阅读说明：本技术 一种基于数字干涉系统的测向方法及系统 (Direction finding method and system based on digital interference system ) 是由 左乐 唐勇 王秀君 聂剑坤 应钱诚 张浩斌 胡泽华 范保华 于 2020-06-19 设计创作，主要内容包括：本发明提供了一种基于数字干涉系统的测向方法,包括：对于N元均匀圆阵天线,空间电磁波转换为数字电压信号,将电压信号处理得到每路天线的电压相位；在来波以仰角为0°入射圆阵天线时,记每一路天线的相位为测试相位；根据电压相位和测试相位构造每路天线对应的复数；根据仰角<Image he="77" wi="110" file="DDA0002547610730000011.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>方位角<Image he="80" wi="112" file="DDA0002547610730000012.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>初始相位<Image he="84" wi="117" file="DDA0002547610730000013.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>计算每路天线的理论相位；引入向量X和方向向量G,结合构造的复数计算迭代次数k+1的二维入射角的仰角<Image he="78" wi="127" file="DDA0002547610730000014.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>和方位角<Image he="78" wi="152" file="DDA0002547610730000015.GIF" imgContent="drawing" imgFormat="GIF" orientation="portrait" inline="no"></Image>计算迭代次数为k+1与迭代次数为k的二维入射角之差,并于门限值比较,小于门限值进入输出仰角和方位角；否则,k的值加1,再次计算相位差。本方法优势在于采用复数运算,避免了相位模糊问题及逻辑判断等运算,提高了测向精度。(The invention provides a direction finding method based on a digital interference system, which comprises the following steps: for the N-element uniform circular array antenna, converting space electromagnetic waves into digital voltage signals, and processing the voltage signals to obtain the voltage phase of each antenna; when incoming waves are incident to the circular array antenna with the elevation angle of 0 degree, recording the phase of each path of antenna as a test phase; constructing a complex number corresponding to each antenna according to the voltage phase and the test phase; according to the elevation angle Azimuth angle Initial phase Calculating the theoretical phase of each path of antenna; introducing a vector X and a direction vector G, and calculating the elevation angle of the two-dimensional incident angle of the iteration number k +1 by combining the constructed complex number And azimuth angle Calculating the difference between the two-dimensional incident angles with the iteration times of k +1 and the iteration times of k, comparing the difference with a threshold value, and outputting an elevation angle and an azimuth angle when the difference is smaller than the threshold value; otherwise, the value of k is added to 1 and the phase difference is calculated again. The method has the advantages that complex operation is adopted, the operations such as phase ambiguity problem, logic judgment and the like are avoided, and the direction finding precision is improved.)

1. A direction finding method based on a digital interference system is characterized by comprising the following processes:

step 1, for an N-element uniform circular array antenna, converting space electromagnetic waves of a receiving antenna of a digital interferometer system into digital voltage signals, performing discrete Fourier transform on the digital voltage signals received by each antenna, and then taking a phase to obtain a voltage phase of each antenna;

step 2, when the incoming wave enters the circular array antenna with the elevation angle of 0 degree, recording the phase of each path of antenna as the test phase

Step 3, constructing a plurality number corresponding to each path of antenna according to the voltage phase and the test phase;

step 4, setting the initial elevation angle as

step 5, when the iteration number is k, according to the elevation angle

step 6, introducing a vector X and a direction vector G, and calculating the elevation angle of the two-dimensional incident angle of the iteration times k +1 by combining the constructed complex number

Step 7, calculating the difference between the two-dimensional incident angles with the iteration times k +1 and the iteration times k, comparing the result with a threshold value, and entering step 8 if the result is smaller than the threshold value; otherwise, adding 1 to the value of the iteration times k, and entering the step 5;

step 8, outputting the two-dimensional incident angle

2. The direction finding method based on the digital interference system according to claim 1, wherein in the step 1, N is greater than or equal to 3 in the N-element uniform circular array antenna, and the specific method for obtaining the voltage phase of each path of antenna comprises:

wherein phi'_iThe voltage phase of the ith antenna is shown, i is 1,2,3 … N, arg is complex phase operation, M is the number of sampling points, M is more than or equal to 3, f is signal frequency, j is an imaginary unit,

3. the direction-finding method based on digital interference system as claimed in claim 1, wherein in step 3, the specific method for constructing the complex number is

Step 31, calculating the normalized phase value of the received voltage of each antenna,

step 32, constructing a complex number for the normalized phase value:

wherein, V_iAnd the complex number corresponding to the phase value of the ith antenna is represented.

4. The direction-finding method based on the digital interference system according to claim 2, wherein in the step 5, the specific method for calculating the theoretical phase of each antenna is as follows:

wherein the content of the first and second substances,

5. The method of claim 3, wherein in step 6, the elevation angle of the two-dimensional incident angle is calculatedAnd azimuth angle

step 61, setting vectors

Wherein T represents a matrix transpose;

step 62, calculating a direction vector G ═ G₁,g₂,g₃]^TWherein:

step 63, updating the vector X to obtain the value of the vector X at the (k + 1) th time;

X^(k+1)＝X^(k)+G

wherein the content of the first and second substances,

step 64, according to X^(k+1)Calculating the elevation angle of the k +1 st two-dimensional incident angleAnd azimuth angle

Wherein, | | represents a complex modulus, real represents the operation of taking a complex real part, and arg represents the operation of solving a complex phase.

6. The direction-finding method based on digital interference system according to claim 4, wherein in step 7, the specific method for calculating the difference between the two-dimensional incident angle with the iteration number k +1 and the iteration number k is as follows:

wherein mod (x,2 π) is the remainder modulo 2 π by x.

7. The method according to claim 1, wherein the threshold value in step 7 is the required direction-finding accuracy.

8. The direction-finding method based on digital interference system according to claim 1, wherein the interference system in step 1 comprises N low noise amplifiers, N mixers, N LPFs, N gain control amplifiers, N ADCs, local oscillator circuit, and sync signal generation circuit; each antenna is sequentially connected with a low noise amplifier, a mixer, an LPF, a gain control amplifier and an ADC, the ADC outputs converted digital signals, the local oscillator circuit is connected with each mixer, and the synchronous signal generating circuit is connected with each ADC.

9. A direction finding system based on a digital interference system, comprising: the antenna comprises N-element uniform circular array antennas, N paths of low-noise amplifiers, N paths of frequency mixers, N paths of LPFs, N paths of gain control amplifiers, N paths of ADCs, local oscillation circuits, synchronous signal generating circuits and signal processing modules, wherein each path of antenna is sequentially connected with one path of low-noise amplifier, one path of frequency mixer, one path of LPF, one path of gain control amplifier and one path of ADC; the signal processing module is used for executing the direction finding method of any one of claims 1 to 8 and outputting the elevation angle and the azimuth angle of the radiation source.

Technical Field

The invention relates to the technical field of radio monitoring, in particular to a direction finding method and system based on a digital interference system.

Background

The interferometer direction-finding system belongs to a phase direction-finding system, and solves the direction information of incoming waves by utilizing different signal phases received by each antenna unit caused by different antenna spatial positions when the incoming waves reach a direction-finding antenna array. The interferometer direction finding technology has been widely used in the passive direction finding field due to its high precision, clear principle, wide frequency band and other features.

The phase interferometer is a direction-finding method commonly adopted in the current direction-finding system because of high direction-finding precision. The linear least square method is simple in operation, and the two-dimensional incident angle can be obtained by processing the phase information of the circular array with least squares (see the documents: Y.Wu, H.C.so.simple and secure two-dimensional angle estimate for a single source with unified aperture array [ J ]. IEEE extensions Wireless and Provisioning Letters 2008,7(1): 78-80; B.Liao, Y.T.Wu, S.C.Chan.A generation angle estimate for a single source with unified aperture array 2012 [ J ]. IEEE extensions and protection letter, 11(1): 986). However, the phase-based least square method does not consider the phase ambiguity problem and is not suitable for large-aperture circular arrays.

For a large-aperture circular array, the phase discrimination range of the phase discriminator is only 2 pi, when the antenna spacing is large enough to cause the actual phase difference to exceed 2 pi, the phase value output by the phase discriminator can overturn by taking 2 pi as a period, and multi-value ambiguity occurs, so that the real phase and the actual receiving phase are subjected to many-to-one mapping. When the radius of the circular array is large, the phase value range exceeds 2 pi, so that phase ambiguity occurs. The longer the distance between the two antennas is to obtain high angle measurement precision; to achieve a phase not exceeding 2 pi, the distance between the two antennas should be small enough, which is contrary to the condition of improving the direction-finding accuracy.

The reported literature reports adopt a multi-baseline method (see the literature: summer Shao, Yangjingji, one-dimensional search and long and short baseline combined interferometer design method [ J ] fire control radar technology, 2013,42(02): 33-37; quarterly dawn light, high dawn light; an airborne passive positioning method-interferometer positioning [ J ]. firepower and command control, 2008,33(11):158-, 2008; xileixue, Wang Guangsong, Dynasty, Xuxu, round array phase interferometer two-dimensional direction finding ambiguity resolving new method [ J ]. telemetering and remote control, 2007, (05): 53-59; zhao national Wei, high precision airborne single station passive positioning technology research [ D ]. instructor: plum, brave. northwest university of industry, 2007; yuanxiakang phase interferometer direction finding localization study [ J ]. Shanghai Spaceflight, 1999, (03):3-9), parallel baseline method (see literature: zhang Yi Sail, missile-borne radar direction finding technical research [ D ]. instructor: lyric facing river, university of electronic technology, 2018; cattail, parallel baseline solution fuzzy interferometer direction finding algorithm and realization [ D ]. instructor: koro spring forest, university of electronic technology, 2013; the university of electronic science and technology, a two-dimensional direction-finding method of a circular array phase interferometer based on a parallel baseline, China, CN201110235023.7[ P ]. 2012-04-18; china aerospace science and technology group company, fifth research institute, third research institute, a direction-finding positioning system combining phase difference direction finding and space spectrum direction finding, China, CN201510182536.4[ P ].2015-07-01, an extended baseline method (see literature: china, CN201110226585.5[ P ].2012-04-11), correlation method (see literature: tao, Ling Ming, Rirengang, even odd-even array element number-uniform circular array direction-finding performance research [ J ]. modern radar, 2016,38(11): 24-29; study of two-dimensional direction finding algorithm based on uniform circular array [ D ]. instructor: he, university of electronic technology, 2014; liu Mang surpasses, research on radio direction finding method [ D ]. instructor: yangjianhong, Lanzhou university, 2013; application of correlation operations in phase interferometer disambiguation [ J ] acoustic techniques, 2010,29(05): 538-; china, CN201310116050.1[ P ].2013-08-07), virtual baseline method (see literature: jianlinhong, wideband interferometer signal processing and direction finding algorithm research based on GPU [ D ]. instructor: who, university of electronic technology, 2012; wuvowei micro, Chengting, Jiakexin, He, interferometer direction finding algorithm [ J ] based on virtual array transform modern radar, 2012,34(03): 42-45; li Peng-Fei, broadcasting band direction of arrival base on virtual base evaluation and RBFNN [ J ]. Journal of evaluation, 2012,33(2): 210-.

For high accuracy direction finding, the distance between the antennas is required to be large enough, which results in a large ambiguity range of the phase, and one phase difference corresponds to many possible incident angles, which requires adding multiple sets of antennas to remove multiple values of the incident angle. For the ambiguity resolution methods such as the multi-baseline, the parallel baseline, the extended baseline, the virtual baseline and the like, the higher the accuracy is, the more the number of antennas is, the angle measurement only uses part of the antennas, and the rest antennas are only used for eliminating multiple values, so that the hardware resources are not fully utilized, and the angle measurement accuracy cannot be improved through the added antennas.

In a word, the method has the steps of searching, clustering threshold setting, logic judgment and the like, and has the problems of complex calculation and low precision caused by insufficient antenna application.

Disclosure of Invention

Aiming at the existing problems, a direction-finding method and a direction-finding system based on a digital interference system are provided, and the purpose of high-precision real-time two-dimensional direction finding is achieved.

The technical scheme adopted by the invention is as follows: a direction finding method based on a digital interference system comprises the following processes:

step 1, for an N-element uniform circular array antenna, converting space electromagnetic waves of a receiving antenna of a digital interferometer system into digital voltage signals, performing discrete Fourier transform on the digital voltage signals received by each antenna, and then taking a phase to obtain a voltage phase of each antenna;

step 2, when the incoming wave enters the circular array antenna with the elevation angle of 0 degree, recording the phase of each path of antenna as the test phase

Step 3, constructing a plurality number corresponding to each path of antenna according to the voltage phase and the test phase;

step 4, setting the initial elevation angle asInitial azimuth angle of

Initial phase ofThe iteration number k is 0;

step 5, when the iteration number is k, according to the elevation angleAzimuth angleInitial phase ofEach time of calculationTheoretical phase of the antenna;

step 6, introducing a complex number calculation iteration number k +1 constructed by combining the vector X and the direction vector G to calculate the elevation angle of the two-dimensional incident angle of the iteration number k +1And azimuth angle

Step 7, calculating the difference between the two-dimensional incident angles with the iteration times k +1 and the iteration times k, comparing the result with a threshold value, and entering step 8 if the result is smaller than the threshold value; otherwise, adding 1 to the value of the iteration times k, and entering the step 5;

step 8, outputting the two-dimensional incident angle

Andas the elevation and azimuth of the radiation source.

Further, in the step 1, N in the N-ary uniform circular array antenna is not less than 3, and the specific method for obtaining the voltage phase of each antenna is as follows:

wherein phi'_iThe voltage phase of the ith antenna is shown, i is 1,2,3 … N, arg is complex phase operation, M is the number of sampling points, M is more than or equal to 3, f is signal frequency, j is an imaginary unit,

further, in the step 3, the specific method for constructing the complex number is step 31, calculating the normalized phase value of the received voltage of each antenna,step 32, normalizing the phase valueConstructing a plurality of:

wherein, V_iAnd the complex number corresponding to the phase value of the ith antenna is represented.

10. In step 5, the specific method for calculating the theoretical phase of each antenna is as follows:

wherein the content of the first and second substances,represents the theoretical phase of the ith antenna, c is the wave velocity in space, p represents the radius of the circular array antenna, α_iAnd indicating the angular position of the ith antenna, wherein the angular position of the first antenna is 0.

Further, in the step 6, the elevation angle of the two-dimensional incident angle is calculated

And azimuth angle

The method comprises the following specific steps:

step 61, setting vectors

Wherein T represents a matrix transpose;

step 62, calculating a direction vector G ═ G₁,g₂,g₃]^TWherein:

step 63, updating the vector X to obtain the value of the vector X at the (k + 1) th time;

X^(k+1)＝X^(k)+G

wherein the content of the first and second substances,

step 64, according to X^(k+1)Calculating the elevation angle of the k +1 st two-dimensional incident angle

And azimuth angle

Wherein, | | represents a complex modulus, real represents the operation of taking a complex real part, and arg represents the operation of solving a complex phase.

Further, in step 7, a specific method for calculating a difference between the iteration number k +1 and the two-dimensional incident angle with the iteration number k is as follows:

wherein mod (x,2 π) is the remainder modulo 2 π by x.

Further, in step 7, the threshold value is the required direction finding precision.

Further, the interference system in step 1 includes N low noise amplifiers, N mixers, N LPFs (low pass filters), N gain control amplifiers, N ADCs (analog to digital converters), a local oscillation circuit, and a synchronization signal generating circuit; each antenna is sequentially connected with a low noise amplifier, a mixer, an LPF, a gain control amplifier and an ADC, the ADC outputs converted digital signals, the local oscillator circuit is connected with each mixer, and the synchronous signal generating circuit is connected with each ADC.

The invention also provides a direction-finding system based on the digital interference system, which comprises: the antenna comprises N-element uniform circular array antennas, N paths of low-noise amplifiers, N paths of frequency mixers, N paths of LPFs, N paths of gain control amplifiers, N paths of ADCs, local oscillation circuits, synchronous signal generating circuits and signal processing modules, wherein each path of antenna is sequentially connected with one path of low-noise amplifier, one path of frequency mixer, one path of LPF, one path of gain control amplifier and one path of ADC; the signal processing module is used for the direction finding method and outputs the elevation angle and the azimuth angle of the radiation source.

Compared with the prior art, the beneficial effects of adopting the technical scheme are as follows: complex number operation is adopted, so that the phase ambiguity problem is avoided; the information of all antennas on the circular array is utilized, so that the direction finding precision is improved; and an iterative algorithm is adopted, so that operations such as logic judgment and the like are avoided.

Drawings

FIG. 1 is a digital interferometer-based direction-finding system of the present invention.

Fig. 2 is a direction-finding coordinate system in the present invention.

FIG. 3 is a schematic view of a uniform circular array in the present invention

FIG. 4 elevation RMS error vs. incident elevation (fixed incident azimuth 60, SNR: 0, 5, 10, 15, 20dB)

FIG. 5 azimuthal RMS error vs. incident elevation (fixed incident azimuth 60, SNR: 0, 5, 10, 15, 20dB)

FIG. 6 shows the relationship between the root mean square error in elevation angle and the signal-to-noise ratio (fixed incident azimuth angle 30 DEG, elevation angle: 10 DEG, 20 DEG, 30 DEG, 40 DEG)

FIG. 7 shows the relationship between the root-mean-square error of the azimuth angle and the signal-to-noise ratio (fixed incidence azimuth angle 30 degrees, elevation angle 10 degrees, elevation angle 20 degrees, elevation angle 30 degrees, elevation angle x-axis angle, elevation angle x-,

Detailed Description

The invention is further described below with reference to the accompanying drawings.

The invention adopts a digital interferometer system as shown in fig. 1, which comprises N paths of antennas uniformly distributed on a circular array, N paths of measurement channels which are mutually associated, digital sampling, signal processing and the like. The receiver adopts a digital heterodyne receiver, signals collected by an antenna are sent into a mixer after passing through low noise amplification, are converted into intermediate frequency signals (IF) through frequency mixing with a local oscillator and a Low Pass Filter (LPF), pass through a gain control amplifier and then are subjected to an analog-to-digital converter (ADC), and synchronous signals are obtained through a synchronous clock and are subjected to digital sampling. And carrying out direction-finding signal processing on the digital sampling signal to obtain a two-dimensional incident angle.

The main function of the digital interferometer system is to convert the electromagnetic wave in space into digital signal, and the direction-finding system can be, but not limited to, the form of fig. 1.

Without loss of generality, define the elevation angle theta_sIs included angle between the incoming wave direction and the z-axis, azimuth angle phi_sThe included angle between the incoming wave direction and the x-axis is shown in fig. 2.

For an N-element uniform circular array positioned on the xoy plane, N is more than or equal to 3, the radius is rho, and the angular position of the ith antenna is α_iWithout loss of generality, let the 1 st antenna position be 0, as shown in fig. 3. The specific direction finding method comprises the following steps:

a direction finding method based on a digital interference system comprises the following processes:

step 1, for an N-element uniform circular array antenna, converting space electromagnetic waves of a receiving antenna of a digital interferometer system into digital voltage signals, performing discrete Fourier transform on the digital voltage signals received by each antenna, and then taking a phase to obtain a voltage phase of each antenna;

step 2, recording the phase of each path of antenna as a test phase when incoming waves enter the circular array antenna with the elevation angle of 0 degree;

step 3, constructing a plurality number corresponding to each path of antenna according to the voltage phase and the test phase;

step 4, setting the initial elevation angle asInitial azimuth angle of

Initial phase ofThe iteration number k is 0;

step 5, when the iteration number is k, according to the elevation angle

Azimuth angleInitial phase of

Calculating the theoretical phase of each path of antenna;

step 6, introducing a complex number calculation iteration number k +1 constructed by combining the vector X and the direction vector G to calculate the elevation angle of the two-dimensional incident angle of the iteration number k +1And azimuth angle

Step 7, calculating the difference between the two-dimensional incident angles with the iteration times k +1 and the iteration times k, comparing the result with a threshold value, and entering step 8 if the result is smaller than the threshold value; otherwise, adding 1 to the value of the iteration times k, and entering the step 5;

step 8, outputting the two-dimensional incident angle

Andas the elevation and azimuth of the radiation source.

In a preferred embodiment, in step 1, N is greater than or equal to 3 in the N-ary uniform circular array antenna, and the specific method for obtaining the voltage phase of each antenna is as follows:

wherein phi'_iThe voltage phase of the ith antenna is shown, i is 1,2,3 … N, arg is complex phase operation, M is the number of sampling points, M is more than or equal to 3, f is signal frequency, j is an imaginary unit,

in a preferred embodiment, in step 3, the specific method for constructing the complex number is step 31, calculating the normalized phase value of the received voltage of each antenna,

step 32, constructing a complex number for the normalized phase value:

wherein, V_iAnd the complex number corresponding to the phase value of the ith antenna is represented.

11. In step 5, the specific method for calculating the theoretical phase of each antenna is as follows:

wherein the content of the first and second substances,represents the theoretical phase of the ith antenna, c is the wave velocity in space, p represents the radius of the circular array antenna, α_iAnd indicating the angular position of the ith antenna, wherein the angular position of the first antenna is 0.

In a preferred embodiment, in step 6, the elevation angle of the two-dimensional incident angle is calculated

And azimuth angle

The method comprises the following specific steps:

step 61, setting vectors

Wherein T represents a matrix transpose;

step 62, calculating a direction vector G ═ G₁,g₂,g₃]^TWherein:

step 63, updating the vector X to obtain the value of the vector X at the (k + 1) th time;

X^(k+1)＝X^(k)+G

wherein the content of the first and second substances,

step 64, according to X^(k+1)Calculating the elevation angle of the k +1 st two-dimensional incident angleAnd azimuth angle

Wherein, | | represents a complex modulus, real represents the operation of taking a complex real part, and arg represents the operation of solving a complex phase.

In a preferred embodiment, in step 7, a specific method for calculating a difference between the two-dimensional incident angle with the iteration number k +1 and the two-dimensional incident angle with the iteration number k is as follows:

wherein mod (x,2 π) is the remainder modulo 2 π by x.

In a preferred embodiment, in step 7, the threshold value is the required direction-finding accuracy.

In a preferred embodiment, the interference system in step 1 includes N low noise amplifiers, N mixers, N LPFs, N gain control amplifiers, N ADCs, a local oscillator circuit, and a synchronization signal generating circuit; each antenna is sequentially connected with a low noise amplifier, a mixer, an LPF, a gain control amplifier and an ADC, the ADC outputs converted digital signals, the local oscillator circuit is connected with each mixer, and the synchronous signal generating circuit is connected with each ADC.

The invention also provides a direction-finding system based on the digital interference system, which comprises: the antenna comprises N-element uniform circular array antennas, N paths of low-noise amplifiers, N paths of frequency mixers, N paths of LPFs, N paths of gain control amplifiers, N paths of ADCs, local oscillation circuits, synchronous signal generating circuits and signal processing modules, wherein each path of antenna is sequentially connected with one path of low-noise amplifier, one path of frequency mixer, one path of LPF, one path of gain control amplifier and one path of ADC; the signal processing module is used for the direction finding method and outputs the elevation angle and the azimuth angle of the radiation source.

To verify the effect of the present invention, the root mean square of the direction error was calculated by 1000 monte carlo simulations, and the results are shown in fig. 4 to 7. The working frequency is 6GHz, the number of points M is 256, and the signal noise is white Gaussian noise.

Fig. 4 and 5 show the rms error in elevation and the rms error in azimuth versus the angle of incidence, respectively, at different snr. The simulation conditions are as follows: the array element number N is 5, the array radius r is 180mm, the signal-to-noise ratio is 0, 5, 10, 15 and 20dB, and the incidence azimuth angle is 60 degrees.

Fig. 6 and 7 show the relationship between the root mean square error of elevation angle and the root mean square error of azimuth angle and the signal-to-noise ratio under the incident elevation angles of 10 °,20 °, 30 ° and 40 °, respectively. The simulation conditions are as follows: the array element number N is 8, the array radius r is 240mm, and the incidence azimuth angle is 30 degrees.

The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed. Those skilled in the art to which the invention pertains will appreciate that insubstantial changes or modifications can be made without departing from the spirit of the invention as defined by the appended claims.

All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.

Any feature disclosed in this specification may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.