Wireless communication systems are widely deployed to provide mobile devices with various contents, such as voice, text, image, and moving pictures. For example, multiple channel access techniques allow multiple users to share system resources, such as bandwidth and transmission power. Examples of multiple channel access techniques include code division multiple access (CDMA) systems, time division multiple access (TDMA) systems, frequency division multiple access (FDMA) systems, or orthogonal frequency division multiple access (OFDMA) systems. Such multiple channel access techniques can simultaneously support communication between multiple mobile devices.
Various embodiments of communication devices and communication methods are disclosed herein. In one embodiment, a communication device includes an RF receiver that receives a combined signal including a first signal transmitted from a first node and a second signal transmitted from a second node, a channel estimator that estimates first channel information of the first signal and second channel information of the second signal, respectively, a multiuser detector that detects original signal values of the combined signal using the estimated first and second channel information, and an RF transmitter that transmits a signal generated based on the original signal values detected by the multiuser detector to the first node and the second node during a predetermined period.
In another embodiment, a communication method includes estimating first channel information of a first signal and second channel information of a second signal transmitted simultaneously from different nodes, detecting original signal values of a combined signal including the first signal and the second signal based on the estimated first and second channel information by a multiuser detector, and transmitting a signal generated based on the detected original signal values to the different nodes during a predetermined period.
The foregoing summary is illustrative only and is not intended to be in any way limiting. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the drawings and the following detailed description.
In the following detailed description, reference is made to the accompanying drawings, which form a part hereof. In the drawings, similar symbols typically identify similar components, unless context dictates otherwise. The illustrative embodiments described in the detailed description, drawings, and claims arc not meant to be limiting. Other embodiments may be utilized, and other changes may be made, without departing from the spirit or scope of the subject matter presented herein. It will be readily understood that the aspects of the present disclosure, as generally described herein, and illustrated in the Figures, can be arranged, substituted, combined, separated, and designed in a wide variety of different configurations, all of which are explicitly contemplated herein.
In one embodiment, the present disclosure provides a communication device including a multiuser detector that detects values of a combined signal. The combined signal includes a first signal transmitted from a first node and a second signal transmitted from a second node using estimated first and second channel information.
As depicted in
The transmitted first and second signals s1 and s3 are combined on a physical layer such as, but not limited to, air interface, to generate a combined signal y2. Combined signal y2 is received at relay node 120. When combined signal y2 is distorted after passing through multi path fading channel, the original signal values of combined signal y2 can be detected by a multiuser detector 330 of relay node 120, which will be further described in detail hereinafter. As used herein, the original signal values of combined signal y2 refer to the values of combined signal y2 in which no distortion is occurred. Relay node 120 then transmits signal s2 generated based on the detected original signal values of combined signal y2 to first node 110 and second node 130 during a time slot 2 (as depicted by a broken or dashed directional line in
As depicted in
First and second encoders 111 and 131 perform channel coding on signals s1 and s3 to generate encoded signals w1 and w3, respectively. In some embodiments, first and second encoders 111 and 131 perform the channel coding by selectively inserting redundant bits into signals s1 and s3. By inserting redundant bits, bit errors of signals s1 and s3 can be detected and corrected so that reliable signal transmission is achieved. First node 110 and second node 130 transmit encoded signals w1 and w3, respectively, for reception by relay node 120. Prior to reception by relay node 120, encoded signals w1 and w3 are combined on a physical layer, such as an air interface.
Relay node 120 receives combined signal y2 including encoded signals w1 and w3. Further, relay node 120 detects original signal values of combined signal y2 using multiuser detector 330 and generates signal s2 using the original signal values, which will be further described hereinafter. Relay node 120 transmits signal s2 to both first node 110 and second node 130.
First decoder 113 of first node 110 decodes signal s2 and second decoder 133 of second node 130 decodes signal s2. First and second decoders 113 and 133 provide decoded signal ŝ2 to first and second XOR operators 115 and 135, respectively.
First XOR operator 115 of first node 110 performs an XOR operation on decoded signal ŝ2 and first signal s1 to generate second signal s3 that has been transmitted from second node 130. Since decoded signal ŝ2 is the decoded signal of signal s2 which is generated using combined signal y2, it includes first signal s1 and second signal s3. Thus, first node 110 can receive second signal s3 transmitted from second node 130 using the XOR operation.
Second XOR operator 135 of second node 130 performs an XOR operation on decoded signal ŝ2 and second signal s3 to generate first signal s1 that has been transmitted from first node 110. Since decoded signal ŝ2 includes first signal s1 and second signal s3, as described above, second node 130 can receive first signal s1 using the XOR operation.
In the illustrative embodiment, signals (for example, signal s1 and signal s3) can be transmitted and received between first and second nodes 110 and 130 which are far away from each other during relatively short time periods, for example, two time slots (for example, time slots 1 and 2).
In the above-stated illustrative embodiment, the channel codes used by encoders 111 and 131 and decoders 113 and 133 have linearity. For example, the channel codes may include Linear Block Codes, such as Hamming codes, Golay codes, BCH codes, Reed Solomon codes and (Linear) Convolution Codes. However, the channel codes used by encoders 111 and 131 and decoders 113 and 133 are not limited thereto and any channel code having linearity may be employed.
For example, the combined signal received by relay node 120 (see
y
2
=h
1√{square root over (P1)}x1+h3√{square root over (P3)}x3+n [Equation 1]
Here, x1 denotes a symbol value of first signal s1 transmitted from first node 110 (see
For example, if first node 110 and second node 130 transmit BPSK (Binary Phase Shift Keying) modulated signals, symbol values x1 and x3 are minus one (−1) or one (1). Accordingly, combined signal y2 has four possible symbol candidates as expressed in the following Equation 2.
C
00
=h
1√{square root over (P1)}+h3√{square root over (P3)}, C10=−h1√{square root over (P1)}+h3√{square root over (P3)},
C
11
=−h
1√{square root over (P1)}−h3√{square root over (P3)}, C01=h1√{square root over (P1)}−h3√{square root over (P3)} [Equation 2]
In Equation 2, C00 is a possible symbol candidate when symbol value x1 of first signal s1 is one (1) and symbol value x3 of second signal s3 is one (1). C10 is a possible symbol candidate when symbol value x1 of first signal s1 is minus one (−1) and symbol value x3 of second signal s3 is one (1). C11 is a possible symbol candidate when symbol value x1 of first signal s1 is minus one (−1) and symbol value x3 of second signal s3 is minus one (−1). C01 is a possible symbol candidate when symbol value x1 of first signal s1 is one (1) and symbol value x3 of second signal s3 is minus one (−1).
Referring to
Although the BPSK modulation signals have been illustrated above, it will be apparent to those skilled in the art that any modulation method, such as M-QAM (Quadrature Amplitude Modulation) method can also be used.
RF receiver 310 receives combined signal y2 including first signal s1 transmitted from first node 110 (see
Channel estimator 320 estimates channel information including a received power level and a channel coefficient by using the first and second pilot signals received by RF receiver 310. For example, channel estimator 320 estimates first channel information including a first received power level and a first channel coefficient of first signal s1 by using the first pilot signal transmitted from first node 110 through RF receiver 310. Further, channel estimator 320 estimates second channel information including a second received power level and a second channel coefficient of second signal s3 by using the second pilot signal transmitted from second node 130 through RF receiver 310. Then, channel estimator 320 provides the estimated first and second channel information to multiuser detector 330.
Multiuser detector 330 detects original signal values of combined signal y2 received from RF receiver 310 using the estimated first and second channel information received from channel estimator 320. The values detected by multiuser detector 330 may be, but not limited to, one (1) or zero (0), and can be varied depending on a modulation method.
Multiuser detector 330 employs various detecting methods such as, but not limited to, a joint ML (maximum likelihood) detecting method and any other multiuser detecting method.
To detect the original signal values of combined signal y2, multiuser detector 330 is configured to execute LLR (log likelihood ratio) computation of combined signal y2. For example, if BPSK is used as a modulation method, the LLR (log likelihood ratio) value is calculated by Equation 3 as follows.
Here, As2 denotes the LLR (log likelihood ratio) value, and P(A) denotes a probability of occurrence of an event A. For example, P(s1=0, s3=0|y2) is a probability of occurrence of an event in which, when combined signal y2 is received, the values of first signal s1 and second signal s3 are zero (0), respectively. If As2 is equal to or less than zero (0), the original signal value of combined signal y2 is determined as one (1). If As2 is larger than zero (0), the original signal value of combined signal y2 is determined as zero (0).
Further, assuming that a first probability (the value of first signal s1 is zero (0)) and a second probability (the value of first signal s1 is one (1)) are equal; and that a third probability (the value of second signal s3 is zero (0)) and a fourth probability (the value of second signal s3 is one (1)) are equal, Equation 3 is expressed by the following Equation 4 according to Bayes' rule.
Here, p(α) denotes a probability density function of α. For example, p(y2|s1=0, s3=0) is a probability density function of combined signal y2 when the value of first signal s1 is zero (0) and the value of second signal s3 is zero (0). σ2 denotes a variance, and C00, C01, C10 and C11 denote the symbol candidates of combined signal y2 as expressed in Equation 2, respectively.
Multiuser detector 330 produces a vector L2 composed of the values detected as a result of the LLR (log likelihood ratio) computation and provides vector L2 to decoder 340.
Although relay node 120 has been described to execute the LLR (log likelihood ratio) computation on BPSK modulated signals, it will be apparent to those skilled in the art that the LLR (log likelihood ratio) computation can also be applied to another signals modulated by another modulation method, such as M-QAM.
As described above, multiuser detector 330 produces vector L2 with a multiuser detecting method, such as a joint ML (maximum likelihood) detecting method. Therefore, relay node 120 can decrease multi path fading even if a pre-equalizer, which is used to compensate the multi path fading, is not provided.
Decoder 340 receives vector L2 having the LLR (log likelihood ratio) values and decodes vector L2 using a first channel code to generate decoded vector ŝ2. Further, decoder 340 provides decoded vector to to encoder 350.
Encoder 350 receives decoded vector ŝ2 from decoder 340 and encodes decoded vector ŝ2 using a second channel code to generate an encoded vector ŵ′2. Then, encoder 350 provides encoded vector ŵ′2 to RF transmitter 360. As described previously, the first and second channel codes have linearity, and various channel codes having linearity can be used for the first and second channel codes.
RF transmitter 360 modulates encoded vector ŵ′2 into signal s2 and transmits signal s2 to first node 110 and second node 130 during time slot 2 (as depicted by a broken arrow in
In another embodiment, relay node 120 is configured without decoder 340 and encoder 350. Since decoder 340 and encoder 350 are omitted, the decoding and encoding of vector L2 are also omitted in this embodiment. Particularly, in response to combined signal y2 transmitted from RF receiver 310 and the first and second channel information estimated by channel estimator 320, multiuser detector 330 generates vector L2, and provide it to RF transmitter 360. In response to vector L2, RF transmitter 360 generates signal s2 without the above-mentioned decoding and encoding processes, and transmits generated signal s2 to first and second nodes 110 and 130. First node 110 and second node 130 decodes signal s2 using decoder 113 and 133 (Sec
Accordingly, first and second nodes 110 and 130 obtain signals s3 and s1 respectively by XOR operations of the decoded signals of signal s2 and their own signals s1 and s3. Since all of the channel codes used by first and second nodes 110 and 130, decoder 340 and encoder 350 have linearity, the decoded signals of signal s2 satisfies linearity with respect to signals s1 and s3 and signals s1 and s3 can be obtained respectively by the XOR operation.
Relay node 400 includes two decoders (for example, first decoder 440 and second decoder 450), while relay node 120 depicted in
As in relay node 120 depicted in
Particularly, multiuser detector 430 executes LLR (log likelihood ratio) computation of first signal s1 and second signal s3. For example, if BPSK is used as a modulation method, the LLR (log likelihood ratio) value of first signal s1 is expressed by the following Equation 5.
Further, the LLR (log likelihood ratio) value of second signal s3 is expressed by the following Equation 6.
In Equations 5 and 6, P(A) denotes a probability of occurrence of an event A. For example, P(s1=0, s3=0|y2) is a probability of occurrence of an event in which, when combined signal y2 is received, the values of first signal s1 and second signal s3 are respectively zero (0). If the LLR (log likelihood ratio) As1 or As3 is equal to or less than zero (0), the value of first signal s1 or second signal s3 is determined as one (1). If As1 or As3 is larger than zero (0), the value of first signal s1 or second signal s3 is determined as zero (0).
Further, multiuser detector 430 produces a first vector L1 composed of the LLR (log likelihood ratio) values of first signal s1 and provides first vector L1 to first decoder 440. Furthermore, multiuser detector 430 produces a second vector L3 composed of the LLR (log likelihood ratio) values of second signal s3 and provides second vector L3 to second decoder 450.
First decoder 440 receives first vector L1 composed of the LLR (log likelihood ratio) values of first signal s1 and decodes first vector L1 using a first channel code. Further, first decoder 440 provides a decoded vector ŝ1 to XOR operator 460.
Second decoder 450 receives second vector L3 composed of the LLR (log likelihood ratio) values of second signal s3 and decodes second vector L3 using a second channel code. Further, second decoder 450 provides a decoded vector ŝ3 to XOR operator 460.
XOR operator 460 performs an XOR operation on decoded vector ŝ3 and decoded vector ŝ3. Accordingly, XOR operator 460 generates a combined vector ŝ2 and then provides combined vector ŝ2 to encoder 470.
Encoder 470 encodes combined vector ŝ2 using a third channel code and then transmits an encoded vector ŵ′2 to RF transmitter 480. RF transmitter 480 modulates encoded vector ŵ′2 into signal s2 and transmits signal s2 to both first node 110 (see
Although first decoder 440, second decoder 450 and encoder 470 are shown in
Channel information is estimated by using a pilot signal received by RF receiver 310 (Operation 520). The channel information includes a received power level and a channel coefficient. For example, first channel information is estimated using a first pilot signal transmitted from first node 110. The first channel information includes a first received power level and a first channel coefficient of first signal s1. Further, second channel information is estimated using a second pilot signal transmitted from second node 130. The second channel information includes a second received power level and a second channel coefficient of second signal s3.
Original signal values of combined signal y2 received in operation 510 are detected using the first and second channel information estimated in operation 520 (Operation 530). Further, vector L2 composed of the original signal values is produced by executing LLR (log likelihood ratio) computation (Operation 530). The values detected in operation 530 may be, but not limited to, one (1) or zero (0), and can be varied depending on the modulation method. Since the detailed process for detecting the original signal values of combined signal y2 has already been discussed with reference to
Vector L2 is decoded using a first channel code to generate vector ŝ2 (Operation 540). Vector ŝ2 decoded in operation 540 is encoded using a second channel code to generate vector ŵ′2 (Operation 550). Vector ŵ′2 encoded in operation 550 is modulated into signal s2 and signal s2 is transmitted to first node 110 and second node 130 during a predetermined period (for example, time slot 2) (Operation 560).
Signal s2 is decoded into decoded vector ŝ2 at first node 110 and first node 110 performs XOR-operation on decoded vector ŝ2 and signal s1 to obtain or generate second signal s3 that has been transmitted from second node 130. Further, signal s2 is decoded into decoded vector ŝ2 at second node 130 and second node 130 performs XOR-operation on decoded vector ŝ2 and signal s3 to obtain or generate first signal s1 that has been transmitted from first node 110.
As compared to operation 530 in
Further, first vector L1 is produced by executing LLR (log likelihood ratio) computation of first signal s1 and second vector L3 is produced by executing LLR (log likelihood ratio) computation of second signal s3, respectively (Operation 640). The detected values may be, but not limited to, one (1) or zero (0), and can be varied depending on the modulation method.
First vector L1 is decoded using a first channel code and second vector L3 is decoded using a second channel code (Operation 650). Accordingly, decoded vectors ŝ1 and ŝ3 are generated.
An XOR operation is performed on decoded vectors ŝ1 and ŝ1 and thus combined vector ŝ2 is generated (Operation 660). Then, combined vector ŝ2 is encoded to generate vector ŵ′2 using a third channel code (Operation 670). Encoded vector ŵ′2 is modulated into signal s2 and signal s2 is transmitted to both first node 110 and second node 130 during a predetermined period (for example, time slot 2) (Operation 680).
One skilled in the art will appreciate that, for this and other processes and methods disclosed herein, the functions performed in the processes and methods may be implemented in differing order. Furthermore, the outlined steps and operations are only provided as examples, and some of the steps and operations may be optional, combined into fewer steps and operations, or expanded into additional steps and operations without detracting from the essence of the disclosed embodiments.
The present disclosure is not to be limited in terms of the particular embodiments described in this application, which are intended as illustrations of various aspects. Many modifications and variations can be made without departing from its spirit and scope, as will be apparent to those skilled in the art. Functionally equivalent methods and apparatuses within the scope of the disclosure, in addition to those enumerated herein, will be apparent to those skilled in the art from the foregoing descriptions. Such modifications and variations are intended to fall within the scope of the appended claims. The present disclosure is to be limited only by the terms of the appended claims, along with the full scope of equivalents to which such claims are entitled. It is to be understood that this disclosure is not limited to particular methods, reagents, compounds compositions or biological systems, which can, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular embodiments only, and is not intended to be limiting.
In an illustrative embodiment, any of the operations, processes, etc. described herein can be implemented as computer-readable instructions stored on a computer-readable medium. The computer-readable instructions can be executed by a processor of a mobile unit, a network element, and/or any other computing device.
There is little distinction left between hardware and software implementations of aspects of systems; the use of hardware or software is generally (but not always, in that in certain contexts the choice between hardware and software can become significant) a design choice representing cost vs. efficiency tradeoffs. There are various vehicles by which processes and/or systems and/or other technologies described herein can be effected (e.g., hardware, software, and/or firmware), and that the preferred vehicle will vary with the context in which the processes and/or systems and/or other technologies are deployed. For example, if an implementer determines that speed and accuracy are paramount, the implementer may opt for a mainly hardware and/or firmware vehicle; if flexibility is paramount, the implementer may opt for a mainly software implementation; or, yet again alternatively, the implementer may opt for some combination of hardware, software, and/or firmware.
The foregoing detailed description has set forth various embodiments of the devices and/or processes via the use of block diagrams, flowcharts, and/or examples. Insofar as such block diagrams, flowcharts, and/or examples contain one or more functions and/or operations, it will be understood by those within the art that each function and/or operation within such block diagrams, flowcharts, or examples can be implemented, individually and/or collectively, by a wide range of hardware, software, firmware, or virtually any combination thereof. In one embodiment, several portions of the subject matter described herein may be implemented via Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs), digital signal processors (DSPs), or other integrated formats. However, those skilled in the art will recognize that some aspects of the embodiments disclosed herein, in whole or in part, can be equivalently implemented in integrated circuits, as one or more computer programs running on one or more computers (e.g., as one or more programs running on one or more computer systems), as one or more programs running on one or more processors (e.g., as one or more programs running on one or more microprocessors), as firmware, or as virtually any combination thereof, and that designing the circuitry and/or writing the code for the software and or firmware would be well within the skill of one of skill in the art in light of this disclosure. In addition, those skilled in the art will appreciate that the mechanisms of the subject matter described herein are capable of being distributed as a program product in a variety of forms, and that an illustrative embodiment of the subject matter described herein applies regardless of the particular type of signal bearing medium used to actually carry out the distribution. Examples of a signal bearing medium include, but are not limited to, the following: a recordable type medium such as a floppy disk, a hard disk drive, a CD, a DVD, a digital tape, a computer memory, etc.; and a transmission type medium such as a digital and/or an analog communication medium (e.g., a fiber optic cable, a waveguide, a wired communications link, a wireless communication link, etc.).
Those skilled in the art will recognize that it is common within the art to describe devices and/or processes in the fashion set forth herein, and thereafter use engineering practices to integrate such described devices and/or processes into data processing systems. That is, at least a portion of the devices and/or processes described herein can be integrated into a data processing system via a reasonable amount of experimentation. Those having skill in the art will recognize that a typical data processing system generally includes one or more of a system unit housing, a video display device, a memory such as volatile and non-volatile memory, processors such as microprocessors and digital signal processors, computational entities such as operating systems, drivers, graphical user interfaces, and applications programs, one or more interaction devices, such as a touch pad or screen, and/or control systems including feedback loops and control motors (e.g., feedback for sensing position and/or velocity; control motors for moving and/or adjusting components and/or quantities). A typical data processing system may be implemented utilizing any suitable commercially available components, such as those typically found in data computing/communication and/or network computing/communication systems.
The herein described subject matter sometimes illustrates different components contained within, or connected with, different other components. It is to be understood that such depicted architectures are merely exemplary, and that in fact many other architectures can be implemented which achieve the same functionality. In a conceptual sense, any arrangement of components to achieve the same functionality is effectively “associated” such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as “associated with” each other such that the desired functionality is achieved, irrespective of architectures or intermedial components. Likewise, any two components so associated can also be viewed as being “operably connected”, or “operably coupled”, to each other to achieve the desired functionality, and any two components capable of being so associated can also be viewed as being “operably couplable”, to each other to achieve the desired functionality. Specific examples of operably couplable include but are not limited to physically mateable and/or physically interacting components and/or wirelessly interactable and/or wirelessly interacting components and/or logically interacting and/or logically interactable components.
With respect to the use of substantially any plural and/or singular terms herein, those having skill in the art can translate from the plural to the singular and/or from the singular to the plural as is appropriate to the context and/or application. The various singular/plural permutations may be expressly set forth herein for sake of clarity.
It will be understood by those within the art that, in general, terms used herein, and especially in the appended claims (e.g., bodies of the appended claims) are generally intended as “open” terms (e.g., the term “including” should be interpreted as “including but not limited to,” the term “having” should be interpreted as “having at least,” the term “includes” should be interpreted as “includes but is not limited to,” etc.). It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases “at least one” and “one or more” to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim recitation to embodiments containing only one such recitation, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an” (e.g., “a” and/or “an” should be interpreted to mean “at least one” or “one or more”); the same holds true for the use of definite articles used to introduce claim recitations. In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should be interpreted to mean at least the recited number (e.g., the bare recitation of “two recitations,” without other modifiers, means at least two recitations, or two or more recitations). Furthermore, in those instances where a convention analogous to “at least one of A, B, and C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). In those instances where a convention analogous to “at least one of A, B, or C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “ a system having at least one of A, B, or C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). It will be further understood by those within the art that virtually any disjunctive word and/or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase “A or B” will be understood to include the possibilities of “A” or “B” or “A and B.”
In addition, where features or aspects of the disclosure are described in terms of Markush groups, those skilled in the art will recognize that the disclosure is also thereby described in terms of any individual member or subgroup of members of the Markush group.
As will be understood by one skilled in the art, for any and all purposes, such as in terms of providing a written description, all ranges disclosed herein also encompass any and all possible subranges and combinations of subranges thereof. Any listed range can be easily recognized as sufficiently describing and enabling the same range being broken down into at least equal halves, thirds, quarters, fifths, tenths, etc. As a non-limiting example, each range discussed herein can be readily broken down into a second third, middle third and first third, etc. As will also be understood by one skilled in the art all language such as “up to,” “at least,” and the like include the number recited and refer to ranges which can be subsequently broken down into subranges as discussed above. Finally, as will be understood by one skilled in the art, a range includes each individual member. Thus, for example, a group having 1-3 cells refers to groups having 1, 2, or 3 cells. Similarly, a group having 1-5 cells refers to groups having 1, 2, 3, 4, or 5 cells, and so forth.
From the foregoing, it will be appreciated that various embodiments of the present disclosure have been described herein for purposes of illustration, and that various modifications may be made without departing from the scope and spirit of the present disclosure. Accordingly, the various embodiments disclosed herein are not intended to be limiting, with the true scope and spirit being indicated by the following claims.
This patent application is a continuation of U.S. patent application Ser. No. 12/604,290, filed Oct. 22, 2009, which is incorporated herein by reference.
Number | Date | Country | |
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Parent | 12604290 | Oct 2009 | US |
Child | 13867906 | US |