus, the soft threshold can be expressed as:

\phantom{\rule{1em}{0ex}}{E}_{n}>\left|\rho \right|\phantom{\rule{0.12em}{0ex}}{E}_{\phantom{\rule{0.12em}{0ex}}\text{mean}}\text{,}

(3)

where *E*_{n} is the power of spectral peak, and *E*_{mean} is the mean power of the 22 segment signals. |*ρ*| is determined according to the distance from radar because of the attenuation of the power along with the increasing distance. For human target detection, UWB radar’s performance in terms of power is governed by

\phantom{\rule{1em}{0ex}}\frac{{P}_{r}}{{P}_{t}}=\frac{{G}_{t}{G}_{r}{\xi}_{t}{\xi}_{r}\lambda \sigma}{{\left(4\pi \right)}^{3}{d}^{4}}{e}^{-4\alpha d/8.686}\text{,}

(4)

where *P*_{
t
} and *P*_{
r
} are respectively the transmitting power and the receiving power, *G*_{
t
} and *G*_{
r
} are gains of the transmitting and receiving antennas, *ζ*_{
t
} and *ζ*_{
r
} are the transmitting and receiving coupling efficiencies, *λ* is propagation wavelength of frequency components within the bandwidth of the radar, *σ* is radar cross section of target’s chest, *α* is attenuation coefficient of medium (wall or air) and *d* is the range from the target to the UWB radar. According to the Equation (4), the formula of |*ρ*| is

\phantom{\rule{1em}{0ex}}\left|\rho \right|=4.{e}^{\frac{-d}{9}}\text{,}

(5)

where *d* is the distance from radar in meters.