阅读说明：本技术 一种信道估计方法、装置、电子设备及存储介质 (Channel estimation method, device, electronic equipment and storage medium ) 是由 乔晖 高永胜 程迎辉 于 2020-12-29 设计创作，主要内容包括：本发明实施例涉及通信技术领域,特别涉及一种信道估计方法、装置、电子设备及存储介质,该方法包括：确定导频数据的导频信道估计值；判断相邻导频数据间的业务数据的幅度和/或相位是否发生变化,若是则拆分所述导频信道估计值,得到幅度估计值和相位估计值；根据所述幅度估计值和所述相位估计值进行滤波合并,得到平滑后的导频信道估计值。通过提取射频系统的反馈信息,即在信号增益控制时导致的信号幅度和/或相位是否变化,根据该变化量对导频信道估计值中的幅度估计值和相位估计值进行平滑处理,以能够适应长期平均抑制噪声的信道估计,保证了信道估计的准确性。(The embodiment of the invention relates to the technical field of communication, in particular to a channel estimation method, a device, electronic equipment and a storage medium, wherein the method comprises the following steps: determining a pilot channel estimation value of pilot data; judging whether the amplitude and/or the phase of service data between adjacent pilot frequency data are changed, if so, splitting the pilot frequency channel estimation value to obtain an amplitude estimation value and a phase estimation value; and carrying out filtering combination according to the amplitude estimation value and the phase estimation value to obtain a smoothed pilot channel estimation value. By extracting the feedback information of the radio frequency system, namely whether the signal amplitude and/or phase changes during signal gain control, the amplitude estimation value and the phase estimation value in the pilot channel estimation value are subjected to smoothing processing according to the variable quantity, so that the channel estimation for long-term average noise suppression can be adapted, and the accuracy of the channel estimation is ensured.)

1. A method of channel estimation, comprising:

determining a pilot channel estimation value corresponding to pilot data;

judging whether the amplitude and/or the phase of service data between adjacent pilot frequency data are changed, if so, splitting the pilot frequency channel estimation value to obtain an amplitude estimation value and a phase estimation value;

and carrying out filtering combination according to the amplitude estimation value and the phase estimation value to obtain a smoothed pilot channel estimation value.

2. The channel estimation method according to claim 1, wherein the determining the pilot channel estimation value corresponding to the pilot data specifically includes:

demodulating the received data, separating out the pilot frequency received data on the pilot frequency sub-carrier, and determining the pilot frequency channel estimation value according to the pilot frequency received data of the pilot frequency sub-carrier and the pilot frequency data adopted on the pilot frequency sub-carrier.

3. The channel estimation method according to claim 1, wherein the determining whether the amplitude and/or phase of the traffic data between the adjacent pilot data changes specifically includes:

monitoring front-end equipment used for adjusting amplitude change in a radio frequency system; the front-end equipment comprises a low noise amplifier, an analog mixer, a digital gain controller and a digital filter;

wherein, the low noise amplifier and the analog mixer are used for controlling the amplitude and phase transmission change of the service data, and the digital gain controller and/or the digital filter are used for controlling the amplitude change of the service data;

and judging whether the amplitude and/or the phase of the service data between the adjacent pilot frequency data are changed or not according to the state of the front-end equipment.

4. The channel estimation method according to claim 1, further comprising, after obtaining the smoothed pilot channel estimation value:

and determining the traffic channel estimation value of the traffic data between the two pilot frequency data according to the interpolation method through the pilot frequency channel estimation values of the two pilot frequency data.

5. A channel estimation device, comprising:

the pilot frequency channel estimation module is used for determining a pilot frequency channel estimation value corresponding to the pilot frequency data;

the filtering resetting module is used for judging whether the amplitude and/or the phase of the service data between the adjacent pilot frequency data are changed or not, and splitting the pilot frequency channel estimation value if the amplitude and/or the phase of the service data are changed, so as to obtain an amplitude estimation value and a phase estimation value;

and the filtering and combining module is used for filtering and combining according to the amplitude estimation value and the phase estimation value to obtain a smoothed pilot channel estimation value.

6. The channel estimation device of claim 5, wherein the filter reset module comprises a phase register and an amplitude register, the phase register is connected to the low noise amplifier and the analog mixer, and determines whether the phase of the traffic data between adjacent pilot data changes; the amplitude register is connected with the low noise amplifier, the analog mixer, the digital gain controller and the digital filter, and judges whether the amplitude of the service data between the adjacent pilot frequency data changes; wherein, the low noise amplifier and the analog mixer are used for controlling the amplitude and phase transmission change of the service data, and the digital gain controller and/or the digital filter are used for controlling the amplitude change of the service data.

7. The channel estimation apparatus as claimed in claim 5, wherein the pilot channel estimation module is connected to a data entry of the physical layer receiver, and configured to demodulate received data, separate pilot received data on pilot subcarriers, and determine a pilot channel estimation value corresponding to the pilot data according to the pilot received data of the pilot subcarriers and pilot data used on the pilot subcarriers.

8. An electronic device, comprising:

at least one processor; and the number of the first and second groups,

a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,

the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the steps of the channel estimation method of any one of claims 1 to 4.

9. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the channel estimation method according to any one of claims 1 to 4.

Technical Field

The present disclosure relates to the field of communications technologies, and in particular, to a channel estimation method, an apparatus, an electronic device, and a storage medium.

Background

Channel estimation is to estimate added model parameters of a wireless communication link from a transmitting end to a receiving end from received data, that is, a time domain or Frequency domain impulse response of the channel model, which is one of key technologies in wireless communication. Generally, a channel estimation method based on pilot-assisted modulation is adopted, pilot data is inserted into a proper position of a transmitting end, information of a pilot channel is estimated at a receiving end through the received pilot data, and then an interpolation algorithm is utilized to acquire the information of the whole data channel, namely, channel responses of front and back adjacent 2 pilot data are utilized to calculate channel responses on data subcarriers in front of the data channels.

The basic principle of the LS (Least Square) method is to minimize the Square of the difference between the received signal and the noiseless data, assuming that the transmitted signal is x (i), the channel transfer function is h (i), and the signal received by the receiving end is y (i), then the equation y (i) x (i) h (i) + n, n is noise, and x (i)^*When 1, then there are The mathematical characteristics of (1) and (n) are the same, the LS method in channel estimation is the most basic and commonly used algorithm, which can obtain a single-point channel estimation with noise, and in a system for average noise suppression for a relatively long time, since pilot data is not only affected by the amplitude and phase of a channel, but also affected by signal gain control, large errors exist in channel estimation, and the accuracy of channel estimation cannot be accurately and effectively ensured.

Disclosure of Invention

An object of embodiments of the present invention is to provide a channel estimation method, an electronic device, and a storage medium, which solve the problem in the prior art that the channel estimation method does not consider the influence of signal gain control, so that the channel estimation has a large error and the correctness of the channel estimation cannot be accurately and effectively ensured.

To solve the above technical problem, in a first aspect, an embodiment of the present invention provides a channel estimation method, including:

determining a pilot channel estimation value corresponding to pilot data;

determining a pilot channel estimation value of pilot data;

judging whether the amplitude and/or the phase of service data between adjacent pilot frequency data are changed, if so, splitting the pilot frequency channel estimation value to obtain an amplitude estimation value and a phase estimation value;

and carrying out filtering combination according to the amplitude estimation value and the phase estimation value to obtain a smoothed pilot channel estimation value.

In a second aspect, an embodiment of the present invention provides a channel estimation apparatus, including:

the pilot frequency channel estimation module is used for determining a pilot frequency channel estimation value corresponding to the pilot frequency data;

the filtering resetting module is used for judging whether the amplitude and/or the phase of the service data between the adjacent pilot frequency data are changed or not, and splitting the pilot frequency channel estimation value if the amplitude and/or the phase of the service data are changed, so as to obtain an amplitude estimation value and a phase estimation value;

and the filtering and combining module is used for filtering and combining according to the amplitude estimation value and the phase estimation value to obtain a smoothed pilot channel estimation value.

In a third aspect, an embodiment of the present invention provides an electronic device, including:

at least one processor; and the number of the first and second groups,

a memory communicatively coupled to the at least one processor; wherein the content of the first and second substances,

the memory stores instructions executable by the at least one processor to cause the at least one processor to perform the steps of the channel estimation method according to the embodiment of the first aspect of the present invention.

In a fourth aspect, the embodiments of the present invention further provide a non-transitory computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the steps of the channel estimation method according to the embodiments of the first aspect of the present invention.

Compared with the prior art, the method and the device have the advantages that the feedback information of the radio frequency system is extracted, namely whether the signal amplitude and/or the phase are/is caused during signal gain control is judged, the amplitude estimation value and the phase estimation value in the pilot channel estimation value are subjected to smoothing processing according to the change feedback, so that the channel estimation for long-term average noise suppression can be adapted, and the accuracy of the channel estimation is ensured.

In addition, the determining the pilot channel estimation value corresponding to the pilot data specifically includes:

demodulating the received data, separating out pilot frequency received data on a pilot frequency subcarrier, determining a pilot frequency channel estimation value of the pilot frequency data according to the pilot frequency received data of the pilot frequency subcarrier and the adopted pilot frequency data, and obtaining an amplitude estimation value and a phase estimation value of the pilot frequency channel estimation value.

The method comprises the steps of setting a pilot frequency subcarrier through a preset interval, loading pilot frequency data on the pilot frequency subcarrier, and extracting pilot frequency receiving data corresponding to the pilot frequency data from the receiving data according to the position of the pilot frequency subcarrier.

In addition, the determining whether the amplitude and/or the phase of the service data between the adjacent pilot data change specifically includes:

monitoring front-end equipment used for adjusting amplitude change in a radio frequency system; the front-end equipment comprises a low noise amplifier, an analog mixer, a digital gain controller and a digital filter;

wherein, the low noise amplifier and the analog mixer are used for controlling the amplitude and phase transmission change of the service data, and the digital gain controller and/or the digital filter are used for controlling the amplitude change of the service data;

and judging whether the amplitude and/or the phase of the service data between the adjacent pilot frequency data are changed or not according to the state of the front-end equipment.

In addition, after obtaining the smoothed pilot channel estimation value, the method further includes:

and determining the traffic channel estimation value of the traffic data between the two pilot frequency data according to the interpolation method through the pilot frequency channel estimation values of the two pilot frequency data.

In addition, the filtering resetting module comprises a phase register and an amplitude register, wherein the phase register is connected with the low noise amplifier and the analog mixer and judges whether the phase of service data between adjacent pilot frequency data changes or not; the amplitude register is connected with the low noise amplifier, the analog mixer, the digital gain controller and the digital filter, and judges whether the amplitude of the service data between the adjacent pilot frequency data changes; wherein, the low noise amplifier and the analog mixer are used for controlling the amplitude and phase transmission change of the service data, and the digital gain controller and/or the digital filter are used for controlling the amplitude change of the service data.

In addition, the pilot channel estimation module is connected to a data entry of the physical layer receiver, and is configured to demodulate received data, separate pilot received data on pilot subcarriers, and determine a pilot channel estimation value corresponding to the pilot data according to the pilot received data of the pilot subcarriers and pilot data used on the pilot subcarriers.

Drawings

One or more embodiments are illustrated by way of example in the accompanying drawings, which correspond to the figures in which like reference numerals refer to similar elements and which are not to scale unless otherwise specified.

Fig. 1 is a flow chart of a channel estimation method according to a first embodiment of the present invention;

FIG. 2 is a schematic diagram of a phase variation and amplitude variation extraction process according to an embodiment of the present invention;

fig. 3 is a block diagram of a channel estimation device according to a second embodiment of the present invention;

fig. 4 is a block diagram of an electronic device according to a third embodiment of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention more apparent, embodiments of the present invention will be described in detail below with reference to the accompanying drawings. However, it will be appreciated by those of ordinary skill in the art that numerous technical details are set forth in order to provide a better understanding of the present application in various embodiments of the present invention. However, the technical solution claimed in the present application can be implemented without these technical details and various changes and modifications based on the following embodiments. The following embodiments are divided for convenience of description, and should not constitute any limitation to the specific implementation manner of the present invention, and the embodiments may be mutually incorporated and referred to without contradiction.

The terms "first" and "second" in the embodiments of the present application are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, the terms "comprise" and "have", as well as any variations thereof, are intended to cover a non-exclusive inclusion. For example, a system, product or apparatus that comprises a list of elements or components is not limited to only those elements or components but may alternatively include other elements or components not expressly listed or inherent to such product or apparatus. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless explicitly specifically limited otherwise.

In a Narrow-Band system receiver represented by NB-IoT (Narrow Band Internet of Things), it usually needs to collect channel information for a long time to combine for noise suppression, in this process, the characteristics of a wireless channel can be considered as static or slow fading, pilot data is not only affected by the amplitude and phase of the channel, but also affected by signal gain control, which finally causes a large error in channel estimation, and the accuracy and validity of the channel estimation cannot be guaranteed accurately and effectively.

Therefore, embodiments of the present invention provide a channel estimation method, an apparatus, an electronic device, and a storage medium, which are applied to NB-IoT, and filter resetting is performed on an amplitude estimation value and a phase estimation value in a pilot channel estimation value according to a change of an amplitude or a phase of a signal caused by extracting feedback information of a radio frequency system, that is, the change of the amplitude or the phase of the signal during signal gain control, so as to adapt to channel estimation for long-term average noise suppression, and ensure accuracy of channel estimation. The following description and description will proceed with reference being made to various embodiments.

A first embodiment of the present invention relates to a channel estimation method. The specific process is shown in fig. 1, and comprises the following steps:

step S1, determining a pilot channel estimation value corresponding to the pilot data;

in this embodiment, received data is demodulated, pilot frequency received data on a pilot frequency subcarrier is separated, a pilot frequency channel estimation value of the pilot frequency data is determined according to the pilot frequency received data of the pilot frequency subcarrier and adopted pilot frequency data, and an amplitude estimation value and a phase estimation value of the pilot frequency channel estimation value are obtained.

Specifically, the channel estimation value is obtained by the LS method, and for a general OFDM (Orthogonal Frequency Division Multiplexing) system, there are:

y＝hp+n

where y denotes frequency domain data at the receiver end, i.e. received data on pilot subcarriers, h denotes a frequency domain channel (here an unknown quantity), p denotes pilot data (the pilot sequence is considered known at the receiver), and n is additive (gaussian) noise.

The processing at the receiver side is:

yp*＝hpp*+np*

considering the design characteristics of the pilot data, pp ═ 1; therefore, an LS channel estimate can be obtained:

wherein the content of the first and second substances,the mathematical characteristics of (a) are the same as n.

Step S2, judging whether the amplitude and/or phase of the service data between the adjacent pilot frequency data changes, if so, splitting the pilot frequency channel estimation value to obtain an amplitude estimation value and a phase estimation value;

specifically, the narrowband system receiver usually needs a long time to collect channel information for combining to achieve Noise suppression, in which the characteristics of the wireless channel may be considered static or slow fading, and the receiver usually uses AGC (Automatic Gain Control) to adjust the baseband signal level to a proper position during the channel process, and the specific AGC adjustment may cause the amplitude or phase transmitted by the baseband signal to change, in this embodiment, by receiving the Control command of the device in the radio frequency system, which may affect the amplitude and/or phase of the traffic data, to determine the corresponding amplitude change and phase change according to the Control command, specifically, as shown in fig. 2, these devices are distributed at the radio frequency front end and the digital front end, the device distributed at the radio frequency front end includes a Low Noise Amplifier (Low Noise Amplifier, LNA) and analog mixers (Mixer), distributed in a digital front-end with a digital Gain controller (Gain) and a digital Filter (Filter). The low noise amplifier is responsible for amplifying an analog receiving signal, and generally has a plurality of gain adjustment gears which can affect the continuity of equivalent channel amplitude; except some special designs, the continuity of the phase is generally influenced; the analog mixer is responsible for down-conversion of a receiving end, and may affect the phase and the amplitude, depending on the implementation mode; the digital gain controller is a digital part (equivalent) gain which can affect the amplitude and the phase; the digital filter is an overall (equivalent) addition to the link.

And step S3, filtering and combining according to the amplitude estimation value and the phase estimation value to obtain a smoothed pilot channel estimation value.

Specifically, long-term combination filtering is performed on the amplitude estimation value and the phase estimation value in the time direction, so as to obtain a pilot channel estimation value after correction of the front or rear adjacent pilot data.

The filtering and merging algorithm in this embodiment, for example, an alpha-beta filter, a moving average filter, and the like, is specifically the basic principle of the conversion part:

for any one x ∈ C can be written as:

x＝a+bi＝Ae^iω

wherein:

a,b∈R

A∈R⁺

ω∈[0,2π]

the following two mapping relationships:

a,b＝f(A,ω)

A,ω＝f^-1(a,b)

corresponding to the mathematical meanings of the above-mentioned filtering combination and splitting, respectively.

After the corrected pilot channel estimation value is obtained, an interpolation method can be used to determine the traffic channel estimation value of the traffic data between the two pilot data according to the pilot channel estimation values of the two pilot data before and after.

The filtering and combining algorithm in this embodiment may be alpha-beta filtering or moving average filtering, which is not limited in this embodiment.

The steps of the above methods are divided for clarity, and the implementation may be combined into one step or split some steps, and the steps are divided into multiple steps, so long as the same logical relationship is included, which are all within the protection scope of the present patent; it is within the scope of the patent to add insignificant modifications to the algorithms or processes or to introduce insignificant design changes to the core design without changing the algorithms or processes.

The second embodiment of the present invention relates to a channel estimation device, and based on the channel estimation method in the foregoing embodiment, the channel estimation device includes:

a pilot channel estimation module 10, configured to determine a pilot channel estimation value corresponding to pilot data;

specifically, the received data is demodulated to separate pilot frequency received data on a pilot frequency subcarrier, and a pilot frequency channel estimation value of the pilot frequency data is determined according to the pilot frequency received data of the pilot frequency subcarrier and the adopted pilot frequency data to obtain an amplitude estimation value and a phase estimation value of the pilot frequency channel estimation value.

The Receiver FIFO is a data entry of the physical layer Receiver, logically, a FIFO buffer FIFO, first in first out buffer, and in the context of typical channel estimation, it is considered that both the time offset and the frequency offset of the physical layer are properly processed by other modules.

A filtering resetting module 20, configured to determine whether amplitude and/or phase of service data between adjacent pilot data change, and if so, split the pilot channel estimation value to obtain an amplitude estimation value and a phase estimation value;

specifically, the narrowband system receiver collects channel information for a long time and combines the channel information to achieve Noise suppression, and the channel characteristics are slow due to narrow bandwidth, in the process, the characteristics of the wireless channel may be considered static or slow fading, while the receiver usually uses AGC (Automatic Gain Control) to adjust the baseband signal level to a proper position during the channel, and the specific AGC adjustment may cause the amplitude or phase of the signal transmitted from the baseband to change, in this embodiment, by receiving a Control instruction of a device in the radio frequency system, which affects the amplitude and/or phase of the traffic data, to determine whether the corresponding amplitude and/or phase changes according to the Control instruction, specifically, the devices are distributed at the radio frequency front end and the digital front end, the device distributed at the radio frequency front end includes a Low Noise Amplifier (Low Noise Amplifier, LNA) and analog mixers (Mixer), distributed in a digital front-end with a digital Gain controller (Gain) and a digital Filter (Filter). The low noise amplifier is responsible for amplifying an analog receiving signal, and generally has a plurality of gain adjustment gears which can affect the continuity of equivalent channel amplitude; except some special designs, the continuity of the phase is generally influenced; the analog mixer is responsible for down-conversion of a receiving end, and may affect the phase and the amplitude, depending on the implementation mode; the digital gain controller is a digital part (equivalent) gain which can affect the amplitude and the phase; the digital filter is the overall (equivalent) gain of the link, which in turn affects the amplitude and not the phase.

The filtering resetting module comprises a phase register and an amplitude register, wherein the phase register is connected with the low noise amplifier and the analog mixer and judges whether the phase of service data between adjacent pilot frequency data changes or not; the amplitude register is connected with the low noise amplifier, the analog mixer, the digital gain controller and the digital filter, and judges whether the amplitude of the service data between the adjacent pilot frequency data changes; wherein, the low noise amplifier and the analog mixer are used for controlling the amplitude and phase transmission change of the service data, and the digital gain controller and/or the digital filter are used for controlling the amplitude change of the service data.

The filter resetting module 20 comprises a phase change determining unit 201, an amplitude change determining unit 202 and a splitting unit 203;

the phase change determination unit 201 is connected to a phase register;

the amplitude variation determining unit 202 is connected with an amplitude register;

the splitting unit 203 is configured to receive the pilot channel estimation value output by the pilot channel estimation module 10, and split the pilot channel estimation value to obtain an amplitude estimation value and a phase estimation value.

The filtering and combining module 30 is configured to filter and combine the amplitude estimation value and the phase estimation value in the time direction to obtain a smoothed pilot channel estimation value;

and the traffic channel estimation module 40 is configured to determine a traffic channel estimation value of traffic data between two adjacent pilot data according to a pilot channel estimation value of two adjacent pilot data.

The filtering and merging algorithm in this embodiment, for example, an alpha-beta filter, a moving average filter, and the like, is specifically the basic principle of the conversion part:

for any one x ∈ C can be written as:

x＝a+bi＝Ae^iω

wherein:

a,b∈R

A∈R⁺

ω∈[0,2π]

the following two mapping relationships:

a,b＝f(A,ω)

A,ω＝f^-1(a,b)

and the mathematical meanings of the filtering and merging module and the splitting unit are respectively corresponded.

A third embodiment of the present invention relates to an electronic device, as shown in fig. 4, including a processor (processor)810, a communication Interface (Communications Interface)820, a memory (memory)830 and a communication bus 840, where the processor 810, the communication Interface 820 and the memory 830 complete communication with each other through the communication bus 840. Processor 810 may invoke logic instructions in memory 830 to perform the steps of the channel estimation method as described in the various embodiments above. Examples include:

step S1, determining a pilot channel estimation value corresponding to the pilot data;

step S2, judging whether the amplitude and/or phase of the service data between the adjacent pilot frequency data changes, if so, splitting the pilot frequency channel estimation value to obtain an amplitude estimation value and a phase estimation value;

and step S3, filtering and combining according to the amplitude estimation value and the phase estimation value to obtain a smoothed pilot channel estimation value.

Where the memory and processor are connected by a communications bus, which may include any number of interconnected buses and bridges, connecting together the various circuits of the memory and one or more processors. The bus may also connect various other circuits such as peripherals, voltage regulators, power management circuits, and the like, which are well known in the art, and therefore, will not be described any further herein. A bus interface provides an interface between a communication bus and a transceiver. The transceiver may be one element or a plurality of elements, such as a plurality of receivers and transmitters, providing a means for communicating with various other apparatus over a transmission medium. The data processed by the processor is transmitted over a wireless medium via an antenna, which further receives the data and transmits the data to the processor.

The processor is responsible for managing the bus and general processing and may also provide various functions including timing, peripheral interfaces, voltage regulation, power management, and other control functions. And the memory may be used to store data used by the processor in performing operations.

A fourth embodiment of the present invention relates to a computer-readable storage medium storing a computer program. The computer program, when being executed by a processor, implements the steps of the channel estimation method as described in the embodiments above. Examples include:

step S1, determining a pilot channel estimation value corresponding to the pilot data;

step S2, judging whether the amplitude and/or phase of the service data between the adjacent pilot frequency data changes, if so, splitting the pilot frequency channel estimation value to obtain an amplitude estimation value and a phase estimation value;

and step S3, filtering and combining according to the amplitude estimation value and the phase estimation value to obtain a smoothed pilot channel estimation value.

That is, as can be understood by those skilled in the art, all or part of the steps in the method for implementing the embodiments described above may be implemented by a program instructing related hardware, where the program is stored in a storage medium and includes several instructions to enable a device (which may be a single chip, a chip, or the like) or a processor (processor) to execute all or part of the steps of the method described in the embodiments of the present application. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.

It will be understood by those of ordinary skill in the art that the foregoing embodiments are specific examples for carrying out the invention, and that various changes in form and details may be made therein without departing from the spirit and scope of the invention in practice.