1. Field of the Disclosure
The disclosure relates to a multiuser multiple input multiple output (MU MIMO) system. Particularly, the disclosure relates to a channel information feedback method and an apparatus thereof used for beamforming and power allocation of a MU MIMO system.
2. Description of Related Art
With the development of wireless communication technology, multiple input multiple output (MIMO) systems are widely used to increase transmission capacity and transmission quality of communication systems. The MIMO system can support multiple users to achieve a multiuser MIMO (MU MIMO) system. However, in order to achieve better spatial multiplexing with a high transmission rate, a transmitting end (for example, a base station) has to perform optimal beamforming and power allocation according to channel state. Therefore, a receiving end (for example, a user end) has to measure channel state information (CSI) and feed back the CSI to the transmitting end.
The CSI of the MIMO system can be represented by a matrix having a plurality of complex elements (which is referred to as a CSI matrix hereinafter). The CSI matrix contains a large amount of information, and a magnitude of the information amount thereof relates to the number of antennas (including transmitting antennas and receiving antennas) and the number of users. Therefore, regarding a finite bit rate uplink channel, if the amount of information of the CSI matrix is too large, the uplink channel can be fully occupied.
Presently, some wireless communication standards adopt a codebook-based pre-coding method, by which the receiving end selects a mostly suitable pre-coding matrix from a codebook according to the measured CSI matrix, and feeds back an index thereof to the transmitting end, the transmitting end obtains the pre-coding matrix by looking up the codebook according to the index and pre-codes data to be transmitted, and then transmits data to the receiving end. The pre-coding method only uses a finite bit feedback index; however, by using the predetermined codebook, an optimal transmission performed in an environment with feeding back real-time channel state cannot be achieved, so that system performance is relatively poor.
Generally, the receiving end directly feeds back the CSI matrix, and the transmitting end calculates an optimal beamforming matrix according to the CSI matrix, so as to transmit data to the receiving end to achieve a better performance. A commonly used beamforming technique is a zero-forcing (ZF) beamforming technique, the ZF beamforming technique is used to prevent signals transmitted to a user end by the transmitting end from being influenced by signals transmitted to the other users. Such ZF beamforming technique only requires a direction part of the CSI matrix (which is referred to as a subspace matrix). The transmitting end receives the subspace matrix and performs optimal beamforming on the data to be transmitted, and accordingly transmits data to the receiving end.
The ZF beamforming technique does not require a magnitude part (which is referred to as a magnitude matrix) of the CSI matrix, so that the receiving end is only required to feed back the subspace matrix of the CSI matrix to the transmitting end. However, there are limitations on the number of antennas of the ZF beamforming technique, and when channels corresponding to two users are the same, the transmitting end can only transmit data to one of the users.
Moreover, non-ZF beamforming techniques or other types of the beamforming and power allocation techniques are also provided, and performance of some non-ZF beamforming technique is better than that of the ZF beamforming technique. However, these techniques all require the complete CSI matrix (including the direction part and the magnitude part), so that in case of the finite bit rate of the uplink channel, the receiving end generally uses vector quantization to quantize the whole CSI matrix, and feed back the quantized CSI matrix to the transmitting end.
In consistence with an exemplary embodiment of the disclosure, there is provided a channel information (CSI matrix) feedback method. The channel information feedback method is adapted in a receiving end of a multiuser multiple input multiple output (MU MIMO) system, and includes the following steps. A subspace matrix and a magnitude matrix related to a transmitting end of the MU MIMO system are obtained according to a channel matrix corresponding to the receiving end. A first quantization is performed on the subspace matrix to generate a quantized subspace matrix. A second quantization is performed on an auxiliary information matrix to generate a quantized auxiliary information matrix, where the auxiliary information matrix is related to the magnitude matrix and a residual subspace matrix, and the residual subspace matrix includes residual subspace information of the subspace matrix remained after the first quantization is performed on the subspace matrix. The quantized subspace matrix and the quantized auxiliary information matrix are fed back to the transmitting end through an uplink channel.
In consistence with an exemplary embodiment of the disclosure, there is provided a channel information feedback method. The channel information feedback method is adapted in a transmitting end of a multiuser multiple input multiple output (MU MIMO) system, and includes the following steps. Power allocation and beamforming are performed on multiple user data to be transmitted to a plurality of users of the MU MIMO system by the transmitting end according to a plurality of quantized subspace matrices and a plurality of quantized auxiliary information matrices received from a plurality of receiving ends of the MU MIMO system, so as to generate a transmitting signal. The transmitting signal is transmitted to the receiving ends. wherein each one of the receiving ends obtains a subspace matrix and a magnitude matrix related to the transmitting end according to a channel matrix corresponding to the receiving end, and performs a first quantization and a second quantization on the subspace matrix and an auxiliary information matrix to generate a quantized subspace matrix and a quantized auxiliary information matrix, the receiving ends feed back the quantized subspace matrices and the quantized auxiliary information matrices to the transmitting end through an uplink channel, wherein the auxiliary information matrix is related to the magnitude matrix and a residual subspace matrix, and the residual subspace matrix includes residual subspace information of the subspace matrix remained after the first quantization is performed on the subspace matrix.
In consistence with an exemplary embodiment of the disclosure, there is provided a channel information feedback apparatus. The channel information feedback apparatus is adapted in a receiving end of a multiuser multiple input multiple output (MU MIMO) system, and includes a transmitting end-related extractor device, a first quantizer, a second quantizer and a feedback signal transmitter. The transmitting end-related extractor device is configured for obtaining a subspace matrix and a magnitude matrix related to a transmitting end of the MU MIMO system according to a channel matrix corresponding to the receiving end. The first quantizer performs a first quantization on the subspace matrix to generate a quantized subspace matrix. The second quantizer performs a second quantization on an auxiliary information matrix to generate a quantized auxiliary information matrix, where the auxiliary information matrix is related to the magnitude matrix and a residual subspace matrix, and the residual subspace matrix has residual subspace information of the subspace matrix remained after the first quantization is performed on the subspace matrix. The feedback signal transmitter is configured for feeding back the quantized subspace matrix and the quantized auxiliary information matrix to the transmitting end through an uplink channel.
In consistence with an exemplary embodiment of the disclosure, there is provided a transmitting end. The transmitting end is configured in a multiuser multiple input multiple output (MU MIMO) system, and includes a feedback signal receiver, a power allocation device and a beamforming device. The feedback signal receiver is configured for receiving a plurality of quantized subspace matrices and a plurality of quantized auxiliary information matrices fed back by a plurality of receiving ends of multiple users of the MU MIMO system through an uplink channel. The power allocation device is configured for performing power allocation on multiple user data to be transmitted to the multiple users of the MU MIMO system by the transmitting end according to the quantized subspace matrices and the auxiliary information matrices. The beamforming device is configured for performing beamforming on the multiple power-allocated user data according to the quantized subspace matrices and the quantized auxiliary information matrices, so as to generate a transmitting signal to the receiving ends. wherein each one of the receiving ends obtains a subspace matrix and a magnitude matrix related to the transmitting end according to a channel matrix corresponding to the receiving end, and performs a first quantization and a second quantization on the subspace matrix and an auxiliary information matrix to generate a quantized subspace matrix and a quantized auxiliary information matrix, the receiving ends feed back the quantized subspace matrices and the quantized auxiliary information matrices to the transmitting end through the uplink channel, wherein the auxiliary information matrix is related to the magnitude matrix and a residual subspace matrix, and the residual subspace matrix has residual subspace information of the subspace matrix remained after the first quantization is performed on the subspace matrix.
In consistence with an exemplary embodiment of the disclosure, there is provided a multiuser multiple input multiple output (MU MIMO) system including a transmitting end and a plurality of receiving ends. The receiving ends are corresponding to multiple users of the MU MIMO system, where each one of the receiving ends includes a channel information feedback apparatus, and the channel information feedback apparatus includes a transmitting end-related extractor device, a first quantizer, a second quantizer and a feedback signal transmitter. The transmitting end-related extractor device is configured for obtaining a subspace matrix and a magnitude matrix related to the transmitting end of the MU MIMO system according to a channel matrix corresponding to the receiving end. The first quantizer performs a first quantization on the subspace matrix to generate a quantized subspace matrix. The second quantizer performs a second quantization on an auxiliary information matrix to generate a quantized auxiliary information matrix, where the auxiliary information matrix is related to the magnitude matrix and a residual subspace matrix, and the residual subspace matrix includes residual subspace information of the subspace matrix remained after the first quantization is performed on the subspace matrix. The feedback signal transmitter is configured for feeding back the quantized subspace matrix and the quantized auxiliary information matrix to the transmitting end through an uplink channel. The transmitting end includes a feedback signal receiver, a power allocation device and a beamforming device. The feedback signal receiver is configured for receiving the quantized subspace matrices and the quantized auxiliary information matrices through the uplink channel. The power allocation device is configured for performing power allocation on multiple user data to be transmitted to the multiple users of the MU MIMO system by the transmitting end according to the quantized subspace matrices and the quantized auxiliary information matrices. The beamforming device is configured for performing beamforming on the multiple power-allocated user data according to the quantized subspace matrices and the quantized auxiliary information matrices, so as to generate a transmitting signal to the receiving ends.
According to the above descriptions, the channel information feedback method and the apparatus thereof provided by the exemplary embodiments of the disclosure can be used in the MU MIMO system having a finite bit rate uplink channel, so that the transmitting end of the MU MIMO system can perform power allocation and beamforming on the user data to be transmitted to all of the users according to the fed back quantized CSI.
In order to make the aforementioned and other features and advantages of the disclosure comprehensible, several exemplary embodiments accompanied with figures are described in detail below.
The accompanying drawings are included to provide a further understanding of the disclosure, and are incorporated in and constitute a part of this specification. The drawings illustrate embodiments of the disclosure and, together with the description, serve to explain the principles of the disclosure.
Referring to
The receiving ends 11-1K may transmit quantized subspace matrices {circumflex over (T)}1-{circumflex over (T)}K and quantized auxiliary information matrices Ĝ1-ĜK to the transmitting end 10 through a finite bit rate uplink channel. Regarding k belonging to 1 to K, the receiving end 1k may extract a matrix {tilde over (H)}k related to the transmitting end from the channel matrix Hk, and decomposes the transmitting end-related matrix {tilde over (H)}k into a magnitude matrix Dk and a subspace matrix Tk (or a direction-related matrix). Then, the receiving end 1k respectively quantizes the subspace matrix Tk and an auxiliary information matrix Gk according to different quantization criterions to obtain the quantized subspace matrix {circumflex over (T)}k and the quantized auxiliary information matrix Ĝk, where the auxiliary information matrix Gk is related to the magnitude matrix Dk and information of a residual subspace matrix. Then, the receiving end 1k feeds back the quantized subspace matrix {circumflex over (T)}k and the quantized auxiliary information matrix Ĝk to the transmitting end 10 through the finite bit rate uplink channel. In other exemplary embodiments, the magnitude matrix Dk and the subspace matrix Tk can also be quantized according to a same quantization criterion.
By decomposing the channel matrix Hk (for example, using the singular value decomposition), the channel matrix Hk can be decomposed into a matrix Lk related to the receiving end and a matrix {tilde over (H)}k related to the transmitting end, i.e., Hk=Lk{tilde over (H)}k, where the matrix Lk related to the receiving end satisfies LkHLk=INr. Similarly, by decomposing the transmitting end-related matrix {tilde over (H)}k, the transmitting end-related matrix {tilde over (H)}k can be decomposed into a subspace matrix Tk and a magnitude matrix Dk, i.e., {tilde over (H)}k=DkTk, where the magnitude matrix Dk is a complex matrix of Nr×Nγ, and the subspace matrix Tk is a complex matrix of Nt×Nγ. The quantized auxiliary information matrix Ĝk is obtained by quantizing the magnitude matrix Dk and the information of the residual subspace matrix. Therefore, the transmitting end-related matrix {tilde over (H)}k can be regarded as being composed of the subspace matrix Tk and the auxiliary information matrix Gk, where the auxiliary information matrix Gk is a complex matrix of Nr×Nγ. The information of the residual subspace matrix is information of the remained direction matrix after the subspace matrix Tk is quantized.
The transmitting end 10 may perform power allocation and beamforming according to the quantized subspace matrices {circumflex over (T)}1-{circumflex over (T)}K and the quantized auxiliary information matrices Ĝ1-ĜK, the power allocation and the beamforming can be optimized power allocation and beamforming. The transmitting end 10 respectively multiplies user data x1-xk to be transmitted to the first to the Kth users by square root of powers √{square root over (P1)}-√{square root over (PK)} (which is referred to as powers below) to accomplish the power allocation, where the user data x1-xk are all complex matrices of Nr×1. Then, the transmitting end 10 further multiplies the user data x1-xk multiplied with the powers √{square root over (P1)}-√{square root over (PK)} by beamforming matrices U1-Uk to accomplish the beamforming. In this way, a transmitting signal transmitted by the transmitting end 10 can be represented as:
Regarding the receiving end 1k of a kth user, a receiving signal rk thereof can be represented as:
where, the receiving signal rk is a complex matrix of Nr×1, the noise matrix nk is a complex matrix of Nr×1. Then, the receiving end 1k performs a beamforming filtering to the receiving signal rk according to the channel matrix Hk, and the beamforming filtering can be an optimized beamforming filtering. The receiving end 1k multiplies the receiving signal rk by a beamforming filtering matrix VkH to obtain user data yk of the kth user, and the user data yk is represented as follows:
where, the user data yk is a complex matrix of Nr×1, the beamforming filtering matrix VkH is a complex matrix of Nr×Nr. Ideally, in case that the noises and interferences are all removed, the user data yk is equivalent to the user data xk.
The MU MIMO system 1 can be the long term evolution advanced technology (LTE-A) or the worldwide interoperability for microwave access (WiMAX) system that requires to feed back a large amount of channel state information (CSI). The receiving ends 11-1K can be mobile stations or user equipments, etc., and the transmitting end 10 can be a base station or a relay station, etc. Overall, types of the receiving ends 11-1K and the transmitting end 10 are not limited by the disclosure.
Referring to
In step S20, the measurement device 61 measures the channel matrix Hk of the kth user. In step S24, the bit allocator 66 obtains a bit number BT of the quantized subspace matrix {circumflex over (T)}K and a bit number BG of the quantized auxiliary information matrix ĜK, where a sum of the bit numbers BT and BG is equal to a quantized total bit number B, and the quantized total bit number B is a bit number allowed to be transmitted in the finite bit rate uplink channel The steps S24 and S20 can be simultaneously executed, or the step S24 can be executed before execution of the step S22. In another exemplary embodiment, if the MU MIMO system 1 has already defined the bit numbers BT and BG, the step S24 can be omitted. In another exemplary embodiment, the bit allocator 66 of the channel information feedback apparatus 6 can be removed, and the bit numbers BT and BG can be determined by the transmitting end 10, and information of the bit numbers BT and BG can be transmitted to the receiving end 1k through a reliable downlink channel.
Then, in step S21, the transmitting end-related extractor device 62 obtains the subspace matrix Tk and the magnitude matrix Dk related to the transmitting end according to the channel matrix Hk. Then, in step S22, the first quantizer 64 performs BT bit quantization on the subspace matrix Tk to generate a quantized subspace matrix {circumflex over (T)}K. In step S23, the second quantizer 65 performs a BG bit quantization on the magnitude matrix Dk and the information of the residual subspace matrix (i.e., quantization of the auxiliary information matrix Gk) to generate the quantized auxiliary information matrix ĜK.
In one exemplary embodiment, the objective is to quantize the subspace spanned by the columns of Tk, and {circumflex over (T)}K denotes the quantized subspace. The relation can be described as
where {circumflex over (T)}k{circumflex over (T)}kH={circumflex over (Q)}kH cos(Θk)QkH by SVD decomposition, and {circumflex over (T)}K is a Nt×Nr unitary matrix whose columns are orthogonal to those of Tk·cos(Θk)=diag{[cos θ1 . . . cos θN
In another exemplary embodiment, Gk as a Nt×Nr matrix shown below:
G
k=σn2({circumflex over (Q)}k cos(Θk)QkH)−HDk−2({circumflex over (Q)}k cos(Θk)QkH)−1
which contains the channel magnitude information and the remaining information of Tk after the subspace is quantized. Define ĜK as the quantized Ĝk, and ΔGk=Gk−Ĝk. Consequently, the channel feedback method of the disclosure decomposes the new CSI (Channel State Information) into two parts, Tk and Gk, then the Tk and the Gk are quantized as {circumflex over (T)}K and ĜK. As a result, the performance of user k with quantized CSI is given as follows:
where {circumflex over (B)}k={circumflex over (T)}k⊥ tan(Θk){circumflex over (Q)}kH is defined. The beamforming filters and power allocation matrices are denoted as Ûk and {circumflex over (P)}k for k=1, 2 . . . . K. In this way, only the quantization error of the spanned subspace is multiplied with power and affects the performance in different order depending on the power, though the error of Gk does not. Therefore, the channel information feedback method allocates the quantization bits to the two parts according to the system SNR adaptively.
In step S25, the feedback signal transmitter 63 feeds back the quantized subspace matrix {circumflex over (T)}K and the quantized auxiliary information matrix ĜK to the transmitting end 10 through an uplink channel. In step S26, the beamforming filter 67 performs beamforming filtering on the receiving signal rk according to the channel matrix Hk to obtain the user data yk of the kth user. The step S26 is executed after execution of the step S20.
Referring to both
In step S30, the bit allocator 74 obtains the bit number BT of the quantized subspace matrix {circumflex over (T)}K and the bit number BG of the quantized auxiliary information matrix ĜK. In another exemplary embodiment, if the MU MIMO system 1 has already defined the bit numbers BT and BG, the step S30 can be omitted. In another exemplary embodiment, the bit allocator 74 of the transmitting end 10 can be removed, and the bit numbers BT and BG can be determined by the receiving end 1k, and information of the bit numbers BT and BG can be transmitted to the transmitting end 10 through a reliable uplink channel.
Then, in step S31, the feedback signal receiver 71 forwards the received quantized subspace matrices {circumflex over (T)}1-{circumflex over (T)}K and the quantized auxiliary information matrices Ĝ1-ĜK to the power allocation device 72 and the beamforming device 73. The power allocation device 72 and the beamforming device 73 perform power allocation and beamforming on the user data x1-xk to be transmitted. The power allocation device 72 obtains information of the magnitude matrix Dk and the auxiliary information matrix Gk according to the quantized subspace matrices T1-TK, the quantized auxiliary information matrices Ĝ1-ĜK and the bit numbers BT and BG thereof, and accordingly allocates powers P1-Pk to the user data x1-xk. The beamforming device 73 obtains information of the magnitude matrix Dk and the auxiliary information matrix Gk according to the quantized subspace matrices {circumflex over (T)}1-{circumflex over (T)}K, the quantized auxiliary information matrices Ĝ1-ĜK and the bit numbers BT and BG thereof, and accordingly performs beamforming on the power-allocated user data √{square root over (P1)}x1-√{square root over (PK)}xk to generate a transmitting signal.
The step S21 of
Referring to
Referring to
The disclosure is not limited to the aforementioned exemplary embodiments, and in other embodiments, it is not necessary to find the transmitting end-related matrices {tilde over (H)}′k equal to the transmitting end-related matrix {tilde over (H)}k from the matrix look-up table, or find a plurality of the subspace matrices T′k and the magnitude matrices D′k corresponding to a plurality of the transmitting end-related matrices {tilde over (H)}′k closest to the transmitting end-related matrix {tilde over (H)}k from the matrix look-up table, and extrapolation and/or interpolation can be achieved through direct calculation. Namely, in the step S432, the extrapolation operation unit (and/or the interpolation operation unit) directly calculates whether the transmitting end-related matrices {tilde over (H)}′k equal to the transmitting end-related matrix {tilde over (H)}k exists, where if yes, the subspace matrix T′k and the magnitude matrix D′k corresponding to the transmitting end-related matrix {tilde over (H)}′k are directly output as the subspace matrix Tk and the magnitude matrix Dk; and if not, the extrapolation operation unit (and/or the interpolation operation unit) calculates a plurality of the subspace matrices T′k and a plurality of the magnitude matrices D′k corresponding to a plurality of the transmitting end-related matrices {tilde over (H)}′k closest to the transmitting end-related matrix {tilde over (H)}k, and outputs the calculating results as the subspace matrices Tk and the magnitude matrices Dk.
The disclosure is not limited to the aforementioned exemplary embodiments, and in other embodiments, it is not necessary to use the extrapolation operation unit (and/or the interpolation operation unit) to find the transmitting end-related matrices {tilde over (H)}′k equal to the transmitting end-related matrix {tilde over (H)}k in the matrix look-up table, or find a plurality of the subspace matrices T′k and the magnitude matrices D′k corresponding to a plurality of the transmitting end-related matrices {tilde over (H)}′k relatively closed to the transmitting end-related matrix {tilde over (H)}k in the matrix look-up table. Namely, in the step S432, it is found whether the transmitting end-related matrices {tilde over (H)}′k equal to the transmitting end-related matrix {tilde over (H)}k existing in the matrix look-up table, where if yes, the subspace matrix T′k and the magnitude matrix D′k corresponding to the transmitting end-related matrix {tilde over (H)}′k are directly output as the subspace matrix Tk and the magnitude matrix Dk; and if not, a plurality of the subspace matrices T′k and the magnitude matrices D′k corresponding to a plurality of the transmitting end-related matrices {tilde over (H)}′k closest to the transmitting end-related matrix {tilde over (H)}k are searched in the matrix look-up table, and the searching results are output as the subspace matrices Tk and the magnitude matrices Dk.
Referring to
The disclosure is not limited to the aforementioned exemplary embodiments, and in other embodiments, it is not necessary to find the channel matrix H′k equal to the channel matrix Hk in the channel matrix look-up table, or find a plurality of the subspace matrices T′k and the magnitude matrices D′k corresponding to the channel matrix H′k closest to the channel matrix Hk in the channel matrix look-up table, and extrapolation and/or interpolation can be achieved through direct calculation. Namely, in the step S441, an extrapolation operation unit (and/or an interpolation operation unit) is configured to directly calculate whether the channel matrix H′k equal to the channel matrix Hk exists, where if yes, the subspace matrix T′k and the magnitude matrix D′k corresponding to the channel matrix H′k are directly output as the subspace matrix Tk and the magnitude matrix Dk; and if not, the extrapolation operation unit (and/or the interpolation operation unit) calculates a plurality of the subspace matrices T′k and the magnitude matrices D′k corresponding to the channel matrix H′k closest to the channel matrix Hk, and outputs the calculating results as the subspace matrices Tk and the magnitude matrices Dk.
Referring to
Implementations of the step S24 of
Referring to
The disclosure is not limited to the aforementioned exemplary embodiments, and in other embodiments, it is not necessary to search whether the reference transmission power equal to the current transmission power exists in the bit allocation look-up table, and bit allocation can be achieved through direct calculation. Namely, in the step S521, the extrapolation and/or interpolation operation unit directly calculates according to the current transmission power the bit numbers BT and BG.
The disclosure is not limited to the aforementioned exemplary embodiments, and in other embodiments, it is not necessary to use the extrapolation and/or interpolation operation unit and the look-up table to obtain the bit allocation. Namely, in the step S512, it is directly found according to the current transmission power the bit numbers BT and BG.
Referring to
where, PmaxdB represents a current maximum transmission power, i.e., a maximum power (i.e., a current transmission power) that can be used by the transmitting end 10, currently. Generally, a sum of the powers P1-PK is equal to the power PmaxdB. Moreover, ΓSINR,q(bT,bG,PmaxdB) is defined as follows:
where, avg(SINRq,quanDL) represents an average of signal-to-noise ratios when the user data xk of the kth user is transmitted. Moreover, it should be noticed that when the signal-to-noise ratio is relatively great, only the subspace matrix Tk is quantized (BT=B) without quantizing the auxiliary information matrix Gk (BG=0). In other words, when the signal-to-noise ratio is relatively great (greater than a threshold of 20 dB), the quantized auxiliary information matrix ĜK is not fed back.
In summary, the channel information feedback method and the apparatus thereof provided by the exemplary embodiments of the disclosure can be used in the MU MIMO system having the finite bit rate uplink channel, so that the transmitting end of the MU MIMO system can perform power allocation and beamforming on the user data to be transmitted to all of the users according to the fed back quantized CSI.
It will be apparent to those skilled in the art that various modifications and variations can be made to the structure of the disclosure without departing from the scope or spirit of the disclosure. In view of the foregoing, it is intended that the disclosure cover modifications and variations of this disclosure provided they fall within the scope of the following claims and their equivalents.
Number | Date | Country | Kind |
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99146769 | Dec 2010 | TW | national |
This application claims the priority benefits of U.S. provisional application Ser. No. 61/329,096, filed on Apr. 29, 2010 and Taiwan application serial no. 99146769, filed on Dec. 30, 2010. The entirety of each of the above-mentioned patent applications is hereby incorporated by reference herein and made a part of this specification.
Number | Date | Country | |
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61329096 | Apr 2010 | US |