A phased array RFID access control system and automatic entry and exit identification and judgment method
Through the phased array RFID access control system combined with microwave radar module and phased array RFID reader and writer, the microstrip unequal power splitter and microstrip phase shifter are used to solve the problem that the existing RFID access control system is large, bulky, and costly. The problem of high misreading rate achieves efficient automatic identification and management of multi-target items entering and leaving.
Patent Information
- Application Number
- CN202311483071.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-11-09
- Publication Date
- 2024-12-17
- Estimated Expiration
- 2043-11-09
AI Technical Summary
The existing RFID access control system is large, bulky, and expensive, with high misreading and misreading rates, and cannot automatically identify the entry and exit status of multiple items at the same time.
The phased array RFID access control system is adopted, combined with microwave radar module and phased array RFID reader and writer, and the entry and exit status of the target object is identified through beam scanning, and the microstrip unequal power splitter and microstrip phase shifter are used to replace traditional equipment to achieve Low cost and efficient identification.
It reduces costs, improves recognition rate and misread rate, and can identify the inlet and exit status of multiple target objects at the same time, improving the efficiency of commodity and goods management.
Smart Images

Figure CN117523716B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of warehouse management and security technology, and in particular to a phased array RFID access control system and an automatic entry and exit identification and judgment method. Background Art
[0002] With the rapid development of computer and electronic information technology, in order to manage and register items entering and leaving warehouses, confidential media rooms, weapons and equipment storage rooms and other important places and prevent loss, the following two methods are usually used: 1. Set up an RFID channel machine at the entrance of the place; 2. Install a microwave radar and RFID directional antenna reader system with the function of distinguishing the direction of travel at the entrance and exit of the place. The first method has the following disadvantages: large size, bulky, inconvenient to deploy, multiple antennas need to be deployed, high cost, and high missed reading rate and misreading rate; the second method has the following disadvantages: it cannot eliminate the misreading phenomenon due to the multipath interference of radio wave propagation, the directional antenna has a narrow radiation angle, and the limited coverage range of the working beam is prone to missed reading. In order to reduce missed reading, multiple RFID directional antennas are generally used to expand the reading range to reduce the probability of misreading, but it will also increase the application cost. When two items enter and exit at the same time, the above methods cannot automatically identify and judge which item is in and which item is out. Summary of the invention
[0003] In order to solve the defects of the prior art, the present invention provides a phased array RFID access control system and an automatic entry and exit identification and judgment method.
[0004] In order to solve the above technical problems, the present invention adopts the following technical solutions:
[0005] In a first aspect, an embodiment of the present invention provides a phased array RFID access control system, including a microwave radar module and a phased array RFID reader / writer system;
[0006] The microwave radar module is used to detect the target object. When the target object enters the sensing range of the microwave radar, the microwave radar module detects the target object and triggers the phased array RFID reader system to work;
[0007] The phased array RFID reader system identifies the target object and determines the entry and exit status of the target object through beam scanning. When the target object moves within the beam scanning range of the phased array RFID reader system, the phased array RFID reader system determines the entry and exit status of the target object by comparing the positions of the target objects identified by different beam scanning.
[0008] In some embodiments, the phased array RFID reader / writer system includes an RFID reader / writer and a phased array RFID array antenna, wherein the phased array RFID array antenna includes a feed control network and an antenna array element module.
[0009] In some embodiments, the feed control network includes a microstrip unequal power divider and a microstrip phase shifter.
[0010] In some embodiments, the microstrip unequal power divider includes microstrip lines of unequal line widths and resistors of different resistance values.
[0011] In some embodiments, the microstrip phase shifter includes two microstrip lines of unequal lengths.
[0012] In a second aspect, an embodiment of the present invention provides a method for automatically identifying and judging entry and exit, comprising the following steps:
[0013] The microwave radar module detects the target object within its microwave radar sensing range. When the target object enters the microwave radar sensing range, the microwave radar module detects the target object and triggers the phased array RFID reader system to work;
[0014] The phased array RFID reader system identifies the target object and determines the entry and exit status of the target object through beam scanning. When the target object moves within the beam scanning range of the phased array RFID reader system, the phased array RFID reader system determines the entry and exit status of the target object by comparing the positions of the target objects identified by different beam scanning.
[0015] In some embodiments, the phased array RFID reader / writer system identifies the target object and determines the entry and exit status of the target object by beam scanning, including:
[0016] The phased array RFID reader system controls the amplitude and phase of each beam excitation signal through a feed control network, thereby realizing beam scanning to identify the target object and determine the entry and exit status of the target object.
[0017] In some embodiments, the feed control network includes a microstrip unequal power divider and a microstrip phase shifter.
[0018] In some embodiments, the microstrip unequal power divider includes microstrip lines of unequal line widths and resistors of different resistance values.
[0019] In some embodiments, the microstrip phase shifter includes two microstrip lines of unequal lengths.
[0020] The present invention provides a phased array RFID access control system and an automatic entry and exit identification and judgment method. Compared with the prior art, the present invention has the following technical effects:
[0021] 1. The present invention adopts a low-cost microwave radar module to detect the target object, and uses a phased array RFID reader system to perform beam scanning and identification on the target object and judge the entry and exit status of the target object through dynamic beam switching. Compared with the prior art, the cost is reduced, the recognition rate of the target object is improved and the misreading rate is reduced. In addition, multiple targets can be scanned and identified at the same time and the entry and exit status of all targets can be judged, thereby improving the efficiency of commodity and goods management registration and preventing loss.
[0022] 2. By constructing a microstrip unequal power divider to replace the traditional lumped parameter power divider and attenuator, the amplitude of the excitation signal of each antenna array element can be controlled, thereby reducing costs and increasing service life.
[0023] 3. By constructing a microstrip phase shifter to replace the traditional lumped parameter phase shifter, the phase control of the excitation signal of each antenna array element can be achieved, thereby reducing costs and increasing service life.
[0024] 4. Through dynamic beam switching, the recognition time of the target tag being illuminated by the beam is increased, which helps to improve the recognition rate of the target object tags entering and leaving. At the same time, beam switching can effectively reduce the impact of multipath interference, so it can reduce the misreading rate. BRIEF DESCRIPTION OF THE DRAWINGS
[0025] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings in the following description only involve some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0026] Figure 1 This is a schematic diagram of the structure of a phased array RFID access control system according to an embodiment of the present invention;
[0027] Figure 2 This is a schematic diagram of an application of a phased array RFID access control system according to an embodiment of the present invention;
[0028] Figure 3 A schematic diagram of the structure of a phased array RFID reader / writer system according to an embodiment of the present invention;
[0029] Figure 4 This is a schematic diagram of the structure of an improved phased array RFID reader system according to an embodiment of the present invention;
[0030] Figure 5 A schematic diagram of the amplification structure of a microstrip unequal power divider according to an embodiment of the present invention;
[0031] Figure 6 It is a schematic diagram of the enlarged structure of a microstrip line phase shifter according to an embodiment of the present invention;
[0032] Figure 7 The present invention is a flowchart of an automatic entry and exit identification and judgment method according to an embodiment of the present invention. DETAILED DESCRIPTION
[0033] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solution in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiment of the present invention, not all of the embodiments. Based on the embodiment of the present invention, other solutions obtained by ordinary technicians in this field without creative work should belong to the protection scope of the present invention.
[0034] In order to facilitate those skilled in the art to understand the embodiments of the present invention, the technical terms involved in the present invention are explained below.
[0035] Radio Frequency Identification (RFID) is a type of automatic identification technology that uses radio frequency to perform non-contact two-way data communication and read and write recording media (electronic tags or radio frequency cards) to achieve the purpose of identifying targets and exchanging data.
[0036] A phased array antenna is an antenna that controls the amplitude and phase of the excitation signal of each radiating element in the array antenna to achieve antenna beamforming and switching scanning control.
[0037] Example 1
[0038] Figure 1 A schematic diagram of the structure of a phased array RFID access control system according to an embodiment of the present invention is shown. Figure 1 It can be seen that the phased array RFID access control system includes: a microwave radar module 10 and a phased array RFID reader / writer system 20;
[0039] The microwave radar module 10 is used to detect a target object. When a target object enters the sensing range of the microwave radar, the microwave radar module detects the target object and triggers the phased array RFID reader system 20 to operate.
[0040] The phased array RFID reader system 20 identifies the target object and determines the entry and exit status of the target object through beam scanning. When the target object moves within the beam scanning range of the phased array RFID reader system 20, the phased array RFID reader system 20 determines the entry and exit status of the target object by comparing the positions of the target object identified by different beam switching scans.
[0041] The phased array RFID access control system of this embodiment is generally applied in the following manner: Figure 2 As shown, the microwave radar module 10 preferably adopts low-cost target proximity sensing technology, and the operating frequency is usually below 30GHz, such as 5.8GHz, 10GHz or 24GHz, etc. Its cost is only a few tenths of the radar module used for positioning and position tracking in the prior art. Therefore, the phased array RFID access control system of this embodiment greatly reduces the cost. Figure 2 As shown, when the phased array RFID access control system starts to operate, the microwave radar module 10 first detects whether there is a target object, such as a person, cargo or commodity, in its microwave radar sensing area. If no target object is detected in the microwave radar sensing area, it continues to detect. When a target object enters the microwave radar sensing area, the microwave radar module 10 detects the target object and triggers the phased array RFID reader system 20 to work, that is, the phased array RFID reader system 20 repeatedly performs beam scanning on its working range through antenna array elements to identify the target object and determine the entry and exit status of the target object. When the target object moves within the beam scanning range of the phased array RFID reader system 20, the phased array RFID reader system 20 compares the different positions of the same target object scanned by different beams and determines the entry and exit status of the target object. Figure 2 As shown, at a certain moment, Person A is scanned and identified by Beam 1 at Position 1, and at a later moment, Person A is scanned and identified by Beam 2 at Position 2. The phased array RFID reader system 20 can determine that Person A is entering by comparing the two. For another example, at a certain moment, Person B is scanned and identified by Beam 3 at Position 3, and at a later moment, Person B is scanned and identified by Beam 2 at Position 2. Similarly, it can be determined that Person B is leaving. Since the beam scanning of the phased array RFID reader system 20 of this embodiment is relatively fast, Person A and Person B enter and leave at the same time, respectively. The phased array RFID reader system 20 can determine that Person A is entering and Person B is leaving. In addition, the phased array RFID reader system 20 of this embodiment can perform beam scanning and identification on multiple targets at the same time and determine the entry and exit status of all targets.
[0042] The phased array RFID access control system of this embodiment adopts a low-cost microwave radar module 10 to detect the target object, and uses a phased array RFID reader system 20 to perform beam scanning and identification on the target object and determine the access status of the target object through dynamic beam switching. Compared with the prior art, the cost is reduced, the recognition rate of the target object is improved, and the misreading rate is reduced. In addition, multiple targets can be scanned and identified at the same time and the access status of all targets can be determined, thereby improving the efficiency of commodity and cargo management registration and preventing loss.
[0043] Example 2
[0044] Depend on Figure 3 and Figure 4 It can be seen that the phased array RFID reader system 20 includes an RFID reader 201 and a phased array RFID array antenna (not shown in the figure), wherein the phased array RFID array antenna includes a feed control network 202 and an antenna array element module 203 .
[0045] like Figure 3 As shown, the existing feed control network 202 includes a power divider 2021, an attenuator 2022, a phase shifter 2023 and a radio frequency switch (not shown in the figure).
[0046] Among them, the phased array RFID reader system 20 controls the transmission path of the excitation signal or the RF signal by controlling the RF switch through the RFID reader 201, thereby obtaining the amplitude and phase values of the excitation signals of different paths, that is, realizing the amplitude and phase control function of the excitation signal of the antenna array element module 203.
[0047] The feed control network 202 is used to control the amplitude and phase of the excitation signal of the antenna array element module 203 .
[0048] The antenna array element module 203 is composed of antenna elements (also called antenna array elements) with independent radiation and receiving functions. Figure 3 and 4 As shown, it can be a one-dimensional planar array or a two-dimensional planar array.
[0049] The radio frequency switch is used to control the radio frequency signal transmission path.
[0050] The feed control network 202 of the conventional phased array RFID reader system 20 realizes the amplitude and phase control of the beam excitation signal through a lumped parameter power divider (referred to as power divider 2021), a lumped parameter phase shifter (referred to as phase shifter 2023) and an attenuator, thereby realizing the beam forming and beam scanning functions. Generally, lumped parameter power dividers, attenuators and phase shifters have large insertion losses and are relatively expensive. It is preferred to use Figure 4The improved feed control network 202 shown includes a power divider 2021, a phase shifter 2023 and a radio frequency switch 2024, thereby reducing the attenuator and further reducing the cost. The power divider 2021 preferably adopts a microstrip unequal power divider 2021 constructed on a PCB board, and the microstrip unequal power divider 2021 is used to achieve amplitude control of the excitation signal. Compared with the existing power divider, it is cheaper and can further reduce the cost; the phase shifter 2023 preferably adopts a microstrip phase shifter 2023, and the microstrip phase shifter 2023 is used to achieve phase control of the excitation signal. Compared with the existing phase shifter, it is cheaper and can further reduce the cost. That is to say, this embodiment preferably replaces the traditional lumped parameter power divider and attenuator with the microstrip unequal power divider 2021 to achieve amplitude control of the excitation signal, and replaces the traditional lumped parameter phase shifter with the microstrip phase shifter 2023 to achieve phase control of the excitation signal, thereby achieving beamforming and beam switching. Since the insertion loss of the microstrip unequal power divider 2021 and the microstrip phase shifter 2023 is smaller, the total power loss of the RF signal radiated by the antenna array element module 203 is smaller, so that the activation energy obtained by the target object's tag is higher, thereby increasing the probability of the tag being read, further improving the recognition rate of the target object and reducing the misreading rate.
[0051] Depend on Figure 5 As shown, the microstrip unequal power divider 2021 includes microstrip lines 20211 of unequal line width and resistors 20212 of different resistance values. The RF switch 2024 controls the excitation signal to pass through different microstrip unequal power dividers 2021 to obtain different amplitude values, thereby controlling the beam shape, that is, realizing beamforming.
[0052] The microstrip unequal power divider 2021 preferably adopts a Wilkinson power divider made based on a microstrip line, and the Wilkinson power divider can achieve any power division ratio. The Wilkinson power divider includes multiple power branches, wherein the power branches with wider transmission line width are allocated more power, and the power branches with thinner transmission line width are allocated less power. The greater the power ratio, the greater the difference in line width of the branch printed lines after power division, thereby achieving any power division ratio to meet business needs.
[0053] Depend on Figure 6 As shown, the microstrip phase shifter 2023 includes two microstrip lines of unequal lengths. The RF switch 2024 controls the excitation signal to pass through microstrip lines of different lengths to obtain different phase shift angles, thereby controlling the beam pointing, that is, realizing beam switching.
[0054] Example 3
[0055] Figure 7 A flow chart of an automatic entry and exit identification and judgment method according to an embodiment of the present invention is shown. Figure 7It can be seen that the automatic entry and exit identification and judgment method includes the following steps:
[0056] S1. The microwave radar module detects a target object within its microwave radar sensing range. When a target object enters the microwave radar sensing range, the microwave radar module detects the target object and triggers the phased array RFID reader system to operate.
[0057] S2. The phased array RFID reader system identifies the target object through beam scanning and determines the entry and exit status of the target object. When the target object moves within the beam scanning range of the phased array RFID reader system, the phased array RFID reader system determines the entry and exit status of the target object by comparing the positions of the target objects identified by different beam scanning.
[0058] The microwave radar module preferably adopts low-cost target proximity sensing technology, and its operating frequency is usually below 30 GHz, such as 5.8 GHz, 10 GHz or 24 GHz. Its cost is only a few tenths of the radar module used for positioning and position tracking in the prior art. Therefore, the automatic entry and exit identification and judgment method of this embodiment greatly reduces the cost.
[0059] First, the microwave radar module detects whether there is a target object, such as a person, cargo or commodity, in its microwave radar sensing area. If no target object is detected in the microwave radar sensing area, it will continue to detect. When a target object enters the microwave radar sensing area, the microwave radar module detects the target object and triggers the phased array RFID reader system to work, that is, the phased array RFID reader system repeatedly performs beam scanning on its working range through antenna array elements to identify the target object and determine the entry and exit status of the target object. When the target object moves within the beam scanning range of the phased array RFID reader system, the phased array RFID reader system compares the different positions of the same target object scanned by different beams to identify the different locations of the target object and determine the entry and exit status of the target object. Figure 2 As shown, at a certain moment, Person A is scanned and identified by Beam 1 at Position 1, and at a later moment, Person A is scanned and identified by Beam 2 at Position 2. The phased array RFID reader system can determine that Person A is entering by comparing the two. For another example, at a certain moment, Person B is scanned and identified by Beam 3 at Position 3, and at a later moment, Person B is scanned and identified by Beam 2 at Position 2. Similarly, it can be determined that Person B is leaving. Since the beam scanning of the phased array RFID reader system of this embodiment is relatively fast, Person A and Person B enter and leave at the same time respectively. The phased array RFID reader system can determine that Person A is entering and Person B is leaving. In addition, the phased array RFID reader system of this embodiment can perform beam scanning and identification on multiple targets at the same time and determine the entry and exit status of all targets.
[0060] The automatic entry and exit identification and judgment method of this embodiment adopts a low-cost microwave radar module to detect the target object, and uses a phased array RFID reader system to perform beam scanning and identification on the target object and judge the entry and exit status of the target object through dynamic beam switching. Compared with the prior art, this method reduces costs, improves the recognition rate of the target object and reduces the misreading rate. It can also scan and identify multiple targets at the same time and judge the entry and exit status of all targets, thereby improving the efficiency of commodity and cargo management registration and preventing loss.
[0061] In another embodiment, the phased array RFID reader system controls the transmission path of the excitation signal, ie, the radio frequency signal, by controlling the radio frequency switch through the RFID reader, thereby obtaining the amplitude and phase values of the excitation signal of different paths.
[0062] The traditional phased array RFID reader system controls the amplitude and phase of the excitation signal of the antenna array element through the feed control network. The feed control network realizes the amplitude and phase control of the beam excitation signal through lumped parameter equal power dividers (referred to as power dividers), lumped parameter phase shifters (referred to as phase shifters) and attenuators, thereby realizing beamforming and beam scanning functions. Usually, lumped parameter power dividers, attenuators and phase shifters have large insertion losses and are relatively expensive. It is preferred to use Figure 4 The improved feed control network 202 shown includes a power divider 2021, a phase shifter 2023 and a radio frequency switch 2024, thereby reducing the attenuator and further reducing the cost. The power divider 2021 preferably adopts a microstrip unequal power divider 2021 constructed on a PCB board, and the microstrip unequal power divider 2021 is used to control the amplitude of the excitation signal. Compared with the existing power divider, the price is lower, which can further reduce the cost; the phase shifter 2023 preferably adopts a microstrip phase shifter 2023, and the microstrip phase shifter 2023 is used to control the phase of the excitation signal. Compared with the existing phase shifter, the price is lower, which can further reduce the cost. That is to say, this embodiment preferably replaces the traditional lumped parameter power divider with the microstrip unequal power divider 2021 to control the amplitude of the excitation signal, and replaces the traditional lumped parameter phase shifter with the microstrip phase shifter 2023 to control the phase of the excitation signal, thereby realizing beamforming and beam switching. Since the insertion loss of the microstrip unequal power divider 2021 and the microstrip phase shifter 2023 is smaller, the total power loss of the RF signal radiated by the antenna array element module 203 is smaller, so that the activation energy obtained by the target object's tag is higher, thereby increasing the probability of the tag being read, further improving the recognition rate of the target object and reducing the misreading rate.
[0063] Depend on Figure 5As shown, the microstrip unequal power divider 2021 includes microstrip lines 20211 of unequal line width and resistors 20212 of different resistance values. The RF switch 2024 controls the excitation signal to pass through different microstrip unequal power dividers 2021 to obtain different amplitude values, thereby controlling the beam shape, that is, realizing beamforming.
[0064] The microstrip unequal power divider 2021 preferably adopts a Wilkinson power divider made based on a microstrip line, and the Wilkinson power divider can achieve any power division ratio. The Wilkinson power divider includes multiple power branches, wherein the power branches with wider transmission line width are allocated more power, and the power branches with thinner transmission line width are allocated less power. The greater the power ratio, the greater the difference in line width of the branch printed lines after power division, thereby achieving any power division ratio to meet business needs.
[0065] Depend on Figure 6 As shown, the microstrip phase shifter 2023 includes two microstrip lines of unequal lengths. The RF switch 2024 controls the excitation signal to pass through microstrip lines of different lengths to obtain different phase shift angles, thereby controlling the beam pointing, that is, realizing beam switching.
[0066] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.
Claims
1. A phased array RFID access control system, characterized in that: Includes microwave radar module and phased array RFID reader system; The microwave radar module is used to detect the target object. When the target object enters the sensing range of the microwave radar, the microwave radar module detects the target object and triggers the phased array RFID reader system to work; The phased array RFID reader system identifies the target object and determines the entry and exit status of the target object through beam scanning. The beam scanning identification is a beam dynamic switching mode. When the target object moves within the beam scanning range of the phased array RFID reader system, the phased array RFID reader system determines the entry and exit status of the target object by comparing the positions of the target objects identified by different beam scans; the phased array RFID reader system includes an RFID reader and a phased array RFID array antenna, wherein the phased array RFID array antenna includes a feed control network and an antenna array element module; the feed control network includes a power divider, a phase shifter and a radio frequency switch, and the phased array RFID reader system controls the transmission path of the excitation signal or the radio frequency signal by controlling the radio frequency switch through the RFID reader, thereby obtaining the amplitude and phase values of the excitation signals of different paths.
2. The phased array RFID access control system according to claim 1, characterized in that: The feed control network includes a microstrip unequal power divider and a microstrip phase shifter.
3. The phased array RFID access control system according to claim 2, characterized in that: The microstrip unequal power divider comprises microstrip lines with unequal line widths and resistors with different resistance values.
4. The phased array RFID access control system according to claim 2, characterized in that: The microstrip phase shifter includes two microstrip lines with unequal lengths.
5. A method for automatically identifying and judging entry and exit, characterized in that: The steps include: The microwave radar module detects the target object within its microwave radar sensing range. When the target object enters the microwave radar sensing range, the microwave radar module detects the target object and triggers the phased array RFID reader system to work; The phased array RFID reader system identifies the target object and determines the entry and exit status of the target object through beam scanning. The beam scanning identification is a beam dynamic switching mode. When the target object moves within the beam scanning range of the phased array RFID reader system, the phased array RFID reader system determines the entry and exit status of the target object by comparing the positions of the target objects identified by different beam scans; the phased array RFID reader system includes an RFID reader and a phased array RFID array antenna, wherein the phased array RFID array antenna includes a feed control network and an antenna array element module; the feed control network includes a power divider, a phase shifter and a radio frequency switch, and the phased array RFID reader system controls the transmission path of the excitation signal or the radio frequency signal by controlling the radio frequency switch through the RFID reader, thereby obtaining the amplitude and phase values of the excitation signals of different paths.
6. The automatic entry and exit identification and judgment method according to claim 5 is characterized in that: The phased array RFID reader / writer system identifies the target object and determines the entry and exit status of the target object through beam scanning, including: The phased array RFID reader system controls the amplitude and phase of each beam excitation signal through a feed control network, thereby realizing beam scanning to identify the target object and determine the entry and exit status of the target object.
7. The method for automatically identifying and judging entry and exit according to claim 6, characterized in that: The feed control network includes a microstrip unequal power divider and a microstrip phase shifter.
8. The automatic entry and exit identification and judgment method according to claim 7 is characterized in that: The microstrip unequal power divider comprises microstrip lines with unequal line widths and resistors with different resistance values.
9. The automatic entry and exit identification and judgment method according to claim 7 is characterized in that: The microstrip phase shifter includes two microstrip lines with unequal lengths.
