WO2012041425A1 - Power line communication system using beamforming - Google Patents

Power line communication system using beamforming Download PDF

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Publication number
WO2012041425A1
WO2012041425A1 PCT/EP2011/004118 EP2011004118W WO2012041425A1 WO 2012041425 A1 WO2012041425 A1 WO 2012041425A1 EP 2011004118 W EP2011004118 W EP 2011004118W WO 2012041425 A1 WO2012041425 A1 WO 2012041425A1
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Prior art keywords
codebook
communication device
precoder
unit
entries
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PCT/EP2011/004118
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French (fr)
Inventor
Andreas Schwager
Dietmar Schill
Lothar Stadelmeier
Daniel Schneider
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Sony Corporation
Sony Deutschland Gmbh
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Priority to EP10012403.1 priority
Application filed by Sony Corporation, Sony Deutschland Gmbh filed Critical Sony Corporation
Publication of WO2012041425A1 publication Critical patent/WO2012041425A1/en

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Classifications

    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B3/00Line transmission systems
    • H04B3/54Systems for transmission via power distribution lines
    • H04B3/542Systems for transmission via power distribution lines the information being in digital form
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; Arrangements for supplying electrical power along data transmission lines
    • H04L25/0202Channel estimation
    • H04L25/0204Channel estimation of multiple channels
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; Arrangements for supplying electrical power along data transmission lines
    • H04L25/0202Channel estimation
    • H04L25/024Channel estimation channel estimation algorithms
    • H04L25/0242Channel estimation channel estimation algorithms using matrix methods
    • H04L25/0248Eigen-space methods
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; Arrangements for supplying electrical power along data transmission lines
    • H04L25/03Shaping networks in transmitter or receiver, e.g. adaptive shaping networks ; Receiver end arrangements for processing baseband signals
    • H04L25/03891Spatial equalizers
    • H04L25/03898Spatial equalizers codebook-based design
    • H04L25/03942Spatial equalizers codebook-based design switching between different codebooks
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00Baseband systems
    • H04L25/02Details ; Arrangements for supplying electrical power along data transmission lines
    • H04L25/03Shaping networks in transmitter or receiver, e.g. adaptive shaping networks ; Receiver end arrangements for processing baseband signals
    • H04L25/03891Spatial equalizers
    • H04L25/03949Spatial equalizers equalizer selection or adaptation based on feedback
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00Arrangements affording multiple use of the transmission path
    • H04L5/003Arrangements for allocating sub-channels of the transmission path
    • H04L5/0048Allocation of pilot signals, i.e. of signals known to the receiver
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B2203/00Indexing scheme relating to line transmission systems
    • H04B2203/54Aspects of powerline communications not already covered by H04B3/54 and its subgroups
    • H04B2203/5404Methods of transmitting or receiving signals via power distribution lines
    • H04B2203/5416Methods of transmitting or receiving signals via power distribution lines by adding signals to the wave form of the power source
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B2203/00Indexing scheme relating to line transmission systems
    • H04B2203/54Aspects of powerline communications not already covered by H04B3/54 and its subgroups
    • H04B2203/5429Applications for powerline communications
    • H04B2203/5445Local network
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B2203/00Indexing scheme relating to line transmission systems
    • H04B2203/54Aspects of powerline communications not already covered by H04B3/54 and its subgroups
    • H04B2203/5462Systems for power line communications
    • H04B2203/5495Systems for power line communications having measurements and testing channel
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L5/00Arrangements affording multiple use of the transmission path
    • H04L5/0001Arrangements for dividing the transmission path
    • H04L5/0014Three-dimensional division
    • H04L5/0023Time-frequency-space

Abstract

A communication device (100) may store a codebook table containing a plurality of codebook entries, wherein each codebook entry includes predefined precoder values for each of at least two transmit paths of a transmission channel (300). On the basis of received feedback information, the communication device (100) selects that one from the codebook entries, whose precoder values approximate a perfect precoding matrix for beamforming transmit signals at best among the codebook entries. The communication device (100) may use the precoder values to construct a precoding matrix for beamforming its transmit signals.

Description

DESCRIPTION

POWER LINE COMMUNICATION SYSTEM USING BEAMFORMING

An embodiment of the present invention relates to a communications system using beamforming, wherein information describing a precoding matrix is fed back from a receiving communication device to a transmitting communication device. Further embodiments relate to communication devices and to methods for operating communication devices using beamforming.

Multiple-input multiple-output (MIMO) and multiple-input single-output communications systems (MISO) use beamforming for increasing bandwidth .

Embodiments described in EP 2019496 A l refer to a powerline communications system combining Eigenbeamforming with an adaptive orthogonal frequency division multiplex method, wherein channel state information is fed back from a receiving communication device to a transmitting communication device. Embodiments in EP 206 1 160 A l concern a precoding approach for powerline communications system without exchange of channel state information between the communication devices.

An object of the invention is to provide a wired communications system with enhanced data throughput, a communication device for such a communications system and a method of operating the communications system.

The object is achieved by the subject-matter of the independent claims. Further embodiments are defined in the dependent claims respectively. Details of the invention will become more apparent from the following description of embodiments in connection with the accompanying drawings, wherein features of the various embodiments may be combined unless they exclude each other.

Figure 1 is a schematic block diagram illustrating a wired MIMO communications system with two communication devices in accordance with an embodiment.

Figure 2A is a schematic block diagram illustrating a communication device with a decoder unit and a codebook control unit in accordance with an embodiment. Figure 2B is a schematic block diagram illustrating a communication device with a decoder unit and a codebook control unit using a look-up table in accordance with another embodiment. Figure 3A is a schematic diagram illustrating a codebook table with three precoder values per entry in accordance with an embodiment.

Figure 3B is a schematic diagram illustrating a codebook table with two precoder values per entry in accordance with another embodiment. Figure 4A is a schematic block diagram of a codebook control unit according to an embodiment providing a search through all entries of a codebook table.

Figure 4B is a schematic block diagram of a codebook control unit according to another embodiment including a quantizer unit and providing a search through only a subset of all entries of a codebook table. Figure 4C is a schematic block diagram showing the quantizer unit of Figure 4B in more detail.

Figure 5A is a schematic diagram showing a distribution of codebook entries in a two-dimensional coordinate system and values derived for each codebook entry on the basis of an equalizer matrix according to an embodiment. Figure 5B is a section of the diagram of Figure 5A for illustrating details of an embodiment referring to a codebook search based on a look-up table.

Figure 6A is a schematic block diagram illustrating a communication device with a precoder unit configurable by entries in a codebook table in accordance with an embodiment. Figure 6B is a schematic diagram of a sequence of sub-carriers for illustrating details of an embodiment referring to the interpolation of precoding matrices for sub-carriers between pilot sub-carriers assigned to codebook entries.

Figure 7 is a simplified flow chart illustrating a method of operating a communications system in accordance with further embodiments. Figure 1A shows a communications system 199. The communications system 199 is a wired communications system, for example xDSL (generic Digital Subscriber Line) or DVB-C2 (Digital Video Broadcasting-Cable). According to an embodiment, the communications system 199 is based on an OFDM (Orthogonal Frequency Division Multiplexing) modulation scheme. The communications system 199 may be a system using power distribution wires for data communication. For example, the communications system 199 is a power line communications (PLC), mains communications, power line telecommunications (PLT), broadband power line (BPL) or power band or power line networking (PLN) using a modulated carrier superimposed to the 50 or 60 Hz alternating current of the power lines respectively. The communications system 199 is, for example, a MIMO system with a first communication device 100 on the left hand side. The first communication device 100 includes a transmitter unit 1 10 employing one , two or more interface ports 101 . A second communication device 100 on the right hand side includes a receiver unit 120 employing at least one, for example two, three or four, interface ports 101 . A transmission channel 300 connects the transmitter unit 1 10 of the first communication device 100 on the left hand side and the receiver unit 120 of the second communication device 100 on the right hand side.

The first communication device 100 may be an exclusively transmitting device with the interface ports 101 configured exclusively as transmit ports. According to other embodiments, the first communication device 100 is a bidirectional device including, in addition to the transmitter unit 1 10, a receiver unit 120 which may be of the type of the receiver unit 120 in the second communication device 100, wherein some or all of the interface ports 101 may be bidirectional ports. The second communication device 100 may be an exclusively receiving device . According to other embodiments, the second communication device 100 is a bidirectional device including, in addition to the receiver unit 120 , a transmitter unit 1 10 which may be of the same type as the transmitter unit 1 10 in the first communication device 100, and wherein some or all of the interface ports 101 may be bidirectional ports. The communication devices 100 may be stand-alone devices or may be integrated in an electronic device for consumer applications, for example in a storage unit, a television set, an audio receiver, a video recorder, or in sensor devices like fire detectors.

The transmission channel 300 may be a multi-wire connection. In accordance with an embodiment the transmission channel is a power cable containing two or more electrical conductors used for transmission of AC (alternating current) electric power and installed as permanent wiring within buildings or buried in the ground . A plurality of m transmit signals tx define a transmit vector tm and a plurality of n receive signals ry define a reveive vector rn. For example, each of the transmitter units 1 10 may supply two differential transmit signals tx using the live or phase wire (L, P), the neutral wire (N), and protective earth (PE), wherein the differential transmit signals tx are modulated on a carrier superposing the AC frequency of the mains voltage. According to an embodiment, the receiver units 120 receive three differential receive signals between live wire and neutral wire, between neutral wire and protective earth, and between live wire and protective earth. According to another embodiment, the receiver unit 120 may receive the three differential receive signals and a common mode signal resulting from a leakage current from the wiring as a fourth receive signal. In a real transmission channel 300 the transmit signals tx interfere with each other, for example through capacitive coupling between the wires. In a channel matrix Hn m, which describes the receive vector rn as a function of the transmit vector tm, the entries of each line describe one of the receive signals ry in dependence of all transmit signals tx, wherein typically none of the entries h, j of Hn m is equal 0 when crosstalk occurs.

( 1 ) I"n = Hn m tm

For enhancing the signal-to-noise ratio (SNR) the principle of beamforming provides a decoupling of the receive signals by precoding the transmit vector with a precoding matrix Pm m such that after applying a suitable decoding scheme for the resulting equivalent channel matrix Hn m Pm m on the receiving side a diagonal matrix results and each decoded signal depends on only one single transmit signal.

For example, the receiving communication device 100 may comprise a channel estimator unit for determining the channel matrix Hn m describing the channel state information (CSI) of the transmission channel 300 by comparing a received training symbol sequence with a nominal training symbol sequence. Then singular value decomposition of Hn m may be used to obtain a suitable precoding matrix Pm m and a suitable decoding matrix. As shown in equation (2), singular value decomposition (SVD) decomposes the channel matrix Hn m in a first unitary marix Un n, the Hermitian transpose Vm m H of a second unitary matrix Vm m and a diagonal matrix Dn m, wherein the diagonal entries of Dn m are the singular values of the channel matrix Hn m.

(2) Hn m Un n Dn_m m m According to an embodiment, the receiving communication device 100 transmits feedback information containing information describing the second unitary matrix Vm m to the transmitting communication device 100. In accordance with an embodiment, the feedback information is transmitted via the transmission channel 300. In accordance with other embodiments, the feedback information is transmitted via an alternative transmission path. For example, an operator may configure the transmitting device on the basis of available channel state information during an installation phase of a communications system comprising the receiving and transmitting communication devices 100.

The feedback information may be a sequence of bits enclosed in a data section of a precoding initialisation message transmitted from the receiving communication device 100 to the transmitting communication device 100 during an installation period. The feedback information may also be included in a message sent by the receiving communication device 100 periodically or after the receiving communication device 100 has detected a significant change in the channel state information. According to an embodiment the feedback information is a binary number between 0 and 2n- l , where n is the number of bits used for coding the feedback information. The number of bits may be between 2 and 12. For example, the feedback information includes 5 , 6, 7, or 8 bits.

The transmitting communication device 100 comprises a precoder control unit configured to generate a precoding matrix on the basis of the feedback information. For example, the feedback information is an index identifying one of a plurality of entries of a table the transmitting communication device 10 stores in a memory unit and the precoder control unit uses precoder values assigned to the identified entry for obtaining the precoding matrix. Each codebook entry may contain at least one precoder value for each interface port used for simultaneous transmission of transmit signals.

From the precoder values addressed by the index contained in the feedback information, the precoder control unit obtains a precoding matrix that at least approximates the second unitary matrix Vm m and uses the approximated second unitary matrix Vm m as precoding matrix Pm m. Then equation (3 ) describes the receive vector rn received by the receiver unit 220:

Figure imgf000007_0001

In equation (3 ) the channel matrix Hn m can be replaced by its SVD description in equation (2): (4) rn = Un.n Dn,m Vm, m H m.m tm

The product of a unitary matrix and its Hermitian transpose is the identity matrix. Decoding the receive vector using the Hermitian transpose Un n H of the first unitary matrix Un n results in a decoded receive vector yn: f v - T T

*^-i*l^ J n ~~ ^ n . nH n w n . n n '-'n . m v v m . mH v m. m t Lm (6) y„ = Dn m tm

With regard to the decoded receive vector yn, the transmission channel 300 is decomposed into a set of parallel and independent paths.

Typically, the described precoding/ decoding scheme uses beamforming for decomposition of interfering signals in order to increase signal-to-noise ratio of payload data. The beamforming precoding/ decoding scheme may be applied to the payload data exclusively. According to other embodiments, the beamforming precoding/ decoding scheme may be applied also for the transmission of synchronization data and training symbols. Figure 2A shows a receiving communication device 100 including a receiver unit 120 in more detail. The communication device 100 receives receive signals at one, two, three , four or more interface ports 101 . According to an embodiment, each interface port 101 includes wire connectors, for example, connectors to a communications wiring or to an electric power wiring. According to an embodiment, the communication device 100 may have three interface ports 101 each of them configured to receive differential signals between the live and neutral wires, or between the live wire and protective earth, or between the neutral wire and protective earth. According to another embodiment, the communication device 100 further comprises a fourth interface port configured to receive a common mode signal caused by a leakage current.

The receiver unit 120 recovers from the at least one receive signal at least a first transmit signal transmitted to the receiving communication device 100 via a transmission channel connecting the receiving communication device 100 with a transmitting communication device with which the receiving communication device 100 establishes a communication link, for example a point-to-point communication link. The receiver unit 120 may include an input signal processing unit 12 1 that may condition and sample analogue receive signals to obtain one or more, for example two, digital receive signals. The signal levels of the receive signals may be adjusted in response to information included in the received signals. According to an embodiment, the input signal processing unit 12 1 may transform the digital receive signals into the frequency domain, wherein for each digital receive signal a digital data stream is generated. Amplitude and phase information may be obtained from the receive signals for further adjusting the signal levels. In embodiments referring to multi-carrier transmission techniques, the input signal processing unit 12 1 may use OFDM to decompose , in the frequency domain, each data stream into orthogonally modulated components. According to an embodiment, synchronization information included in the receive signals may be used for the demodulation.

The communication device 100 includes a channel estimation unit 150 that estimates the channel state information, for example on the basis of training symbols contained in the receive signals. The channel estimation unit 150 may compare selected symbols included in a receive signals burst with an equivalent nominal signal. Typically, a predefined set of training symbols is known at both the transmitter and the receiver side and the training symbols are selected for channel estimation. Based on the result of the comparison the channel estimation unit 150 may determine the channel matrix Hn m. The channel estimation unit 150 may calculate the channel matrix Hn m or may select, from a plurality of predefined channel matrices, that one that models best the actual transmission channel.

The channel estimation unit 150 may further forward the channel state information or information derived from the channel state information to a codebook control unit 183. Based on the received channel state information, the codebook control unit 183 consults a table stored in a codebook memory unit 188 for generating a feedback information for the transmitter side. The table may be of the type of a look-up table and is denoted as codebook table in the following. Accordingly, an entry in the codebook table is denoted as codebook entry in the following. The feedback information may be a binary value representing an index identifying a matching entry in the codebook table, wherein precoder values identified by the matching entry represent or at least approximate the perfect precoding matrix. An index referring to an entry in the codebook table is denoted as codebook index in the following. According to an embodiment the feedback information represents a codebook index determining a codebook entry that, among all entries in the codebook table, approximates the second unitary matrix Vm.m at best. In the receiving communication device 100, the stored codebook table may be used for determining the codebook index to be transmitted to the transmitting communication device with which the receiving communication device establishes a communication link. In the transmitting communication device , the same codebook table is stored. The transmitting communication device determines the precoding matrix by using the received codebook index for accessing a corresponding entry in its own codebook table. The communication device 100 may use the same codebook table from the same codebook memory unit 188 both, as receiving device , for determining the codebook index and, as transmitting device , for generating the precoding matrices on the basis of received codebook indices.

The receiving communication device 100 may include an output unit that outputs the codebook index identifying the matching entry. According to an embodiment, the output unit is a transmitter unit 1 10 configured to output the codebook index via at least one of the interface ports 101 . These outbound transmit signals may be balanced to the receive signals with respect to frequency range , modulation method and transmit power, in other words, the outbound transmit signals may use the same frequency range, the same modulation techniques and almost the same transmit power as the transmit signals transmitted by the transmitting communication device with which the communication device 100 establishes a communication link. The channel estimation unit 150 may further provide information required for determining or directly describing the first unitary matrix Un n to a decoder control unit 189.

The decoder control unit 189 receives information for determining the decoding matrix, which is, for example, the Hermitian transpose Un n H of the first unitary matrix Un n, and configures a decoder unit 124 in the receive path of the receiver unit 120 accordingly.

The decoder unit 124 decodes the receive signals according to the beamforming scheme as discussed above to generate the decoded receive signals. The decoder unit 1 24 is defined be coefficients derived from the decoding matrix. The decoder unit 124 is programmable to realize different decode matrices. For example, during a learning phase , the decoding matrix may be selected to realize an equalizer or detection function for detecting the transmitted MIMO paths, for example a zero forcing receiver. During an operational phase, the decoding matrix may be approximately equal to the Hermitian transpose Un n H of the second unitary matrix Un n.

Demodulators 127 may demodulate each of the data streams output by the decoder unit 124. The demodulators 127 may be quadrature amplitude demodulators generating a demodulated data signal, which may be output to a demultiplexer unit 1 28 that combines the demodulated data signals to one, two or more data streams which are transmitted to a control unit 190 for further processing. Figure 2B refers to details of an embodiment of a receiver unit 120 of a communication device 100. The illustrated embodiment refers to a transmitting communication device (not shown) driving two transmit signals, and a receiving communication device 100 receiving two or more, for example three or four, receive signals via interface ports 101 . An input signal processing unit 12 1 samples the analogue receive signals and may output an equivalent number of digital receive signals, wherein the signal levels of the receive signals may be adjusted in response to information derived from the receive signals. The input signal processing unit 12 1 may further Fourier transform the digital receive signals into the frequency domain, wherein a digital data stream is generated for each digital receive signal, and may use OFDM to decompose , in the frequency domain, each data stream into orthogonally modulated components , wherein synchronization information included in the receive signals may be used for the demodulation.

According to an embodiment, the input signal processing unit 12 1 may output the resulting data streams to an equalizer unit 122 performing a channel equalizing using the Q and R matrices obtained by a QR decomposition of the channel matrix. The equalizer unit 122 may output the equalized data streams to a decoder unit 124. According to another embodiment, no channel equalization is performed and the input signal processing unit 12 1 may directly output the resulting data streams to the decoder unit 124. The decoder unit 124 decodes the data streams using a decoder matrix UH. A demodulator unit 129 may perform a QAM demodulation that may or may not use tonemap information derived from the channel state information and recombines the two or more receive signals to a resulting receive signal. A forward error correction may be performed that u ses included code redundancy for detecting and correcting data errors.

The channel estimation unit 150 may be configured to determine the parameters of a channel matrix H describing attenuation and mutual effects between the receive signals. The channel estimation unit 150 may perform a singular value decomposition to obtain the decoder matrix UH for the decoder unit 124. According to another embodiment, a decoder control unit 189 may use information delivered from the channel estimation unit 150 to determine the decoder matrix UH, for example by singular value decomposition of the channel matrix H . A pseudo inversion unit 182 may use information obtained by the channel estimation unit 150 to determine coefficients of the equalizer unit 122 , for example by a QR decomposition of the channel matrix H . Further, the information obtained by the channel estimation unit 150 may be used, directly or indirectly, for generating a codebook index that identifies, in a codebook table, a codebook entry with precoder values with which the perfect precoder matrix V can be approximated at best among all codebook entries. The channel estimation unit 150 may supply the channel matrix H, or in the case of an embodiment including a pseudo-inversion unit 182 the pseudo-inversion unit 182 may supply the orthogonal matrix Q and / or the upper triangle matrix R or a derivative of at least one of them, for example R" 1 to a codebook control unit 183. Based on the received information, the codebook control unit 183 generates a binary value representing the codebook index, wherein the codebook index identifies a matching entry in the codebook table stored in a codebook memory unit 188. Precoder values identified by the matching entry at least approximate the perfect precoding matrix for the transmitter side at best among all codebook entries. According to an embodiment the codebook index identifies an entry in the codebook table that represents or approximates the second unitary matrix V.

The codebook control unit 183 includes a codebook search unit 183a that may search all entries of the codebook table stored in the codebook memory unit 188 for the best matching entry. In accordance with an embodiment, the codebook control unit 183 contains a look-up table memory unit 183b and the codebook search unit 183a selects a subset of codebook indices assigned to one of the entries of a look-up table stored in the look-up table memory unit 183b for the search for the best matching entry in the codebook table. The tables of Figure 3A and 3B refer to embodiments of the codebook table for a MIMO scheme with two transmit ports, for example an in-home PLC system using two transmit ports. The number of available MIMO data streams depends on the number of receive ports. A commu nication devices with at least two receive ports allows support of two MIMO streams where different symbols are transmitted via the two transmit ports. In this case, the precoding matrix is a 2x2 matrix with column vectors V] and V^ :

(7) y = [v, v2 ] The perfect precoding matrix V decomposes the MIMO channel into two independent logical MIMO streams where the first path is stronger and provides better SNR than the second path. The columns of the perfect precoding matrix V might be toggled to change the two logical MIMO paths, wherein then the second path would be stronger than the first one .

For embodiments where the receiving communication device comprises only one receive port or only a simplified decoder supporting not more than one receive stream , for example where spot beamforming is used, the precoding matrix V shrinks to a 2x 1 precoding vector

(8) V = [ l ] and the elements of the precoding vector V| describe the precoding matrix V completely. Where V is a 2x2 matrix and the transmitting communication device uses two transmit ports with Vj and being orthogonal the second column vector V>2 can be derived from the elements Vj and V2 of the first column vector

Figure imgf000013_0001
a consequence of the properties of the precoding matrix V, Vj is a real fficient, whereas V2 is a complex coefficient:

( 10) V2 = v2| - e p( <p2 )

The absolute value of V2 depends on Vj

Figure imgf000013_0002

In other words, j and the phase angle 2 °f ^2 suffice to determine V2. The parameters Vj and 2 completely describe the 2x1 precoding vector V and the 2x2 precoding matrix V for the above described cases.

Figure 3A refers to a codebook table 3 10 with m entries 305 identifying predefined precoding matrices on the basis of three real-valued parameters Vj , Re V2 }-, and \m.\ V2 }-. Based on a received codebook index and without further calculations a transmitting communication device has direct access to all values of that one of the predefined precoding matrices that fits best with the perfect precoding matrix. Figure 3B refers to a codebook table 320 having a codebook length m and containing m entries 305 identifying predefined precoding matrices on the basis of only two real-valued parameters Vj and A transmitting communication device may calculate the parameter V from the precoder values of a codebook entry 305 identified by a received codebook index in order to generate that one of the predefined precoding matrices that fits best with the perfect precoding matrix. Since the codebook table 320 includes only two real-valued parameters per entry the codebook table 320 requires less memory space than the codebook table 3 10 of Figure 3A.

The codebook length m determines the minimum number of data bits assigned to a codebook index information transmitted from the receiving communication device to the transmitting communication device. For example , a codebook length m of 32 , 64, 1 28 , 256 entries require at least five , six, seven or eight data bits for the codebook index information. The codebook index information may directly give the binary value of the corresponding entry.

From the values Vj and a precoder control unit in the transmitting communication device may construct the precoding matrix or the precoding vector V according to one of equations ( 12 ) or ( 13)

Figure imgf000014_0001

In accordance with an embodiment, the codebook entries predefine precoding matrices based on u niformly distributed precoding vectors pointing on equidistantly arranged coordinate points in a codespace with linearly scaled axes. In accordance with other embodiments, the codebook entries predefine precoding matrices depending on properties of the expected channels. For example , the codebook table may be designed on the basis of statistically evaluated properties of real transmission channels. For example, the codebook table includes the first and at least one of the second, third and fourth columns of one of the codebook tables defined in tables 1 to 6. According to another embodiment, each commu nication device may adaptively improve its codebook table by a self- training process.

According to other embodiments the codebook table may be designed to optimize both Vj and the orthogonal V2 simultaneously such that a codebook search algorithm searching a codebook table for a codebook entry that fits best with the respective perfect precoding matrix may check which one of the predefined precoding vector is closest to either the first column vector Vj or the second column vector V - For example , the codebook table includes the first and at least one of the second, third and fourth column of one of the codebook tables defined in tables 7 to 1 2.

According to an embodiment, uniformly distributed codebook may be defined for the cases the orthogonal vectors are included or not included . The exclusion of the orthogonal vectors may allow maximizing the SNR always on the one and the same transmission path .

In accordance with an embodiment , the codebook table contains an entry (A) as follows:

(A)

Figure imgf000015_0001

In this case , the precoding matrix is the identify matrix and no precoding is performed . A spatial multiplexing MIMO approach can be applied .

In accordance with another embodiment, the codebook table in addition or in the alternative, contains an entry (B ) as follows :

(B )

Figure imgf000015_0002

In this case, the logical MIMO paths are flipped. Apart from that no fu rther precoding is performed and a spatial multiplexing MIMO approach can be applied .

In accordance with a further embodiment , the codebook table in addition or in the alternative contains an entry (C) as follows:

Figure imgf000016_0001

In this case, a MISO approach is applied where only one symbol is transmitted and energy is uniformly distributed among the two transmit ports.

According to an embodiment, the precoding scheme is applied to a communications system using a single-carrier approach. According to other embodiments, the precoding scheme is embedded in a multi-carrier approach, for example in a communications system using OFDM, wherein a transmitting communication device comprises a precoder unit configured to precode multi- carrier signals and the receiving communication device comprises a decoder unit configured to decode multi-carrier signals.

Figure 4A refers to an embodiment of a codebook control unit 183 that is assigned to a codebook memory unit 188 storing a codebook table whose entries may have, for example , two independent precoder values respectively. By using one of the equations ( 12) or ( 13) the codebook table with two precoder values per entry allows constructing a precoding matrix that approximates the perfect precoding matrix V for a transmitting communication device that is adapted to send two transmit signals simultaneously.

The codebook control unit 183 makes use of the fact that in the receiver unit the SNR after equalization depends on both the equalizer matrix and the applied precoding matrix, if a zero-forcing receiver is used. Therefore, from the equalizer matrix, a parameter w (or w l and w2 for the different logical MIMO paths) reflecting the SNR can be derived for each precoding matrix predefined in the codebook table. Thereby the maximum value for the respective parameter w, w, , w2 represents that one of the predefined precoding matrices that, when applied to the channel, results in the lowest SNR.

A parameter calculation unit 410 receives values defining the channel matrix H or a derivative of it, for example, the equalizer matrix or a derivative of the equalizer matrix. If zero-forcing detection is applied, the equalizer matrix is the pseudo- inverse matrix of the channel matrix H, wherein the pseudo-inverse matrix may be obtained by a QR decomposition of the channel matrix H into the orthogonal matrix Q and the upper triangular matrix R. According to an embodiment the parameter calculation unit 410 receives values defining the inverse matrix R 1 of the upper triangular matrix R as input. According to other embodiments, for example such embodiments providing no equalization or no QR decomposition for other purposes, the full equalizer matrix may be used as input.

From the equalizer matrix or the matrix R" 1 the parameter calculation unit 410 calculates parameters P I , P2 and P I 2 that describe the actual channel.

From the parameters P I , P2 and PI 2 a search index unit 490 calculates the parameter w l for predetermined codebook entries of a codebook table stored in the codebook memory unit 188 thereby recording that codebook index identifying that codebook entry which, when combined with the parameters P I , P2, P 12 result in the minimum value for the parameter w l . The search index unit 490 outputs the recorded codebook index Codelnd. According to an embodiment, the search index unit 490 calculates the parameter w l for all codebook entries. According to other embodiments, the search index unit 490 calculates the parameter w l for a preselected subset of all codebook entries.

In Figure 5A black squares 502 represent the predefined precoding matrices defined by their precoder values V j and cp2 in an orthogonal coordinate system 500 with V j plotted against horizontal axis and φ2 plotted against the vertical axis. Contour lines 55 1 , 552 show lines connecting value pairs V j and cp2 resulting in the same value for | w l | 2, wherein dark contour lines 55 1 indicate high values and bright contour lines 552 indicate low valu es for | w l | 2. In multi- carrier systems, the contour lines 55 1 , 552 vary for different channels. The illustrated codebook table contains 128 entries. The bright squares 504 refer to values ψ2 ± 1 ' l .

The codebook control unit 183 of Figure 4A outputs the codebook index Codelnd identifying the codebook entry closest to the perfect precoding matrix, which is denoted by a diamond 506 in Figure 5A. A six-pointed star 508 indicates the perfect orthogonal precoding matrix.

Figure 4B refers to an embodiment of a codebook control unit 183 where the search index unit 490 processes and checks only a subset of all codebook entries. To this purpose, the codebook control unit 183 comprises a look-up table memory unit 183b storing a look-up table, wherein each entry of the look-up table is assigned to one of a plurality of possible combinations of quantized precoder values . Each look-up table entry contains a predefined number of codebook indices, wherein the predefined number of codebook indices is smaller than the total number of codebook entries . According to an embodiment the predefined number of codebook indices is between two and twelve , for example four. Each look-up table entry contains codebook indices identifying codebook entries with precoder values nearest to the combination of quantized precoder values the respective look-up table is assigned to. The codebook search u nit 183a includes a coarse quantizer u nit 450 receiving at least a subset of the parameters P I , P2 and P I 2 , for example the parameters P I and P 1 2. On the basis of these parameters the coarse quantizer unit 450 calculates a quantized version of the perfect precoding matrix with a coarse quantization to obtain a combination of quantized precoder values v 1 Q and p2Q, wherein the combination of quantized precoder values v i g , φ represents the coarsely quantized perfect precoding matrix.

The combination of quantized precoder valu es identifies that one of the entries of the look- up table that contains codebook indices that identify entries of the codebook table representing those predefined precoder matrices closest to the quantized perfect precoder matrix. The coarse qu antizer unit 450 selects , in the look-up table memory unit 183b, that one of the look-up entries that is addressed by the obtained combination of quantized precoder values . The look-up table memory unit 188 returns a predefined number of selected codebook indices identifying that codebook entries closest to the coarsely quantized perfect precoding matrix. The coarse quantization unit 450 outputs the selected codebook indices to the search index unit 490. The search index unit 490 performs the calculation of the parameter w l and the search for the codebook index identifying the codebook table entry with the minimum value for the parameter w l only for the codebook entries identified by the selected codebook indices .

Figu re 4C shows details of an embodiment of the coarse quantizer unit 450. A first subu nit 45 1 may derive angle information φ and an absolute value of a parameter P 12 received from the parameter calculation unit 4 10. From the angle information φ a second subunit 452 derives a quantized angle ^2Q - From the absolute value of P 1 2 and another parameter P I output by the parameter calculation unit 410 , a third subunit 453 derives a quantized precoding value Vj g . With the quantized values (p2Q anc* VI Q αειϊη1ηβ a quantized perfect precoding matrix VQ , the coarse quantization unit 450 identifies an entry in the look-up table 183b. Each entry of the look-up table 183b contains a predefined number, for example four, of binary values (codebook indices) representing codebook entries defining predefined precoding matrices close to the quantized perfect precoding matrix Vg. The look-up table 183b contains for each possible quantized precoding matrix VQ a subset of codebook indices, wherein the codebook indices identify a codebook entry representing those predefined precoding matrices which are closest to the quantized precoding matrix VQ.

In accordance with an embodiment where the receiving communication device applies singular value decomposition, the receiving communication device may calculate the precoder values of the perfect quantized precoding matrix directly. Then the precoder values of the perfect quantized precoding matrix may be used for accessing the look-up table 183b and the coarse quantization unit 450 may be omitted.

Figure 5B shows a section of Figure 5A in more detail. A black diamond 506 marks the position of the perfect precoding matrix. Crosses 522 mark the positions of possible quantized precoder values. A five-pointed star 524 marks the position of the coarsely quantized perfect precoding matrix which maps on one of the positions for the possible quantized precoder values. Filled squares 526 mark four codebook entries contained in the look-up table entry identified by the coarsely quantized perfect precoding matrix marked by the five-pointed star 524.

The precoder values contained in these four codebook entries are checked with regard to the parameter w l . The search over these four codebook entries provides the codebook entry marked by the filled square with the number one as identifying a codebook entry representing the best approximation for the (non- quantized) perfect precoder matrix available in the codebook table . The codebook control unit outputs the codebook index identifying this codebook entry as resulting codebook index Codelnd.

For comparison, the numbered circles 528 show the order of the codebook entries approximating the perfect precoder matrix at best (number 1 ), second best (number 2 ) and so on.

Figure 6A refers to an embodiment concerning the transmitting side . A communication device 100 includes a transmitter unit 1 10. A data source, for example a controlling unit of the communication device 100, outputs a primary data stream, which contains payload data, to an editing unit 1 1 1 of the transmitter unit 1 10. The editing unit 1 1 1 may insert code redundancy according to an error detection scheme for facilitating error correction at the receiver side. The editing unit 1 1 1 may split up the primary data stream into at least two complementary data streams or multiplies, for example doubles, the data stream in two or more identical data streams. According to an embodiment, the editing unit 1 1 1 may insert in each of the output data streams training symbols and/ or synchronization sequences. According to other embodiments, training symbols and synchronization sequences are inserted into the precoded data stream later.

A modulator unit 1 12 receives and modulates each data stream output by the editing unit 1 1 1 , for example by using a plurality of sub-carriers and QAM (quadrature amplitude modulation), respectively. The modulator unit 1 12 may use constellation data describing frequency dependent channel characteristics for adapting the QAM scheme accordingly. A constellation control unit 18 1 may derive the constellation data ConDat from feedback information which may be received, for example , via a receiver unit as described with regard to Figures 2A and 2B.

A precoder unit 1 14 precodes the modulated data signals using a precoding matrix or precoding vector V provided by a precoder control unit 184. The precoder control unit 184 may configure parameters of the precoder unit 1 14. For example, the precoder control unit 184 may provide the precoding matrix or vector V on the basis of a codebook index information received, for example, via the receiver unit. According to an embodiment the precoder control unit 184 receives a binary value identifying an entry in a codebook table stored in a codebook memory unit 188. The codebook table returns precoder values from which the precoder control unit 184 derives a precoding matrix or vector which matches best the perfect precoding matrix or vector. For example, the codebook table returns the parameters v , and φ2 · From Vj and cp2 , the precoder control unit 184 may calculate Re-j

Figure imgf000020_0001
Then the precoder control unit 184 may construct the precoding matrix or vector V on the basis of the equations ( 12) or ( 13). A finalizing unit 1 19 of the transmitter unit 1 10 may modulate the precoded modulated data streams on a frequency carrier using, for example, OFDM. The finalizing unit 1 19 may combine the orthogonal signals and performs an inverse Fourier transformation for obtaining digital output signals describing the transmit signals in the time domain, converts the digital output signals in analogue transmit signals, and couples each analogue transmit signal to a corresponding interface port 101 . The precoder unit 1 1 4 and the precoder control unit 1 84 may be adapted to apply different precoding matrices to different sub-carriers . According to an embodiment the precoder control unit 184 receives one codebook index for each sub-carrier and applies for each sub-carrier the corresponding precoding matrix. According to another embodiment each codebook entry is assigned to a plurality of sub-carriers and the precoder control unit 184 controls the precode u nit 1 1 4 to apply the same precoding matrix for a predefined number of neighbouring sub - carriers in the vicinity of a pilot sub-carrier for which the respective predefined precoding matrix has been selected such that overhead resulting from the feedback of the codebook indices is reduced. For example , the precoder control unit 184 may use the same codebook index for all sub-carriers included in a group of neighbouring sub-carriers.

According to a further embodiment codebook indices are transmitted for pilot sub - carriers representing a subset of all available sub- carriers and the precoder control unit 184 interpolates the values of precoding matrices for the sub-carriers between the pilot sub-carriers for obtaining better matching precoding matrices at low feedback overhead.

Figure 6B refers to an embodiment providing interpolation of precoding matrices . Figure 6B shows pilot sub-carriers 602 for which the respective codebook index is known to the precoder control u nit and further sub- carriers 604 for which no codebook index is transmitted. According to an embodiment the pilot sub-carriers are distributed uniformly. With N sub-carriers in total and K pilot sub-carriers , the number of sub-carriers between two successive pilot sub-carriers is N/ K- l .

The precoder control unit calculates a subspace angle between the pilot sub- carriers . With V] (c) representing the precoding vector of the c -th pilot sub- carrier, equation ( 1 4) gives the subspace angle for the first two pilot sub-carriers : ( 14) cp =

Figure imgf000021_0001

The calculation for the other pilot sub-carriers and sub-carriers is similar and can be derived from equation ( 14) simply by selecting the respective sub -carrier indices. With equation ( 1 4) , \≤m≤ N I K— 1 , and V°r'h being the orthogonal vector to V| according to e . g. the calculation of the second column in equations ( 1 2 ) and ( 13) , a precoding vector for a sub-carrier m between the pilot sub- carriers may be calculated on the basis of equation ( 1 5 ):

( 1 5 ) Vj (m) = v, (0) * cos(m * φ) - v°r (0) * sin(m * p)

Typically the first entry νλ of an interpolated precoding vector Vj is not real- valued. Accordingly the precoder control unit may derive such precoding matrices that are based on interpolated values for V ! and φ2 on the basis of equations ( 16 ) and ( 1 7) below. According to another embodiment, the interpolated precoding vectors Vj may be phase-rotated in the way that V j becomes real-valued such that the precoder control unit can construct the precoding matrices on the basis of equations ( 1 2) and ( 13 ).

Figure imgf000022_0001

According to the described embodiment, a pilot sub-carrier is a sub-carrier used for interpolation. The codebook index of this sub-carrier is fed back from a receiving communication device to a transmitting communication device. On the basis of equations ( 1 4) and ( 15) , the transmitting communication device interpolates the beamform vectors of sub-carriers for which no codebook index information is fed back, i.e the sub-carriers in between the pilot sub-carriers.

Elements of the above described embodiments, for example the precoder and decoder units, the precoder and decoder control units, the codebook control unit and sub-units of these units may be embodied in various forms by hardware only, for example by integrated circuits, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs) or digital signal processors (DSPs), by software only, which is implemented, for example, in a DSP or a computer program , or by a combination of hardware and software.

According to a method of operating a communications system like a PLC system, evaluation of the beamform vectors is part of a channel estimation procedure. Similar to the bit loading of the carriers, different beamform vectors could be used at different times within an AC line cycle period. The codebook index may be transmitted from a receiving communication device to a transmitting communication device in a new type of message or may be integrated in an existing type of message . According to an embodiment, the codebook index is sent in a message of the type CM CHAN EST.IND (Channel Estimation Indication message sent to or from a Connection Manager).

The new or adapted existing message may include further information , for example a dedicated information bit or flag for indicating that an operation mode called Spot Beamforming will or shall be applied.

With Spot Beamforming the 2nd of two logical MIMO paths does not carry information. All physical transmitting paths are used to apply Spot-Beamforming. According to an embodiment Spot Beamforming may be applied if the receiving communication device is connected to an outlet where additional MIMO paths are not available, for example, where only live and neutral wires are connected. Alternatively, Spot Beamforming may be applied where the SNR on most carriers on the 2nd transmission path is very low such that few or no information can be transported via the 2nd logical path. Alternatively, Spot Beamforming may be applied where the receiver modem is a low cost implementation with only one logical reception path or only one decoder included. According to an embodiment the message of the type CM CHAN EST.IND includes an information bit indicating that Spot Beamforming shall or will be used. According to another embodiment a receiving communication device performing a channel estimation of a transmission channel connecting the receiving communication device with a transmitting communication device with which the receiving communication device establishes a communication link, and which identifies the best fitting predefined precoding matrix transmits the corresponding codebook indices to the transmitting communication device and uses temporarily or permanently the same precoding matrix for precoding data streams transmitted to the transmitting communication device. For example, in the case of a symmetric differential channel, the precoding matrices may be identical for each direction.

Usually all PLC channels are symmetric where they are identically terminated on both sides. Instead , in a common mode (CM), a CM path is used at the receiving side only. Due to regulatory constraints feeding via CM is not possible such that in the CM neither channel estimation nor a codebook table can be applied for the transmit signals based on the received signals. Here different precoding matrices have to be applied for the two communication directions. Accordingly an embodiment provides that a message exchanged between a transmitting and a receiving communication device contains information about whether or not a codebook index exchange is performed between the devices. For example , the message of the type CM CHAN EST.IND may contain an information bit or flag indicating whether codebook indices will or shall be exchanged between the transmitting and receiving communication devices or whether both sides apply the beamforming vectors derived at their sides respectively.

According to an embodiment, interpolation of precoding matrices is performed on the basis of a predefined pilot sub-carrier raster or step size known to both the transmitting and the receiving communication device. In accordance with another embodiment, the pilot sub-carrier raster or step size is configurable in at least one of the transmitting and the receiving communication devices. In this case, for example the receiving communication device may send a message indicating the pilot sub-carrier step size, for example by sending a binary value indicating the number of sub-carriers between adjacent pilot sub-carriers. For example the message of the type CM CHAN EST.IND may contain an information bit of flag indicating whether or not interpolation is used. In addition the message of the type CM CHAN EST.IND may contain a data field indicating the number of sub- carriers between adjacent pilot sub-carriers.

According to an embodiment, the transmitting and the receiving communication devices use codebook tables of a predefined resolution or length . In accordance with another embodiment, at least one of the transmitting and the receiving communication devices stores codebooks of different length or resolution. In this case , for example the receiving communication device may send a message indicating the codebook resolution or length, for example by sending a binary value indicating the codebook length or resolution. For example the message of the type CM CHAN EST. IND may contain a data field indicating the codebook length or resolution. Depending on the information in this data field the corresponding codebook will be selected. According to a further embodiment, the transmitting and receiving communication devices support both beamforming and an Alamouti scheme and both may be allowed to switch between a beamforming mode and an Alamouti mode. For example, the Alamouti mode may be applied, when the receiving communication device supports only one physical reception path or when the receiving communication device is connected to only one reception path, for example a PLC device connected to an outlet, where only one reception path is available , e.g. without connection to protective earth. For coordinating a switch between the operation modes, for example the receiving communication device may send a message indicating that the Alamouti scheme will or shall be applied. For example the message of the type CM CHAN EST.IND may contain an information bit or flag indicating a change of the operation mode or the requested operation mode.

Figure 7 refers to a method of operating a communications system comprising a first and a second communication device connected by a wired transmission channel. Both communication devices store the same codebook table comprising a plurality of codebook entries, wherein each codebook entry includes at least one predefined precoder value for each of at least two transmit signals. The first communication device identifies, in the codebook table, on the basis of channel state information describing the transmission channel , that one of the codebook entries, whose precoder values approximate a perfect precoding matrix for beamforming transmit signals at best among all or a subset of the codebook entries. The relevant codebook entry gives a codebook index ( 702).

The first and / or the second communication device may use the codebook index for constructing a precoding matrix for beamforming the respective transmit signals on the basis of the precoder values assigned to the codebook entry identified by the codebook index (704).

Table 1 (5 bit) vl real (v2) imag ( v2 ) angle ( 2 )

+ 0, .5429118123 + 0. .7325414029 + 0, .4106456589 + 0. .5109272538

+ 0. .8890378263 + 0. .1804094684 -0. .4207899322 -1. .1657621497

+ 0. .8520230127 -0. .4242616312 -0. .3066901598 -2. .5156755927

+ 0, .9583699224 + 0. .2622585825 -0. .1129049504 -0. .4065284205

+ 0, .7845428042 -0. .1379849364 -0. .6045268776 -1. .7952046406

+ 0. .7208801863 + 0. .2438249187 -0. .6487535480 -1. .2112929532

+ 0. .7895094007 + 0. .5132647486 -0. .3365029034 -0. .5803107874

+ 0. .3678133423 -0. .2445837675 + 0. .8971578043 + 1. .8369491567

+ 0, .4194919393 -0. .7898742375 -0. .4473535535 -2. .6262754399

+ 0, .2789402854 -0. .0495744116 -0. .9590279948 -1. .6224427089

+ 0, .9493270518 + 0. .2248511744 + 0. .2195907514 + 0. .7735626971

+ 0, .8349743073 + 0. .2006290213 + 0. .5124118481 + 1. .1976054683

+ 0. .6437778772 -0. .5296176025 -0. .5523180606 -2. .3352162299

+ 0. .7515049899 + 0. .5231669119 + 0. .4019162007 + 0. .6550710142

+ 0. .3154816246 + 0. .6055763516 + 0. .7305810201 + 0. .8786819854

+ 0. .9339951934 -0. .1163966601 + 0. .3377940144 + 1. .9026334400

+ 0. .6058703520 -0. .6968905692 + 0. .3837507669 + 2. .6382417583

+ 0. .9974148629 -0. .0662278106 + 0. .0278831213 + 2. .7430993563

+ 0. .3545051951 -0. .8948992442 + 0. .2710745457 + 2. .8474676471

+ 0. .6921350912 -0. .7194854156 -0. .0573563622 -3. .0620422954

+ 0. .5307601623 -0. .0547795048 -0. .8457498779 -1. .6354763166

+ 0. .0383121179 -0. .9477381321 + 0. .3167406110 + 2. .8190561069

+ 0. .5156760692 + 0. .6028865201 -0. , 6087742074 -0. , 7902573132

+ 0. .9526501184 -0. .0948727896 -0. ,2888890891 -1. ,8881053686

+ 0. .5971425452 + 0. ,2532717747 + 0. , 7611006431 + 1. ,2495524869

+ 0. .8469389995 + 0. .5256289112 + 0. ,0800535994 + 0. , 1511391618

+ 0. .6289801775 + 0. , 7730414887 -0. , 0824062679 -0. , 1061990035

+ 0. .5914770000 -0. .3603891509 + 0. , 7213006436 + 2. , 0341542272

+ 0. .9177609510 -0. , 3969777000 + 0. , 0111149657 + 3. , 1136009993

+ 0. .7726056604 -0. , 1260646301 + 0. , 6222444877 + 1. ,7706873855

+ 0. .8190726488 -0. .4597451218 + 0. ,3431536377 + 2. ,5003996982

+ 0. .3091478225 + 0. .9343053665 -0. , 1774855095 -0. , 1877283626

Table 2 (6 bit) vl real (v2 ) imag ( v2 ) angle ( v2 )

+ 0 .5370545358 -0 .1855474350 -0 .8228879480 -1 .7925706697

+ 0 .8384124707 -0, .5446977253 -0 .0192072159 -3 .1063451024

+ 0 .8726365170 + 0, .4878962574 + 0 .0215116531 + 0, .0440620922

+ 0. .9959431368 + 0, .0562311975 + 0 .0702518373 + 0, .8957974147

+ 0 .7124662060 -0, .6820405895 + 0 .1649622365 + 2 .9042843163

+ 0 .8001176514 -0, .5483103928 -0 .2432436167 -2 .7240536962

+ 0 .8070029620 + 0, .3346201991 -0 .4865958711 -0, .9683896224

+ 0 .2687047193 -0, .8360541367 -0 .4783421937 -2 .6219084317

+ 0 .9440520070 -0, .1127762428 -0 .3099150323 -1 .9197949218

+ 0 .8799164606 -0, .1312542481 + 0 .4566391844 + 1 .8506864428

+ 0 .9282229308 -0, .3569673078 + 0 .1047689456 + 2 , .8561122523

+ 0, .9183604277 + 0. .2674778994 -0 .2916671017 -0, .8286322600

+ 0. .8824289340 -0. .3105185571 -0, .3534082654 -2 , .2916840746

+ 0, .3732044063 -0. .4735026723 + 0, .7978180811 + 2 , .1064205205

+ 0, .9686776061 -0. .1346593940 + 0, .2086397447 + 2 , .1439421792

+ 0, .8308013261 -0. .0839352753 -0, .5502036225 -1, .7221822663

+ 0. .5653353832 + 0. .3581176545 + 0, .7430663834 + 1 , .1216961899

+ 0, .5214077647 -0, .6653388823 + 0 .5342828040 + 2 , .4650107889

+ 0. .3265207182 + 0, .9156699443 -0 .2343774170 -0, .2505827623

+ 0. .9868755405 -0. .1581712059 -0, .0325351671 -2 , .9387263226

+ 0. .5173607870 + 0. .8517732567 + 0, .0825841102 + 0. .0966534058

+ 0. .1869679277 -0. .2939958967 + 0, .9373416702 + 1. .8747272584

+ 0. .7555948274 -0. , 2232625836 + 0. .6158167549 + 1. .9186049508

+ 0. .0600016333 -0. .4871113467 -0. .8712762707 -2. .0805824428

+ 0. .8487683522 + 0. .2738351930 + 0. .4523345790 + 1. .0264288991

+ 0. .6649767787 + 0. .4177867256 -0. .6190800722 -0. .9771491177

+ 0. .9367940037 + 0. .0350272498 + 0. .3481236653 + 1. .4705165620

+ 0. .2945556475 -0. .8789475759 + 0. .3750841630 + 2 , .7382471375

+ 0. .9824201600 + 0. .0606530887 -0. .1765554645 -1. .2398919992

+ 0. .5403210814 + 0. , 6950135216 + 0. .4743514877 + 0. .5988888616

+ 0. .8030958367 + 0. , 0480358982 + 0. .5939104559 + 1. .4900912952

+ 0. .7171617233 + 0. , 1056318437 -0. .6888548296 -1. .4186374529

+ 0. .7172625048 + 0. , 6951466795 + 0. .0480165931 + 0. .0689645026

+ 0. .2899682464 + 0. , 4920228933 -0. .8208726385 -1. .0308254386

+ 0. .7252078766 + 0. , 3248125960 + 0. .6070999202 + 1. .0795242146

+ 0. .7344223090 + 0. , 5850292197 -0. .3440416896 -0. .5316057733

+ 0. .5836664489 -0. , 730405125 + 0. .2484790582 + 2. .8305923204

+ 0. .9401761036 + 0. , 2553869953 + 0. .2254914118 + 0. .7233093752

+ 0. ,8866466031 + 0. 1075855428 -0. ,4497589934 -1. , 3360012009

+ 0. 1412279570 + 0. 8632288323 + 0. ,4846551839 + 0. ,5115873860

+ 0. .5958421040 + 0. 7641504586 -0. ,2470754210 -0. ,3127238440

+ 0. , 6396444809 -0. 5569270499 -0. ,5297992065 -2. , 3811522112

+ 0. .6531713929 + 0. 0203413973 + 0. ,7569368263 + 1. , 5439294839

+ 0. ,5135078730 -0. 7875611786 -0. , 3406714755 -2. ,7333317927

+ 0. 7843161996 -0. 3784187351 -0. ,4915764029 -2. ,2268535887

+ 0. 3611153600 + 0. 4452488515 + 0. ,8193589915 + 1. , 0730257666

+ 0. 8294727167 -0. 5076319558 + 0. ,2329910077 + 2. ,7112992043

+ 0. 2973638436 -0. 2072267913 -0. 9320041853 -1. 7895825975

+ 0. 9589399172 + 0. 2801736008 -0. 0440112331 -0. 1558123060

+ 0. 5015828956 + 0. 6652934310 -0. 5529911839 -0. 6934773017

+ 0. 8485421665 + 0. 4866646919 -0. 2076864689 -0. 4033559970

+ 0. 4473921579 -0. 0404210742 + 0. 8934239720 + 1. 6160083759

+ 0. 7029118578 -0. 2195961595 -0. 6765297088 -1. 8846591974

+ 0. 8305397871 + 0. 4858567340 + 0. 2722992764 + 0. 5108321886

+ 0. 5821292785 -0. 3527594192 + 0. 7325887628 + 2. 0195545723 +0.4238950361 -0.9056675283 +0.0089065525 +3.1317587299 +0.9245914011 -0.3594312596 -0.1262533592 -2.8037969329 +0.6591708476 -0.7365179258 -0.1517733131 -2.9383686453 + 0.8724454181 -0.3288260032 +0.3615417710 + 2.3088410186 +0.7213952222 -0.5080642040 +0.4705950468 + 2.3944620132 +0.6907592035 +0.5969629956 +0.4080280684 +0.5995704991 +0.4988766087 +0.2143087516 -0.8397582321 -1.3209268257 +0.3432442229 +0.8496337693 +0.4003821443 + 0.4403767466 +0.4443477116 -0.5684575522 -0.6923952069 -2.2582125646

table 3 (7 bit) vl real (v2) imag ( v2 ) angle ( v2 )

+ 0 .6317736337 + 0. 7238481520 + 0. ,2773191817 + 0 .3658686672

+ 0 .6106276958 -0. 3125280924 -0. ,7276400268 -1 .9764801068

+ 0 .6950914471 -0. 6157145944 -0. ,3711380046 -2 .5991344475

+ 0 .6100571752 -0. 0333070436 -0. ,7916570494 -1 .6128440951

+ 0 .5995506391 + 0. 7258933546 -0. ,3370724979 -0 .4347275404

+ 0 .5981134001 + 0. 1640861692 + 0. ,7844336107 + 1 .3645916468

+ 0. .6301042649 -0. 7648413642 -0. 1341130231 -2 , .9680098305

+ 0, .3013116427 + 0. 5158354554 + 0. 8019507946 + 0 , .9991980235

+ 0 , .7538002344 -0. 6253031951 -0. 2019433603 -2 , .8292135728

+ 0, .5882469008 + 0. 2375951112 -0. 7729903925 -1 , .2725906082

+ 0, .7126897012 + 0. 6899172353 + 0. ,1268368958 + 0, .1818134420

+ 0, .8497712596 + 0. 0281703101 -0. ,5263983662 -1 , .5173321332

+ 0, .9093227347 + 0. 3992401893 -0. ,1172153375 -0, .2855712936

+ 0. .4829533864 + 0. 7262484516 -0. 4892026299 -0, .5927888406

+ 0, .9383003240 -0. 0318738915 + 0. 3443494692 + 1, .6630959506

+ 0. .7749910322 -0. 6270158022 + 0. 0789942015 + 3, .0162685341

+ 0, .1993472259 -0. 9154479748 -0. 3495936054 -2 , .7768016639

+ 0. .3652433356 + 0. 9289266539 + 0. 0607665825 + 0, .0653228388

+ 0. .1080676645 -0. 8526190750 + 0. 5112358486 + 2 , .6014626201

+ 0, .3483369396 + 0. 6361832923 -0. 6884273347 -0, .8248187874

+ 0. .9980685734 + 0. 0474729116 + 0. 0400680104 + 0. .7010111648

+ 0. .4913681458 -0. 8671896177 -0. 0808672510 -3. .0486094595

+ 0. .5601156584 -0. 5087949528 -0. 6537569466 -2. .2321418603

+ 0, .9635567540 -0. 1774140601 -0. 2002064761 -2. .2959096382

+ 0. .3259274700 + 0. 8407719365 + 0. 4322890642 + 0. .4749092301

+ 0. .3574216567 -0. 2358272879 -0. 9036787314 -1. .8260667927

+ 0. .4961731867 + 0. 7641439340 + 0. 4121846878 + 0. .4946741313

+ 0. .3516886085 + 0. 2254711463 -0. 9085581351 -1. .3275466936

+ 0. .2463405697 + 0. 9423449983 -0. 2264999511 -0. .2358832468

+ 0. .5919203439 -0. 7517513017 -0. 2906893305 -2. .7726190352

+ 0. .0490053971 + 0. 9648624124 + 0. 2581453005 + 0. .2614233805

+ 0. .4663774743 -0. 8165043860 -0. 3403125609 -2. .7466946780

+ 0. .8239821537 + 0. 5107919419 + 0. 2452447805 + 0. .4476228350

+ 0. .4863184928 + 0. 0914979337 -0. 8689778200 -1. .4658891309

+ 0. .9335120204 + 0. 1960111899 + 0. 3002247844 + 0. .9923981548

+ 0. , 8006009055 + 0. 0384095462 + 0. 5979656318 + 1. , 5066507488

+ 0. .7179148968 -0. 2762553914 -0. 6389688252 -1. .9788723165

+ 0. ,3715729080 + 0. 8699346223 -0. 3242642858 -0. , 3567927295

+ 0. ,5633144111 -0. 6413080554 + 0. 5209614691 + 2. , 4593712771

+ 0. , 9488441314 -0. 3013187162 + 0. 0943495919 + 2. , 8381410036

+ 0. , 8448396019 + 0. 4592951402 -0. 2743975604 -0. ,5385290393

+ 0. , 8511158488 + 0. 2577531481 + 0. 4573457406 + 1. , 0575831198

+ 0. 7953101618 -0. 5571693454 + 0. 2388389983 + 2. 7366218170

+ 0. ,8806153808 -0. 4713095859 + 0. 0488244326 + 3. 0383677323

+ 0. ,9673344247 + 0. 2209276586 + 0. 1243184637 + 0. 5125498685

+ 0. ,7594503312 -0. 4188442250 -0. 4977998690 -2. 2702710188

+ 0. , 8791381839 -0. 4171842780 + 0. 2303765000 + 2. 6370484666

+ 0. , 9021693959 -0. 3294772655 -0. 2784512750 -2. 4399324066

+ 0. , 6046827111 + 0. 7963828109 + 0. 0115428480 + 0. 0144930800

+ 0. 5864926108 + 0. 6299381353 + 0. 5091211675 + 0. 6797259419

+ 0. 9458872731 + 0. 1263919973 -0. 2988684152 -1. 1707041964

+ 0. 4556689198 -0. 8745251554 + 0. 1660469456 + 2. 9539552377

+ 0. 8007902108 -0. 4397364589 + 0. 4066532737 + 2. 3952620154

+ 0. 4043567632 -0. 3405656790 + 0. 8488289736 + 1. 9523524818 +0.9103782182 -0.0320116191 -0.4125369753 -1.6482381120 + 0.8313017730 -0.5100030850 -0.2209846501 -2.7327123712 +0.4532876467 +0.2896524476 + 0.8429897798 +1.2398331747 + 0.8591974203 -0.1469751593 +0.4900796829 +1.8621618669 +0.6964405573 -0.7174431073 -0.0156824091 -3.1197373846 +0.9382208559 -0.1944106762 +0.2862623176 + 2.1673810552 + 0.9915754066 -0.1278243236 -0.0209560307 -2.9790942229 + 0.6039404631 -0.2354148749 +0.7614694700 + 1.8706342311 +0.8818169744 -0.3060645715 +0.3587802972 + 2.2770697659 +0.6879346876 +0.0032447053 +0.7257653460 +1.5663256205 +0.8067555856 +0.3810920657 -0.4515686686 -0.8698371459 +0.9069527033 +0.3492839388 +0.2354517446 +0.5931300182 +0.7564516125 -0.1579564765 +0.6346894591 +1.8147131228 +0.9656793568 +0.2578122352 -0.0315631309 -0.1218205999 +0.5034726798 +0.8457730539 -0.1765876607 -0.2058315523 +0.7395360689 +0.2213624141 +0.6356768711 +1.2356982921 +0.7974907213 +0.6023978161 +0.0335472892 +0.0556321293 +0.8836466089 +0.0790075989 +0.4614395626 +1.4012208517 +0.5784950444 -0.6602681825 -0.4789461460 -2.5140346224 +0.9597323722 -0.2680045189 -0.0841864099 -2.8372297746 +0.2936947163 -0.5722512380 -0.7656839650 -2.2126137966 +0.5715766722 -0.7534498454 +0.3249822123 +2.7343763831 +0.9826165920 -0.1012532525 +0.1556033802 +2.1476731115 + 0.8840517465 +0.4657226280 +0.0394327685 +0.0844686042 +0.5023809145 -0.4875592891 +0.7140723747 + 2.1698762440 +0.8857454044 +0.1482734448 -0.4398523208 -1.2456611888 +0.4862609003 -0.0525511146 +0.8722320318 +1.6309725930 +0.5581448706 +0. 362820549 +0.7057848624 +1.0171368548 +0.4337857134 -0.6231426179 -0.6507866260 -2.3344980966 +0.8419321901 -0.2912144414 -0.4542514022 -2.1408799235 +0.4143404761 -0.7609704892 +0.4992453150 +2.5609663464 +0.1786270657 + 0.8816225713 +0.4368455256 +0.4600425368 +0.1903259722 +0.5717110973 -0.7980742106 -0.9491724752 +0.3623847908 -0.9300985091 -0.0599502032 -3.0772259364 +0.1686825679 +0.0046949336 +0.9856592458 +1.5660331207 +0.4806440138 +0.4291749302 -0.7647157716 -1.0593786040 +0.6071617024 -0.7879417707 +0.1024813800 +3.0122565588 +0.7765762773 -0.0097799293 -0.6299473299 -1.5863200748 +0.6966222961 +0.7041715907 -0.1373307958 -0.1926069940 +0.7938554882 +0.4243614384 +0.4355580712 +0.7984179867 +0.8843614249 +0.3091437239 -0.3497642464 -0.8469684917 +0.7588531775 -0.3345675980 +0.5587543086 + 2.1103139290 +0.4891892313 -0.2469811946 -0.8364772474 -1.8579020580 +0.3335960145 +0.0422838380 +0.9417673684 +1.5259280707 +0.8127848898 +0.5647287164 -0.1430461458 -0.2480827281 +0.9758267505 +0.0698350086 +0.2070874804 +1.2455476616 +0.9039912908 -0.1779259166 -0.3887700020 -2.0000050792 +0.7426457039 +0.5835403107 -0.3285697251 -0.5128167339 +0.5783084262 +0.5445184765 -0.6075022575 -0.8400162246 +0.4245649628 +0.6204512033 +0.6593822083 +0.8158075930 +0.5063894189 +0.8471300283 +0.1610604593 +0.1878824320 +0.7223864418 +0.1256255213 -0.6799823947 -1.3881080420 +0.1063876553 -0.3325702638 -0.9370585288 -1.9118374796 +0.2482791229 -0.1299972578 -0.9599261378 -1.7054016678 +0.8273551724 -0.4313368871 -0.3597664638 -2.4464179946 +0.6272136116 -0.4256506250 +0.6522458362 +2.1489917600 +0.7075658348 +0.5016891015 -0.4976531270 -0.7813595544 +0.8225995601 -0.5639907295 -0.0724183737 -3.0138879536 +0.6931110677 -0.5435049170 +0.4734970465 + 2.4249235650 +0.6909784146 +0.3349971755 -0.6405667202 -1.0889420340 +0.9578692419 -0.0729725637 -0.2777796254 -1.8276912708 + 0.8037830442 +0.2303065730 -0.5485359608 -1.1732900381 +0.2864657220 -0.9141766823 +0.2867374822 +2.8376545002 +0.9085490897 -0.4029687721 -0.1102484483 -2.8745372681 +0.6971682910 -0.6701070089 +0.2547802398 +2.7782636484 +0.9883017639 +0.0556017256 -0.1420143358 -1.1976199362 +0.3367231338 -0.8349070774 -0.4353707652 -2.6609246906 +0.8230805551 -0.1608203598 -0.5446789988 -1.8578962076 +0.6841667907 +0. 086352535 +0.6040968731 +0.9760580949 +0.6666039422 -0.5034436914 -0.5497123191 -2.3122894149 +0.9426889166 +0.2656139735 -0.2019574797 -0.6500872460 +0.7105932712 +0.5762010980 +0.4037938802 +0.6112535396 +0.7098063460 -0.1180267778 -0.6944383564 -1.7391476558 +0.2794117654 -0.5983260544 +0.7509560560 +2.2435538974

table 4 (8 bit) vl real (v2) imag ( 2 ) angle (v2)

+ 0 .8909402196 + 0 .1356014147 -0 .4334025627 -1 .2675686224

+ 0 .7801305003 + 0 .6194043211 + 0 .0879470833 + 0 .1410437709

+ 0 .4605040367 + 0. .5304757763 -0 .7117102521 -0 .9302755722

+ 0 .8690485029 -0 .0927698858 + 0 .4859510756 + 1 .7594303962

+ 0 .2074053916 + 0 .9586694037 + 0 .1947716047 + 0 .2004405101

+ 0 .6311597071 -0 .4454653253 + 0 .6349787934 + 2 .1825575309

+ 0 .7297945686 + 0 .0011364906 + 0 .6836655586 + 1 .5691339796

+ 0 .9287951424 + 0, .3106438808 + 0 .2020889972 + 0 .5767609083

+ 0 .7315091601 -0, .1623082680 + 0, .6622313605 + 1 .8111513275

+ 0 .8654404094 -0, .3451943029 + 0 .3631167733 + 2 .3308967820

+ 0 .9774419950 + 0. .1461541109 + 0 .1524667908 + 0 .8065344596

+ 0 .3226018604 + 0, .8665657160 -0 .3807780187 -0 .4140128292

+ 0 .8812253145 + 0, .3074054292 -0 .3590875203 -0 .8627866424

+ 0. .9015159785 + 0. .4281232371 + 0, .0630827576 + 0 .1462945119

+ 0. .4098284032 -0. .0399730297 + 0, .9112863638 + 1 .6146326264

+ 0, .8038391632 -0. .3492961158 + 0. .4814922878 + 2 .1983960637

+ 0, .7316461051 + 0. .4716434094 -0. .4921854033 -0 .8067078443

+ 0, .9596128553 -0. .1086028338 + 0 .2595160734 + 1 .9671333351

+ 0. .8995554706 + 0. .1153958006 + 0. .4212882203 + 1, .3034421193

+ 0. .7776075410 -0. .6264177047 + 0. .0541051895 + 3, .0554340997

+ 0. .9307610248 -0. .1810749674 -0. .3176409464 -2 , .0889114937

+ 0. .9468196717 + 0. .3123429563 + 0, .0772941582 + 0, .2425919904

+ 0. .4754862767 -0. .1478982763 -0. .8672017646 -1 , .7397176424

+ 0. .3866161872 + 0. .5777035564 -0, .7188786578 -0, .8938534078

+ 0. .8892302607 + 0. , 4250732565 -0. .1690629175 -0. .3785449666

+ 0. .6782698102 + 0. .6115729126 + 0. .4073433897 + 0. .5875815068

+ 0. .4982285619 + 0. , 7707089859 + 0. .3972102203 + 0. .4758780472

+ 0. .7054902896 + 0. .5001980206 + 0. .5020810606 + 0, .7872769194

+ 0. .8402284199 -0. .0115762343 -0. .5421090233 -1. .5921471523

+ 0. , 1148849877 -0. .8740435200 + 0. .4720692373 + 2. .6463834473

+ 0. .4883522981 + 0. .8670709229 -0. .0984888200 -0. .1131031978

+ 0. , 9940100953 + 0. , 1091764577 + 0. .0049428307 + 0. .0452428827

+ 0. ,7286123567 + 0. .3389312963 + 0. .5951887180 + 1. .0531416509

+ 0. .8103117225 + 0. .2603711415 + 0. .5249778862 + 1. .1103811847

+ 0. , 5505836355 -0. .8342431861 + 0. .0299327035 + 3. .1057279693

+ 0. 9846785462 -0. 0534523151 + 0. .1659849710 + 1. .8823405762

+ 0. 6863876900 + 0. 2458879152 + 0. , 6844056343 + 1. .2258851979

+ 0. 8448369767 -0. 5310310980 -0. .0652415190 -3. .0193470721

+ 0. 4806513866 -0. 5653700618 -0. , 6703215182 -2. .2714644630

+ 0. 7533281147 + 0. 3595538621 -0. ,5506521332 -0. .9923430187

+ 0. 5178028700 -0. 6896499372 + 0. , 5062244087 + 2. .5083903075

+ 0. 2373453639 -0. 9396475447 + 0. 2464339059 + 2. ,8851069325

+ 0. 2981040126 + 0. 8213564811 + 0. ,4863203971 + 0. , 5345861217

+ 0. 8059242581 + 0. 4071354651 -0. , 4297985614 -0. ,8124702608

+ 0. 9368367352 -0. 3410049241 -0. , 0777982866 -2. , 9172875642

+ 0. 1149624948 + 0. 2795281336 + 0. ,9532301125 + 1. ,2855500119

+ 0. 5949849162 -0. 1443170541 -0. 7906741031 -1. 7513330398

+ 0. 6403778011 + 0. 4236255484 + 0. 6406697017 + 0. 9865718834

+ 0. 6472939793 + 0. 0446749795 -0. 7609301220 -1. 5121526316

+ 0. 8995729683 -0. 3203467244 -0. 2968946796 -2. 3941711540

+ 0. 6627071719 + 0. 4742966270 -0. 5795359470 -0. 8849315818

+ 0. 4558207444 + 0. 5016768332 + 0. 7352195618 + 0. 9720146946

+ 0. 4205305938 + 0. 8887105603 + 0. 1826131422 + 0. 2026601626

+ 0. 4798584641 + 0. 7775112873 -0. 4064628551 -0. 4817005473 +0.9360459504 +0.0525696065 +0.3479287501 +1.4208375803 + 0.8251112025 -0.2680913030 -0.4973113277 -2.0652181315 +0.5515889147 +0.8340590132 +0.0097586707 +0.0116996823 +0.3058928880 +0.9439481007 -0.1240625818 -0.1306804423 +0.8946280497 +0.3262277443 +0.3053131367 +0.7522934706 +0.9340332030 +0.3289498700 -0.1391903686 -0.4002903421 +0.7524316836 +0.5412005260 +0.3754311551 +0.6064856874 +0.5851969478 +0.0870559763 +0.8062045580 +1.4632306237 +0.6761653310 +0.7161466115 -0.1730158258 -0.2370504350 +0.5816676839 +0.7475973224 +0.3205634868 +0.4050778177 +0.9752210079 -0.0541428352 -0.2145053359 -1.8180399344 +0.8580800640 +0.1554302505 +0.4894282796 +1.2632945543 +0.7353975447 +0.6378811647 -0.2286877149 -0.3442372074 +0.1873656604 +0.7288848248 +0.6584990671 +0.7347089024 +0.9386809708 +0.0807696623 -0.3351929247 -1.3343393869 +0.6583323272 -0.2976231761 -0.6913891755 -1.9772920464 +0.6764170439 -0.5580123900 +0.4807100533 +2.4304781437 +0.7410750058 +0.1755312700 +0.6480714537 +1.3062908112 +0.5802587125 +0.7075977729 -0.4032433735 -0.5179753423 +0.5672093369 +0.0753541314 -0.8201190907 -1.4791716517 +0.4955494428 +0.2210143013 -0.8399901359 -1.3135123985 +0.9603351648 -0.0155127920 +0.2784164589 +1.6264567169 +0.9216021925 +0.3081750070 -0.2359609369 -0.6534558957 +0.5956405604 -0.5837600243 -0.5517576976 -2.3843700591 +0.3704547391 +0.4644041272 +0.8044203459 +1.0472238214 +0.9253321609 -0.0718061621 +0.3722959403 +1.7613305517 +0.6097709750 +0.2155968216 -0.7626908735 -1.2953049640 +0.9624681500 -0.1849716214 -0.1985964742 -2.3206880785 +0.9709008409 +0.2280597798 + 0.0730773154 +0.3100934316 +0.5294461920 -0.7905767065 +0.3076933554 + 2.7704301618 +0.3207949781 +0.9304283725 +0.1771824642 +0.1881779576 +0.7381240731 -0.6042783887 +0.3000341341 +2.6807358009 +0.2271441370 +0.6327359364 -0.7403045156 -0.8635818121 +0.9915469382 +0.0183887185 -0.1284387964 -1.4285916478 +0.6109111657 -0.7554291721 +0.2368845997 + 2.8377276445 +0.7913617971 -0.0160446652 +0.6111375253 +1.5970440694 +0.6374012229 +0.7081779359 +0.3036506087 +0.4050656818 +0.8332225173 -0.4128949153 -0.3677744223 -2.4139274501 +0.3156563240 -0.0723344860 +0.9461124707 +1.6471023074 +0.4928357614 +0.0141598710 +0.8700071323 + 1.5545221834 +0.6984400519 +0.1978362216 -0.6877807233 -1.2907132033 +0.9479443905 -0.0823699072 -0.3075981647 -1.8324417038 +0.7906530084 +0.0991243619 -0.6041872071 -1.4081826622 +0.3802001800 +0.7427936364 -0.5510947622 -0.6383109567 +0.1164006758 +0.5092872213 -0.8526883422 -1.0323848209 +0.8116286667 +0.5834614172 -0.0288388975 -0.0493870649 +0.7079819218 -0.5313628285 -0.4652044097 -2.4224835298 +0.2627849958 -0.2611965631 -0.9288274336 -1.8449277079 +0.3931902665 +0.8013707543 +0.4507841263 +0.5124018564 +0.8615282146 +0.0824415986 -0.5009715742 -1.4076947411 +0.3612391203 -0. 561968066 -0.8132593507 -2.0820065995 +0.8003832600 +0.1339630685 +0.5843291310 +1.3454312439 +0.9217603851 +0.1901158112 -0.3379552793 -1.0583709781 +0.2169470497 +0.1670554082 -0.9617829631 -1.3988186596 +0.8668555861 -0.4244155172 +0.2615967537 +2.5892236719 +0.5634180396 -0.5652763583 +0.6025136940 +2.3243182787 +0.5288598655 +0.8076380311 -0.2608218804 -0.3123712220 +0.2317999262 -0.6654747865 +0.7095154000 +2.3241756709 + 0.8992308481 + 0, .0257846608 + 0.4367139030 + 1. ,5118223366

+ 0 .7732069641 -0, .5531334100 -0 .3101522552 -2. , 6305573651

+ 0 .7834536828 -0, .6113872082 -0 .1113822629 -2. , 9613893456

+ 0 .9927060102 -0, .0988966945 -0 .0689508607 -2. , 5327477768

+ 0 .4951890175 -0, .1843407461 + 0 .8490031368 + 1. .7846037667

+ 0. .8167377077 + 0, .5501117523 -0 .1741165608 -0. .3065350650

+ 0 .6177171903 -0, .7754722992 -0 .1306452676 -2. .9746880789

+ 0, .4571962645 -0, .5868652507 + 0 .6682520132 + 2. .2914411944

+ 0 .8956906825 + 0, .4101220332 + 0 .1718665738 + 0. .3968304065

+ 0 .7927741800 -0, .4655833611 + 0 .3933716225 + 2. .4400665621

+ 0 .9062407378 -0, .3654484958 -0 .2125444004 -2. .6148133545

+ 0. .9330041409 + 0. .1830178778 + 0, .3098511407 + 1. ,0372699017

+ 0, .7546614369 + 0. .6471683361 -0, .1079780548 -0. ,1653240708

+ 0. .1176061059 -0. .4891759210 -0, .8642197187 -2. ,0858647167

+ 0, .5557191368 + 0. .6615153115 + 0, .5035610526 + 0. , 6506455872

+ 0, .4275528798 -0. .7684138411 + 0, .4761708766 + 2. ,5868279301

+ 0, .8550357868 -0. .2325675486 + 0, .4634934073 + 2. ,0358597287

+ 0, .7060699277 -0. .6733204161 -0, .2193282348 -2. 8266904643

+ 0. .7060699277 -0. .6733204161 -0, .2193282348 -2. , 8266904643

+ 0. .5812699293 -0. .4111884754 -0, .7021746983 -2. , 1005549665

+ 0. .7789809438 + 0. .4196100371 + 0, .4659571932 + 0. ,8376865814

+ 0, .3934366478 + 0. .9174505067 -0, .0590946024 -0. , 0643229029

+ 0. .7417670367 + 0. .1149192162 -0. .6607384029 -1. 3985934815

+ 0. .9043258345 -0. .0198723454 -0. .4263799654 -1. 6173697512

+ 0. .9695164792 + 0. .0725749753 + 0. .2340313430 + 1. 2700921928

+ 0. .4523402355 + 0. .6928895450 -0. .5615090291 -0. 6810427707

+ 0. .9679255239 -0. .2491108213 + 0. .0326186889 + 3. 0113929175

+ 0. .5956962848 + 0. .7936494797 + 0. .1235574348 + 0. 1544428415

+ 0. .3251367104 + 0. .6236293190 + 0. .7108956267 + 0. 8506964869

+ 0. .1991749513 -0. , 1648291161 + 0. .9660024334 + 1. 7397988461

+ 0. .4152658272 -0. ,2036273226 + 0. .8866172829 + 1. 7965490557

+ 0. .8773083574 + 0. ,2444193289 + 0. .4130245000 + 1. 0364434237

+ 0. .7920705916 + 0. , 5017041416 -0. .3477314081 -0. 6060804252

+ 0. .6086573001 + 0. ,7642700556 -0. .2131374512 -0. 2719671768

+ 0. .7386184591 -0. 3082744937 + 0. ,5995078052 + 2. 0457492951

+ 0. ,3258283513 -0. 4934177505 + 0. , 8064581880 + 2. 1198711767

+ 0. .8788411106 + 0. 4744503645 -0. , 0503503121 -0. 1057277320

+ 0. ,8146974340 + 0. 4710709457 + 0. , 3381719313 + 0. 6226247710

+ 0. ,5256800318 + 0. 3727306276 -0. ,7646779606 -1. 1172513347

+ 0. ,4358836078 + 0. 6665961775 + 0. , 6046941513 + 0. 7367443096

+ 0. , 6960877347 + 0. 6594562912 + 0. ,2838648720 + 0. 4064802206

+ 0. , 9461686453 -0. 2116078394 + 0. ,2449224714 + 2. 2833500711

+ 0. 7552097716 -0. 2270958904 -0. , 6148867029 -1. 9245864870

+ 0. 4463752228 -0. 8877580386 + 0. ,1124047389 + 3. 0156464314

+ 0. 9027022869 -0. 4300809784 -0. ,0126068705 -3. 1122882615

+ 0. 7814907956 + 0. 2347244070 -0. 5780800889 -1. 1850927820

+ 0. 9305740111 -0. 3634694122 + 0. 0438405781 + 3. 0215555631

+ 0. 6688158100 + 0. 6534908603 -0. 3544504306 -0. 4969859977

+ 0. 6844852730 -0. 4247085537 -0. 5925390750 -2. 1926825492

+ 0. 9520396599 + 0. 2151839654 + 0. 2175232103 + 0. 7908041798

+ 0. 6693877566 -0. 6578000634 + 0. 3452812011 + 2. 6582217267

+ 0. 5356360076 -0. 4515275314 + 0. 7135943916 + 2. 1349499550

+ 0. 9485608119 -0. 2817750530 -0. 1443440527 -2. 6681796968

+ 0. 6073554103 + 0. 2305992137 + 0. 7602258929 + 1. 2762874215

+ 0. 7035382882 -0. 7096901400 -0. 0370645673 -3. 0894136515

+ 0. 7322529246 -0. 4510057443 + 0. 5102935165 + 2. 2945978849

+ 0. 5495738073 + 0. 5283843078 + 0. 6471310946 + 0. 8860734322

+ 0. 9218335521 -0. 3599130665 + 0. 1438244996 + 2. 7614233933 +0.3490444356 -0.1082254095 -0, .9308357764 -1..6865435576

+0.5945485686 +0.5784212783 -0, .5585166285 -0. .7678927073

+0.9787220976 -0.2003300221 -0. .0443952467 -2. .9235066692

+0.9612651871 -0.2352714316 + 0, .1435847954 + 2. .5936382356 +0.3381755714 -0.9338643602 + 0. .1163384706 + 3. .0176536983

+0.3630873657 -0.7398855734 -0, .5663363868 -2. .4882843413

+0.9687787025 +0.2462445849 -0. .0288345284 -0. .1165662656

+0.5663350150 -0.1001861435 + 0. .8180631928 + 1. .6926569979

+0.5895722345 +0.4376336624 -0. .6788824330 -0. .9981995078 +0.1061409494 +0.9902987221 -0, .0896802094 -0. .0903124020

+0.5709274552 -0.3075047730 + 0. .7612375815 + 1. .9547064524

+0.0134484414 -0.9282986139 + 0. .3715922805 + 2. .7608329327

+0.7805584700 -0.5974916329 + 0, .1836633426 + 2. .8433693119

+0.9648512791 +0.2238704553 -0. .1376373074 -0. .5512365151 +0.8056755281 -0.5218284718 + 0, .2803247927 + 2. .6486319561

+0.2182255609 -0.8938911070 -0. .3915817837 -2. .7287086667

+0.6507956275 -0.1345125299 + 0. .7472425514 + 1. .7489007636

+0.6452815829 -0.7611654299 + 0, .0651065820 + 3. .0562649534

+0.8532036572 +0.4398994857 -0. .2802355470 -0. .5672136813 +0.7269174758 +0.6727951951 + 0, .1376139848 + 0. .2017577588

+0.7525284906 +0.5712896462 -0, .3276110666 -0. .5206752448

+0.6445484879 +0.7644539234 + 0, .0129400823 + 0. .0169256069

+0.8482006122 +0.0311743711 + 0, .5287569197 + 1. .5119066477

+0.6921252172 +0.5747346477 -0. .4366265779 -0. .6496809944 +0.6520696908 +0.3250047675 -0. .6849649768 -1. .1277692684

+0.8555949206 -0.4920858045 + 0. .1606514640 + 2. .8260313765

+0.9663805264 +0.0670960014 -0. .2482071813 -1. .3067838707

+0.3883235217 +0.2082069141 + 0. .8976941146 + 1. .3428906933

+0.5180521836 +0.8328068359 + 0. .1950761626 + 0. .2300910318 +0.5180521836 +0.8328068359 + 0. .1950761626 + 0. .2300910318

+0.6683211647 +0.0397918655 + 0. .7428078003 + 1. .5172779504

+0.2190452190 +0.9163320932 -0. .3351935067 -0. .3506798792

+0.8346727904 -0.5101333935 -0. .2075698768 -2. .7551579094

+0.6236515055 +0.6005436988 + 0. .5004059008 + 0. .6946919084 +0.8410396127 +0.2132239237 -0. .4971799756 -1. .1656551338

+0.9942903297 +0.0429995210 + 0. .0976615664 + 1. .1560455727

+0.5906075122 -0.6785309394 + 0. .4367820175 + 2. .5696468713

+0.5433023434 +0.3773487881 + 0. .7499536358 + 1. .1046216623

+0.8787738843 -0.2751710440 -0. .3899196799 -2. .1853456500 +0.9074450492 -0.2213743477 + 0. .3571230611 + 2. .1257071991

+0.6480092808 -0.3041765550 + 0. .6982553941 + 1. .9816307700

+0.8527760237 +0.5197099036 + 0. .0517172068 + 0. .0991851463

+0.8210865764 +0.3195864084 -0. .4729496396 -0. .9765451115

+0.4856271799 +0.2664331 17 + 0. .8325740947 + 1. .2610831065 +0.9294597487 +0.3665236678 -0. .0420116232 -0. .1141238029

+0.4083318883 +0.1033660175 -0. .9069622569 -1. .4573164872

+0.9898594603 -0.1198000878 + 0. .0763294684 + 2. , 5743108022

+0.8999701394 -0.1312308514 -0. .4157309368 -1. , 8765601381

+0.8597907217 +0.4526755816 + 0. .2363149014 + 0. ,4811239888 +0.4074379353 +0.8643081508 -0. .2948995581 -0. ,3288112979

+0.9999984653 +0.0017232240 + 0. .0003160976 + 0. , 1814170108

+0.5192784403 +0.6668787443 -0. .5344367519 -0. , 6755941332

+0.4961596819 -0.7200088432 -0. .4851936064 -2. , 5486185012

+0.8431750809 -0.1368515322 -0. .5199302271 -1. , 8281700256 +0.6723319595 +0.7192858844 + 0. .1749215615 + 0. ,2385569885

+0.2752683297 +0.3289984756 + 0. .9033201812 + 1. ,2215185471

+0.7110560511 +0.3277009825 -0. .6221023696 -1. , 0859676666

+0.7662378147 -0.3996182393 -0. .5031747948 -2. ,2419867854 + 0..7791921091 + 0.5756259475 + 0..2480210187 + 0..4068336286

+ 0. .3299436157 + 0. 2753821256 -0. .9029406932 -1. .2747736939

+ 0. .7227870273 + 0. 0104541399 -0. .6909917685 -1. .5556682994

+ 0. .4994238044 + 0. 0229922216 -0. .8660526666 -1. .5442542665

+ 0. .8206507575 + 0. 5395971841 + 0. .1880617270 + 0. .3353579013

+ 0. .4884941360 -0. 3400141399 + 0. .8035943403 + 1. .9710706733

+ 0. .8029403439 -0. 1689656988 + 0. .5716094793 + 1. .8582082320

+ 0. .8928255090 -0. 4338620721 -0. .1209392944 -2. .8697429339

+ 0. .7187494042 + 0. 6952452918 -0. .0057687162 -0. .0082971922

+ 0. .5802650788 -0. 7493339240 -0. .3190471888 -2. .7390662801

+ 0. .2666612715 -0. 5942457064 -0. .7587910165 -2. .2351768914

+ 0. .3644949458 -0. 9116198615 -0. .1899806900 -2. .9361343065

+ 0. .7777698533 -0. 0542668701 -0. .6262021736 -1. .6572406622

+ 0. .6620950236 -0. 6532002296 -0. .3673685340 -2. .6292690134

+ 0. .7029570106 -0. 1397463344 -0. .6973681977 -1. .7685678528

+ 0. .8647308416 -0. 4997123702 + 0. .0502804013 + 3. .0413114797

+ 0. .3337207472 -0. 8095004033 + 0. .4830523366 + 2. .6035817985

+ 0. .4824127577 -0. 3421419889 -0. .8063602115 -1. .9720774404

+ 0. .7003340113 -0. 6907202499 + 0. .1801049943 + 2. .8865226345

+ 0. .4140401953 -0. 4139039733 + 0. .8107121669 + 2. .0428432577

+ 0. .3008515857 + 0. 6234909280 -0. .7216282880 -0. .8582272392

+ 0. .8356293323 + 0. 3440875579 + 0. .4281674572 + 0. .8938468164

+ 0. .4705737366 -0. 8526101726 -0. .2271921037 -2. .8811770884

+ 0. .9073901234 -0. 3195771135 + 0. .2729718529 + 2. .4346850721

+ 0. .9839051142 + 0. 1215947464 -0. .1309406121 -0. .8223894292

+ 0. .9496500986 + 0. 1945428796 -0. .2455967391 -0. .9008767880

+ 0. .4299713008 + 0. 3795396729 -0. .8191912580 -1. .1369289250

+ 0. .5364948439 + 0. 5315738888 -0. .6554406787 -0. .8893733824

Table 5 (9 bit) vl real ( v2 ) imag ( 2 ) angle ( v2 )

+ 0 .8849664064 + 0 .0504737955 + 0, .4629112826 + 1 .4621897997

+ 0 .3552782612 -0, .6239635574 -0, .6960221520 -2 .3016581866

+ 0 .4319731382 -0 .3206448151 + 0, .8429626981 + 1 .9342739620

+ 0 .9491159414 -0 .2821692218 -0, .1398551394 -2 .6814368869

+ 0 .7068243617 -0 .5717230493 + 0, .4165718144 + 2 .5119123536

+ 0, .8713805998 + 0, .2777505940 -0. .4044137211 -0 .9689857271

+ 0, .8633308251 -0, .0117204695 + 0, .5045022468 + 1 .5940238974

+ 0. .6738477447 -0, .1521654937 -0. .7230317279 -1 .7782240664

+ 0. .6016132073 + 0, .7306407976 -0. .3228398578 -0 .4160628741

+ 0, .9121437820 -0, .4036894584 -0, .0709122144 -2 .9677063726

+ 0. .9998105035 -0, .0188831027 -0, .0047313257 -2 .8960882207

+ 0, .6409182920 -0, .2926755834 + 0. .7096229604 + 1 .9619790515

+ 0, .7993138716 + 0, .3100551666 + 0, .5147456929 + 1 .0286533873

+ 0 , .3898517790 -0, .7336624228 + 0, .5565564120 + 2 .4926101420

+ 0. .8406028447 + 0. .4836659474 -0. .2438321325 -0, .4669488160

+ 0. .7686250597 -0. .5793714767 -0. .2711903568 -2 , .7038081494

+ 0. .1425407156 -0. .9266561965 + 0. .3478367979 + 2 , .7824996620

+ 0. .2361615775 + 0. .7817213331 + 0. .5771823513 + 0, .6360020004

+ 0. .9500860769 -0. .1083901388 + 0. .2925543098 + 1, .9256122610

+ 0. .9016965912 + 0, .2870561879 + 0. .3233295569 + 0 .8447553140

+ 0. .4383816424 -0, .8775854135 -0. .1940757005 -2 .9239482176

+ 0. .8540775190 -0. .1328247506 -0. .5029007628 -1 .8290170211

+ 0. .4464161273 + 0, .5061145823 + 0. .7379435418 + 0, .9696339509

+ 0. .9505375607 -0. .2061470074 -0. .2323397450 -2 , .2965309988

+ 0. .8879331370 -0. .4007371713 + 0. .2257973952 + 2 , .6284779681

+ 0. .7812450693 + 0. .0264721912 + 0. , 6236628615 + 1 , .5283754745

+ 0. .3661960311 -0. .8512254721 -0. , 3759197552 -2. .7257278155

+ 0. .8086878210 -0. .0549259730 + 0. ,5856681191 + 1 , .6643062601

+ 0. .1848329633 + 0. .0745368211 + 0. .9799393032 + 1 , .4948798158

+ 0. .8635353156 -0. .3359974909 -0. .3760484608 -2 , .3000059647

+ 0. .6469437390 + 0. .3560910157 -0. , 6742870213 -1. .0849221992

+ 0. .6558964432 + 0. .0422053729 -0. .7536700620 -1. .5148549548

+ 0. .8331170113 -0. .5528303428 -0. , 0171655936 -3. .1105522442

+ 0. .5862071865 + 0. , 3747165985 -0. ,7182956253 -1. .0899597540

+ 0. ,7390056711 -0. , 2461900018 -0. , 6271053349 -1. .9448911988

+ 0. .3419774748 + 0. , 8911801406 + 0. ,2980761039 + 0. .3227763160

+ 0. , 7565871548 -0. , 5252225164 -0. ,3895089029 -2. .5034844842

+ 0. ,5164225300 + 0. , 8518176975 + 0. , 0878315476 + 0. .1027476286

+ 0. ,3163508572 + 0. ,2872775576 + 0. ,9040983022 + 1. .2631353911

+ 0. , 9372217378 -0. , 3217342472 + 0. , 1345454883 + 2. .7455057205

+ 0. ,3648325536 + 0. , 0504898990 -0. ,9297031666 -1. .5165420749

+ 0. , 8201265147 + 0. ,4702531118 -0. 3259670394 -0. .6061297758

+ 0. ,8838773709 -0. ,2432113909 -0. 3995109668 -2. .1176414224

+ 0. 6533284925 + 0. 1394684129 -0. 7441172238 -1. , 3855179197

+ 0. 9362264337 + 0. 3199249088 + 0. 1453551426 + 0. , 4264583964

+ 0. 8663611739 -0. 3616373518 + 0. 3444368478 + 2. ,3805504329

+ 0. 7217373631 -0. 1980606169 + 0. 6632248267 + 1. ,8609982408

+ 0. 4374232543 -0. 2301016920 -0. 8693181857 -1. , 8295543773

+ 0. 3897980336 + 0. 8266625386 + 0. 4058158946 + 0. ,4563482144

+ 0. 9483924062 + 0. 2492319898 + 0. 1960491243 + 0. , 6665246693

+ 0. 7473335402 + 0. 5656915363 -0. 3485479385 -0. , 5522062252

+ 0. 9686971138 -0. 0885914329 -0. 2318996759 -1. , 9357114787

+ 0. 3845920865 -0. 1824836402 + 0. 9048694094 + 1. 7697956803

+ 0. 4589814549 + 0. 1652988720 + 0. 8729331630 + 1. 3836518791 + 0..4834999459 -0..8702058678 + 0..0947077076 + 3, .0331856479

+ 0, .5092966432 + 0. .7082970032 + 0, .4888070012 + 0, .6040614701

+ 0. .9435226084 + 0. .1316451396 + 0, .3040306641 + 1, .1621695503

+ 0. .8070464402 -0. .3337424703 + 0, .4871262741 + 2 , .1714692664

+ 0, .9963142387 -0. .0747704349 -0. .0420395021 -2 , .6293949018

+ 0, .4214726120 -0. .9063625695 + 0. .0294572574 + 3, .1091035668

+ 0. .6370567030 -0. .6824501149 + 0, .3583581978 + 2 , .6580630786

+ 0. .9445883503 + 0. .1688956825 + 0, .2814730838 + 1. .0303459176

+ 0. .4218807483 + 0. .1350123837 -0. .8965424086 -1. .4213271627

+ 0. .7072232341 + 0. .1733574497 -0, .6854068075 -1. .3230653435

+ 0. .7715745679 + 0. .5771651250 -0, .2674941207 -0, .4339923859

+ 0. .6273365540 -0. .5546928763 -0. .5465936892 -2 , .3635486534

+ 0. .3407947045 + 0. .9232397870 -0. .1774465135 -0, .1898842529

+ 0. .6991846829 + 0. .6567633036 + 0. .2824937915 + 0. .4062080134

+ 0. .5560474738 -0. .7557670134 -0. .3458719826 -2 , .7124004681

+ 0. .7995824138 -0. .5752018645 -0. .1726579816 -2. .8499804805

+ 0. .4150684407 + 0. .8889481708 + 0. .1936216391 + 0, .2144602763

+ 0. .7297987345 -0. .6413853340 -0. .2366826155 -2 , .7880769242

+ 0. .6964218502 + 0. .3675147082 -0. .6163842517 -1 , .0331440102

+ 0. .6967177863 + 0. .5993396812 -0. .3941779709 -0. .5817601831

+ 0. .9172362327 -0. .1807852410 -0. .3549568848 -2. .0418689756

+ 0. .4901073099 + 0. .5962108419 + 0. .6358674836 + 0. .8175738415

+ 0. .1898681028 -0. .8493742189 -0. .4924566374 -2, .6161678113

+ 0. .4655285660 + 0. .7944802294 + 0. .3899798960 + 0. .4563102596

+ 0. .8977245107 + 0. .1188934634 -0. .4242110882 -1. .2975376600

+ 0. .0126695856 + 0. .5559330936 + 0. .8311304814 + 0. .9812575463

+ 0. .6191181891 -0. .2345786551 -0. .7494434752 -1. .8741401066

+ 0. .9144360966 -0. .2627655738 -0. .3078325493 -2. .2773761217

+ 0. .2866969610 + 0. , 1906309415 + 0. .9388635133 + 1. .3704752185

+ 0. .9838388830 -0. , 1394405527 + 0. .1123271316 + 2. .4634732602

+ 0. .7023265985 + 0. , 5552651350 -0. .4454413305 -0. .6760893377

+ 0. .4476665250 + 0. ,4446095987 -0. .7758330924 -1. .0504108615

+ 0. .8195060745 -0. , 3118206659 -0. .4808093866 -2. .1461394442

+ 0. .8984768183 -0. , 3250598902 -0. .2950855379 -2. .4044912951

+ 0. .4830114815 -0. , 0821787084 -0. .8717491432 -1. .6647873207

+ 0. .8598621685 -0. ,4324796817 + 0. .2712902064 + 2. .5813482467

+ 0. .6871818128 -0. , 7237808170 -0. .0626297465 -3. .0552762904

+ 0. .8236010763 + 0. , 1680943979 -0. .5416876780 -1. .2699023129

+ 0. .6036382721 + 0. ,7232866325 + 0. .3353763314 + 0. .4341749697

+ 0. .7228970919 + 0. , 6845254794 -0. .0940460662 -0. .1365339268

+ 0. .4417951342 + 0. 7360616405 + 0. .5128648173 + 0. .6085541089

+ 0. .9853741170 + 0. , 0309590130 -0. .1675690578 -1. .3881026652

+ 0. .5769353326 -0. , 3612282400 -0. .7325706660 -2. .0289061286

+ 0. .8894654422 + 0. ,4553500556 -0. .0388272332 -0. .0850632156

+ 0. , 6050348672 -0. 1393046073 -0. .7839177482 -1. .7466635531

+ 0. .2346534283 + 0. 2610718409 + 0. .9363649195 + 1. .2988875490

+ 0. .2764326811 + 0. 7029517230 -0. , 6553196532 -0. .7503443741

+ 0. .5461971188 -0. 5873921498 + 0. , 5971927409 + 2. .3479212397

+ 0. , 9616500297 + 0. 2308094657 -0. .1481762833 -0. .5707203331

+ 0. ,1178521292 + 0. 4379651128 + 0. ,8912336594 + 1. .1140407048

+ 0. ,5839769998 -0. 7147280351 + 0. ,3848827089 + 2. .6476196660

+ 0. , 6014838500 -0. 5618050963 + 0. ,5679720169 + 2. .3507360158

+ 0. ,7838336727 -0. 3851725022 -0. ,4870799904 -2. ,2398892047

+ 0. ,8263816879 + 0. 2269185754 + 0. ,5153651774 + 1. , 1560327958

+ 0. , 0517616502 -0. 8483273778 -0. ,5269358515 -2. ,5857689653

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+ 0. .4919371423 -0. .8700431351 -0. .0319811044 -3. .1048511278

+ 0. .4318662034 -0. , 0402660792 -0. .9010384149 -1. .6154551404

+ 0. .4250807268 -0. , 8812695929 + 0. .2065678588 + 2. .9113512331

+ 0. .1997052456 + 0. .4880154736 + 0. .8496815359 + 1. .0494498946

+ 0. .8106526329 -0. , 5798513147 -0. .0813311850 -3. .0022396227

+ 0. .8096433747 -0. .4708318834 + 0. .3504210943 + 2. .5017756101

+ 0. .3665841731 -0. ,4038241011 + 0. .8381778686 + 2. .0197685342

+ 0. .4980295326 + 0. , 8385011004 + 0. .2210938474 + 0. .2578095753

+ 0. .9800385959 -0. , 1961346043 + 0. .0324894984 + 2. .9774343147

+ 0. .8607562972 -0. , 5047960334 -0. .0654183570 -3. .0127172738

+ 0. .3346938777 -0. , 1420538026 -0. .9315582244 -1. .7221211012

+ 0. .6630990230 -0. 4907434728 + 0. .5652172410 + 2. .2857840521

+ 0. .6871093381 + 0. 4935878209 + 0. ,5331527179 + 0. .8239135717

+ 0. , 4261516796 -0. 6059355672 + 0. , 6717416426 + 2. .3047354995

+ 0. , 4334953469 + 0. 8841909632 -0. , 1740348376 -0. .1943451217

+ 0. .7530077947 -0. 1979313894 + 0. , 6275367927 + 1. .8763301116

+ 0. , 9717736165 -0. 2275445060 -0. ,0622859222 -2. , 8744068616

+ 0. ,4064214006 + 0. 8550388689 -0. ,3220716965 -0. , 3602382830

+ 0. , 9377130042 + 0. 0794209524 + 0. ,3382109314 + 1. , 3401486157

+ 0. , 6116756333 + 0. 2480904874 + 0. ,7512017237 + 1. ,2518159909

+ 0. .9666062111 + 0. 2428982172 + 0. 0816877516 + 0. ,3244221726

+ 0. .2856876759 + 0. 3150048880 -0. 9050715289 -1. ,2358649378

+ 0. 5626705062 + 0. 7832346347 -0. 2644719426 -0. ,3256451438

+ 0. 8581031798 + 0. 0508353297 -0. 5109546967 -1. 4716317842

+ 0. 9018288504 -0. 3818930599 -0. 2021445410 -2. , 6547632459

+ 0. 9913553065 + 0. 1051303825 -0. 0785000566 -0. 6413808757

+ 0. 9169547471 -0. 0110347736 -0. 3988385960 -1. 5984565366

+ 0. 8164068896 -0. 4178791592 -0. 3985684368 -2. 3798422084 +0.2996336795 -0.0621909188 +0.9520251823 +1.6360285103 +0.6719578127 -0.7111959184 -0.2065745956 -2.8589101529 +0.9368962907 +0.3321053194 -0.1092309358 -0.3177593275 +0.4903418475 -0.0602531468 +0.8694448982 +1.6399864122 +0.7100339744 +0.4771409700 -0.5178689506 -0.8263075621 +0.9990694591 +0.0103284302 +0.0418752850 +1.3289755319 +0.2720055025 +0.1076532923 +0.9562550785 +1.4586903315 +0.9734130753 -0.1736572908 -0.1493657600 -2.4312538238 +0.5755623309 +0.6058018240 -0.5493015140 -0.7365234759 +0.5755623309 +0.6058018240 -0.5493015140 -0.7365234759 +0.3255184951 -0.3845170454 -0.8638196288 -1.9895978295 +0.2651856466 -0.3483345181 -0.8990771026 -1.9404246620 +0.7636704683 -0.0008396035 -0.6456056930 -1.5720968157 +0.6812799589 +0.0204948383 +0.7317360038 +1.5427951331 +0.7990330817 -0.5999026440 +0.0407793093 +3.0737205211 +0.3261992517 +0.9399174894 +0.1007430458 +0.1067752225 +0.9832441998 -0.0712415654 -0.1677959564 -1.9723049064 +0.4297972907 +0.9026084391 +0.0239226799 +0.0264977367 +0.9289208832 +0.3174619355 -0.1905883319 -0.5406769499 +0.7307150281 -0.6803820964 -0.0559977725 -3.0594743204 +0.9984000770 +0.0306935157 -0.0474888858 -0.9970050405 +0.5661566251 +0.8034508461 +0.1842102431 +0.2253785817 +0.2635728406 -0.0057851351 -0.9646221488 -1.5767935619 +0.9751439032 +0.1565353042 +0.1568153901 +0.7862920048 +0.8685040243 +0.1906379344 -0.4575564859 -1.1760249495 +0.4788317910 -0.8280330257 -0.2916872028 -2.8029012835 +0.9051739796 +0.0637662861 +0.4202308026 +1.4202040241 +0.8095909328 +0.5869164010 -0.0095739136 -0.0163107805 +0.4798822804 -0.8536478258 +0.2024805829 +2.9087020456 +0.1712227886 +0.6917372202 +0.7015571073 +0.7924460099 +0.7879490842 +0.4668356728 +0.4014980638 +0.7102948772 +0.3936401015 +0.3368470814 +0.8553253850 +1.1956259898 +0.6700561595 +0.2427004658 -0.7015135259 -1.2377189704 +0.0793615654 +0.3446316910 -0.9353773246 -1.2177880611 +0.0805969725 +0.9383519093 +0.3361544622 +0.3439959482 +0.2640995845 -0.6073662464 -0.7492380478 -2.2519946383 +0.3571197816 -0.5477290738 +0.7566097563 +2.1973998385 +0.7501597874 +0.6414176465 +0.1607597468 +0.2455733384 +0.1784603957 -0.9711457415 -0.1582018833 -2.9801088156 +0.7021626537 -0.5702559454 -0.4263516911 -2.4995974293 +0.5340530963 -0.7592586557 +0.3719053429 +2.6861165644 +0.8225029234 -0.4010922786 +0.4032541694 +2.3535067360 +0.8461379349 -0.2299413138 -0.4808093045 -2.0168833201 +0.5017401529 +0.8329852804 -0.2332216579 -0.2729928723 +0.5943046737 +0.5651067324 +0.5722380063 +0.7916681888 +0.9473553072 +0.3147740592 +0.0586106961 +0.1840910881 +0.6993727012 -0.6441793022 +0.3096947715 +2.6934562731 +0.9166971997 +0.2877547580 +0.2772425711 +0.7667945813 +0.6446893456 -0.7640270423 -0.0252651213 -3.1085363392 +0.8137816377 +0.4824239017 +0.3240781160 +0.5915276659 +0.7604215448 -0.3767167000 +0.5290024595 + 2.1896146397 +0.4558473822 -0.7963403451 +0.3975490145 +2.6785692519 +0.8750095781 +0.4642568257 +0.1371999926 +0.2873472293 +0.5809499246 +0.8006971733 -0.1462231919 -0.1806293980 +0.9070554339 -0.1004121049 -0.4088616502 -1.8116195889 +0.8393170556 +0.3098539256 +0.4466961214 +0.9643400555 +0.6882416959 +0.7037564484 +0.1762107530 +0.2453419121 +0.4915445562 +0.0658992868 -0.8683554763 -1.4950517570 +0.9867888967 +0.0765712824 -0.1427743393 -1.0785245196 +0.7320490385 -0.0846020325 -0.6759783291 -1.6953038824 +0.7149315721 -0.5039136762 +0.4847100723 +2.3756166305 +0.6632505282 +0.7480559432 -0.0226062550 -0.0302108114 +0.9847727916 +0.1662526394 -0.0508193747 -0.2966555959 +0.7712704734 +0.1470121638 -0.6192974088 -1.3377250089 +0.9936567857 +0.0450411858 +0.1030411755 +1.1587062889 +0.6895461600 -0.1399765208 +0.7105861432 +1.7652934902 +0.2980137337 -0.7840820267 -0.5444292331 -2.5346670933 +0.2733372980 +0.8419752935 +0.4651497895 +0.5047227529 +0.5637235164 +0.4912854582 -0.6639686706 -0.9337759800 +0.5347974188 +0.6266516311 +0.5668328273 +0.7353189286 +0.7970242831 +0.4485339093 -0.4044374170 -0.7337466375 +0.5555858823 -0.1070022121 +0.8245452407 +1.6998463110 +0.4098100012 +0.6583255601 +0.6313978301 +0.7645225101 +0.6975111109 -0.1074686450 -0.7084692940 -1.7213399689 +0.5987192688 +0.0452370521 -0.7996804651 -1.5142876423 +0.4179328398 -0.0343757292 +0.9078273242 +1.6086441783 +0.3089109054 +0.5976444166 -0.7398616112 -0.8913302673 +0.5549754362 -0.0463942763 -0.8305719934 -1.6265965640 +0.9416702410 +0.2152156636 +0.2587264488 +0.8769476522 +0.7591629503 -0.2881727231 +0.5836335294 +2.0294364993 +0.9232056091 -0.3610988540 -0.1315257426 -2.7922908249 +0.7927982297 -0.5464433539 +0.2699456020 +2.6827527524 +0.7696262199 +0.2361105730 -0.5932345902 -1.1920106104 +0.7925308406 +0.0781941631 -0.6047979328 -1.4422198494 +0.5207237320 +0.6423084542 -0.5623936740 -0.7191594916 +0.6818097515 +0.3937244782 +0.6165358855 +1.0024715858 +0.6721990172 -0.6698251203 -0.3154089241 -2.7015091883 +0.9363784095 -0.0489933237 +0.3475559357 +1.7108388777 +0.4505625999 +0.6491339146 -0.6128772345 -0.7566767769 +0.1181537846 -0.9869963490 -0.1089857344 -3.0316165680 +0.3756260559 +0.9236355488 -0.0761737427 -0.0822854250 +0.6079293169 -0.7108112879 -0.3537926774 -2.6797620446 +0.5703857491 +0.6800994400 +0.4605701347 +0.5952663523 +0.6624637059 +0.6594642052 -0.3553150720 -0.4941987322 +0.6286905605 +0.4126333624 +0.6591524007 +1.0114739177 +0.9724380814 -0.0121277579 -0.2328456472 -1.6228342713 +0.6318561358 -0.0581361152 -0.7729023326 -1.6458728841 +0.6233100444 -0.4196446173 +0.6598355733 +2.1372550164 +0.6757077954 -0.7345157897 +0.0624942383 +3.0567148436 +0.3355492081 +0.1476957914 +0.9303723352 +1.4133609569 +0.8851478283 -0.4437083261 +0.1401293811 +2.8356913165 +0.8298651703 +0.3953553624 -0.3937231726 -0.7833296907 +0.8789038463 +0.3870626603 +0.2787660774 +0.6241607963 +0.6992934105 -0.2059372550 -0.6845279929 -1.8630287476 +0.1626653083 +0.8925335111 +0.4206232626 +0.4403996733 +0.8177322494 +0.3909691657 +0.4224418064 +0.8240710484 +0.2233969336 +0.9050284949 -0.3619630277 -0.3804603020 +0.4995050187 +0.0456535693 +0.8651072118 +1.5180730815 +0.9590688063 +0.0658584881 +0.2754082139 +1.3360737069 +0.9345324994 +0.2313465901 -0.2704214541 -0.8631156705 Table 6 (10 bit) vl real ( v2 ) imag ( v2 ) angle ( v2 )

+ 0 .7393308570 + 0 .2441256533 + 0 .6275289230 + 1 .1997851326

+ 0, .6094372697 -0 .1435708610 + 0 .7797266329 + 1 .7528864997

+ 0, .3615414294 + 0 .8078477257 + 0 .4654780843 + 0 .5227321356

+ 0 .5288322589 -0 .5309347582 + 0 .6621515872 + 2 .2466537366

+ 0. .6247313201 + 0 .7694918778 + 0 .1326387111 + 0 .1706944443

+ 0, .5660637671 -0 .5800939600 -0 .5857156385 -2 .3513724035

+ 0. .5350787109 -0 .0516961557 + 0 .8432189992 + 1 .6320277881

+ 0. .8264081922 + 0, .0018685678 -0, .5630683868 -1, .5674777939

+ 0. .9736340403 + 0 , .0891629024 -0, .2099684083 -1 , .1692229048

+ 0. .4369312608 + 0, .0212501001 -0, .8992438527 -1, .5471696478

+ 0. .8418419196 -0 , .1220764501 -0, .5257371233 -1 , .7989536988

+ 0. .4088056652 + 0, .3769367680 -0, .8311417455 -1, .1450216559

+ 0. .4468074033 -0, .8926326570 + 0, .0597501798 + 3, .0747553266

+ 0. .3911724160 + 0, .4196628446 + 0, .8190648557 + 1 .0973031293

+ 0. .4314083251 + 0, .2392811872 + 0, .8698456015 + 1 .3023514039

+ 0. .7543255713 + 0, .6363715050 + 0, .1613203030 + 0 .2482702450

+ 0, .8635196786 -0, .4727758019 -0, .1755471610 -2 .7860595237

+ 0. .5388496835 + 0, .5731689120 -0, .6173478897 -0 .8224902187

+ 0. .8742168972 -0. . 849848436 + 0. .0231196466 + 3, .0939578511

+ 0. .1628877703 -0. .9140415900 + 0. .3714775176 + 2 , .7555708969

+ 0. .6670096852 -0. .6050938494 -0. .4346947357 -2 , .5186292489

+ 0. .6277656724 + 0, .7583847970 -0. .1753931590 -0, .2272761315

+ 0. .3160036615 -0. .9272926942 + 0. .2006737281 + 2 , .9284709170

+ 0. .9450220966 + 0. .3254987286 -0. .0313658206 -0, .0960657313

+ 0. .1973791308 + 0. .3673681711 -0. .9088905905 -1. .1866796242

+ 0. .5486887567 + 0. .1025137204 -0. .8297177746 -1, .4478667981

+ 0. .8488486285 -0, .4531671879 + 0. .2722048964 + 2, .6006790925

+ 0. .5734944450 -0. .3901871240 -0. .7203180755 -2. .0672350013

+ 0. .6494235719 -0. .1014645987 -0, .7536272019 -1. .7046265710

+ 0. ,4756402880 + 0. , 3129387513 -0. ,8220922420 -1. .2070715335

+ 0. , 9711286383 -0. , 1988905346 -0. .1317259396 -2. .5566166416

+ 0. , 9118754266 -0. , 1749363931 -0. .3713225885 -2. .0110717396

+ 0. ,3846239446 -0. .4103585721 -0. .8268435545 -2. .0314757882

+ 0. ,2439239120 -0. , 6644929376 -0. ,7063641136 -2. .3256601887

+ 0. , 9354761451 -0. , 1061987183 -0. ,3370552095 -1. .8760282088

+ 0. , 6036504671 -0. .5145559731 -0. .6089649120 -2. .2723618967

+ 0. , 2030011074 + 0. , 5695228609 + 0. .7965138174 + 0. .9500611663

+ 0. ,8126455390 + 0. , 0539370778 + 0. .5802568565 + 1. .4781088704

+ 0. ,5649000337 + 0. , 8211899056 + 0. .0808399089 + 0. .0981262421

+ 0. ,5839610012 -0. , 0300585980 + 0. .8112250179 + 1. .6078327253

+0. 5615438925 -0. 5167420267 + 0. ,6462554716 + 2. ,2452896865

+ 0. 9355657590 -0. 0262971298 + 0. ,3521720766 + 1. , 6453292572

+ 0. 7617474321 + 0. 4302849278 + 0. ,4843508342 + 0. , 8444414104

+ 0. 3198779688 + 0. 7464796969 + 0. 5834776321 + 0. , 6634444996

+ 0. 3424415523 + 0. 3679770288 -0. .8644805895 -1. ,1683646111

+ 0. 9201997796 -0. 3828671472 -0. 0815175638 -2. , 9318117107

+ 0. 6251256091 -0. 0540276882 -0. 7786520287 -1. , 6400714734

+ 0. 9651642916 + 0. 1972096857 -0. 1719483355 -0. ,7170750351

+ 0. 5540004271 + 0. 6871622882 + 0. 4699909749 + 0. ,5998790129

+ 0. 8538478654 -0. 5125846675 -0. 0905581657 -2. ,9667273888

+ 0. 7344260695 + 0. 6294503777 + 0. 2537923767 + 0. ,3832591959

+ 0. 8901621727 -0. 4512681586 + 0. 0629948835 + 3. 0028937208

+ 0. 9519102438 -0. 3026377143 -0. 0477210823 -2. 9851965329

+ 0. 7477353287 + 0. 3393564022 -0. 5707268265 -1. 0343539875 + 0.9081328414 + 0, .1540640419 -0.3893058096 -1.1939673923

+ 0 .6884656031 + 0, .3064911400 + 0 .6573266269 + 1 .1344956291

+ 0 .2773131202 + 0 .9225659655 + 0 .2682712670 + 0 .2829842938

+ 0 .7916859405 + 0, .6035739774 + 0 .0945083350 + 0 .1553200281

+ 0 .6023354184 + 0 .4618739909 -0 .6510487388 -0 .9537690065

+ 0. .9345147310 -0, .2497689306 + 0, .2535699094 + 2 , .3486431028

+ 0. .9177077610 + 0, .1896528697 -0, .3490619637 -1, .0730950185

+ 0. .9921650404 -0, .0805611744 -0, .0954904699 -2 , .2715962297

+ 0. .7481548432 + 0, .5717960361 + 0, .3366208900 + 0, .5320751683

+ 0. .9694737088 -0, .0926486210 -0, .2270175343 -1, .9582763424

+ 0, .8814725031 + 0, .0672072169 + 0, .4674285147 + 1, .4279942659

+ 0, .6422827440 + 0, .4475757472 -0, .6222128473 -0, .9472153248

+ 0, .4708336873 -0, .8817251663 -0, .0296035472 -3, .1080306863

+ 0 .7198119097 -0 , .6379361370 + 0 .2736938065 + 2 .7363134309

+ 0. .5106561203 + 0. .8007688298 + 0, .3130488908 + 0, .3726677340

+ 0. .5478337068 + 0. .3164425878 -0, .7744303186 -1 , .1828867487

+ 0. .4369972092 + 0. .1219652277 -0, .8911553862 -1, .4347794687

+ 0. .5855699505 -0. .0769922232 -0, .8069572670 -1, .6659189184

+ 0. .8537722552 + 0. .4784690784 + 0. .2052809714 + 0, .4052851066

+ 0, .2258835091 + 0. .7943534522 + 0, .5638964739 + 0, .6173268128

+ 0. .7124462969 -0. .6785940266 -0 , .1786908534 -2 , .8841125506

+ 0, .8447237583 -0, .4961469618 -0, .2006986910 -2 , .7572004468

+ 0. .6934731833 -0. .4404403353 -0, .5701817738 -2 , .2285150606

+ 0. .0943510121 + 0. . 854839810 + 0. .8691393391 + 1. .0613895450

+ 0. .7294837145 -0. .1432544890 -0. .6688285742 -1. .7817954251

+ 0. .7806418140 + 0. .6239694483 + 0. .0355033220 + 0. .0568378503

+ 0. .8353594121 + 0. .2527636364 -0. .4881446474 -1. .0930065551

+ 0. .8012511704 -0. .2581375161 -0. .5397792000 -2. .0168751078

+ 0. .3630782024 -0. .5532078432 -0. .7497568280 -2. .2064757787

+ 0. .4008303982 -0. .8344799411 -0. .3781246088 -2. .7161421358

+ 0. .8673539779 + 0. .3416133781 -0. .3619355978 -0. .8142754288

+ 0. .7788886390 + 0. .2700283388 -0. .5660540471 -1. .1256878488

+ 0. .4868513504 + 0. , 6021120321 + 0. , 6328008086 + 0. .8102440152

+ 0. .2243459918 -0. , 2225449922 -0. , 9487584531 -1. .8011954791

+ 0. .6213674986 -0. ,7647430870 + 0. , 1705005647 + 2. , 9222289232

+ 0. .7513013068 + 0. , 1666536083 + 0. , 6385709993 + 1. ,3155114953

+ 0. .7728648185 + 0. , 2903629224 + 0. ,5642422756 + 1. .0955316638

+ 0. .8650674640 -0. , 4788892583 + 0. , 1494100433 + 2. .8391698462

+ 0. .7780222127 + 0. , 1744803801 + 0. , 6035213612 + 1. .2893656858

+ 0. .9984843297 + 0. , 0163146411 + 0. .0525630656 + 1. .2698419840

+ 0. .1116170910 -0. , 7724079328 + 0. .6252420414 + 2. .4611031607

+ 0. .9588216958 -0. , 2571572066 -0. .1205451235 -2. .7032475403

+ 0. ,9882330013 -0. 1311963686 -0. , 0786323601 -2. , 6016522601

+ 0. ,5927418158 + 0. 2281131874 -0. ,7724127870 -1. ,2836335686

+ 0. , 8070948413 + 0. 1716269236 -0. ,5649266468 -1. ,2758533715

+ 0. , 6809214487 -0. 7219478733 + 0. , 1230335280 + 2. , 9727954371

+ 0. , 9032019779 + 0. 3915580277 + 0. ,1758081286 + 0. ,4220189837

+ 0. ,5152374872 + 0. 2616435828 + 0. ,8161329348 + 1. ,2605588055

+ 0. ,0728609046 + 0. 3694383101 -0. 9263944212 -1. , 1913321109

+ 0. , 9673917179 + 0. 2519519321 + 0. ,0259516489 + 0. , 1026404148

+ 0. ,3706511179 + 0. 7443483670 + 0. ,5554847049 + 0. , 6411095015

+ 0. 8604460188 + 0. 3569407504 + 0. 3636288622 + 0. 7946795980

+ 0. 8122582568 -0. 4699172666 + 0. 3455637233 + 2. 5075197669

+ 0. 4433272251 + 0. 8047211122 + 0. 3948226223 + 0. 4561258569

+ 0. 7149857061 + 0. 6579461236 -0. 2364367538 -0. 3449851708

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+ 0. .5532726304 + 0. ,8310499948 -0 .0569675569 -0 .0684418251

+ 0. .8571447095 -0. ,5108240488 + 0 .0660434572 + 3 .0130178079

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+ 0. .9783464890 + 0. ,0604879370 + 0 .1979377603 + 1 .2742183825

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+ 0. ,5151129691 + 0. 1176922849 -0, .8490036249 -1 .4330501810

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+ 0. 9920605348 + 0. 0546771545 + 0. .1132532740 + 1 .1210140845

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+ 0. .3879591956 -0, .9193322020 -0, .0656960033 -3 .0702533526

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+ 0. .8658079313 + 0, .2293877776 + 0, .4446997566 + 1 , .0945680815

+ 0. .9908375239 -0, .0673214333 + 0. .1170846949 + 2 , .0926160604

+ 0. .7165070085 + 0, .6791137578 + 0, .1594434404 + 0, .2306050162

+ 0, .4826112405 -0, .7498222794 -0, .4526068270 -2 , .5985165162

+ 0, .5841713697 + 0, .0318481529 -0, .8110052441 -1. .5315465230

+ 0. .8018895079 -0, .0488129484 -0, .5954750315 -1 , .6525865785

+ 0, .8018895079 -0, .0488129484 -0, .5954750315 -1 , .6525865785

+ 0. .8021735642 + 0, .1615384628 + 0, .5748242321 + 1 , .2968398406

+ 0. .8021735642 + 0. .1615384628 + 0. .5748242321 + 1. .2968398406

+ 0. .6262497710 -0. .7580205648 -0. .1822527029 -2. .9056388638

+ 0. .9347441165 -0. .3536207586 -0. .0347245709 -3 , .0437092613

+ 0. .6410388454 + 0. .7639636989 + 0. .0736794775 + 0, .0961463269

+ 0. .7945721908 -0. .1865779785 -0. .5777920833 -1 , .8831416490

+ 0. .8403844380 + 0, .4075624315 -0, .3572770085 -0, .7197462718

+ 0. .7048263332 + 0. .3274952338 -0, .6292588593 -1 , .0909260565

+ 0. .7327061257 -0. .5007092804 -0, .4609034062 -2 , .3975657842

+ 0. .7327061257 -0, .5007092804 -0, .4609034062 -2 , .3975657842

+ 0. .2988883430 -0. .9438373021 -0. .1408435497 -2. .9934613308

+ 0. .9667582390 + 0. .1118013957 + 0. .2299542458 + 1. .1182578366

+ 0. .9798016222 -0. .1909769505 -0. .0593008057 -2. .8405191246

+ 0. .9685405297 + 0. .1587514250 + 0. .1916434906 + 0. .8789952977

+ 0. .5509430417 + 0. .7867163548 -0. .2784585103 -0. .3401896969

+ 0. .8150086037 -0. .3515376058 + 0. .4606324866 + 2. .2226685787

+ 0. .9566268340 -0. .1398324730 + 0. .2555620864 + 2. .0714538565

+ 0. .9961807532 + 0. .0556917569 + 0. .0672483101 + 0. .8791242675

+ 0. .8195027812 + 0. .5167826402 -0. .2476911270 -0. .4469465050

+0. .9574306516 -0. , 1888860499 -0. ,2182856101 -2. .2841152394

+ 0. ,4930663004 -0. , 8424450393 -0. ,2171911122 -2. .8892766199

+ 0. ,7206518486 + 0. , 1061805868 -0. , 6851179432 -1. .4170381208

+ 0. ,4627598029 -0. , 8297052418 -0. ,3121579352 -2. .7817462467

+ 0. , 9834049919 + 0. , 0800529659 -0. ,1628070775 -1. .1138071467

+ 0. ,5712301482 -0. , 6849369898 -0. ,4522802647 -2. .5579940599

+ 0. , 6182156552 + 0. , 5934626999 + 0. .5153750357 + 0. .7150912508

+ 0. ,7033904439 -0. ,7055832800 -0. ,0859890597 -3. .0203212063

+ 0. , 9593672897 + 0. .0715142948 + 0. .2729470812 + 1. .3145484181

+ 0. 9720574601 -0. , 0108860455 + 0. ,2344904864 + 1. , 6171872707

+ 0. 9643191006 + 0. ,2576724107 -0. ,0607750029 -0. ,2316282231

+ 0. 6930219609 -0. ,7196264011 + 0. ,0431092171 + 3. ,0817591616

+ 0. 5111975817 + 0. ,7528569321 + 0. ,4145883166 + 0. , 5033702924

+ 0. 9675875218 -0. ,2123494137 + 0. ,1366825307 + 2. ,5696816105

+ 0. 3489144964 -0. , 3339543191 + 0. ,8756330207 + 1. , 9351540375

+ 0. , 6868260782 -0. , 0181151757 + 0. ,7265960217 + 1. ,5957227277

+ 0. 9599472339 + 0. , 2424561305 -0. , 1404148597 -0. ,5249363777

+ 0. 3696728730 + 0. ,2044621496 + 0. , 9063868911 + 1. ,3489305362

+ 0. 6321248438 -0. 2724594348 + 0. 7253854411 + 1. 9300985544

+ 0. 7190962082 -0. 0289411496 + 0. 6943076070 + 1. 6124556790

+ 0. 8449164565 + 0. 0446528772 -0. 5330312393 -1. 4872198715

+ 0. 3028697552 -0. 3030091508 + 0. 9035791974 + 1. 8943546804

+ 0. 8297252773 + 0. 1975922216 -0. 5220280435 -1. 2089529802

+ 0. 6983379578 + 0. 7032933244 -0. 1330511050 -0. 1869732452

+ 0. 8092584968 -0. 4743720828 -0. 3465137984 -2. 5107094246

+ 0. 9171475470 + 0. 3396404197 + 0. 2085300036 + 0. 5506303683 + 0.4935106354 + 0.0366701993 -0.8689663683 -1.5286215590

+ 0, .6584343860 + 0 .5297406533 -0 .5346391302 -0 .7900003199

+ 0, .6827352532 + 0 .7302437423 + 0 .0248324565 + 0 .0339926106

+ 0. .4153740987 -0 .6042285540 + 0 .6799795678 + 2 .2972762050

+ 0, .4541253844 + 0 .5023065536 -0 .7358384751 -0 .9718224012

+ 0. .4541253844 + 0, .5023065536 -0 .7358384751 -0 .9718224012

+ 0. .6333656477 + 0, .2898198620 -0 .7175321623 -1, .1869220783

+ 0, .4092727459 + 0, .5961122516 -0 .6907575573 -0, .8588128994

+ 0, .9013562930 + 0. .2853514427 + 0 .3257781256 + 0, .8514526818

+ 0. .7907156207 + 0. .5925058391 + 0 .1539663530 + 0, .2542334180

+ 0. .2429152873 + 0. .8568729870 -0 .4547096297 -0, .4878749858

+ 0. .5609711237 -0, .7919895568 -0, .2409646039 -2 , .8462392932

+ 0. .3964591901 + 0, .8312552784 + 0, .3896598166 + 0, .4383453425

+ 0. .2059357720 -0. .8818005961 -0, .4242854776 -2 , .6931318852

+ 0. .9344309132 + 0. .1447386849 -0 , .3254067939 -1 , .1522809197

+ 0. .7065911798 -0. .1113367005 + 0, .6988083026 + 1 , .7287920673

+ 0. .4183545373 + 0. .7546261860 + 0, .5054886750 + 0, .5902053391

+ 0. .7322370412 -0. .6792049076 -0, .0500959982 -3. .0679691401

+ 0. .7322370412 -0. .6792049076 -0 , .0500959982 -3. .0679691401

+ 0. .5178187833 + 0. .8378021988 -0, .1730641018 -0. .2037040127

+ 0. .2849485710 + 0. .0584623399 -0, .9567583115 -1. .5097676009

+ 0. .5355117470 + 0. .4374623974 -0, .7223945042 -1. .0262893180

+ 0. .7830544823 -0. .4529462775 + 0, .4262221808 + 2. .3865821482

+ 0. .5687189294 + 0. .1631148215 -0, .8061962133 -1. .3711647955

+ 0. .4025643053 -0. .9006663677 -0. .1635300409 -2. .9619836515

+ 0. .7170789071 + 0. .6941540282 + 0. .0628333194 + 0. .0902718241

+ 0. .9365352054 + 0. .2944298932 -0. .1902967343 -0. .5737858044

+ 0. , 9365352054 + 0. .2944298932 -0. .1902967343 -0. .5737858044

+ 0. , 3466042817 -0. .9120030448 + 0. .2193534094 + 2. .9055576717

+ 0. .9007461075 + 0. , 0396469760 + 0. .4325327353 + 1. .4793893850

+ 0. , 9291854739 + 0. ,2144444837 -0. .3010447118 -0. , 9518401652

+ 0. .8390962957 -0. , 4993324611 + 0. .2158344270 + 2. ,7336006767

+ 0. ,3483413836 + 0. , 0242581305 + 0. .9370537997 + 1. , 5449144471

+ 0. .8913970568 -0. , 4264856648 -0. .1533664400 -2. ,7963866686

+ 0. 8552233305 + 0. , 0154949938 + 0. .5180279531 + 1. ,5408937413

+ 0. 8552233305 + 0. 0154949938 + 0. .5180279531 + 1. , 5408937413

+ 0. 8674466043 -0. 2880176239 -0. .4056873637 -2. ,1881687786

+ 0. 9336320069 + 0. 3559658963 + 0. , 0402437130 + 0. , 1125769604

+ 0. 5897831091 + 0. 7047881291 + 0. .3942455799 + 0. 5100175046

+ 0. 8213111575 + 0. 4887349747 + 0. ,2942551733 + 0. 5419439341

+ 0. 6944845540 + 0. 2242368739 + 0. , 6836731885 + 1. 2538639026

+ 0. 0941176083 -0. 1249273038 + 0. , 9876917761 + 1. 6966123196

Table 7 (5 bit, Codebook optimized including orthogonal precoding vectors) vl real ( v2 ) imag ( v2 ) angle ( v2 )

+ 0. .8868707849 + 0. .4618952503 + 0. .0106296123 + 0, .0230089754

+ 0. .9337412276 + 0. .3154378798 -0. .1691929785 -0, .4923223792

+ 0. .7728530345 -0. .2933029007 + 0. .5627358132 + 2 , .0512667191

+ 0. .5908364455 -0. .7742251893 + 0. .2269089044 + 2 , .8564977180

+ 0. .7320805228 -0. .6659323432 + 0. .1434999035 + 2 , .9293508553

+ 0. .4591559629 + 0. .5473755421 -0. .6996826550 -0, .9069293985

+ 0. .9149189768 -0. .0166002174 + 0. .4032960434 + 1 , .6119344737

+ 0. .6774622269 -0. .0651096162 + 0. .7326702321 + 1 , .6594296933

+ 0. .8156779110 -0. .0154336120 + 0. .5783003970 + 1 , .5974778742

+ 0. .3184846599 -0. .5616832483 -0. .7635963921 -2 , .2050020425

+ 0. .3418481620 + 0. .9180995345 -0. .2005818509 -0, .2150953002

+ 0. .5428840615 + 0. .7413848505 -0. .3944938520 -0, .4889997522

+ 0. .7102884428 -0. .2509334044 -0. .6576646216 -1 , .9352990092

+ 0. .1857306992 -0. .4508656337 + 0. .8730545732 + 2 , .0474960045

+ 0. .9718577907 -0. .1058940388 + 0. .2104254910 + 2 , .0370307348

+ 0. .5027996612 -0. .7542386322 -0. .4222754863 -2 , .6312033994

+ 0. .1499672138 + 0. .9347809800 + 0. .3220160775 + 0. .3317513924

+ 0. .8503001398 -0. .0440620252 -0. .5244503887 -1 , .6546151027

+ 0. .9971360769 + 0. .0490047775 + 0. .0576036098 + 0. .8658820513

+ 0. .5231794805 -0. , 6413996163 + 0. .5611503929 + 2. .4228282412

+ 0. .8458055052 -0. ,2911356100 -0. .4470493305 -2. .1480415080

+ 0. , 5340994093 + 0. , 8422806899 + 0. .0728083816 + 0. .0862276017

+ 0. .7493379790 + 0. ,4905209459 + 0. .4448390663 + 0. .7365981182

+ 0. ,5901007419 + 0. , 6878083454 + 0. .4227301674 + 0. .5510890174

+ 0. , 6744282076 -0. , 7201708760 -0. , 1627897483 -2. .9192854755

+ 0. , 8495796058 + 0. ,2453837005 + 0. ,4669061287 + 1. .0869162737

+ 0. , 9161147911 + 0. , 1375686797 -0. ,3765747574 -1. .2205428942

+ 0. ,7177634833 + 0. , 5388733824 -0. ,4409433748 -0. .6857817215

+ 0. , 9246319214 -0. ,3322668698 -0. , 1861572915 -2. .6309030913

+ 0. , 3266361514 + 0. 3301758751 + 0. ,8856030240 + 1. .2139329484

+ 0. , 9622781839 + 0. ,2688055703 + 0. , 0420031197 + 0. .1550049105

+ 0. ,5945174836 -0. 3599055575 + 0. ,7190389081 + 2. .0348734207

Table 8 (6 bit, Codebook optimized including orthogonal precoding vectors) vl real ( v2 ) imag ( v2 ) angle ( 2 )

+ 0 .9273716336 + 0 .3246533257 -0 .1859625535 -0 .5201819671

+ 0 .6179634900 -0 .6443196655 -0 .4505255750 -2 .5313858069

+ 0 .9252378169 -0 .3500544499 + 0 .1462766701 + 2 .7457780643

+ 0 .2063172598 + 0, .9402642101 + 0 .2708069488 + 0 .2804222500

+ 0 .4684326185 -0, .5812423405 + 0 .6653782559 + 2 .2888054902

+ 0 .5214576025 + 0, .7581839443 -0 .3914576291 -0 .4766099730

+ 0 .6727514533 + 0, .6667293262 -0 .3207452067 -0 .4483913547

+ 0 .0742827590 + 0, .8689268141 -0 .4893345108 -0 .5128816723

+ 0 .6779939200 -0 , .7349396641 + 0 .0137089248 + 3 .1229416870

+ 0 .6113759150 + 0, .4314359867 + 0 .6633871267 + 0 .9941728023

+ 0 .3450834000 -0, .0841670317 + 0 .9347905422 + 1 .6605925785

+ 0 .6026979262 + 0, .1399536811 + 0 .7856005199 + 1 .3944972033

+ 0 .3737211492 + 0, .8311273697 + 0 .4117763933 + 0 .4599955185

+ 0. .9650410057 + 0, .1846633653 -0 .1859981152 -0, .7889991421

+ 0, .9956020883 + 0. .0843760640 -0 .0407082489 -0, .4495190692

+ 0, .9004705376 + 0. .4304486232 -0 .0621835487 -0, .1434696414

+ 0. .5054592423 -0, .7433613861 -0 .4380922322 -2, .6090486293

+ 0, .7517315124 + 0. .0868697303 -0 .6537227113 -1 , .4386856415

+ 0, .5323653437 -0. .3010565622 + 0 .7911713387 + 1 , .9343976939

+ 0. .2316418927 + 0. .8436596581 -0, .4843350234 -0, .5211487402

+ 0. .6616827242 + 0. .2893385702 -0, .6917074268 -1, .1746175548

+ 0. .8850043139 + 0. .2329979062 + 0, .4030872611 + 1 , .0466853431

+ 0. .6296491548 + 0. .7593331481 -0, .1641801209 -0. .2129383253

+ 0. .9534294514 + 0. .1085939700 + 0, .2813887542 + 1. .2024851898

+ 0. .9739837398 + 0. .1956563039 + 0, .1143428413 + 0. .5288748765

+ 0. .8572963866 + 0. .4511211468 -0, .2480576876 -0. .5027428912

+ 0. .3403052379 + 0. , 9400800591 + 0, .0210196913 + 0. .0223557443

+ 0. .5760894271 -0. , 5287103478 + 0. .6233669386 + 2. .2742169561

+ 0. .3725668939 -0. , 6946545967 -0. .6153445383 -2. .4166627526

+ 0. .6080400422 -0. ,7619680701 + 0. .2229169514 + 2. .8569807984

+ 0. .8826936550 + 0. , 0604817553 + 0. .4660406298 + 1. .4417397777

+ 0. .8111948305 + 0. , 3547420313 + 0. .4648881997 + 0. .9189830414

+ 0. .7071821496 + 0. , 1016276439 + 0. .6996893806 + 1. .4265581951

+ 0. .9304472102 -0. , 0705123005 + 0. .3595775360 + 1. .7644368019

+ 0. .9917439857 -0. , 0699540844 -0. .1074722892 -2. .1478064033

+ 0. .9921886010 + 0. 0446975435 + 0. .1164641993 + 1. .2043435946

+ 0. .6290480912 + 0. 0352540893 -0. .7765665768 -1. .5254300934

+ 0. .5882358033 -0. 2193089063 -0. .7783843802 -1. , 8454260033

+ 0. ,5157814306 + 0. 8165623666 + 0. .2592207889 + 0. .3073915108

+ 0. .6173770002 -0. 7567730727 -0. .2148025976 -2. ,8650265240

+ 0. ,7676416388 + 0. 2850329794 -0. , 5740056751 -1. , 1098979044

+ 0. ,8618752221 -0. 1827643104 -0. , 4730415504 -1. , 9394890231

+ 0. ,5237351622 + 0. 4154501763 -0. ,7437087003 -1. ,0613595583

+ 0. ,5709884897 + 0. 6656282721 + 0. ,4805321510 + 0. , 6252881577

+ 0. 3754662004 + 0. 2783704025 + 0. ,8840447112 + 1. ,2657421999

+ 0. 6994420939 + 0. 5165257330 + 0. ,4939452646 + 0. 7630554035

+ 0. 8736972401 -0. 4849372867 + 0. , 0385870528 + 3. 0621887330

+ 0. 6981853355 -0. 2960745485 -0. , 6518259730 -1. 9971568015

+ 0. 8118307021 -0. 4117126696 + 0. 4140333186 + 2. 3533841309

+ 0. 8697009071 + 0. 0253589194 -0. 4929272334 -1. 5193960771

+ 0. 6794415446 + 0. 6767880977 + 0. 2834026434 + 0. 3965619712

+ 0. 2983577584 + 0. 5711668848 + 0. 7646901579 + 0. 9292655465

+ 0. 7029961458 -0. 4987729573 + 0. 5069733287 + 2. 3480411520

+ 0. 6238415094 + 0. 7762419139 + 0. 0909409817 + 0. 1166238335 +0.8869315223 -0.3097210131 -0.3426738519 -2.3057268072 +0.3892763374 -0.3901733698 +0.8344031847 +2.0081959696 +0.8391062875 +0.5437102311 +0.0167279082 +0.0307565174 +0.9148854685 +0.3907245050 +0.1015821868 +0.2543532324 +0.9611228936 +0.2737193167 -0.0363389456 -0.1319880604 +0.4095133351 +0.6036188796 -0.6840636495 -0.8477895983 +0.2359262874 +0.3414584320 -0.9098048836 -1.2117543262 +0.6328652830 -0.6531553408 +0.4157759426 + 2.5747200024 +0.9782279749 +0.0196684539 -0.2065990829 -1.4758813123 +0.8540098170 -0.1010801186 +0.5103430631 + 1.7663287711

Table 9 (7 bit, Codebook optimized including orthogonal precoding vectors) vl real (v2) imag ( v2 ) angle ( 2 )

+ 0 .5809413615 + 0, .7842335412 + 0, .2179102735 + 0 .2710269001

+ 0 .5982471968 -0 .3537775777 -0, .7189865903 -2 .0280639860

+ 0 .7143483868 -0 .5665504922 -0, .4107638276 -2 .5142674304

+ 0 .6365481899 -0 .0078575688 -0, .7711969013 -1 .5809847714

+ 0 .6509687276 + 0 .6897368486 -0, .3170217586 -0 .4308309356

+ 0 .6227345860 + 0 .2471720964 + 0, .7423662103 + 1 .2493892760

+ 0 .6566562329 -0 .7289006393 -0, .1936658201 -2 .8818969151

+ 0. .2061480264 + 0, .6813508854 + 0. .7023275319 + 0 .8005570612

+ 0, .7868204647 -0, .5594789679 -0. .2605702225 -2, .7057289337

+ 0, .5531449600 + 0 , .3329374898 -0. .7636643773 -1 , .1596677979

+ 0, .7157159233 + 0, .6968533676 + 0. .0463260318 + 0, .0663812062

+ 0, .8352186103 + 0, .0610630506 -0. .5465173162 -1, .4595265934

+ 0, .8839929771 + 0, .4064879097 -0. .2309198904 -0 .5166223292

+ 0, .4629649762 + 0, .7323743464 -0, .4992907445 -0 .5983672522

+ 0. .9506709131 -0, .0190534640 + 0. .3096155365 + 1 , .6322579270

+ 0. .7503467683 -0, .6500984036 + 0. .1197989688 + 2 .9593588836

+ 0, .1857539411 -0, .9167585642 -0, .3536229749 -2 .7734465948

+ 0, .3778026764 + 0, .9170825056 -0, .1273766688 -0 .1380104082

+ 0. .1087997835 -0. .9091855279 + 0. .4019257183 +2. .7253509473

+ 0. .3905706117 + 0. .6147848521 -0. .6851964556 -0, .8395088408

+ 0. .9939201075 + 0. .0475772273 + 0. .0992936418 + 1, .1239618523

+ 0. .4651189867 -0. .8600664556 -0. .2096426008 -2 , .9025033995

+ 0. .5590499980 -0. .5083217426 -0. .6550359575 -2 , .2307440356

+ 0. .9016737689 -0. .2118567860 -0. .3769630178 -2 , .0828130813

+ 0. .3834674462 + 0. .8663998125 + 0. .3198500939 + 0, .3536509617

+ 0. .3738207711 -0. .1372512833 -0. .9172895488 -1 , .7193214623

+ 0. .4524734468 + 0. .7583810682 + 0. .4691758043 + 0, .5540231867

+ 0. .1693542866 + 0. .3394164544 -0. .9252651491 -1, .2192061924

+ 0. .2550778487 + 0. .9446996628 -0. .2061015242 -0, .2148004803

+ 0. .5754827100 -0. .7720097366 -0. ,2698529545 -2. .8053223006

+ 0. .0956355383 + 0. .6541083746 + 0. ,7503306458 + 0. .8538042215

+ 0. .4985175102 -0. .7675902784 -0. ,4028466911 -2. .6582868094

+ 0. .7654203843 + 0. ,5664976833 + 0. , 3053064201 + 0. .4943096935

+ 0. .4100234369 + 0. .1483201216 -0. , 8999343991 -1. .4074525865

+ 0. .9337335058 + 0. .1883323430 + 0. , 3044218597 + 1. .0167721607

+ 0. .8366983882 + 0. .0645341179 + 0. , 5438484668 + 1. .4526866675

+ 0. .6759278812 -0. .4399231176 -0. , 5912606448 -2. .2104737953

+ 0. .3590571853 + 0. .8499338137 -0. .3856040067 -0. .4259158866

+ 0. .5612676019 -0. .7515987818 + 0. , 3465226548 + 2. .7095897903

+ 0. .8828791982 -0. .4440800915 + 0. , 1526996850 + 2. .8104016185

+ 0. ,8339650528 + 0. , 324104263 -0. 3428170269 -0. , 6703381514

+ 0. , 8945743463 + 0. ,2583236952 + 0. 3646993383 + 0. .9545085239

+ 0. ,8154968517 -0. , 5505683914 + 0. 1784357902 + 2. , 8281806192

+ 0. ,8475368679 -0. , 5274330414 -0. 0591239745 -3. , 0299610864

+ 0. , 9692591498 + 0. , 1587047653 + 0. 1880146217 + 0. .8697324634

+ 0. ,7494407615 -0. ,4682466851 -0. ,4680636568 -2. .3563899684

+ 0. ,8370401396 -0. , 4767693403 + 0. 2684302533 + 2. , 6288089361

+ 0. ,9123943947 -0. , 3031393768 -0. 2750327014 -2. ,4047692434

+ 0. ,5851759702 + 0. ,8091231899 -0. 0537470683 -0. ,0663288674

+ 0. ,5669537650 + 0. ,5644863006 + 0. 5999322001 + 0. .8158296251

+ 0. ,9224035591 + 0. 1852012620 -0. 3389279669 -1. ,0706961917

+0. 4066331880 -0. 9124568120 + 0. 0455194098 + 3. ,0917473300

+ 0. 7948800956 -0. 4613917725 + 0. 3940599776 + 2. ,4347416050

+ 0. 3107547247 -0. 1328348192 + 0. 9411622665 + 1. 7110093209 +0.8712977785 -0.0042248210 -0.4907365201 -1.5794052573 +0.8519131775 -0.4691990734 -0.2325858282 -2.6813843752 +0.3271327866 +0.5825021449 +0.7440936709 +0.9066101868 +0.8631913123 -0.0789571715 +0.4986647406 +1.7278298607 +0.6751059455 -0.7342014203 +0.0719738619 +3.0438747438 +0.9380013059 -0.1148331833 +0.3270579307 +1.9084593230 +0.9620467986 -0.2052635743 +0.1798132986 +2.4221899266 +0.6485038729 -0.4135972361 +0.6390462058 +2.1452078663 +0.8866408108 -0.2202717681 +0.4066305703 + 2.0672448292 +0.7304265220 -0.1708300651 +0.6612822278 +1.8236009500 +0.7611630150 +0.4895688060 -0.4253859997 -0.7153642796 +0.9473881949 +0.3162272586 +0.0495573304 +0.1554499349 +0.8008722385 -0.1164918456 +0.5873953588 +1.7665753230 +0.9636712677 +0.2653323059 -0.0306015568 -0.1148256156 +0.4964581654 +0.8619537141 -0.1027865981 -0.1186879261 +0.7775183433 +0.1588605612 +0.6084640892 + 1.3154126782 +0.7951658039 +0.6019977122 +0.0728704246 +0.1204616023 +0.8882139897 +0.0592169171 +0.4555977010 +1.4415445995 +0.5761447276 -0.6652624389 -0.4748506504 -2.5216784843 +0.9545998766 -0.2937391118 -0.0495621816 -2.9744384688 +0.2869061670 -0.8256773618 -0.4857383509 -2.6098273906 +0.6034204817 -0.7695725531 +0.2089062179 +2.8765228787 +0.9633044350 -0.1171814798 +0.2414809853 +2.0225839513 +0.8631347261 +0.5049736409 -0.0002579582 -0.0005108349 +0.5140001302 -0.4645909229 +0.7210819236 +2.1431519580 +0.8869471101 +0.1342286953 -0.4419360601 -1.2759221643 +0.4015765917 +0.1965971263 +0.8944751595 +1.3544458762 +0.4937606763 +0.5653251051 +0.6607631346 +0.8630809694 +0.4843651270 -0.6536501396 -0.5814911166 -2.4145498364 +0.8355630411 -0.2584140085 -0.4848263654 -2.0604966005 +0.3592440164 -0.8780081182 +0.3162996698 +2.7958185505 +0.1770727972 +0.9639796082 +0.1984654619 +0.2030442937 +0.1399657571 +0.8355391334 -0.5313040028 -0.5663860818 +0.3868868738 -0.8539017481 -0.3480953196 -2.7545066131 +0.1631231844 -0.2840416359 +0.9448339408 +1.8628273222 +0.5080211710 +0.5926423830 -0.6250515944 -0.8120071166 +0.5899490625 -0.8051930190 +0.0602022079 +3.0669640849 +0.7217439533 +0.0121827775 -0.6920529212 -1.5531943213 +0.6779443238 +0.7154516447 +0.1688799512 +0.2318035858 +0.7083356157 +0.2855664424 +0.6455326966 +1.1543028212 +0.8908306057 +0.3118523458 -0.3304072432 -0.8142801578 +0.7416354420 -0.3107668917 +0.5944752394 +2.0524844074 +0.4927629027 -0.3238753861 -0.8076443871 -1.9521751280 +0.3186457883 +0.3182328525 +0.8928564908 +1.2284126829 +0.8777648402 +0.4608223077 -0.1310407802 -0.2770498440 +0.9750457783 +0.0314749736 +0.2197613622 +1.4285403404 +0.8610863734 -0.1396102449 -0.4889163907 -1.8489444130 +0.7605973054 +0.5692419020 -0.3121784683 -0.5016223600 +0.5942645533 +0.4807183991 -0.6447941232 -0.9301571410 +0.3111132673 +0.8139837377 +0.4905497014 +0.5423679164 +0.4230580889 +0.9029197821 +0.0758796443 + 0.0838410767 +0.7632372295 +0.1119663536 -0.6363430421 -1.3966263019 +0.0123673211 -0.4121337901 -0.9110394000 -1.9956256821 +0.2949875380 -0.3437096493 -0.8915413784 -1.9387605185 +0.8158573706 -0.4684659483 -0.3389932243 -2.5151869474 +0.5842996463 -0.5064202142 +0.6341391724 +2.2446798220 +0.6971483119 +0.4813261481 -0.5313279311 -0.8347350566 +0.7794212145 -0.6246057866 -0.0486845119 -3.0638055447 +0.7146874724 -0.5738247818 +0.3999336652 + 2.5329089987 +0.7662506124 +0.2427423618 -0.5949253271 -1.1833939935 +0.9137884804 +0.0424074221 -0.4039705727 -1.4662029000 +0.8277062855 +0.2106509496 -0.5201235261 -1.1859855282 +0.2336360902 -0.8229244580 +0.5178894803 +2.5798870537 +0.8742883592 -0.4666085500 -0.1337771508 -2.8623809617 +0.6890979318 -0.6885331786 +0.2259781017 + 2.8244672088 +0.9762128412 -0.0454664999 -0.2119935992 -1.7820668978 +0.3798958471 -0.7138237752 -0.5883321879 -2.4522699501 +0.7974915588 -0.0532898687 -0.6009720489 -1.6592378004 +0.6398055637 +0.4262592733 +0.6394934500 +0.9828691763 +0.6344166582 -0.5611857107 -0.5315882823 -2.3832725451 +0.9352794198 +0.2794876928 -0.2171152607 -0.6604542251 +0.6937562102 +0.6614605787 +0.2849073949 +0.4067094919 +0.7113962414 -0.1323414489 -0.6902181747 -1.7602357356 +0.2776387724 -0.5234697161 +0.8055409167 + 2.1470564486

Table 10 (8 bit, Codebook optimized including orthogonal precoding vectors) vl real (v2) imag ( v2 ) angle ( v2 )

+ 0. .7756558849 + 0. .0384581078 + 0. .6299832713 + 1. .5098257536

+ 0. .4492053963 + 0. .4964587818 + 0. .7427941774 + 0. .9816178040

+ 0. .9106430412 -0. .4067173725 -0. .0728713279 -2. .9643043165

+ 0. .9352287003 -0. .3381002663 -0. .1050499312 -2. .8403426063

+ 0. .7846709884 + 0. .5309793126 + 0. .3199256314 + 0. .5422703483

+ 0. .8616463760 -0. .2535146826 + 0. .4396542146 + 2. .0938493940

+ 0. .6639633467 + 0. .6475250576 + 0. .3739839222 + 0. .5237553067

+ 0. .5096342401 -0. .7057483792 + 0. .4921302333 + 2. .5326697351

+ 0. .8139488988 + 0. .0720712075 + 0. .5764485503 + 1. .4464154743

+ 0. .6813272081 + 0. .2665718761 + 0. .6817130411 + 1. .1980444769

+ 0. .3068846118 -0. .3956683378 + 0. .8656029121 + 1. .9995400960

+ 0. .3839944983 + 0. .7568007488 + 0. .5289620514 + 0. .6100175171

+ 0. .7460863961 -0. .3611503374 -0. .5593974646 -2. .1440763870

+ 0. .5165598777 + 0. .5745252139 + 0. .6348910705 + 0. .8352699914

+ 0. .6991627464 -0. .7144811947 -0. .0262312092 -3. .1048954902

+ 0. .9002856832 -0. .3980943445 -0. .1760868581 -2. .7251400289

+ 0. .7818659303 + 0. .4538919874 -0. .4273964562 -0. .7553426772

+ 0. .9359660733 + 0. .2331461599 -0. .2638377868 -0. .8470756061

+ 0. .6814674670 + 0. .6660532506 -0. .3032740655 -0. .4272775548

+ 0. .7955544817 -0. .5712239331 + 0. .2019809023 + 2. .8017203525

+ 0. .5829728208 -0. .5311824670 + 0. .6148071868 + 2. .2833519806

+ 0. .8221511037 + 0. .5459798734 -0. .1611630865 -0. .2870301903

+ 0. .7760981159 -0. .5578898079 + 0. .2939909467 + 2. .6566029076

+ 0. .7064386309 -0. .3254879633 + 0. .6284918826 + 2. .0486511603

+ 0. .6473224756 + 0. .7614782521 + 0. .0335333298 + 0, .0440087135

+ 0. .4758508799 + 0. .0881505349 -0. .8750973793 -1. .4704027192

+ 0. .5387392250 -0. .7689905795 -0. .3441126795 -2. .7208311631

+ 0. .7631886297 + 0. .2781381835 -0. .5832514606 -1. .1258190706

+ 0. .7887253209 + 0. .0574465554 -0. .6120557665 -1. .4772121228

+ 0. .2147964630 -0. .3194174832 -0. .9229490511 -1. .9039778513

+ 0. .7753180742 + 0. .6194824555 -0. .1229771163 -0. .1959681329

+ 0. .1530113531 + 0. .4644150637 + 0. .8722993605 + 1. .0815633495

+ 0. .5314878670 + 0. .6721350232 + 0. .5155144594 + 0. .6542803533

+ 0. .9478056397 -0. .1060908231 -0. .3006812374 -1. .9099944007

+ 0. .8094131198 + 0. .5862410428 -0. .0342321671 -0. .0583264166

+ 0. .8233921300 -0. .1279332041 + 0. .5528639033 + 1. .7981948215

+ 0. .9754783086 + 0. .2134056488 -0. .0538525634 -0. .2471876510

+ 0. .7151362935 + 0. .6710989882 -0. .1954641393 -0. .2834190754

+ 0. .7957470917 + 0. .3367138166 -0. .5033988198 -0. .9812624123

+ 0. .3626290543 -0. .8493989126 + 0. .3834340312 + 2. .7175600721

+ 0. .4787796819 + 0. .2896833537 + 0. .8287662944 + 1. .2345352547

+ 0. .6728287078 -0. .4881373859 + 0. .5558987520 + 2. .2913821176

+ 0. .6301970492 + 0. .1300996300 -0. .7654578796 -1. .4024419879

+ 0. .9654306830 -0. .2239802061 + 0. .1333284052 + 2. .6046593160

+ 0. .6573512651 + 0. .3239580635 -0. .6803973011 -1. .1264258208

+ 0. .0032289983 -0. .4548147128 -0. .8905802325 -2. .0429631414

+ 0. .9356342410 -0. .0354413228 + 0. .3511872431 + 1. .6713743953

+ 0. .1586354334 + 0. .9136505094 -0. .3742693494 -0. .3887904565

+ 0. .9629083970 -0. .2496360482 -0. .1024171004 -2. .7522680068

+ 0. .6426052600 -0. .5008348989 -0. .5798472936 -2. .2832109099

+ 0. .8075056792 -0. .2889889474 + 0. .5142178199 + 2. .0828037153

+ 0. .0813298092 + 0. .8658286612 + 0. .4936863292 + 0. .5182114748

+ 0. .9174567332 + 0. .0871077423 -0. .3881821529 -1. .3500538627

+ 0. .3929513910 + 0. .7369399394 -0. .5500079363 -0. .6411547493 + 0.7806917982 + 0.2200573207 -0.5848889568 -1.2109409244

+ 0 .9346424861 -0 .2026066277 -0 .2922224794 -2 .1770317769

+ 0 .1978944792 + 0 .3572474236 -0 .9128044990 -1 .1977487014

+ 0 .6740988383 -0 .7348211168 + 0 .0750245455 + 3 .0398461584

+ 0 .7441028354 + 0 .0915186213 -0 .6617668112 -1 .4333736223

+ 0 .4139577381 + 0 .1881867689 -0 .8906316473 -1 .3625633420

+ 0 .8430998552 + 0 .0833343547 + 0 .5312607829 + 1 .4152027298

+ 0 .8110513873 -0 .4347288296 + 0 .3914160087 + 2, .4085741702

+ 0 .8159468530 + 0 .3962738182 + 0 .4209486834 + 0, .8155825635

+ 0 .3467357751 -0 .6034625715 -0 .7180579552 -2, .2696960676

+ 0 .8767794930 -0 .4783122710 + 0 .0497502966 + 3, .0379531551

+ 0 .7654177110 + 0 .1189796549 + 0 .6324393800 + 1, .3848416227

+ 0 .4654463452 -0 .6219724798 + 0 .6296903478 + 2 .3500284764

+ 0 .9749415698 -0 .2157367831 + 0 .0542823713 + 2 , .8950956126

+ 0 .4647556176 + 0 .6910844956 -0 .5535381069 -0 , .6753322655

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+ 0 .2590454170 + 0. .0702954667 + 0. .9633037004 + 1 .4979521273

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+ 0 .7990571705 + 0. .3258804368 + 0. .5052816830 + 0 .9979807663

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+ 0. .4570837443 + 0. 8063557018 -0. .3753197743 -0. .4356291487

+ 0, .8896414066 + 0. 1804095107 + 0. .4195123074 + 1 , .1646596063

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+ 0. .7064489301 + 0. 4725618829 + 0. 5268919964 + 0. .8397045144 + 0.7376675893 + 0.1802499707 -0.6506584940 -1.3005466083

+ 0 .0948921381 + 0 .0212318959 + 0 .9952611159 + 1 .5494665717

+ 0 .4838083764 + 0 .0850556970 + 0 .8710309888 + 1 .4734554891

+ 0 .6186633755 + 0 .0940975822 + 0 .7800008159 + 1 .4507387026

+ 0 .1387877087 -0 .4785544921 -0 .8670199363 -2 .0751379350

+ 0, .2101309455 + 0 .9317575895 + 0 .2960958968 + 0 .3076897810

+ 0, .5172880011 -0 .8557575440 -0 .0095994737 -3 .1303756084

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+ 0, .7238354357 + 0, .6039041967 + 0 .3337094293 + 0 .5048269943

+ 0, .6058583268 -0, .6183822984 -0, .5005387305 -2 .4611265916

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+ 0. .3590421320 -0. .8556621197 -0, .3727346030 -2 .7307700394

+ 0, .4902390111 -0. .8582195410 + 0, .1520688377 + 2 , .9662218197

+ 0. .9855658198 + 0. .0117674449 -0 , .1688832202 -1 , .5012307629

+ 0. .9446019428 + 0, .1461587869 + 0, .2938788502 + 1 , .1092760363

+ 0. .5384692283 -0. .6176309845 + 0 , .5732214731 + 2, .3934694199

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+ 0. .3214813837 + 0. .9130919924 -0, .2508241084 -0, .2680849785

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+ 0. .9199624773 + 0. .1868144749 + 0. .3446293550 + 1, .0740590053

+ 0. .4422221640 -0. .5110494703 + 0. .7370671588 + 2 , .1770488713

+ 0. .3349195523 -0. .9297487508 -0. .1529580131 -2. .9785378012

+ 0. .9595189736 + 0. .1734505556 -0, .2218969221 -0. .9073314879

+ 0. .3926687024 + 0. .0028412451 + 0. .9196756045 + 1. .5677069374

+ 0. .9955882059 -0. .0794020286 + 0. .0499944203 + 2. .5796661272

+ 0. .9193866585 + 0. .3151952784 + 0. .2353297868 + 0. .6413317244

+ 0. .8999294135 -0. .4360338199 -0. .0012484769 -3. .1387294044

+ 0. .5680203874 -0. .7384060255 + 0. .3634685420 + 2. .6841771339

+ 0. .6238722783 + 0. .2517237165 -0. .7398773891 -1. .2428574427

+ 0. .2189863154 -0. .7101488321 + 0. .6691290084 + 2. .3859257998

+ 0. .7759729796 + 0. .5807882688 + 0. .2460709690 + 0. .4007558531

+ 0. , 6056256946 + 0. .6360672631 + 0. .4781589221 + 0. .6446155045

+ 0. .9091616208 + 0. .0951647879 + 0. .4054242351 + 1. .3402412865

+ 0. ,8643785614 + 0. .2136532598 + 0. .4551944498 + 1. .1319540241

+ 0. , 6791229091 -0. , 5635975709 + 0. ,4702657254 + 2. .4462252911

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+ 0. .9958432829 + 0. .0101403447 + 0. .0905170109 + 1. .4592345266

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+ 0. .4017560096 + 0. .1947197812 + 0. .8948051830 + 1. .3565255185

+ 0. .5511459977 + 0. .8299467162 + 0. .0861773604 + 0. .1034640358

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+ 0. .8406130943 + 0. .5354305560 + 0. .0817541762 + 0. .1515184049

+ 0. .8336149056 -0. .2286454287 + 0. .5027996192 + 1. .9975888808

+ 0. .9102196410 + 0. .2755397260 + 0. .3091570223 + 0. .8428302026

+ 0. .6919874643 -0. .3230643120 -0. .6455871743 -2. .0347793569

+ 0. .8876998509 + 0. .0856914728 -0. .4523781009 -1. .3835899357

+ 0. .8805087566 + 0. .4608548962 + 0. .1109824053 + 0. .2363188009

+ 0. .9649354022 + 0. .0001043894 + 0. .2624874446 + 1. .5703986339

+ 0. .8512151589 + 0. .3053036418 -0. .4268752037 -0. .9499378286

+ 0. .4464133179 + 0. .5065869728 -0. .7376210332 -0. .9689947415

+ 0. .8377010782 -0. .1286043962 -0. .5307709608 -1. .8085123999

+ 0. .7022769401 + 0. .0153788861 -0. .7117377251 -1. .5491921700

+ 0. .8609227691 + 0. , 2215475660 -0. .4579614194 -1. .1202175774

+ 0. .8325510073 + 0. , 4524470485 + 0. .3196099006 + 0. .6150102891

+ 0. .5013185312 + 0. .8612473753 + 0. .0832627701 + 0. .0963774338

+ 0. .9059822253 + 0. , 1555728666 -0. .3936918726 -1. .1944658295

+ 0. .9783955504 + 0. , 1525871658 + 0. .1394966081 + 0. .7406103159

+ 0. .5150132621 + 0. , 8259462440 -0. .2292905185 -0. .2707906140

+ 0. .5771934818 + 0. , 5403410719 -0. .6122738036 -0. .8477256268

+ 0. .5115863010 + 0. , 5575489947 -0. .6537725714 -0. .8646685613

+ 0. .3329216070 -0. , 1685196632 -0. .9277738554 -1. .7504761100

+ 0. .2977742543 + 0. , 6499736638 -0. .6991886225 -0. .8218601570

+ 0. .5247526192 -0. , 0621519138 + 0. .8489828198 + 1. , 6438734692

Table 11 (9 bit, Codebook optimized including orthogonal precoding vectors) vl real ( 2 ) imag ( 2 ) angle ( v2 )

+ 0. 6892282875 + 0. .4960891507 + 0. .5280718911 + 0, .8166162518

+ 0. 9151397305 + 0. .0935728835 -0. .3921267514 -1 , .3365479139

+ 0. 5918771401 -0. .7025676707 + 0, .3950697648 + 2 , .6293378719

+ 0. 7195887275 + 0. .1314315981 + 0. .6818488089 + 1. .3803741304

+ 0. 9286573332 -0. .3423916118 + 0. .1427008818 + 2. .7467076924

+ 0. 6089832683 -0. .7505038545 + 0. .2566775084 + 2 , .8120562922

+ 0. 9380857344 + 0. .0743555594 -0. .3383288426 -1. .3544625111

+ 0. 7011463258 -0. .6967518680 + 0. .1514287433 + 2. .9275854929

+ 0. 9578865817 -0. .2854988223 + 0. .0307200109 + 3. .0344038792

+ 0. 8540900952 + 0. .4616998758 -0. .2395064381 -0, .4785342109

+ 0. 6115795592 + 0. .4477641728 + 0. .6522865078 + 0, .9692201398

+ 0. 8962122044 -0. .2096718093 -0. .3909493791 -2. .0630717340

+ 0. 7402519247 -0. .0430703413 -0. .6709486073 -1. .6349015738

+ 0. 2428459854 -0. .9693917541 -0. .0361310737 -3. .1043379973

+ 0. 1189576373 -0. .9877914593 -0. .1005838630 -3, .0401153972

+ 0. 3413278717 + 0. .9279523786 -0. .1496651829 -0. .1599083384

+ 0. 5715524017 + 0. .7364963149 -0. .3618024742 -0, .4566216722

+ 0. 9918805390 + 0. .1212814253 -0. .0382598004 -0. .3055819607

+ 0. 8123645807 -0. .3442458394 + 0. .4707001063 + 2. .2022532557

+ 0. 9907013486 + 0. .0675965058 -0. .1180743422 -1. .0508496232

+ 0. 1148670379 + 0. .6904850478 + 0. .7141680211 + 0. .8022569380

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+ 0. 4677240239 + 0. .1371365456 + 0. .8731711203 + 1. .4150131341

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+ 0. 9707759783 -0. .2393181253 -0. .0179118611 -3. .0668865417

+ 0. 6266697735 + 0. , 6909461464 -0. .3603864839 -0. .4807653679

+ 0. 3750534482 + 0. .2559331123 -0. .8909731494 -1. .2910763184

+ 0. 1285757858 -0. , 7762696817 -0. .6171496161 -2. .4698959237

+ 0. 8091986689 -0. .0230305300 + 0. .5870835621 + 1. .6100049310

+ 0. 5806595823 -0. , 6611123993 + 0. .4751471825 + 2. .5184206066

+ 0. 5111450401 -0. , 8484494519 + 0. .1373472810 + 2. .9811045317

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+ 0. 5633882463 -0. , 5589775099 + 0. .6083895359 + 2. .3138919870

+ 0. 4315133434 -0. , 0277360381 + 0. .9016800689 + 1. .6015470288

+ 0. 5464379927 + 0. , 3328003088 + 0. .7685372304 + 1. .1621432125

+ 0. 5681088913 -0. , 0699738514 -0. .8199731384 -1. .6559268367

+ 0. 7274346229 -0. , 6860242989 + 0. .0144751785 + 3. .1204956882

+ 0. 4740894866 -0. , 0096757137 + 0. .8804234999 + 1. .5817857248

+ 0. 5881001118 + 0. .6973397512 + 0. .4097017573 + 0. .5311932406

+ 0. 9302479896 + 0. , 3421069596 + 0. .1326706681 + 0. .3699491345

+ 0. 8852152521 -0. 4038249158 -0. .2309099278 -2. .6221612826

+ 0. 4231972459 + 0. 1173188331 + 0. .8984099190 + 1. .4409461167

+ 0. 7893115825 -0. 2219960593 + 0. .5724552170 + 1. , 9407382742

+ 0. 7320539423 + 0. 3732207513 + 0. ,5699151659 + 0. .9910046716

+ 0. 3404693866 + 0. 9258529485 + 0. , 1639418020 + 0. , 1752545167

+ 0. 6316157577 -0. 6902069385 + 0. , 3530947703 + 2. , 6687255064

+ 0. 9826898122 + 0. 1295216719 + 0. , 1324570474 + 0. , 7966023277

+ 0. 5888541050 -0. 3103607511 -0. ,7462754499 -1. , 9649166402

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+ 0. , 9709560606 + 0. 1652138791 + 0. , 1730569343 + 0. , 8085797383 Table 12 (10 bit, Codebook optimized including orthogonal precoding vectors) vl real (v2) imag ( v2 ) angle ( v2 )

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+ 0. , 6418668888 + 0. 4514674454 -0 .6198258165 -0. ,9412775578

+ 0. ,4461515395 -0. 0738774338 -0 .8919029816 -1. , 6534389117

+ 0. ,4597393513 -0. 5837953148 + 0 .6691956061 + 2. 2881425850

+ 0. , 6339753723 -0. 5176998551 + 0 .5745103023 + 2. 3042271131

Claims

Claims
1 . A communication device for wired data transmission , the communication device ( 100) comprising:
a transmitter unit ( 1 10) configured to transmit at least two transmit signals via different transmission paths of a transmission channel (300);
a codebook memory unit ( 188) configured to store a codebook table comprising a plurality of codebook entries, each codebook entry including at least one predefined precoder value for each of the at least two transmit signals;
a precoder unit ( 1 14) configurable to beamform the transmit signals; and a precoder control unit ( 184) configured to construct, on the basis of precoder values assigned to a codebook entry identified by a codebook index, a precoding matrix for beamforming the at least two transmit signals and to configure the precoder u nit ( 1 14) according to the constructed precoding matrix.
2. The communication device of claim 1 , wherein
the transmitter unit ( 1 10) is configured to transmit and precode multi- carrier signals; and
the precoder control unit ( 184) is configured to construct, for each or a subset of the sub-carriers respectively, on the basis of precoder values assigned to a codebook entry identified by a codebook index for the respective sub-carrier, a precoding matrix for beamforming the at least two transmit signals and to configure the precoder unit ( 1 14) for the respective sub-carrier according to the constructed precoding matrix.
3. The communication device of claim 2 , wherein
the precoder control unit ( 184) is further configured to interpolate the precoder values for precoding matrices for sub-carriers between two pilot sub- carriers on the basis of the precoder values assigned to the codebook entries identified by codebook indices assigned to the two pilot sub-carriers.
4. The communication device of any of the preceding claims, wherein
the entries in the codebook table represent u niformly distributed precoding vectors.
5. The communication device of any of the preceding claims, wherein
the codebook memory unit ( 188) stores at least two codebook tables of different length and the precoder control unit ( 184) is configured to access a selected one of the codebook tables.
6. The communication device of any of the preceding claims, wherein
the codebook table includes the first and at least one of the second, third and fourth column of one of the codebook tables defined in tables 1 to 12.
7. The communication device of any of the preceding claims, further comprising a receiver unit ( 120) configured to receive at least one receive signal containing information about at least two further transmit signals, the at least two further transmit signals received via different transmission paths of the wired transmission channel (300);
a codebook control unit ( 183) configured to identify, on the basis of channel state information describing the transmission channel (300), that one of the codebook entries whose precoder values approximate a perfect precoding matrix for beamforming the at least two further transmit signals at best among all or a subset of the codebook entries.
8. The communication device of claim 7, wherein
the codebook control unit ( 183) is configured to identify that one of the codebook entries whose precoder values approximate the perfect precoding matrix at best among all of the codebook entries.
9. The communication device of any of the preceding claims, wherein
the perfect precoding matrix is obtained by singular value or QR
decomposition of a channel matrix of the transmission channel (300).
10. The communication device of claim 2 , wherein
the codebook table contains a codebook entry for each sub-carrier.
1 1 . A communications system comprising
a first communication device according to any of claims 1 to 10 and a second communication device according to any of claims 7 and 8.
12. A communications method for a communications system comprising a first and a second communication device ( 100) connected by a wired transmission channel (300),
identifying, in the first communication device, in a codebook table comprising a plurality of codebook entries, each codebook entry including at least one predefined precoder value for each transmit signal on the basis of channel state information describing the transmission channel (300), that one of a plurality of codebook entries, whose precoder values approximate a perfect precoding matrix for beamforming transmit signals at best among all or a subset of the codebook entries for obtaining a codebook index; and
using, in the first and / or the second communication device, the codebook index for constructing a precoding matrix for beamforming the transmit signals on the basis of the precoder values assigned to the codebook entry identified by the codebook index.
PCT/EP2011/004118 2010-09-30 2011-08-16 Power line communication system using beamforming WO2012041425A1 (en)

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TWI622279B (en) * 2017-05-02 2018-04-21 國立高雄師範大學 Communication device and method for beamforming

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EP2019496A1 (en) 2007-07-23 2009-01-28 Sony Corporation Method for transmitting a signal between a transmitter and a receiver in a power line network, transmitter, receiver, power line communication modem and powerline communication system
EP2061160A1 (en) 2007-11-14 2009-05-20 Sony Corporation MIMO-Eigenbeamforming without feedback of channel state information
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