JP5846601B2 - Receiving apparatus and receiving method - Google Patents

Description

  The present invention relates to a receiving apparatus and a receiving method for receiving a radio signal in which a plurality of subcarrier signals whose upper sideband is modulated with a first symbol and whose lower sideband is modulated with a second symbol are orthogonal frequency division multiplexed. About.

  A technique that realizes twice the transmission capacity of the normal OFDM system by applying SSB (single sideband) multiplexing to the OFDM (Orthogonal Frequency Division Multiplexing) system has been studied. In the OFDM scheme, even if SSB signals modulated with different information symbols are combined with USB (upper sideband) and LSB (lower sideband) of a plurality of subcarrier signals, the orthogonality of the plurality of subcarrier signals is almost the same. While being maintained, the transmission capacity can be doubled.

  As a technique related to such a transmission method, Non-Patent Document 1 discloses a modulation technique of four orthogonal SSB elements. Non-Patent Document 2 discloses a technique for decoding an SSB-converted QPSK (Quadrature Phase Shift Keying) signal.

G.Ohta, M.Nanri, M Uesugi, T.Sato and H.Tominaga, "A Study of New Modulation Method Consisted of Orthogonal Four SSB Elements Having a Common Carrier Frequency", IEEE, The 11th International Symposium on Wireless Personal Multimedia Communications (WPMC), Lapland, Finland, Sep. 2008 B. Pitakdumrongkija, et al, "Single sideband QPSK with turbo equalization for mobile communications", IEEE, Vehicular Technology Conference-Spring 2005, pp. 538-542, May 2005

  However, in the transmission system in which SSB multiplexing is applied to the OFDM system, when the USB signal and LSB signal of each subcarrier signal are simply separated and demodulated and decoded, the transmission error characteristics deteriorate and the desired reception is achieved. There was a problem that performance could not be obtained.

  Such deterioration of the transmission error characteristic is considered to be caused by interference between the USB and LSB of the subcarrier signal. This interference is considered to be caused by the fact that the Hilbert transform performed on the subcarrier signal at the time of modulation and demodulation of the subcarrier signal at the time of modulation is a pseudo transformation limited to a finite frequency range. It was.

  An object of the present invention is to make it possible to obtain good transmission error characteristics in a receiving apparatus or receiving method that receives an SSB multiplexed OFDM signal.

  A receiving apparatus according to an aspect of the present invention receives a radio signal in which a plurality of subcarrier signals whose upper sideband and lower sideband are modulated by different information symbols are orthogonally frequency division multiplexed. A signal separator for separating the plurality of subcarrier signals; a demodulator for demodulating the subcarrier signals to obtain demodulated data of upper sidebands and demodulated data of lower sidebands; The leakage component based on the lower sideband information symbol included in the upper sideband and the leakage component based on the upper sideband information symbol included in the lower sideband from the demodulation data of the lower sideband and the demodulation data of the lower sideband Each of the filter unit to be removed, the demodulated data of the upper sideband and the demodulated data of the lower sideband that have passed through the filter unit, and the information symbols included in the upper sideband and the lower sideband are included. Information symbol And a decoding unit that estimates the leakage component based on the information symbol of the upper sideband and the information symbol of the lower sideband based on the information symbol estimated by the decoding unit. The structure which produces | generates the leakage component based on this is taken.

  A reception method according to an aspect of the present invention is a reception method for receiving a radio signal in which a plurality of subcarrier signals whose upper sideband and lower sideband are modulated by different information symbols are orthogonally frequency division multiplexed. A signal separation step of separating the plurality of subcarrier signals; a demodulation step of demodulating the subcarrier signal to obtain demodulated data of the upper sideband and demodulated data of the lower sideband; and the upperband The leakage component based on the lower sideband information symbol included in the upper sideband and the leakage component based on the upper sideband information symbol included in the lower sideband from the demodulation data of the lower sideband and the demodulation data of the lower sideband A filter step for removing each of the information symbols, and the upper sideband demodulated data and the lower sideband demodulated data that have passed through the filter step to decode the information symbols included in the upper sideband and the lower side A decoding step for estimating each information symbol included in the band, and the filtering step includes a leakage component based on the information symbol in the upper sideband based on the information symbol estimated in the decoding step, and the lower part. A method of generating a leakage component based on an information symbol in a sideband is used.

  According to the present invention, good transmission error characteristics can be obtained in a receiving apparatus or receiving method that receives an SSB-multiplexed OFDM signal.

The block diagram which shows the receiver of embodiment of this invention Block diagram showing the transmitter The block diagram which shows the principal part of the modulation | alteration part of a transmitter The block diagram which shows the principal part of the demodulation part of a receiver Configuration diagram showing details of Hilbert converter Diagram explaining the characteristics of the Hilbert converter Configuration diagram showing details of leak component removal filter Characteristics diagram showing simulation results of transmission error characteristics

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a block diagram showing a receiving apparatus 10 according to an embodiment of the present invention, and FIG. 2 is a block diagram showing a transmitting apparatus 40 corresponding to the receiving apparatus 10.

  The receiving device 10 and the transmitting device 40 of this embodiment transmit and receive a plurality of subcarrier signals digitally modulated with information symbols different in USB and LSB by the OFDM method.

  As shown in FIG. 2, the transmission device 40 includes a data input unit 46 that inputs data to be transmitted, a convolutional encoding unit 45 that encodes input data, and an interleaver 44 that rearranges the encoded bit strings. It has. The transmission apparatus 40 also includes a symbol mapper 43 that maps the rearranged bit sequence to a QPSK complex symbol sequence, and 4-SSB modulation that digitally modulates a plurality of subcarrier signals in the baseband in accordance with the mapped complex symbol sequence. And an OFDM transmission unit 41 that converts a plurality of subcarrier signals into a transmission band and orthogonally multiplexes them for transmission.

  Two sets of data input unit 46, convolutional code unit 45, interleaver 44 and symbol mapper 43 are provided corresponding to USB and LSB of each subcarrier signal for SSB multiplexing.

  As illustrated in FIG. 1, the receiving device 10 includes an OFDM receiving unit 11, a 4-SSB demodulating unit 12, a leakage component removal filter 13, a decoding unit 21, and the like.

  The decoding unit 21 includes an LC MMSE equalizer (low complexity-minimum mean square error equalizer) 14, a deinterleaver 16, a MAP (Maximum a posteriori probability) decoding unit 17, an interleaver 15, an output unit 18, and the like. Yes.

  The OFDM receiver 11 receives an OFDM signal from the transmitter 40, separates a plurality of subcarriers in the transmission band, converts the subcarrier into a baseband, and outputs the baseband to the 4-SSB demodulator 12.

  Although described in detail later, the 4-SSB demodulator 12 performs demodulation of each subcarrier signal and softly determines two QPSK information symbols included in the USB and LSB of the subcarrier signal. Then, the 4-SSB demodulation unit 12 outputs demodulated data (for example, log likelihood ratio data), which is the result of the soft decision, to the leakage component removal filter 13.

  The leak component removal filter 13 removes interference components (mutual leak components) between the USB and LSB of the subcarrier signal from the demodulated data representing the likelihood of two information symbols, as will be described in detail later. Then, the leakage component removal filter 13 outputs the demodulated data after removal to the decoding unit 21. This interference component is calculated based on the information symbol estimated by the decoding unit 21 from the demodulated data. Therefore, the interference component removal processing of the leakage component removal filter 13 and the decoding processing of the decoding unit 21 are recursively repeated, so that the above-described interference component removal is normally performed.

  The decoding unit 21 performs a hard decision on each demodulated data based on the demodulated data sequence sequentially input from the leakage component removal filter 13 and decodes information symbols.

  The LC MMSE equalizer 14 performs equalization processing on the input demodulated data string so that the mean square error between the estimated value of the demodulated data obtained from the decoding result and the output of the demodulated data is minimized. Then, the LC MMSE equalizer 14 outputs the demodulated data string after the equalization processing to the deinterleaver 16.

  The deinterleaver 16 rearranges the demodulated data sequence in order to decode the convolutionally encoded information symbol sequence, and then outputs the demodulated data sequence to the MAP decoding unit 17.

  The MAP decoding unit 17 determines each demodulated data by a recursive algorithm so that the encoded information symbol sequence matches the determination value of the demodulated data sequence with a high probability. Then, the MAP decoding unit 17 outputs the determination result of each demodulated data to the output unit 18 and the interleaver 15.

  The interleaver 15 rearranges the information symbol sequence decoded for the above equalization processing and returns it to the MMSE equalizer 14.

  The LC MMSE equalizer 14 and the MAP decoding unit 17 recursively repeat equalization processing and decoding processing on a series of demodulated data strings, thereby improving the decoding characteristics.

  The output unit 18 outputs the decoded data to the outside and feeds back the hard-decided information symbols (u, v, p, r) to the leakage component removal filter 13.

  FIG. 3 is a configuration diagram illustrating a main part of the 4-SSB modulation unit of the transmission apparatus.

  The 4-SSB modulation unit 42 of the transmission apparatus 40 digitally modulates (for example, QPSK modulation) two information symbols (d1 = u + jv, d2 = p + jr (where u, v, p, and r are information bits)). A plurality of modulators (not shown in FIG. 3), a plurality of adders 2 for adding and subtracting the modulated signal, and a Hilbert transform with the baseband frequency of the subcarrier signal as the center frequency for the modulated signal And a plurality of Hilbert transformers F1.

  In FIG. 3, “u” and “p” are the in-phase components of the two modulated signals digitally modulated by the information symbols d1 and d2, respectively, and “v” and “p” are the two modulated signals. Each quadrature component is represented.

The output of the 4-SSB modulation unit 42 is obtained by the 4-SSB in-phase signal (S _{4SSB, I} ) and 4-SSB quadrature signal shown in the following equation 1 by the plurality of adders 2 and the plurality of Hilbert transformers F1. (S _{4SSB, Q} ).

Here, H _run (x) represents a signal obtained by converting the modulated signal x by the Hilbert transformer F1.

  FIG. 4 is a configuration diagram illustrating a main part of the 4-SSB demodulation unit of the reception apparatus.

  As shown in FIG. 4, the 4-SSB demodulator 12 of the receiver 10 performs a Hilbert transform on the baseband subcarrier signal separated and extracted by the OFDM receiver 11 with the frequency of the subcarrier as the center. A plurality of Hilbert transformers F2 for performing the above, an adder 2 for performing addition / subtraction of the subcarrier signals, and demodulated data (d11, d12) subjected to soft detection by performing detection on the signals after the Hilbert transformation and addition / subtraction, respectively. , D21, d22) are provided.

The four demodulated data (d11, d12, d21, d22) obtained by the 4-SSB demodulator 12 have a value of the following expression 2 if there is no noise and distortion of the transmission path.

  FIG. 5 is a block diagram showing details of the Hilbert transformer, and FIG. 6 is a diagram for explaining the characteristics of the Hilbert transformer.

As shown in FIG. 5, the Hilbert transformer F1 included in the 4-SSB modulation unit 42 of the transmission device 40 and the Hilbert converter F2 included in the 4-SSB demodulation unit 12 of the reception device 10 have the number of taps “N + 1”. FIR (Finite Impulse Response Filter) filter. That is, the Hilbert transformers F1 and F2 include a plurality of delay blocks _{dnN / 2− dn + N / 2} that sequentially transmit signals with a certain delay, and a plurality of these delay blocks _{dnN / 2− dn +.} A plurality of multipliers 3 respectively corresponding to _{N / 2} and a plurality of adders 2 for adding the outputs of the plurality of multipliers 3 are provided.

With such a configuration, when signals are transmitted to a plurality of delay blocks _{dnN / 2− dn + N / 2} , each delay block _{dnN / 2− dn + N / 2} is a signal corresponding to the signal amplitude. Is output to the corresponding multiplier 3, and the signal is multiplied by a coefficient h- _{N / 2-} h _{+ N / 2} corresponding to each delay block _{dnN / 2- dn + N / 2} by a plurality of multipliers 3. Is done. The multiplied signals are added by a plurality of adders 2 and output. As the coefficient h _{−N / 2} −h _{+ N / 2} multiplied by each multiplier 3, a value similar to that of a known Hilbert transformer is adopted as shown in the signal response diagram of FIG. The signal response diagram of FIG. 6 represents the response output when a pulse signal is input to the Hilbert transformer.

The Hilbert transformers F1 and F2 perform a pseudo Hilbert transform (Truncated Hilbert Transform) in which the impulse response time is finitely cut off with respect to the input signal. That is, the number of taps of the Hilbert transformers F1 and F2 is finite, and the coefficient sequence of taps H _t = (h _{−N / 2} ,..., H _{+ N / 2} ) is as shown in FIG. This corresponds to a finite range of impulse response times. In other words, the Hilbert transformers F1 and F2 perform Hilbert transform with a finite frequency range, and do not perform complete Hilbert transform.

In FIG. 6, the range of the coefficient sequence “H _t + H _c ” represents an infinite range of impulse response time. Here, the coefficient sequence H _c, wherein each tap coefficient in the range of braces of the right and left in FIG. 6, a coefficient sequence in which the coefficients of the middle of the range corresponding to the coefficient sequence H _t to zero. Further, the coefficient sequence H _c, the scope of the braces of the right and left of Figure 6 represents the coefficient sequence of infinite length. A complete Hilbert transformer is realized by an FIR filter having a tap number and a coefficient sequence over such an infinite range. Further, in FIG. 6, the range of the coefficient sequence “H ^to _i = H _t + H ^to _c ” represents a finite range of impulse response times larger than those of the Hilbert transformers F1 and F2. The FIR filter having a finite number of taps and a coefficient sequence over a wide range in this way performs a conversion that approximates a perfect Hilbert transform. If the impulse response time of the FIR filter is lengthened, the delay of the conversion time increases, causing inter-symbol interference before and after. Therefore, there is a limit on the magnitude of the impulse response time of the Hilbert transformers F1 and F2.

Since the Hilbert transformers F1 and F2 are Hilbert transformers having a finite impulse response time as described above, for a certain signal (for example, u, v, p, r) as shown in the following equation (3): Even if the Hilbert transform is performed twice, it does not return to the original signal (the original signal with the sign reversed). There is a slight difference between the signal before conversion and the signal after conversion.

On the other hand, four demodulated data shown in Formula 2 (d11, d12, d21, d22) is the Hilbert transform _{H trun} (x) is, if the ideal Hilbert transform H (x), such as the following equation 4 Result. In Equation 4, “u, v, p, r” represents the detected values of the modulated signals u, v, p, r with the same symbol. The hat symbol indicates the detection value of the signal after the Hilbert transform.

However, since the Hilbert transformers F1 and F2 having a finite impulse response time are used, the four demodulated data (d11, d12, d21, and d22) shown in the equation 2 have the result as the following equation 5. That is, the demodulated data includes a component of the function G corresponding to the interference component between the USB and LSB of the subcarrier signal (the leakage component from USB to LSB and the leakage component from LSB to USB). The right side of Equation 5 represents the detection value of the signal.

  Therefore, the leakage component removal filter 13 described above removes the component of the function G from the four demodulated data (d11, d12, d21, d22).

  FIG. 7 is a configuration diagram showing details of the leakage component removal filter.

  The leakage component removal filter 13 includes a buffer 131 that receives bit data (u, v, p, r) that is hard-decided from the output unit 18, and a G operation unit 132 that calculates the value of the function G using the bit data as an argument. , A buffer 133 for receiving the demodulated data d1 and d2 input from the 4-SSB demodulator 12, an adder / subtractor 134 for adding and subtracting the values converted from the demodulated data d1 and d2 by the G operation unit 132, and the like. The data fed back from the output unit 18 to the buffer 131 may be soft decision data.

The G calculation unit 132 obtains a component related to the function G of Expression 5 based on the fed back bit data (u, v, p, r) as follows. Here, as shown in Expression 7, a matrix notation of the Hilbert transform is introduced. The transformation by the Hilbert transformers F1 and F2 can be expressed by a matrix H _t determined based on the tap coefficient sequence (h _{−N / 2} ,..., H _{+ N / 2} ) as shown in Equation 7. it can. Here, “x” indicates a vector in which the values of the signal x are arranged in each element in time series.

The transformation matrix H _t of the Hilbert transformers F1 and F2 having a finite impulse response time is obtained from the ideal Hilbert transformation transformation matrix H _i as shown in Expression 8 and ranges from the left and right infinite lengths shown in FIG. a value obtained by subtracting the transformation matrix H _c of the FIR filter is determined by the tap coefficients.

Therefore, the conversion by the function G can be expressed by matrix notation as shown in Equation 9.

Here, an FIR filter approximating the ideal Hilbert transform is introduced. In other words, by introducing a FIR filter with increased number of taps than Hilbert transformer F1, F2 of the above and the transformation matrix and H ^~ _i. Further, in the FIR filter that approximates the ideal Hilbert transform, the transform matrix of the FIR filter with the tap coefficient in the range to zero corresponding to the transformation matrix H _t Hilbert transformer F1, F2 and H ^~ _c. Then, the transformation matrices H _i and H _c appearing in Equation 9 are approximately represented by the transformation matrices H ^to _i and H ^to _c as shown in Equation 10.

Thereby, the conversion by the function G can be approximately expressed as shown in Equation 11 using the above-described conversion matrices H ^to _i and H ^to _c .

  Based on the fed back decoded bit (u, v, p, r), the G calculation unit 132 of the leakage component removal filter 13 calculates the value of the function G using the decoded bit as an argument. Specifically, assuming a baseband subcarrier signal modulated by the information symbol of the decoded bit, the subcarrier signal is converted by a function G, and a data value obtained by demodulating the converted signal is expressed as follows: The G calculation unit 132 calculates.

Note that the value of the function G with the decoded bit as an argument is uniformly determined according to the value of the decoded bit. Therefore, the leakage component removal filter 13 holds the exact value of the function G for each decoded bit value, and extracts the value held according to the decoded bit value, thereby obtaining the value of the function G. Can be requested. Further, the leakage component removal filter 13 can actually calculate the value of the function G by actually performing the matrix operation of Expression 11. Alternatively, the leakage component removal filter 13 includes a Hilbert transformer corresponding to the transformation matrix H ^to _i and an FIR filter corresponding to the transformation matrix H ^to _c , and using these, the value of the function G can be obtained. it can. In this case, the leakage component removal filter 13 converts the decoded bit that is fed back into a frequency signal of a subcarrier in the base band, passes this frequency signal through the Hilbert transformer and the FIR filter, performs demodulation processing, and performs the function G The value can be determined.

  The leakage component removal filter 13 is soft-demodulated demodulated data (d11, d12) based on the function values (G (u), G (v), G (p), G (r)) calculated as described above. , D21, d22), the interference component (the term including the function G) between the USB and LSB of the subcarrier signal described above is removed. Then, the leakage component removal filter 13 outputs the demodulated data from which the interference component is removed to the decoding unit 21. Such interference component removal processing by the leakage component removal filter 13 and decoding processing by the decoding unit 21 are recursively repeated by temporarily storing data in the buffers 131 and 133. As a result, the decoding unit 21 can perform more accurate decoding of information bits.

  FIG. 8 is a characteristic diagram showing a simulation result of transmission error characteristics. This figure shows data received by the receiving device 10 when the noise ratio per bit (Eb / No: bit energy to noise power density ratio) is changed by additive white Gaussian noise (AWGN). Represents the bit error rate (BER). Further, this figure shows a case where transmission data is transmitted after being turbo-encoded and decoded by the receiving apparatus 10 by repeated decoding five times.

  As shown in FIG. 8, according to the receiving apparatus 10 of this embodiment, the transmission of the OFDM method in which the USB and LSB of each subcarrier signal are respectively subjected to QPSK modulation (represented by “4SSB” in FIG. 8). Even if it is, sufficient wireless transmission performance can be obtained.

  The embodiment of the present invention has been described above.

  In the above embodiment, each of the leakage component based on the information symbol of the lower sideband included in the upper sideband and the leakage component based on the information symbol of the upper sideband included in the lower sideband, Equipped with a decoding step for estimation and a filtering step for removal, which were extracted independently as a configuration corresponding to only one of the upper sideband or the lower sideband. It is also possible to easily extract the remaining sideband information symbols using the sideband information symbols. Moreover, although the example which applied the convolutional code | cord | chord and MAP decoding to the code | symbol and decoding of transmission data was shown, it is not restricted to these, Various error correction codes | symbols and decoding can be applied. Also, the modulation / demodulation method is not limited to QPSK modulation / demodulation, and various digital modulation / demodulation methods can be applied.

  Further, although cases have been described with the above embodiment as examples where the present invention is configured by hardware, the present invention can also be realized by software in cooperation with hardware. Each functional block used in the description of the above embodiment is typically realized as an LSI which is an integrated circuit. These may be individually made into one chip, or may be made into one chip so as to include a part or all of them. The name used here is LSI, but it may also be called IC, system LSI, super LSI, or ultra LSI depending on the degree of integration. Further, the method of circuit integration is not limited to LSI's, and implementation using dedicated circuitry or general purpose processors is also possible. An FPGA (Field Programmable Gate Array) that can be programmed after manufacturing the LSI or a reconfigurable processor that can reconfigure the connection and setting of circuit cells inside the LSI may be used. Further, if integrated circuit technology comes out to replace LSI's as a result of the advancement of semiconductor technology or a derivative other technology, it is naturally also possible to carry out function block integration using this technology.

  The present invention is useful for a digital broadcasting system or a mobile communication system.

DESCRIPTION OF SYMBOLS 10 Receiving device 11 OFDM receiving unit 12 4-SSB demodulating unit 13 Leakage component removal filter 21 Decoding unit F1, F2 Hilbert transformer 40 Transmitting device 41 OFDM transmitting unit 42 4-SSB modulating unit 45 Convolution coding unit

Claims (4)

Using a first Hilbert transformer with a finite impulse response time , a radio signal in which a plurality of subcarrier signals whose upper sideband and lower sideband are modulated by different information symbols is orthogonal frequency division multiplexed is received. A receiving device,
A signal separator for separating the plurality of subcarrier signals;
A demodulator that demodulates the subcarrier signal using a second Hilbert transformer having a finite impulse response time to obtain demodulated data of the upper sideband and demodulated data of the lower sideband;
First leakage component based on lower sideband information symbol included in upper sideband from upper sideband demodulated data and lower sideband demodulated data, and upper sideband information symbol included in lower sideband A filter unit for removing each of the second leakage components based on
The demodulated data of the upper sideband and the demodulated data of the lower sideband that have passed through the filter unit are decoded to estimate information symbols included in the upper sideband and information symbols included in the lower sideband, respectively. A decryption unit;
Comprising
The filter unit is
The function G corresponding to the first leakage component and the second leakage component is obtained from the following equation using the information symbol estimated by the decoding unit as an argument, and the demodulated data of the upper sideband based on the function G And removing the first leakage component and the second leakage component from the demodulated data of the lower sideband, respectively.
Receiver device.

here,
x: Any of the information symbols estimated by the decoding unit
H ^to _i : FIR filter transformation matrix that approximates an ideal Hilbert transform and has a larger number of taps than the first and second Hilbert transformers
H ~ _^c: the ideal transformation matrix FIR filter tap coefficient in the range was zero in FIR filters that approximate Hilbert transform corresponding to the transformation matrix H _t of the first and second Hilbert transformer The filter unit holds an accurate value of the function G for each decoded bit value, and obtains a value of the function G by extracting a value held in accordance with the value of the decoded bit;
The receiving device according to claim 1. The filter unit includes a Hilbert transformer corresponding to the transformation matrix H ^to _i and an FIR filter corresponding to the transformation matrix H ^to _c , and using these, the value of the function G is obtained.
The receiving device according to claim 1 . Using a first Hilbert transformer with a finite impulse response time , a radio signal in which a plurality of subcarrier signals whose upper sideband and lower sideband are modulated by different information symbols is orthogonal frequency division multiplexed is received. Receiving method,
A signal separation step of separating the plurality of subcarrier signals;
A demodulation step of demodulating the subcarrier signal using a second Hilbert transformer having a finite impulse response time to obtain demodulated data of the upper sideband and demodulated data of the lower sideband;
First leakage component based on lower sideband information symbol included in upper sideband from upper sideband demodulated data and lower sideband demodulated data, and upper sideband information symbol included in lower sideband Filter steps for respectively removing second leakage components based on
The upper sideband demodulated data and the lower sideband demodulated data that have passed through the filter step are decoded to estimate information symbols included in the upper sideband and information symbols included in the lower sideband, respectively. A decryption step;
Comprising
The filtering step includes
The function G corresponding to the first leakage component and the second leakage component is obtained from the following equation using the information symbol estimated by the decoding step as an argument, and the demodulated data of the upper sideband based on the function G And removing the first leakage component and the second leakage component from the demodulated data of the lower sideband, respectively.
Reception method.

here,
x: Any of the information symbols estimated by the decoding step
H ^to _i : FIR filter transformation matrix that approximates an ideal Hilbert transform and has a larger number of taps than the first and second Hilbert transformers
H ~ _^c: the ideal transformation matrix FIR filter tap coefficient in the range was zero in FIR filters that approximate Hilbert transform corresponding to the transformation matrix H _t of the first and second Hilbert transformer

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