Radio frequency fingerprint extraction method and system based on repetitive characteristics of wireless signal preamble

Abstract

The present invention provides a radio frequency fingerprint extraction method and system based on the repetitive characteristics of wireless signal preamble codes, which are carried out by extracting the signal preamble code from the wireless signal; dividing the signal preamble code into multiple sub-signal segments according to the repetitiveness of the signal preamble code; calculating the characteristic coefficients between the sub-signal segments; and arranging all the characteristic coefficients of the multiple sub-signal segments of the signal preamble code in order to construct a radio frequency fingerprint feature that highlights the carrier offset information. The radio frequency fingerprint feature constructed by the present invention highlights the carrier offset feature. The radio frequency fingerprint identification method based on this feature is resistant to wireless channel fading and greatly reduces the computational complexity. It can effectively alleviate the impact of channel fading and receiver changes, and improve the generalization capability of the receiver. In addition, the present invention can directly extract the radio frequency fingerprint feature from the received signal preamble code, without the need for additional signal processing of the received signal, thereby avoiding the fingerprint loss problem caused by channel equalization.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and more specifically, to a method and system for extracting radio frequency fingerprints based on the repetitive nature of wireless signal preambles. This invention utilizes the repetitive nature of preamble signals to construct radio frequency fingerprint features that can be used for device identification, thereby improving the generalizability of the identification system across different receivers. Background Art

[0002] Due to manufacturing process variations, wireless devices cannot have identical hardware features. Therefore, their transmitted signals contain a unique RF fingerprint characteristic specific to each wireless device, making it difficult to impersonate. Therefore, extracting RF fingerprints from wireless signals plays a significant role in wireless device identification. Hardware defects in wireless devices are often correlated, making it difficult to accurately represent the RF fingerprint using a single feature. Thanks to the feature extraction capabilities of neural networks, deep learning technology is currently widely used in the field of RF fingerprint extraction for wireless devices. However, fading in wireless transmission channels can cause severe distortion in received signals, making it impossible for neural networks to extract a valid RF fingerprint. This significantly reduces the performance of the identification system, especially when the identification system is deployed on an unknown receiver.

[0003] In his paper "Radio frequency fingerprint identification for LoRa using deep learning," (IEEE J.Sel.Areas Commun., vol. 39, no. 8, pp. 2604-2616, Aug. 2021), G. Shen disclosed a wireless radio frequency fingerprint recognition method based on deep learning. The method first converts the input signal into different signal representations, including in-phase and quadrature (IQ) samples, fast Fourier transform (FFT) spectrum, and short-time Fourier transform (STFT) time-frequency spectrum. Secondly, a multilayer perceptron (MLP), convolutional neural network (CNN), and long short-term memory (LSTM) network are designed for different signal representations. Finally, by combining the signal representation and the neural network architecture, the recognition results of the recognition system under different combinations are obtained. This method comprehensively compares the radio frequency fingerprint extraction capabilities of different neural networks. However, this method still has a drawback: it does not consider the impact of wireless transmission channel fading on RF fingerprint extraction. Because fading in the wireless transmission channel causes severe distortion in the received signal, the neural network is usually unable to extract an effective RF fingerprint from it, resulting in a decrease in the performance of the recognition system.

[0004] To address this issue, M. Cekic, S. Gopalakrishnan and U. Madhow disclosed a method for device identification using preprocessed signals in "Wireless fingerprinting via deep learning: the impact of confounding factors," (in Conf. Rec. Asilomar Conf. Signals Syst. Comput., Oct. 2021, pp. 677-684.). The implementation steps of this method are: 1) collecting signals from wireless devices; 2) performing frequency offset compensation and channel equalization on the collected signals; 3) using the processed device signals and using neural networks to perform device identification to obtain identification results. Although signal preprocessing can alleviate the impact of channel fading and improve the performance of the identification system. However, this method does not take into account the differences between different receivers. The information loss caused by signal preprocessing is different on different receivers, resulting in a significant decrease in performance when the identification system is deployed on different receivers. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a method and system for extracting radio frequency fingerprints based on the repetitive characteristics of wireless signal preamble codes. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] In a first aspect, the present invention provides a radio frequency fingerprint extraction method based on the repetitive characteristics of a wireless signal preamble, which is applied to a receiver. The radio frequency fingerprint extraction method includes:

[0007] S100, receiving a wireless signal and extracting a signal preamble from the wireless signal;

[0008] S200, dividing the signal preamble into a plurality of sub-signal segments according to the repetitiveness of the signal preamble;

[0009] S300, calculating characteristic coefficients between sub-signal segments;

[0010] S400: Arrange all characteristic coefficients of the plurality of sub-signal segments of the signal preamble in order to construct a radio frequency fingerprint feature that highlights carrier offset information.

[0011] In a second aspect, the present invention provides a radio frequency fingerprint extraction system based on the repetitive characteristics of a wireless signal preamble, comprising a plurality of receivers, each of which performs the following process:

[0012] S100, receiving a wireless signal and extracting a signal preamble from the wireless signal;

[0013] S200, dividing the signal preamble into a plurality of sub-signal segments according to the repetitiveness of the signal preamble;

[0014] S300, calculating characteristic coefficients between sub-signal segments;

[0015] S400: Arrange all characteristic coefficients of the plurality of sub-signal segments of the signal preamble in order to construct a radio frequency fingerprint feature.

[0016] Beneficial effects:

[0017] The present invention provides a radio frequency fingerprint extraction method and system based on the repetitive characteristics of wireless signal preamble codes, which receives a wireless signal through a receiver and extracts a signal preamble code from the wireless signal; divides the signal preamble code into multiple sub-signal segments according to the repetitiveness of the signal preamble code; calculates the characteristic coefficients between the sub-signal segments; and arranges all the characteristic coefficients of the multiple sub-signal segments of the signal preamble code in order to construct a radio frequency fingerprint feature that highlights the carrier offset information. The radio frequency fingerprint feature constructed by the present invention highlights the carrier offset feature. Compared with the traditional radio frequency fingerprint recognition method based on deep learning, the radio frequency fingerprint recognition method based on this feature is resistant to wireless channel fading and greatly reduces the computational complexity, can effectively alleviate the impact of channel fading and the receiver, and improves the generalization capability of the receiver. In addition, the present invention can directly extract radio frequency fingerprint features from the received signal preamble code without the need for additional signal processing of the received signal, thereby avoiding the fingerprint loss problem caused by channel equalization.

[0018] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a flow chart of a radio frequency fingerprint extraction method based on the repetitive characteristics of wireless signal preambles provided by the present invention;

[0020] Figure 2 The present invention provides a flow chart of a radio frequency fingerprint extraction system based on the repetitive characteristics of wireless signal preamble codes. DETAILED DESCRIPTION

[0021] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0022] Before introducing the present invention, a brief introduction to the technical concept of the invention is first given.

[0023] Typically, RF fingerprint recognition systems based on deep learning rely on neural networks to directly extract RF fingerprints from signals. However, the fading of wireless channels and the differences in receivers cause the performance of the recognition system on unknown receivers to degrade severely. After experimental analysis, the carrier frequency offset (CFO) feature of wireless devices is an important RF fingerprint. Therefore, the present invention designs a RF fingerprint extraction method based on the repetitiveness feature of the wireless signal preamble, which can effectively alleviate the impact of channel fading and receivers, and enhance the receiver generalization capability of the recognition system. The present invention directly extracts the RF fingerprint features of the device from the received signal without adopting additional signal processing means. The recognition system designed using this feature can be deployed on different receivers and has strong robustness.

[0024] refer to Figure 1 The present invention provides a radio frequency fingerprint extraction method based on the repetitive characteristics of the wireless signal preamble code, which is applied to a receiver. The radio frequency fingerprint extraction method includes:

[0025] S100, receiving a wireless signal and extracting a signal preamble from the wireless signal;

[0026] The wireless signals are transmitted to the receiver by multiple wireless devices. Each wireless device complies with the IEEE 802.11g WiFi protocol and has the same address. Each wireless device transmits the wireless signals using a transmission channel with a center frequency of 2462 MHz and a bandwidth of 20 MHz. The receiver captures the multiple wireless signals transmitted from the wireless devices at a sampling rate of 25 Msps. The center frequency of the wireless signals captured by the receiver is 2462 MHz and the duration is 0.512 seconds.

[0027] In order to demonstrate the advantages of the proposed recognition method in terms of temporal generalization and receiver generalization, the original signal dataset named WiSig is used. The selected dataset contains N D =6 WiFi devices, N R = 12 different receivers, and in N T =4 days of data collection, including signals on March 1, 8, 15, and 23, 2021. All devices implemented the IEEE 802.11g WiFi protocol and were configured with the same address. WiFi channel 11 with a center frequency of 2462 MHz and a bandwidth of 20 MHz was used to avoid any data clues about the device's identity. The USRP then captured the signal at a sampling rate of 25Msps with a center frequency of 2462 MHz for a duration of 0.512 seconds. For each WiFi-USRP pair, more than N B =1000 signals.

[0028] S200, dividing the signal preamble into a plurality of sub-signal segments according to the repetitiveness of the signal preamble;

[0029] According to the IEEE 802.11g protocol, the preamble of a WiFi signal is 320 bytes long and consists of a short training sequence (STS) of 160 bytes and a long training sequence (LTS) of 160 bytes. The first two segments of the LTS sequence are guard intervals (GI2) of 32 bytes. The preamble signal is segmented into 10 segments of STS, 2 segments of GI2, and 8 segments of LTS, for a total of 20 segments. The segmentation results are shown in the figure below. Figure 2 shown.

[0030] S300, calculating characteristic coefficients between sub-signal segments;

[0031] The signal preamble of the present invention is divided into L sub-signal segments, and the number of characteristic coefficients is The characteristic coefficient is expressed as:

[0032]

[0033] in, represents the characteristic coefficient between the k-th segment signal and the i-th segment signal, represents the conjugate transpose operation, and |·| represents the modulo operation. L is the length of the sub-signal segment, y(i,n) represents the nth sample point of the i-th sub-signal segment, and y(k,n) represents the nth sample point of the k-th sub-signal segment. The value of i ranges from 1 to L-1, and the value of k ranges from i+1 to L.

[0034] If the wireless signal includes a WiFi signal, the preamble portion of the WiFi signal has a length of 320 and consists of a short training sequence (STS) of 160 and a long training sequence (LTS) of 160. The first two sub-signals of the LTS sequence are guard intervals (GI2) of 32. The preamble signal is segmented according to a length of 16: the STS is divided into 10 sub-signals, the GI2 is divided into 2 segments, and the remaining LTS is divided into 8 sub-signals, resulting in 20 sub-signal segments.

[0035] Calculating characteristic coefficients between sub-signal segments includes: calculating cyclic characteristic coefficients in STS, calculating characteristic coefficients in GI2, and calculating cyclic similarity coefficients in LTS.

[0036] The cyclic characteristic coefficient in the STS is calculated using formula (1). At the transmitter, the 10 sub-signals divided by the STS are exactly the same, but due to transmitter hardware defects and wireless channel variations, there are certain differences in the received STS. The characteristic coefficient of the signal is calculated using the above formula.

[0037] The characteristic coefficient in GI2 is calculated by using formula (1) to calculate the manual features of GI2. According to the similarity between GI2 and LTS, the two GI2 sequences are respectively operated with the LTS sequences with sequence numbers 5 and 6 and sequence numbers 9 and 10 to calculate the cyclic similarity coefficient.

[0038] Calculating the cyclic similarity coefficient in LTS is to calculate the manual features of LTS using formula (1). LTS can be divided into two identical sub-signals of length 64. Based on the similarity of LTS, the sub-signals numbered 3, 4, 5, and 6 are matched with the sub-signals numbered 7, 8, 9, and 10 to calculate the cyclic similarity coefficient.

[0039] The logical principle of the present invention is described in detail below:

[0040] From the perspective of waveform, formula (1) represents the similarity between the kth sub-signal segment and the ith sub-signal segment. Where L is the length of the sub-signal segment. In addition, The value of ranges from 0 to 1; therefore, no additional normalization is required. The received signal can be rewritten as

[0041] y(m,n)=h(m,n)x(m,n) (2)

[0042] For ease of understanding, the present invention ignores the influence of thermal noise. It can be expressed as

[0043]

[0044] The maximum time interval between the first and last sub-segments is set to 7.2 μs; therefore, it is reasonable to assume that h(i,n)≈h(k,n) because the wireless channel does not change dramatically in such a short time. The adjacent spectra in the spectrum diagram are used to remove channel-related information. where |h| 2 is the average channel gain, then can be rewritten as

[0045]

[0046] It is worth noting that the proposed This reduces the variation of the wireless channel. In addition, the L-times accumulation operation can be regarded as an average filter, which further reduces the error.

[0047] Different receivers have different oscillator-induced drifts. Assuming the receiver generates a time-varying carrier offset, It can be expressed as

[0048]

[0049] in and are the carrier offsets on the ith and kth sub-signal segments respectively. Although the carrier offset is time-varying, it will not change dramatically in a short period of time of about 7.2us; therefore, the present invention can also assume that Based on the properties of the conjugate operation, is simplified to the above formula, which means that the proposed The carrier offset caused by the receiver can be mitigated.

[0050] Following the above principle, two identical signal segments can be written as

[0051]

[0052] in is the carrier offset information. Therefore, Essentially, it includes the carrier offset characteristics between multiple groups of subcarrier signals, highlights the carrier offset damage, and is robust to wireless channel changes and receiver differences.

[0053] S400: Arrange all characteristic coefficients of the plurality of sub-signal segments of the signal preamble in order to construct a radio frequency fingerprint feature for highlighting carrier frequency offset (CFO) information.

[0054] In this step, all characteristic coefficients of the plurality of sub-signal segments of the signal preamble are arranged in order to be converted into row vectors to obtain characteristic row vectors.

[0055] The present invention converts the extracted manual features into row vectors, which are suitable for training various types of classifiers such as neural networks. The three received feature coefficients are arranged in sequence to obtain a row vector with a length of 53, such as Figure 2 shown.

[0056] It's worth noting that carrier frequency offset information varies over time and can affect RF fingerprinting. Existing technologies typically filter out carrier frequency offset information through a channel equalization method called zero-forcing equalization. Specifically, all subcarrier signals are stacked in chronological order, and the superimposed signal is divided into multiple subsegments based on the transmission protocol. Each segment is then Fourier transformed to obtain the received symbol Y, from which symbols on valid subcarriers are selected. Equalization is then performed on the selected symbols using the following method:

[0057]

[0058] in This is channel estimation. For each segment, existing technologies obtain a number of equalized symbols equal to the number of subcarriers from the active subcarriers. Finally, an inverse fast Fourier transform is performed on each segment to recover the time domain signal. During this operation, subcarriers without signals are reset to zero, resulting in a loss of information about these subcarriers. Furthermore, the carrier frequency offset information also contains RF fingerprint information, which is eliminated by the channel equalization operation.

[0059] The fingerprint feature proposed in the present invention can be directly extracted from the preamble of the received signal without the need for additional signal processing of the received signal, thereby avoiding the fingerprint loss problem caused by channel equalization.

[0060] As an optional embodiment of the present invention, the radio frequency fingerprint extraction method based on the repetitive characteristics of the wireless signal preamble provided by the present invention further includes:

[0061] S510, inputting the feature row vector into multiple classifiers to obtain multiple recognition results;

[0062] Among them, the multiple classifiers include a classifier based on a KNN neural network and a classifier based on a CNN neural network.

[0063] S520: Compare the multiple recognition results to verify the classification effect of the feature row vector.

[0064] In this embodiment of the present invention, wireless signals from six WiFi devices were captured from five different receivers. When constructing the recognition system, only the captured signal from a single receiver was used, and testing was performed on the signals from the other receivers. Using the designed RF fingerprint features, recognition systems based on the K-Nearest Neighbor (KNN) algorithm and the Convolutional Neural Network (CNN) were trained, respectively. The recognition results were compared to determine the classification outcome of the RF fingerprint features.

[0065] The proposed RF fingerprint recognition method was compared with deep learning algorithms based on signal FFT and STFT time-frequency patterns to verify the effectiveness of the present invention in improving RF fingerprint recognition capabilities. The performance results of the different recognition systems are shown in Tables 1 and 2.

[0066] The present invention provides a radio frequency fingerprint extraction system based on the repetitive characteristics of wireless signal preamble codes, comprising a plurality of receivers, each of which performs the following process:

[0067] S100, receiving a wireless signal and extracting a signal preamble from the wireless signal;

[0068] S200, dividing the signal preamble into a plurality of sub-signal segments according to the repetitiveness of the signal preamble;

[0069] S300, calculating characteristic coefficients between sub-signal segments;

[0070] S400: Arrange all characteristic coefficients of the plurality of sub-signal segments of the signal preamble in order to construct a radio frequency fingerprint feature.

[0071] The effects of the present invention are further described below in conjunction with simulation experiments:

[0072] 1. Simulation conditions:

[0073] The hardware platform of the simulation experiment of the present invention is: Intel(R) Core(TM) i7-8700k CPU, the main frequency of the processor is 3.20GHz, the memory is 16GB, and the RTX3060 graphics card is used for training.

[0074] The software platforms for the simulation experiment of the present invention are: MATLAB R2020a and Python 3.7 software platforms.

[0075] 2. Simulation content and result analysis:

[0076] This patent analyzes the performance of the proposed RF fingerprint feature on different classifiers and compares it to the performance of a traditional deep learning-based RF fingerprint recognition system. Specifically, a RF fingerprint constructed from 53 characteristic coefficients (abbreviated as Cyclic53) was used as input to construct recognition systems based on KNN and CNN. For comparison, the signal was channel-equalized and a CNN-based recognition system was constructed using the signal's FFT and STFT time-frequency spectrum. We only used the captured signal from a single receiver and tested it on signals from other receivers.

[0077] Table 1 shows the construction of an RFID system using only the signal from receiver 1, and testing the performance of the system on other receivers. When the signal comes from the same receiver 1, different identification systems can achieve high recognition performance. When the identification system is deployed on other receivers, the system performance will decline due to the differences between the receivers. The deep learning-based identification systems FFT-CNN and STFT-CNN have an average recognition accuracy of 71.83% and 70.56% on all receivers, respectively. The RFID fingerprint identification systems Cyclic53-KNN and Cyclic53-CNN designed based on the present invention have an average recognition accuracy of 83.09% and 83.98% on all receivers, respectively. Therefore, the invented RFID fingerprint feature can bring a 12% performance improvement.

[0078] Table 1

[0079]

[0080]

[0081] To avoid random results on a single receiver, we conducted the same experiment on all remaining receivers. We used the signal from each receiver to build an RFID system and tested it on all remaining receivers. The results are shown in Table 2. As can be seen, the RFID fingerprint recognition system designed based on this invention achieves good recognition performance across different receivers, achieving a 13% performance improvement over a deep learning-based recognition system.

[0082] Table 2

[0083]

[0084] It is concluded that the RF fingerprint feature based on the repetitive characteristics of the preamble code can effectively alleviate the impact of channel fading and the receiver, and improve the receiver generalization capability of the recognition system.

[0085] The method of the present invention can be used in the identification scenario of wireless signal device targets.

[0086] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature identified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0087] Although the present application is described herein with reference to various embodiments, those skilled in the art will be able to understand and implement other variations of the disclosed embodiments in practicing the claimed application by reviewing the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0088] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art of the present invention, without departing from the concept of the present invention, several simple deductions or substitutions can be made, which should be considered to fall within the scope of protection of the present invention.

Claims

1. A radio frequency fingerprint extraction method based on the repetitive characteristics of wireless signal preamble code, characterized in that: Applied to a receiver, the radio frequency fingerprint extraction method includes: S100, receiving a wireless signal and extracting a signal preamble from the wireless signal; the wireless signal includes a WiFi signal, the preamble portion of the WiFi signal is 320 characters long and consists of a short training sequence (STS) of 160 characters and a long training sequence (LTS) of 160 characters; the first two segments of the LTS sequence are a guard interval (GI2) of 32 characters; S200, dividing the signal preamble into a plurality of sub-signal segments according to the repetitiveness of the signal preamble; S200 includes: The preamble signal is divided into 16 segments, STS is divided into 10 sub-signals, GI2 is divided into 2 segments, and the remaining LTS is divided into 8 sub-signals, resulting in 20 sub-signal segments; S300, calculating characteristic coefficients between sub-signal segments; the signal preamble is divided into sub-signal segments, the number of characteristic coefficients is ; The characteristic coefficient is expressed as: in, Indicates the Section signal and The characteristic coefficients between the segment signals, represents the conjugate transpose operation, Represents the modulo operation; Indicates the The first segment signal Sample points, Indicates the The first segment signal Sample points, The value of arrive Traverse between, The value of arrive traverse between; S400, arranging all characteristic coefficients of the plurality of sub-signal segments of the signal preamble in order to construct a radio frequency fingerprint feature highlighting carrier offset information; S400 includes: All characteristic coefficients of the plurality of sub-signal segments of the signal preamble are arranged in sequence to be converted into row vectors to obtain characteristic row vectors, and the characteristic row vectors are determined as radio frequency fingerprint features.

2. The radio frequency fingerprint extraction method based on the repetitive characteristics of the wireless signal preamble according to claim 1 is characterized in that: The wireless signal is transmitted to the receiver by multiple wireless devices, each of which complies with the IEEE 802.11g WiFi protocol and has the same address; each wireless device transmits the wireless signal using a transmission channel with a center frequency of 2462 MHz and a bandwidth of 20 MHz.

3. The radio frequency fingerprint extraction method based on the repetitive characteristics of the wireless signal preamble according to claim 2 is characterized in that: Receiving wireless signals in S100 includes: The receiver captures a plurality of wireless signals transmitted from the wireless device at a sampling rate of 25 Msps. The center frequency of the wireless signals captured by the receiver is 2462 MHz and the duration is 0.512 s.

4. The radio frequency fingerprint extraction method based on the repetitive characteristics of the wireless signal preamble according to claim 1 is characterized in that: After S400, the radio frequency fingerprint extraction method based on the repetitive characteristics of the wireless signal preamble code further includes: S510, inputting the feature row vector into multiple classifiers to obtain multiple recognition results; S520: Compare the multiple recognition results to verify the classification effect of the feature row vector.

5. A radio frequency fingerprint extraction system based on the repetitive characteristics of wireless signal preamble codes, characterized in that: It includes multiple receivers, each of which performs the following process: S100, receiving a wireless signal and extracting a signal preamble from the wireless signal; the wireless signal includes a WiFi signal, the preamble portion of the WiFi signal is 320 characters long and consists of a short training sequence (STS) of 160 characters and a long training sequence (LTS) of 160 characters; the first two segments of the LTS sequence are a guard interval (GI2) of 32 characters; S200, dividing the signal preamble into a plurality of sub-signal segments according to the repetitiveness of the signal preamble; S200 includes: The preamble signal is divided into 16 segments, STS is divided into 10 sub-signals, GI2 is divided into 2 segments, and the remaining LTS is divided into 8 sub-signals, resulting in 20 sub-signal segments; S300, calculating characteristic coefficients between sub-signal segments; the signal preamble is divided into sub-signal segments, the number of characteristic coefficients is ; The characteristic coefficient is expressed as: in, Indicates the Section signal and The characteristic coefficients between the segment signals, represents the conjugate transpose operation, Represents the modulo operation; Indicates the The first segment signal Sample points, Indicates the The first segment signal Sample points, The value of arrive Traverse between, The value of arrive traverse between; S400, arranging all characteristic coefficients of the plurality of sub-signal segments of the signal preamble in order to construct a radio frequency fingerprint feature; S400 includes: All characteristic coefficients of the plurality of sub-signal segments of the signal preamble are arranged in sequence to be converted into row vectors to obtain characteristic row vectors, and the characteristic row vectors are determined as radio frequency fingerprint features.

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