阅读说明：本技术 一种基于时域人工噪声的通信方法 (Communication method based on time domain artificial noise ) 是由 董宇涵 阳帆 李志德 耿祖航 权进国 金爽 于 2021-01-11 设计创作，主要内容包括：本发明公开了基于时域人工噪声的通信方法,包括：初始化人工噪声向量并进行预编码,以生成与合法信道正交的目标人工噪声；对发射信号的频域复数信号作厄米特对称,之后进行快速傅里叶反变换,生成时域信号向量,对时域信号向量插入循环前缀,并叠加目标人工噪声,形成最终发射信号；对合法用户和窃听者接收的时域信号分别先进行循环前缀的消除,再进行快速傅里叶变换,分别得到合法用户和窃听者的接收频域信号,再分别作厄米特反对称,分别得到合法用户频域信号Y-B和窃听者频域信号Y-E；利用Y-B和合法信道的频域信道矩阵恢复出合法用户的最终接收信号；利用Y-E和窃听信道的频域信道矩阵恢复出窃听者的最终接收信号。(The invention discloses a communication method based on time domain artificial noise, which comprises the following steps: initializing artificial noise vectors and carrying out precoding to generate target artificial noise orthogonal to a legal channel; carrying out Hermite symmetry on a frequency domain complex signal of a transmitting signal, then carrying out inverse fast Fourier transform to generate a time domain signal vector, inserting a cyclic prefix into the time domain signal vector, and overlapping target artificial noise to form a final transmitting signal; respectively eliminating cyclic prefixes of time domain signals received by a legal user and an eavesdropper, then performing fast Fourier transform to respectively obtain receiving frequency domain signals of the legal user and the eavesdropper, and then respectively performing Hermite inversion symmetry to respectively obtain frequency domain signals Y of the legal user B And an eavesdropper frequency domain signal Y E (ii) a Using Y B Recovering the frequency domain channel matrix of the legal channelFinal received signals of the legal user; using Y E And recovering the final received signal of the eavesdropper by the frequency domain channel matrix of the eavesdropping channel.)

1. A communication method based on time domain artificial noise is characterized by comprising the following steps: constructing artificial noise, constructing a transmitting signal and processing a receiving signal;

constructing the artificial noise includes steps S11-S12:

s11, initializing an artificial noise vector;

s12, pre-coding the initialized artificial noise vector to generate target artificial noise orthogonal to a legal channel; the legal channel is a transmission channel from a transmitting terminal to a legal user;

constructing the transmission signal includes steps S21 to S23:

s21, carrying out Hermitian symmetry on the frequency domain complex signal of the transmitting signal;

s22, performing inverse fast Fourier transform on the frequency domain signal subjected to Hermite symmetry to generate a time domain signal vector;

s23, inserting a cyclic prefix into the generated time domain signal vector, and overlapping the target artificial noise to obtain a final transmitting signal;

the processing of the received signal includes steps S31 to S33:

s31, eliminating the cyclic prefix of the time domain signal received by the legal user and the time domain signal received by the eavesdropper, and then performing fast Fourier transform to correspondingly obtain the receiving frequency domain signal of the legal user and the receiving frequency domain signal of the eavesdropper;

s32, respectively making Hermite inversion symmetry on the receiving frequency domain signal of the legal user and the receiving frequency domain signal of the eavesdropper, and correspondingly obtaining the frequency domain signal of the legal user and the frequency domain signal of the eavesdropper;

s33, restoring the final received signal of the legal user by using the frequency domain signal of the legal user and the frequency domain channel matrix of the legal channel; and restoring the final received signal of the eavesdropper by using the eavesdropper frequency domain signal and the frequency domain channel matrix of the eavesdropper channel.

2. The time-domain artificial noise-based communication method according to claim 1, wherein the insertion and removal of the cyclic prefix are implemented in the form of matrix transformation, and the insertion matrix and the removal matrix are respectivelyAndwherein the content of the first and second substances,representing an identity matrix I of 2 Nx 2N_2NLast N_cpA matrix of rows, the superscript T representing the transpose of the matrix,the expression size is 2 NXN_cpZero matrix of, N_cpAnd 2N is the OFDM subcarrier number of the communication system for the length of the cyclic prefix.

3. The time-domain artifact-based communication method as claimed in claim 2, wherein the artifact vector is initialized to a length N in step S11_cpA vector z ofWhereinFor the real number domain, z follows a zero mean Gaussian distribution, and the covariance matrix is ∑_z＝E{zz^TDenotes mathematical expectation, z^TRepresenting the transpose of z.

4. The time-domain artificial noise based communication method according to claim 3, wherein the precoding matrix for precoding the initialized artificial noise vector in step S12 isAnd the column vector of G is located at R^cpH_BIn the null space of (1), i.e. R^cpH_BG＝0，The time domain channel matrix from the transmitting terminal to the legal user is a normal diagonal matrix; thus, the precoding matrixWhereinRepresents H_BThe inverse of (1);

the generated target artificial noise a is Gz, andeach element in vector a represents an artificial noise symbol transmitted in each slot in one OFDM period.

5. A time-domain artificial noise based communication method according to claim 3, wherein the power allocated to the information part and the artificial noise part satisfies a preset constraint condition under a total power limit of the final transmitted signal.

6. The time-domain artificial noise based communication method according to claim 5, wherein the preset constraint condition is:

in the case where the total power limit of the final transmission signal is P, the power allocated to the information part and the artificial noise part is P_sAnd P_aUsing α ∈ [0,1 ]]Indicates assignment to P_aIn a ratio of (i.e. P)_a＝αP，P_sFor power P, (1- α) P_sAnd P_aThe following constraints are satisfied:

where E {. denotes a mathematical expectation, vector a denotes the target artificial noise, and vector s denotes the time-domain signal vector.

7. The time-domain artifact-based communication method as claimed in claim 2, wherein said final transmitted signal formed in step S23 is x_A＝T^cps + a, vector s representing the time-domain signal vector, and vector a representing the target artifact.

8. The time-domain artifact-based communication method as claimed in claim 1, wherein in step S33:

restoring the final received signal of the legal user by using the frequency domain signal of the legal user and the frequency domain channel matrix of the legal channel, wherein the restoring comprises the following steps:whereinI.e. the final received signal of the legitimate user,frequency domain channel matrix for legal channelInverse of (A), (B), (C), (_BThe legal user frequency domain signal;

restoring the final received signal of the eavesdropper by using the frequency domain signal of the eavesdropper and the frequency domain channel matrix of the eavesdropper channel, wherein the method comprises the following steps:whereinI.e. the final received signal of the eavesdropper,frequency domain channel matrix for eavesdropping on channelInverse of (A), (B), (C), (_EIs the eavesdropper frequency domain signal.

9. The time-domain artifact-based communication method as recited in claim 5, further comprising: in the case where the power allocated to the information part and the artificial noise part satisfies a preset constraint condition, by adjusting the covariance matrix Σ_zTo maximize the privacy rate of the communication system.

Technical Field

The invention relates to the technical field of wireless optical communication, in particular to a communication method based on time domain artificial noise.

Background

Wireless Optical Communication (OWC) is a technology for Communication by using Wireless Optical waves, has the advantages of wide spectrum and high speed, is considered as a key technology for future indoor multiple access, and is included in the IEEE 802.15.7 standard. At the same time, however, due to the broadcast nature of optical communications, it is very easy to eavesdrop, especially in public places like conference rooms, libraries, shopping malls, etc., and therefore there is a need to increase security using information security techniques.

Conventional information security techniques have mainly focused on upper-layer protocols for communication, using encryption techniques to prevent eavesdropping. However, the encryption technology itself is based on the assumption that the calculation capability of the eavesdropper is limited, and once the key is leaked or the eavesdropper has the calculation capability of brute force cracking, the security cannot be guaranteed. Accordingly, physical layer security techniques have attracted the attention of students in recent years. Among the many physical layer security technologies in the field of Radio Frequency (RF) communication, there is a technology called Artificial Noise (AN), which has a core idea of constructing Artificial Noise by using orthogonality of channels, thereby only interfering with AN eavesdropper and not affecting a legitimate user. This requires the transmitting end to have more degrees of freedom than the legitimate user, which is usually from multiple antennas in radio frequency communication, and this is not applicable to a Single-antenna system like Single-Input Single-Output (SISO). For this reason, there is a document that proposes to utilize the degree of freedom provided by a Cyclic Prefix (CP) in a SISO Orthogonal Frequency Division Multiplexing (OFDM) system.

As described above, the OWC system is also affected by an eavesdropper. However, the OWC system cannot directly use the physical layer security technology in the RF communication system because unlike the RF communication system which transmits complex signals, the OWC system generally transmits unipolar real signals by using an amplitude Modulation and Direct Detection (IM/DD) method. This requires redesigning the physical layer security techniques of the OWC system. For example, the scholars MostafaA and Lampe L first propose to apply AN to AN OWC system to improve the security performance of the system; then Arfaoui MA, Zaid H, Rezki Z, etc. further explore AN AN-based optimal beamforming scheme in a Multiple-Input Single-Output (MISO) OWC system; furthermore Cho S, Chen G and Coon J P propose a non-orthogonal AN scheme for optimizing OWC system security performance in the case of random distribution of eavesdroppers. However, the above-mentioned secure communication scheme using AN utilizes spatial freedom, requires support of multiple light sources, and is not suitable for SISO single light source system.

Disclosure of Invention

Based on the above, the present invention provides a signal processing method based on time domain artificial noise, which is used for improving the security performance of a wireless Optical communication system of direct current biased Optical OFDM (DC-biased Optical OFDM, DCO-OFDM), and the core idea is to use a cyclic prefix in DCO-OFDM to construct artificial noise orthogonal to a legal channel, so as to improve the security rate of the system.

A communication method based on time domain artificial noise comprises the following steps: constructing artificial noise, constructing a transmitting signal and processing a receiving signal; constructing the artificial noise includes steps S11-S12: s11, initializing an artificial noise vector; s12, pre-coding the initialized artificial noise vector to generate target artificial noise orthogonal to a legal channel; the legal channel is a transmission channel from a transmitting terminal to a legal user; constructing the transmission signal includes steps S21 to S23: s21, carrying out Hermitian symmetry on the frequency domain complex signal of the transmitting signal; s22, performing inverse fast Fourier transform on the frequency domain signal subjected to Hermite symmetry to generate a time domain signal vector; s23, inserting a cyclic prefix into the generated time domain signal vector, and overlapping the target artificial noise to obtain a final transmitting signal; the processing of the received signal includes steps S31 to S33: s31, eliminating the cyclic prefix of the time domain signal received by the legal user and the time domain signal received by the eavesdropper, and then performing fast Fourier transform to correspondingly obtain the receiving frequency domain signal of the legal user and the receiving frequency domain signal of the eavesdropper; s32, respectively making Hermite inversion symmetry on the receiving frequency domain signal of the legal user and the receiving frequency domain signal of the eavesdropper, and correspondingly obtaining the frequency domain signal of the legal user and the frequency domain signal of the eavesdropper; s33, restoring the final received signal of the legal user by using the frequency domain signal of the legal user and the frequency domain channel matrix of the legal channel; and restoring the final received signal of the eavesdropper by using the eavesdropper frequency domain signal and the frequency domain channel matrix of the eavesdropper channel.

The invention has the beneficial effects that: the cyclic prefix in DCO-OFDM is utilized to construct time domain artificial noise orthogonal to a legal channel, and when the artificial noise passes through the legal channel, the artificial noise is mutually offset in the time domain due to multipath effect caused by reflection, so that the influence on a legal user is eliminated, only an eavesdropper is interfered, and the confidentiality of a communication system is improved. Meanwhile, the covariance matrix of the artificial noise is optimized according to the expression of the confidentiality rate, and the confidentiality performance of the system is further improved through the mode.

Drawings

FIG. 1 is a flow chart of the artifact assisted DCO-OFDM of the present invention;

FIG. 2 is a diagram of the secret rate R of the present invention_sA graph of the variation of the SNR with respect to the signal-to-noise ratio;

FIG. 3 is a diagram of the secret rate R of the present invention_sAnd (3) a change relation diagram of the artificial noise power ratio alpha.

Detailed Description

The invention is further described with reference to the following figures and detailed description of embodiments.

The embodiment of the invention provides a communication method based on time domain artificial noise, namely, the artificial noise is superposed on information to be transmitted in an optical signal transmitted by a transmitting terminal, and the artificial noise is used for improving the confidentiality of a DCO-OFDM wireless optical communication system. The core idea is that cyclic prefix in DCO-OFDM is utilized to construct artificial noise orthogonal to a legal channel, and when the artificial noise passes through the legal channel, the artificial noise is mutually offset in a time domain due to multipath effect caused by reflection, so that the artificial noise does not exist in a received signal of a legal user, the influence on the legal user is eliminated, and only interference is caused to an eavesdropper.

The embodiment of the invention considers a DCO-OFDM wireless optical communication system of three users. The transmitting end includes a single user named Alice, which transmits an optical signal using a single Light source, such as a Light Emitting Diode (LED) or a Laser Diode (LD). The receiving end includes a legitimate user named Bob and an eavesdropper named Eve, which receive the optical signal with a single photodetector such as a Photodiode (PD), respectively. The system flow is shown in fig. 1, and it should be noted that S/P in fig. 1 represents serial-to-parallel conversion, and P/S represents parallel-to-serial conversion.

The number of DCO-OFDM subcarriers is represented as 2N, and the length of the cyclic prefix is represented as N_cpIn which N is_cpDepending on the delay spread of the actual channel, 1/8 is typically taken for the number of OFDM subcarriers 2N. The insertion and elimination of cyclic prefix can be expressed by matrix transformation, and the insertion matrix and the elimination matrix are respectivelyAndwherein the content of the first and second substances,representing an identity matrix I of 2 Nx 2N_2NLast N_cpA matrix of rows, the superscript T representing the transpose of the matrix,the expression size is 2 NXN_cpThe zero matrix of (2). For the receiving end, due to the multipath effect caused by the reflection of the light wave, the PD of the receiving end receives multiple paths of light signals, and the impulse responses of the first path of signals received by the legal user Bob and the eavesdropper Eve are respectively defined as h_B(l) And h_E(l) Where L is 0,1, …, L, and L denotes the maximum delay. h is_B(l) And h_E(l) The Line-of-Sight (LOS) component is indicated when l is 0, and the Non-Line-of-Sight (NLOS) component is indicated when l > 0.

The communication method based on the time domain artificial noise provided by the embodiment of the invention comprises the steps of constructing the artificial noise, constructing a transmitting signal and processing a receiving signal; wherein, constructing the artificial noise comprises steps S11-S12: s11, initializing an artificial noise vector z; s12, pre-coding the initialized artificial noise vector z to generate a target artificial noise a orthogonal to a legal channel; wherein, the legal channel is a transmission channel between a transmitting terminal and a legal user. Constructing the transmission signal includes steps S21 to S23: s21, carrying out Hermitian symmetry on the frequency domain complex signal S of the transmitting signal; s22, and converting the frequency domain signal S after Hermite symmetry^SPerforming inverse fast Fourier transform to generate a time domain signal vector s; s23, inserting cyclic prefix into the generated time domain signal vector S, and superposing the target artificial noise to obtain a final emission signal x_A. The processing of the received signal includes steps S31 to S33: s31, eliminating the cyclic prefix of the time domain signal received by the legal user and the time domain signal received by the eavesdropper, and then performing Fourier transform to correspondingly obtain the received frequency domain signal of the legal userAnd the received frequency domain signal of the eavesdropperS32, receiving frequency domain signals of legal users respectivelyAnd the received frequency domain signal of the eavesdropperMaking Hermite inverse symmetry to correspondingly obtain legal user frequency domain signal Y_BAnd an eavesdropper frequency domain signal Y_E(ii) a S33, utilizing legal user frequency domain signal Y_BAnd frequency domain channel matrix of legal channelRecovery of the final received signal of a legitimate userUsing the eavesdropper frequency domain signal Y_EAnd eavesdropping the frequency domain channel matrix of the channelRecovering the final received signal of the eavesdropperThe method comprises the following specific steps:

s11, the initial artificial noise can be expressed as a length N_cpVector of (2)WhereinFor the real number domain, z follows a zero mean Gaussian distribution, and the covariance matrix is ∑_z＝E{zz^TDenotes mathematical expectation, z^TRepresenting the transpose of z.

S12, constructing a precoding matrix to precode the initialized artificial noise vector z, wherein the precoding matrix isAnd the column vector of G is located at R^cpH_BIn the null space of (a), i.e.:

R^cpH_BG＝0 (1)

wherein the content of the first and second substances,the time domain channel matrix representing the time domain channel from the transmitting end to the legal user is a normal diagonal matrix, which can be written as:

similarly, h is_B(l) Is replaced by h_E(l) A time domain channel matrix H between the transmitting end and the eavesdropper can be obtained_E. Due to H_BIs a lower triangular matrix and the diagonal element is greater than 0, so H_BIs a reversible matrix, whereby the precoding matrix is

WhereinRepresents H_BThe inverse of (a) is,is expressed as size N_cp×N_cpThe identity matrix of (2).

And precoding the initialized artificial noise vector z by using a precoding matrix, namely:

a＝Gz (4)

wherein a is the vector representation of the target artificial noise obtained by pre-coding, andeach element in vector a represents an artificial noise symbol transmitted in each slot in one OFDM period. The target artificial noise a generated by pre-coding is orthogonal to the legal channel, so that it does not appear in the received signal of the legal user.

S21, since the transmitted time domain signal is real, hermitian symmetry is required for the complex signal in the frequency domain. Each OFDM block thus carries only (N-1) frequency domain symbols, with one complex vector S ═ S₁,S₂,…,S_N-1]^TRepresenting a frequency domain complex signal. The frequency domain signal obtained after Hermite symmetry is expressed asWherein

Wherein [ ·]^*Representing conjugation.

S22, and then S^SGenerating a time-domain signal vector s ═ F through Inverse Fast Fourier Transform (IFFT)^HS^S＝[s₁,s₂,…,s_2N-1]^TWherein F and F^HFast Fourier Transform (FFT) matrix and IFFT matrix are shown, respectively. The nth element of s can be represented as

Where Φ { · } represents the real part of the complex number, e is a natural constant. Will matrix 2F^HThe middle 2 nd column to the Nth column form a submatrix defined asThen s can also be expressed as

After the time-domain signal S is generated S23, a cyclic prefix needs to be inserted to combat inter-symbol interference. The insertion of the cyclic prefix can be expressed in the form of a matrix transformation using a matrix of T^cp. Finally, adding the constructed target artificial noise a to form a final transmitting signal x_AIs shown as

Considering the total power limit of the transmitted signal as P, the power allocated to the information part and the artificial noise part is P_sAnd P_a. By alpha epsilon [0,1]Indicates assignment to P_aIn a ratio of (i.e. P)_a＝αP，P_s＝(1-α)PFor power P_sAnd P_aThe following constraints are satisfied:

where | · | | represents the euclidean norm and E {. denotes the mathematical expectation.

S31, after the legal user Bob receives the time domain signal, firstly eliminating the cyclic prefix, then carrying out fast Fourier transform, wherein the elimination of the cyclic prefix adopts a matrix R^cpMatrix transformation is carried out, and after fast Fourier transformation, the receiving frequency domain signal of a legal user is obtainedIs composed of

Similarly, the receiving frequency domain signal of the eavesdropper is obtainedIs composed of

Wherein the content of the first and second substances, andrespectively indicating the reception of a legal user and an eavesdropper in the ith time slotTo a frequency domain signal.Andrespectively representing Additive White Gaussian Noise (AWGN) received by Bob and Eve, and the noise power is sigma²，The expression size is (N)_cp+2N)×(N_cp+2N) identity matrix.

Order toEquivalent to FR^cpH_BT^cpF^HAnd orderEquivalent to FR^cpH_ET^cpF^HThen, thenAndcan be written in the form of a diagonal matrix, i.e. Wherein H_B,iAnd H_E,iRespectively representing the frequency responses of the ith subcarrier from the transmitting end Alice to the legitimate user Bob and the eavesdropper Eve.

S32, receiving frequency domain signal to legal userMaking Hermite inverse symmetry to obtain legal user frequency domain signal Y_B＝[Y_B,1,...,Y_B,N-1]^T(ii) a Receiving frequency domain signal for eavesdropperMaking Hermite inverse symmetry to obtain eavesdropper frequency domain signal Y_E＝[Y_E,1,...,Y_E,N-1]^TWherein:

s33, the frequency domain channel matrices of the legitimate user and the eavesdropper can be defined as:

wherein the content of the first and second substances,the definition given above is that of the matrix 2F^HA submatrix formed by the 2 nd column to the Nth column; whileIs thatIs transposed, thereforeCan be composed ofAnd (6) obtaining.

Thus, Y_BAnd Y_ECan be rewritten as:

finally, the signals recovered at the legal user receiving end and the eavesdropper receiving end are respectively:

in addition, in the case where the power allocated to the information part and the artificial noise part satisfies a preset constraint condition, the covariance matrix Σ is adjusted_zTo maximize the privacy rate of the communication system. Secret rate R_sExpressed as:

R_s＝[Θ(S；Y_B)-Θ(S；Y_E)]⁺ (20)

wherein [ theta (S; Y)_B)-Θ(S；Y_E)]⁺Representing 0 and [ theta (S; Y)_B)-Θ(S；Y_E)]The largest of (A), Θ (S; Y)_B) Frequency domain complex signal S representing transmission signal and legal user frequency domain signal Y_BMutual information between theta (S; Y)_E) Frequency domain complex signal S representing transmission signal and eavesdropper frequency domain signal Y_EThe mutual information between them.

The goal of artificial noise optimization is to satisfy the power constraint (9) by adjusting sigma_zMaximizing the privacy rate. The optimization problem is expressed as follows:

whereinRepresenting a covariance matrix ∑_zSemi-positive nature of (2), constraint of E { | | a | | non-phosphor cells in (9)²}＝Tr{GΣ_zG^TAnd (4) represents the trace of the matrix.

Covariance matrix sigma of complex signal S in frequency domain_S＝E{SS^TAt fixed, the mutual information in equation (20) depends on the probability distribution of S. Using signal processing techniques such as probability shaping, the mutual information can be maximized, and in particular, can be represented as

Wherein K is equivalent toI_N-1An identity matrix of size (N-1) × (N-1) is represented. It can be seen that the expression in equation (22) is equal to ∑_zIndependently, for equation (23), it can be approximated as:

it can be seen that the final expression of equation (24) has only the last term log₂det(KΣ_zK^H+4σ²I_N-1) And sigma_zIn this regard, optimization problem equation (21) may then be rewritten as:

this is a convex optimization problem that can be solved using algorithms such as gradient descent or interior point methods to maximize the privacy rate.

The effect of the present invention is verified by a specific example.

Consider a SISO DCO-OFDM OWC system comprising a single light source sender Alice, a single photodetector legitimate user Bob and a single photodetector eavesdropper Eve. OFDM comprises 64 subcarriers with 2N, length N of cyclic prefix_cp8. Suppose AWGN has a power of σ²The Signal-to-Noise Ratio (SNR) can be expressed as SNR of 10log 1₁₀And P. The elements of the frequency domain complex signal S are assumed to be independent and uniformly distributed random variables, and the variance is beta_sI.e. covariance matrix of ∑_S＝E{SS^T}＝β_sI_N-1，I_N-1Is an identity matrix of (N-1) × (N-1). Wherein, beta_sSatisfies the power constraint (8), i.e. beta_sIs equivalent to

In addition, for the channel part, it is assumed that the line-of-sight channel gain is h_B(0)＝h_E(0) 1. The non-line-of-sight channels have 6 channels and the gains are respectively h_B(l)＝γθ_B,lAnd h_E(l)＝γθ_E,lWhere l ═ 1.. 6. { θ }_B,lAnd { theta }_E,lAnd the independent and uniformly distributed random variables are uniformly distributed between 0 and 1, and the gamma is 0.3 to represent the attenuation coefficient of the reflection. FIG. 2 shows the secret rate R_sRegarding the variation relationship of the SNR, the target artificial noise power ratio to be added is, in order, 0,0.1,0.2, 0.5. FIG. 3 shows R_sRegarding the α variation relationship, the SNR is 10,20,30dB in order. Each R_sChannel simulations were performed 100 times and then averaged. It can be seen that compared with the case of not adding artificial noise, i.e. α is 0, the security performance of the system can be significantly improved after adding artificial noise, and the security performance can be improved along with the improvement of α. However, when α reaches a threshold value, increasing α will causeThe power of the signal portion becomes less and less, which in turn impairs the security performance. As can be seen from fig. 3, the privacy performance is optimized when α ≈ 0.7 under the current channel conditions. In the case of a general channel, a is 0.5, which can achieve better security performance.

The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several equivalent substitutions or obvious modifications can be made without departing from the spirit of the invention, and all the properties or uses are considered to be within the scope of the invention.