# Stepped-Frequency Continuous-Wave Signal Processing Method for Human Detection Using Radars for Sensing Rooms through the Wall

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Characteristics of Site, Radar, Targets and Sensing Conditions

#### 2.1. Radar Measurement Site Description

_{FW}from the AS. This distance is assumed to be short and typically 5–20 cm. FW was actually a big block equipped with a wheeled rack at the bottom in order to make it easy to change where it was put up or to remove it completely.

#### 2.2. Characteristics of Radar

_{r}. The parameters of the signal used will define the main characteristics of the radar system. Their list is the following:

- f
_{0}is the carrier frequency of the first pulse (the initial frequency); - Δf—the frequency change step;
- N—the number of pulses;
- T
_{s}—the duration of one frame.

_{max}and the range resolution ΔR by the following ratios [34,43]:

_{r}.

**S**. In order to increase the duration of the scanning and use the fast Fourier transform (FFT) instead of DFT, each column of the matrix

**S**was padded with tail zeros to the total number ${N}_{p}={2}^{p}>N$ [22]. This leads to the matrix stacked by columns:

**X**. The absolute values $\left|{g}_{n}^{(k)}\right|$ of the vector components ${G}^{(k)}={[{g}_{1}^{(k)}\hspace{0.17em}{g}_{2}^{(k)}\hspace{0.17em}\dots \hspace{0.17em}\hspace{0.17em}{g}_{{N}_{p}}^{(k)}]}^{\mathrm{T}}$ characterize the reflective properties of the objects located over the ranges for the k-th probing period

**S**

^{(k)}and

**G**

^{(k)}(k = 1,…, K) are also called frames, and the integers n and k respectively denote the indices of the ‘fast’ and ’slow’ time [10,23].

**G**

^{(k)}, whose envelope, provided there is no noise, exhibits the waveform of a certain function visually resembling the envelope of the absolute values of the spectrum of a rectangular radio pulse defined by its samples in discrete time domain [22].

_{0}= 1 GHz, Δf = 5 MHz, N = 375, where the distance to the reflecting target was 5 m. The forming of the range profile using reverse FFT operations required N

_{p}= 2048 points, so the values of discrete samples in the figure were represented as a continuous interpolating line for the sake of easing visual perception.

**S**

^{(k)}on the window function.

**S**(or

**G**) consisted of samples describing the results of probing in one corner sector, which could cover the entire controlled space of the observed room. If it was necessary to resolve targets by azimuth, the improved radar system containing several sensing channels could be used. However, the basic processing of each channel was organized similar to one-channel leading to the set of two-dimensional matrices, similar to

**S**. The possible scenario of cooperative processing their data can be found in [42].

_{0}can be set in the range from 900 MHz to 3 GHz; the frequency change step Δf was varied from 1 to 10 MHz, the number of pulses N ≤ 3000, the probing period T

_{r}= 0.01…0.5 s.

**G,**were displayed on the tablet-type screen and had the form of a “floating” strip with a stacked display showing the latest frame. The control program settings window or the results of inter-frame signal processing could be displayed on the same screen.

#### 2.3. Characteristics of Targets

## 3. Signal Processing Algorithms

#### 3.1. Algorithm Based on Interperiodic Subtraction

**V**, containing samples of the difference signals

**V**. As a result, we get the matrix

**X**using the Equation (7) where values ${G}^{(k)}$ are substituted instead of ${S}^{(k)}$.

**X**were used to calculate the critical statistics by accumulating the energy of the observed signal in each range resolution cell:

_{0}is the number of accumulation periods.

_{0}= 2, the columns ${Y}^{(k)}$ of the matrix $Y=\left\{{y}_{n}^{(k)},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}n=1,\dots ,{N}_{p},\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}k=2,\dots ,K\right\}$ can be considered as a range profile where moving targets are being highlighted in each probing period with a number $k=2,\dots ,K$.

_{0}= 2 is made and the values ${G}^{(k)}$ are involved, is shown in Figure 4. The comparison between curves shown in Figure 3b and Figure 4 shows that using the interperiodic subtraction algorithm, the level of the signal of interest, corresponding to the target which is at a distance of 4 m, has significantly increased. Thus, the signal happens to exceed the reflection from the wall by about 4 times, i.e., by 6 dB, while the average level of interference from the stationary objects is lower by more than 15 times (or about 12 dB).

#### 3.2. Algorithm Based on Local Variance

_{0}> 2 slow time instants. The term “local variance” highlights the fact that the value ${K}_{0}\ll K$, and the evaluation of the variance of samples ${s}_{n}^{(k)}$ for each fixed value n is actually carried out in a sliding window where $k\ge {K}_{0}$.

**G**according to the local variance algorithm is determined as follows:

_{0}. This is achieved by two proposals. First, the differences between the current values of the instant and their average value for K

_{0}frames are used, and, second, the accumulation is not performed over the absolute values of the differences but over their squared values. The latter corresponds to energy-like accumulation that made the scheme more robust.

**D**

^{(k)}and

**V**

^{(k)}involves complex-valued samples rather than their absolute values. Since the difference between the values of ${s}_{n}^{(k)}$ or ${g}_{n}^{(k)}$ ordered by the index k is likely to be determined by the amplitudes of the signals as well as by their phases, this important feature points out the effectiveness of the algorithms under consideration.

#### 3.3. Algorithm Based on the Normalized Difference Samples of the SFCW Signal

_{0}frames. However, the fundamental difference here is the normalization of difference samples, which is carried out before the reconstruction of the range profile, i.e., before the IDFT is applied. In other words, this algorithm performs the operation similar to the range compression.

_{0}subsequent frames. Thus, it takes on different values at each observation period numbered with k = K

_{0},…,K.

**Z**is defined as

**I**.

**Z**can be used in the evaluation of the statistics designed for reliable detecting or accurate measuring of the coordinates of targets in a similar way to the statistics considered for inter-periodic subtraction algorithms as the elements of matrix

**X**or for local variance as elements of matrix

**D**. However, if the normalization operation (13) has been excluded, the outputs of the local variance and NDS algorithms will inevitably coincide.

**Z**, allows one to improve the SNR in comparison with the cases where the statistics of inter-periodic subtraction and local variance are primarily exploited. This result has been confirmed by numerous experimental data from the radar system when observing single and multiple moving and stationary targets and described in more detail in paragraph 5. Despite the fact that there is still no rigorous theoretical substantiation supporting the advantages of the proposed method of processing SFCW signals found so far, the next section presents the results of computer modeling of the simple signals, for which quantitative estimates of the gains have been achieved in the form of a valuable SNR gain.

## 4. Computer Simulation Results

_{t}, ${\phi}_{0}=2\pi {f}_{0}{\tau}_{0}+{\tilde{\phi}}_{0}$ is the initial phase, depending on the distance to the target and including the random component ${\tilde{\phi}}_{0}$, that occurs when the signal is reflected from the target, and the last term $\eta ({t}_{n}^{(k)})$ denotes complex samples of white Gaussian noise with zero mean and variance ${\sigma}_{\eta}^{2}$; n = 0,…, N is the “fast time” index.

_{0}= 1 GHz, Δf = 1 GHz, N = 500, Δt = T

_{s}/N = 10

^{−5}s. The frequency relating to the acquisition of discrete samples taken out of the complex exponent in (18) is chosen to be f

_{p}= Δfτ

_{0}/Δt = 4 kHz, that corresponds to the maximal target range R

_{t}= 6 m, or as the time value τ

_{0}= 4 × 10

^{−8}s. The variance of the noise is chosen ${\sigma}_{\eta}^{2}=0.3$, which yields the additional average amplitude value of the SFCW signal samples $\overline{a}({t}_{n}^{(k)})=0.855$, that corresponds to SNR q = 6 dB.

## 5. Results of Field Experiments

^{2}total area was assembled with a brick wall of 0.5 m thick. During the experiments, the following parameters of the emitted SFCW signal were set: initial frequency f

_{0}= 1 GHz, frequency change step Δf = 4 MHz, which give final frequency f

_{N}

_{−1}= 2.5 GHz for the number of pulses N = 375, the duration of one pulse Δt = 50 μs, probing period T

_{r}= 0.1 s yielding the frame rate 10 Hz. Thus, the maximum unambiguous range R

_{max}= 37.5 m, and the range resolution ΔR = 0.1 m can be found using (1).

**Y**,

**D**,

**Z**were formed as the outputs of those algorithms. The number of averaging frames K

_{0}= 5, corresponding to averaging time K

_{0}T

_{r}= 0.5 s, was set for the second and third one. The range profile restoration was performed by IDFT transformation with the number of points N

_{p}= 1024 for all three algorithms.

**S**) are two-dimensional arrays

**Y**,

**D**,

**Z**, which are presented in the form of color images shown in Figure 7, where the vertical axis corresponds to the range values at the interval (0, 10) meters (the range origin is the inner boundary of the room wall), and the horizontal axis corresponds to the instants of slow time ${t}^{(k)}=(k-1){T}_{r}$, $(k=1,\dots ,K)$ taken out of the interval (0, 40) seconds.

**Y**,

**D**,

**Z**corresponding to the algorithms of interperiodic subtraction, local variance and NDS, are determined by the formulae:

**Y**,

**D**,

**Z**for this experiment are shown in Figure 9a–c respectively.

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Normalized response functions of a point target when using a rectangular window (

**a**) and a Kaiser window (

**b**).

**Figure 3.**The response function of the target—A human facing the radar at a distance of 4 m: (

**a**) in open space; (

**b**) when sensing through a brick wall 0.5 m thick.

**Figure 4.**Range profile in one frame after applying the interperiod subtraction algorithm for the signal shown in Figure 3b.

**Figure 5.**Discrete samples of the SFCW signal without normalization (

**a**) and with normalization of samples (

**b**). The in-phase components of the signals are depicted with blue lines and the quadrature components are with red lines.

**Figure 6.**Results of SFCW signals compression: (

**a**) compression of non-normalized samples; (

**b**) compression of normalized samples.

**Figure 7.**Two-dimensional matrices of signals after processing according to the interperiodic subtraction algorithm (

**a**), local variance algorithm (

**b**) and NDS algorithm (

**c**). The warmer tones correspond to more intensive reflection.

**Figure 8.**The values of statistics accumulated for 400 frames depending on the range when using the basic interperiod subtraction algorithm (yellow line), local variance algorithm (red line), normalized difference samples algorithm (blue line).

**Figure 9.**The results of the work of the inter-periodic subtraction algorithm (

**a**), local variance algorithm (

**b**) and difference samples normalization algorithm (

**c**). The warmer tones correspond to more intensive reflection.

Research Group | Freq, GHz | d, m | Tx Power | Steps | Application | TWR | Signal Processing |
---|---|---|---|---|---|---|---|

This work | 1–2.5 | 1–8 | 6 dBm | 375 | Vital sign detection, Movement detection | yes | NDS ^{1}, FFT ^{2} |

Nahar et al. [41] | 2–3 | 1 | 8 dBm | 51 | Vital sign detection | no | FFT ^{2} |

Qui et al. [44] | 2–3 | 3.5 | 10 dBm | 101 | Vital sign detection | yes | Isophase method |

Su et al. [52] | 8.5–9.5 | 4 | 0 dBm | 101 | Vital sign detection | no | FFT ^{2} |

Quaiyum et al. [53] | 2–4 | 0.75 | 12 dBm | 100 | Vital sign detection | no | FFT ^{2} |

Šipoš et al. [54] | 0.5–2.5 | 1 | −10 dBm | 200 | Conductive object detection | yes | EC ^{3} method |

Li et al. [30] | 1.75–2.25 | 2 | 20 dBm | 125 | Vital sign detection | yes | VMD ^{4}, FFT ^{2} |

^{1}Normalized difference samples;

^{2}Fast Fourier transform;

^{3}Echo cancellation;

^{4}Variational mode decomposition.

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**MDPI and ACS Style**

Kozlov, R.; Gavrilov, K.; Shevgunov, T.; Kirdyashkin, V.
Stepped-Frequency Continuous-Wave Signal Processing Method for Human Detection Using Radars for Sensing Rooms through the Wall. *Inventions* **2022**, *7*, 79.
https://doi.org/10.3390/inventions7030079

**AMA Style**

Kozlov R, Gavrilov K, Shevgunov T, Kirdyashkin V.
Stepped-Frequency Continuous-Wave Signal Processing Method for Human Detection Using Radars for Sensing Rooms through the Wall. *Inventions*. 2022; 7(3):79.
https://doi.org/10.3390/inventions7030079

**Chicago/Turabian Style**

Kozlov, Roman, Konstantin Gavrilov, Timofey Shevgunov, and Vladimir Kirdyashkin.
2022. "Stepped-Frequency Continuous-Wave Signal Processing Method for Human Detection Using Radars for Sensing Rooms through the Wall" *Inventions* 7, no. 3: 79.
https://doi.org/10.3390/inventions7030079