JP2008005067A - Single carrier modulation method, and single carrier modulation apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a technology for determining a proper metric and determining a metric adaptable to reduction in peak power in single carrier modulation for applying QAM modulation to a single carrier. <P>SOLUTION: The single carrier modulation has a form of a metric value provided to symbols of a QAM constellation to suppress the peak power and a form of a transition metric applicable to transition between the symbols obtained by QAM mapping. The metric value is provided to the symbols of the QAM constellation so as to suppress occurrence of symbols increasing the peak power, a dispersion in an instantaneous power is fixed as the metric on the basis of a relationship between the peak power and the dispersion in the instantaneous power, and encoding is executed to minimize the transition metric to reduce the peak power. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to single carrier modulation for QAM modulation of a single carrier by trellis shaping, and more particularly to reduction of peak power in multilevel QAM.

  In the 4th generation mobile communication system (4G), the adoption of OFDM having excellent resistance to frequency selective fading is dominant, but OFDM has very poor PAR (Peak-to-Average Ratio) characteristics. There are drawbacks. This defective PAR characteristic causes a problem of nonlinearity of a power amplifier in signal amplification performed at the time of transmission, and causes problems such as signal distortion and out-of-band power radiation.

  In order to prevent this nonlinear distortion of the power amplifier, the power amplifier requires a large amount of back-off, which causes a problem that the power added efficiency is significantly reduced. Since the battery-powered portable terminal is required to save power, the low power added efficiency is a serious problem. In addition, since high-performance power amplifiers are expensive, it is difficult to mount a high-performance power amplifier in a form terminal in view of cost, considering that mobile terminals are mass-produced.

  For these reasons, it is difficult to use OFDM on the uplink, and it has been considered to adopt a single carrier method instead.

  Further, in the fourth generation mobile communication system (4G), high speed communication of 1 [Gbps] when stationary and 100 [Mbps] even when moving is set as a target, and considering the depletion of frequency resources, the modulation is high. Frequency utilization efficiency is required. For example, there is a target of 4 to 10 [bit / sec] per 1 [Hz]. In order to achieve such modulation with high frequency utilization efficiency, multi-level modulation such as QAM is required. However, even in a single carrier, there is a problem that PAR deteriorates when QAM modulation is used, but when QAM value modulation is used for large-capacity transmission, a large peak power is generated and power utilization efficiency is reduced. Invite.

Shaping is known as a technique for reducing electric power. This shaping refers to the distribution of symbols after modulation to be close to the normal distribution, and to reduce the average power and close to the channel capacity, but generally is not limited to the normal distribution, and to the characteristics of the channel, The input bit sequence is encoded so that the distribution of symbols is favorable. As this shaping, there is known trellis shaping capable of arbitrary shaping by appropriately defining a code word search metric according to the Viterbi algorithm. It has been studied to reduce not only the average power but also the dynamic range of the signal by this trellis shaping (Non-Patent Document 1).
ISMorrison: “Trellis shaping applied to reducing the envelope fluctuations of MQAM and band-limited MPSK”, Proc. Int / Conf. Digital Satellite Commum. (ICDSC'92), pp. 143-149 (1992)

  Trellis shaping is originally intended to lower the average power by selecting the inner symbol points as much as possible in the QAM constellation. In the above-mentioned non-patent literature, trellis shaping is applied for the purpose of reducing the dynamic range of signals for QAM.

  In trellis shaping, it is important to define a codeword search metric. In the above non-patent literature, PSK is mainly handled for a single carrier, and the smaller the phase difference between symbol transitions, the smaller the probability that a peak will appear. The phase difference between two consecutive symbols is used as a metric.

  However, in QAM, unlike PSK, there is no relationship that the probability of peaking is smaller as the phase difference between symbol transitions is smaller, so no appropriate metric has been proposed, and it is mainly set based on empirical rules. ing. Also in the above document, since the metrics in the Viterbi algorithm are based on empirical rules, the performance of trellis shaping is not sufficiently exhibited.

  Therefore, conventionally, in single carrier modulation in which a single carrier is QAM modulated by trellis shaping, a good technique for reducing peak power in multilevel QAM has not been proposed.

  In addition, in shaping, the communication path capacity is reduced because a restriction is placed on the appearance of symbols. In trellis shaping, a 1-bit redundancy is added at the time of encoding. If an attempt is made to maintain the same information rate as when no shaping is performed, a constellation that is one size larger is required, leading to deterioration of error rate characteristics. .

  The peak power problem is a problem that always exists in communication, but becomes an increasingly important problem in high-speed communication such as the fourth generation mobile communication system (4G).

  Therefore, the present invention aims to solve the above-described conventional problems and to determine an appropriate metric in single carrier modulation for QAM modulation of a single carrier, and in particular to determine a metric suitable for peak power reduction. And

  It is another object of the present invention to suppress deterioration of error rate characteristics caused by shaping.

  The present invention uses a shaping code called trellis shaping and introduces a systematic metric to dynamically suppress peak power. Conventionally proposed metrics are based on heuristics, and the performance of trellis shaping has not been fully demonstrated. By introducing a systematic metric, the present invention enables not only reduction of peak power but also reduction of average power.

  Although the bit error rate is increased by the shaping code, the present invention substantially maintains the error rate at the same frequency utilization efficiency by combining the shaping code and the error correction code TCM (trellis coded modulation). The peak power is reduced.

  Further, the present invention improves the bit error rate by performing MAP (maximum a posteriori) decoding using the fact that the information source becomes a Markov information source by shaping.

  The present invention includes two aspects of a single carrier modulation method and a single carrier modulation apparatus in the aspect of QAM modulating a single carrier by trellis shaping.

  Each aspect of the single carrier modulation method and apparatus according to the present invention is configured to reduce the peak power between the form of the metric value (first form) given to the symbol of the QAM constellation and the symbol obtained by the QAM mapping. There are two characteristic forms of metrics, the form of transition metrics for transitions (second form).

  In the first form of the metric, a metric value is assigned to a symbol of the QAM constellation so that generation of a symbol that increases peak power is suppressed. Further, in the second mode, based on the relationship between the peak power and the variation in the instantaneous power, the variation in the instantaneous power is a metric (hereinafter referred to as a transition metric to distinguish it from the metric value assigned to each symbol). The peak power is reduced by encoding so that the transition metric is minimized.

  The single carrier modulation method of the present invention is a single carrier modulation method for QAM modulating a single carrier by trellis shaping.

  In the first mode, in giving a metric value to a symbol, in the QAM mapping, a metric value that is sufficiently large to be considered as infinite for a symbol that exists outside the set radius range from the center of the QAM constellation is set. Peak power is reduced by making the appearance probability of this symbol substantially zero.

  In the second embodiment, the transition metric for the transition between symbols obtained by QAM mapping is determined by the variation in instantaneous power.

  The single carrier modulation method of the present invention can be a combination of the first and second embodiments described above. According to this embodiment, the range of the set radius from the center of the QAM constellation in QAM mapping. A symbol that exists within the range of the set radius obtained by QAM mapping by setting a sufficiently large metric value to be regarded as infinite with respect to a symbol existing outside, and making the appearance probability of this symbol substantially zero The transition metric for the transition between symbols is determined by the variation in instantaneous power.

  Further, in the method for obtaining the transition metric determined by the variation in instantaneous power, more specifically, a continuous signal is formed from discrete symbols, the instantaneous power is calculated from the signal waveform of the continuous signal, and the calculated instantaneous power with respect to the reference power is calculated. A statistical moment is obtained, and the obtained statistical moment is used as a transition metric.

  Also, as a technique for forming a continuous signal from discrete symbols. The instantaneous value of the complex symbol point is calculated by squaring the sampling value of the complex symbol obtained by oversampling the signal waveform of the continuous signal, and the difference between the calculated instantaneous power and the preset reference power is raised to the power of the moment, The obtained power value is accumulated for the number of oversampling, and this accumulated value is used as a transition metric.

  The reference power for obtaining the transition metric becomes a parameter of the transition metric, and the peak power is reduced by setting the reference power to be equal to or less than the maximum value of the instantaneous power of the complex symbol points existing within the set radius range. In addition, the average power can be reduced by performing trellis shaping so that the transition metric obtained by setting the reference power to 0 is minimized.

  Furthermore, by increasing or decreasing the reference power between the maximum value of the instantaneous power of the complex symbol point existing within the set radius and 0, and performing trellis shaping so that the transition metric obtained from the reference power is minimized. The increase / decrease between the peak power and the average power can be adjusted.

  In addition, the single carrier modulation method of the present invention reduces peak power while maintaining the error rate substantially at the same frequency utilization efficiency by combining trellis shaping and error correction code TCM (trellis coded modulation). Can do. This combination of trellis shaping and TCM (trellis coded modulation) is performed by trellis coding and modulating at least a part of bits in the information code string that are not subjected to trellis shaping, and performing trellis coding modulation in the information code string. This can be done by trellis-shaping at least some of the bits that are not to be performed, and mapping the trellis-coded modulation information and the trellis-shaped information by the mapper in the TCM-QAM constellation, thereby causing the shaping. The error rate can be improved by TCM (trellis coded modulation) error correction.

  Also, the single carrier modulation method of the present invention can improve the bit error rate by performing MAP (maximum a posteriori) decoding using the fact that the information source becomes a Markov information source by shaping, and is encoded. In the decoding of the information, at the symbol point of the information, the occurrence probability of the symbol point is calculated from the posterior probability before the temporary point, and the symbol point that maximizes the calculated occurrence probability is selected, so that QAM modulation is performed by trellis shaping. MAP decoding is performed using the probability of occurrence of the single carrier symbol point.

  In addition to the above-described method aspect, the present invention may be an apparatus aspect. The single carrier modulation device of the present invention is a single carrier modulation device that QAM modulates a single carrier by trellis shaping.

  Also in each aspect of the single carrier modulation apparatus of the present invention, in order to suppress the peak power, the form of the metric value (first form) given to the symbol of the QAM constellation and the transition between symbols obtained by QAM mapping The transition metric form for (second form) has two characteristic forms with respect to the metric.

  In the first embodiment, the codeword that minimizes the metric by the Viterbi algorithm based on the inverse syndrome that encodes the bits to which the information sequence is shaped, the encoded bits, and the bits that are not subjected to the shaping of the information sequence And a mapper for mapping information obtained by adding a code word to encoded bits to a complex symbol point, and the generator is configured to detect a symbol existing outside a set radius from the center of the QAM constellation. By setting a metric value sufficiently large to be regarded as infinite, and making the appearance probability of this symbol substantially zero, the use of symbols that may increase peak power is suppressed.

  In the second mode, the codeword that minimizes the metric by the Viterbi algorithm based on the inverse syndrome that encodes the bits to which the information sequence is shaped, the encoded bits, and the bits that are not subjected to the shaping of the information sequence And a mapping unit that maps information obtained by adding the codeword to the encoded bits to complex symbol points, and the generator determines a transition metric for a transition between symbols obtained by QAM mapping as a variation in instantaneous power. Determined by

  Further, in the calculation of the transition metric, the transition metric may be prepared in a table in advance, and the transition metric may be read from this table based on the continuous signal. As a result, the calculation speed can be improved.

  Furthermore, the single carrier modulation device of the present invention can be configured by combining the first mode and the second mode, and according to this mode, the inverse syndrome, the generator, the mapper, The generator sets a metric value large enough to be considered infinite for symbols that are outside the set radius range from the center of the QAM constellation, and substantially reduces the probability of this symbol to appear. 0, and the transition metric for the transition between symbols obtained by QAM mapping is determined by the variation in instantaneous power.

  In a more detailed configuration, the generator calculates the instantaneous power from the signal waveform of the continuous waveform and the partial waveform calculation unit that forms a continuous signal by convolving a plurality of bits for shaping the information sequence, and calculates the instantaneous power A metric calculation unit that obtains a statistical moment with respect to the reference power, and uses the obtained statistical moment as a transition metric, a traceback unit that obtains a trellis that minimizes the transition metric, and a decoder that obtains a codeword from the trellis.

  The metric calculation unit included in the generator of the present invention squares the sampling value of the complex symbol obtained by oversampling the signal waveform of the continuous signal, calculates the instantaneous power of the complex symbol point, and presets the calculated instantaneous power The difference from the reference power is raised to the power of the moment order, the obtained power value is accumulated for the number of oversampling, and this accumulated value is used as the transition metric.

  Further, the metric calculation unit provided in the generator of the present invention reduces the peak power by setting the reference power to be equal to or less than the maximum value of the instantaneous power of the complex symbol points existing within the set radius range.

  Further, the metric calculation unit provided in the generator of the present invention sets the reference power to 0, thereby reducing the average power by performing trellis shaping so that the obtained transition metric is minimized.

  The metric calculation unit may prepare the transition metrics in a table in advance and read the transition metrics from this table based on the continuous signal. Thereby, the calculation speed of the metric calculation unit can be improved.

  Furthermore, the metric calculation unit included in the generator of the present invention increases or decreases the reference power between the maximum value of the instantaneous power of the complex symbol points existing within the set radius range and 0, and the transition metric obtained from the reference power is obtained. The trellis shaping is performed so as to minimize the difference between the peak power and the average power.

  In addition, the single carrier modulation apparatus of the present invention includes a TCM coder that trellis-code-modulates at least a part of bits that are not subjected to trellis shaping in the information code string, and information that is trellis-coded and modulated by the TCM coder. The TCM-QAM mapper also maps the information trellis-shaped with the inverse syndrome to the TCM-QAM using the constellation.

  With this configuration, trellis shaping and TCM (trellis coded modulation) that is an error correction code can be combined, and peak power can be reduced while maintaining the error rate substantially at the same frequency utilization efficiency.

  The single carrier modulation apparatus of the present invention further includes an inverse mapper that decodes symbol points from information output from the mapper. This inverse mapper calculates the occurrence probability of a symbol point from the posterior probability before the temporary point, and selects the symbol point that maximizes the calculated occurrence probability, so that the symbol point of a single carrier that is QAM modulated by trellis shaping MAP decoding is performed using the occurrence probability of.

  This makes it possible to improve the bit error rate by performing MAP (maximum a posteriori) decoding using the fact that the information source becomes a Markov information source by shaping.

  Further, the present invention sets a set power as a metric value limiter in single carrier modulation in which a single carrier is subjected to multilevel PSK modulation by trellis shaping, and for power exceeding the set power, the power value is set as a metric value. For the following power, 0 is used as the metric value. By setting this metric value, the power lost in the limiter can be minimized.

  As described above, according to the present invention, systematic metrics can be determined regardless of empirical rules in single carrier modulation in which a single carrier is QAM modulated.

  In addition, according to the present invention, the generation of this symbol is suppressed by giving an infinite metric to a symbol outside the predetermined circle of the QAM constellation in the metric value set for the symbol, and the peak power Reduce.

  Furthermore, in the transition between symbols in the QAM constellation, the variation in instantaneous power is used as a transition metric, and the peak power is reduced and the average power is adjusted by adjusting the reference power as a reference parameter in calculating the transition metric. The reduction relationship can be adjusted.

  Further, by combining the shaping code and TCM (trellis coded modulation), it is possible to suppress the deterioration of the error rate characteristic caused by the shaping.

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

  FIG. 1 is a block diagram for explaining a schematic configuration of single carrier modulation according to the present invention. The configuration example shown in FIG. 1 shows an example in which the single carrier modulation device of the present invention is applied to a general trellis shaping configuration.

  In FIG. 1, single carrier modulation includes a transmitter side shown in FIG. 1 (a) and a doctor side shown in FIG. 1 (b).

  Trellis shaping is a technique for controlling a transmission sequence, and is performed by converting an information sequence so as to be orthogonal to a code, and adding a code word to it with modulo-2. Due to the orthogonality between the information sequence and the code, the information sequence can be decoded on the receiving side. The code used here is a convolutional code, and the codeword is searched by the Viterbi algorithm so as to minimize a certain metric.

  The transmitter of the single carrier modulation according to the present invention includes a generator 1 that generates a codeword v, an inverse syndrome 2 that encodes a shaping bit s, and complex symbol points, as in a generally known trellis shaping configuration. A mapper 3 for mapping and forming a transmission signal is provided.

  In FIG. 1A, Gs is a 1 × ns generator matrix as a convolutional code, and Hs is a syndrome corresponding to this generator matrix.

Between Gs and H,
GsHs ^T = 0 (1)
There is a relationship.

Hs ⁻¹ is the left-side inverse matrix of the syndrome (called inverse syndrome)
Hs ^-1 Hs ^T = I (2)
There is a relationship.

First, the transmission sequence is divided into a bit s to be shaped and a bit u to be mapped as it is, and s is encoded by inverse syndrome 2 to obtain s ^* .
s ^* = s (Hs-1) ^T (3)

Since inverse syndrome 2 is a matrix of (ns−1) × ns, this process adds 1-bit redundancy. Next, based on s ^* and u, a codeword v that minimizes the metric is found by the Viterbi algorithm, and this codeword v is added to s ^* by modulo-2. Finally, z = s ^* + v and u are mapped to complex symbol points by the mapper 3 and transmitted.

  In FIG. 1B, on the receiving side, the signal A sent from the mapping device 3 of the transmitter is received by the inverse mapping device 13 and divided into z and u. z is a signal related to the shaped bit s, and u is the unshaped bit u. By passing the signal z through the syndrome 11, the original information s can be decoded.

This decryption is
zHs ^T = (s ^* + v) Hs ^T
= (S (Hs ^-1 ) ^T + v) Hs ^T
= S (Hs ^-1 ) ^T Hs ^T + vHs ^T
As long as the codeword v is a valid codeword, vHs ^T = 0 holds,
= S + 0 = s (4)
Because it becomes.

  Normally, trellis shaping is aimed at reducing the average power, so that one symbol is associated with one branch of the trellis and shaping is performed using the square value of the symbol corresponding to power as a metric. On the other hand, since the present invention aims to reduce peak power, a metric is obtained by associating a continuous signal waveform with one branch of a trellis instead of discrete symbol points.

  The generator 1 includes a partial waveform calculation unit 1a, a metric calculation unit 1b, a traceback unit 1c, and a decoder 1d as a configuration for obtaining a metric by associating a continuous signal waveform with one branch of a trellis. Note that the traceback unit 1c for obtaining the trellis having the smallest metric based on the obtained metric, and the decoder 1d for obtaining the codeword v corresponding to the obtained trellis are the same as in a normal trellis shaping generator using discrete values. It is.

  The generator 1 of the present invention includes a partial waveform calculation unit 1a and a metric calculation unit 1b as a configuration for obtaining a metric by associating a continuous signal waveform with one branch of a trellis. The partial waveform calculation unit 1a obtains a continuous signal waveform (hereinafter referred to as a partial waveform) by passing a signal of a plurality of consecutive symbols through a convolution filter.

  Also, the metric calculation unit 1b samples this partial waveform, obtains a value corresponding to the instantaneous power obtained by squaring the value of this sampling point, and calculates the square value and the reference power Pref (reference power). Is obtained as a metric.

  In this metric calculation, in order to reduce peak power, the metric value of a symbol located outside a circle with a predetermined radius is set to infinity in the QAM constellation. FIG. 2 is a diagram for explaining setting of the metric value. In FIG. 2, each point indicates a symbol point arranged in the QAM constellation. Here, for a symbol existing outside a circle with a predetermined radius rs (indicated by a broken line in the figure), a sufficiently large value is set so that the metric value can be regarded as infinite. The black circles in FIG. 2 indicate symbols inside the circle, and the white circles indicate symbols outside the circle. Infinity is given to the branch metric of the symbol represented by the white circle.

  By assigning infinity to the branch metric, when a trellis having the smallest metric (transition metric) is obtained by the traceback unit 1c, the path passing through the symbol to which the infinity is assigned is removed.

  In the QAM constellation, symbols existing outside a circle with a predetermined radius are assumed to have a high peak power. Therefore, peak power can be suppressed by avoiding such symbols that exist outside the circle.

  This metric value is set so that a symbol outside the circle with a predetermined radius rs is not selected in the trellis. If the trellis path is interrupted at the symbol position in the metric value comparison, it is not necessarily infinite. It doesn't have to be big.

  Further, in order to avoid a symbol outside the circle and to select a path having the smallest metric from paths using only the symbols within the circle, the statistical moment described above is used as a metric. Since this statistical moment is obtained based on the difference between the value corresponding to the instantaneous power and the standard power Pref (reference power), the standard power Pref (reference power) is a kind of parameter. By doing so, it is possible to adjust peak power reduction, average power reduction, or peak power reduction and average power reduction.

  For example, the peak power can be reduced by setting the reference power Pref (reference power) to be equal to or less than the maximum value of the instantaneous power of the complex symbol points existing within the set radius range. On the other hand, by setting the reference power to 0, the average power can be reduced by performing trellis shaping so that the obtained transition metric is minimized.

  Also, trellis shaping is performed by increasing or decreasing the reference power between the maximum value of the instantaneous power of the complex symbol point existing within the set radius range and 0 and minimizing the transition metric obtained from the reference power. The increase / decrease between the peak power and the average power can be adjusted.

  Hereinafter, in the single carrier modulation according to the present invention, PAR is reduced by combining trellis shaping and TCM (trellis coded modulation), and the error rate due to shaping is suppressed, and the error rate is substantially maintained with the same frequency utilization efficiency. A description will be given using a configuration example in which the peak power is reduced as it is. In this configuration, trellis shaping is used to reduce PAR, and the loss in BER caused by trellis shaping is recovered by TCM. Further, the point that the BER is further recovered by utilizing the fact that the information source becomes a Markov information source by shaping will be described.

Unencoded M-QAM is
R (M) = log ₂ M (5)
It has a bit information rate represented by In addition, MSED (Minimum squared Euclidean Distance) that determines the error rate in a region where the signal-to-noise power ratio is large is:
MSED (M) ≈6.4 / M (6)
It is known that it is proportional to the reciprocal of M as follows. Since shaped M-QAM is a redundant bit in which 1 bit of mapped bits is added by inverse syndrome, the information rate is
Rs (M) = R (M) -1 = log ₂ M-1
= Log ₂ (M / 2) = R (M / 2) (7)
Thus, it is equal to that of M / 2-QAM, but MSED is unchanged MSEDs (M) = MSED (M)
= 1/2 · MSED (M / 2) (8)
Therefore, the error rate deteriorates under the condition that the information rate is constant.

Further, since 1-bit redundancy is added by shaping, 2M-QAM having twice the number of symbols must be used instead of M-QAM in order to send log ₂ M-bit information. Therefore, it can be said that as the number of symbols increases twice, the Euclidean distance between the symbol points is shortened, and a loss occurs in the BER characteristics (bit error rate).

  Therefore, in the present invention, trellis shaping is configured to combine error correction codes in order to compensate for this loss.

  FIG. 3 is a diagram for explaining a configuration example in which trellis shaping and TCM are combined.

  The configuration example shown in FIG. 3 combines trellis shaping and TCM in parallel, encodes unshaped bits, and shapes uncoded bits. Here, a configuration example using an inverse syndrome with a coding rate of 2/3 and a TCM with a coding rate of 2/3 is shown.

  In FIG. 3, the lower 2 bits of the information code are passed through the TCM coder 4 and encoded by trellis coding modulation, and the upper 2 bits are passed through the inverse syndrome 2 for shaping. The generator 1 inputs the bit output encoded through the TCM coder 4, the bit output through the inverse syndrome 2, and any non-encoded bits, and uses the Viterbi algorithm to generate a codeword v for lowering the PAR. Explore. In this generator, a metric calculation is performed to lower the PAR.

  The codeword v generated by the generator 1 is added modulo-2 to the output from the inverse syndrome 2, and is mapped to a TCM-QAM constellation by the TCM-QAM mapper 3A.

  Note that the broken lines in FIG. 3 are bits necessary for 128 QAM and 256 QAM, and represent directly mapped bits. In 32QAM, the encoded bit by the TCM coder 4 is handled as 1 bit. Further, since the number of bits is insufficient for 16QAM, this combination of trellis shaping and TCM (trellis coded modulation) cannot be applied.

  Since 1-bit redundancy is added by shaping and 1-bit redundancy is added by TCM, a total of 2-bit redundancy is added.

The overall information rate is
Rt (M) = Rs (M) -1 = log ₂ (M / 2) -1
= Log ₂ (M / 4) = R (M / 4) (9)
MSED is equal to that of M / 4-QAM, but considering that set partitioning is performed three times with a rate 2/3 encoder, MSED is MSEDt (M) ≈4MSED (M / 4)
= MSED (M) (10)
Therefore, it is possible to reduce PAR without any loss in error rate characteristics.

  In the configuration shown in FIG. 3, 1-bit redundancy is added during shaping. On the other hand, according to the configuration of multi-dimensional trellis shaping shown in FIG. 4, a plurality of symbols can be simultaneously shaped, and the redundancy can be halved. Although FIG. 4 shows the case of 2 symbols, the same can be applied to 3 bits or more. Note that a multi-dimensional configuration can be used in the TCM coder instead of the configuration in inverse shaping.

  Next, the configuration and metrics of the Viterbi algorithm for reducing PAR will be described.

  Since the present invention aims to reduce peak power, a metric is obtained in association with one branch of a trellis by using a continuous signal waveform instead of discrete symbol points.

  FIGS. 5A and 5B schematically show the relationship between a trellis and symbols for the purpose of reducing average power. Here, one branch of the trellis corresponds to each discrete symbol point in the QAM constellation.

  On the other hand, FIGS. 5C and 5D schematically show the relationship between a trellis and symbols for the purpose of reducing peak power. Here, since the signal after passing through the filter is an object, it is necessary to associate a continuous waveform in one QAM constellation with one branch of the trellis.

  In order to perform metric calculation using continuous signal waveforms instead of discrete symbol points, continuous signal waveforms are acquired by the following method.

  First, the output before the temporary point is held in the trellis. A continuous signal waveform can be obtained by performing a convolution operation of two pulses of the output before the temporary point and the current symbol. This signal waveform is a partial waveform (partial waveform). FIG. 6A shows an impulse response of a pulse corresponding to the two symbols at this time, and a partial waveform example obtained by passing these impulse responses through a filter.

FIG. 7A shows a circuit example for acquiring the current symbol and the symbol before the temporary point. In FIG. 7A, as a shaping code, Gs = [1 + D ² 1 + D + D ² ] (11)
, A circuit for acquiring a current symbol can be configured by memories (registers) 11a and 11b and adders 12a and 12b that constitute two delay units. A circuit for acquiring a symbol before one point in time adds a memory (register) 11c to the above circuit and outputs it from the adders 12c and 12d. As a result, the output before the temporary point is
DGs = D [1 + D ² 1 + D + D ² ]
= [D + D ³ D + D ² + D ³ ] (12)
Given in.

  However, the output before the temporary point is necessary only for calculating the branch metric on the trellis, and is not necessary when outputting the codeword.

  The impulse responses and partial waveform examples shown in FIGS. 6A and 6B are schematically shown.

  The actual signal waveform is a convolution of the impulse responses of all symbols, and inaccuracy is included in the partial waveform obtained from only two symbols. Therefore, the accuracy of the partial waveform can be increased by increasing the number of signals used for the convolution calculation. FIG. 7B shows a configuration example in which a partial waveform is obtained from three consecutive symbols. Further, as shown in FIG. 6B, a more accurate one can be obtained by obtaining a partial waveform from four consecutive symbols. However, in order to obtain a partial waveform from these four consecutive symbols, it is necessary to add two more memories and add a total of three memories, which increases the amount of calculation of the Viterbi algorithm.

  FIG. 8 shows a configuration for obtaining a convolutional code for shaping by adding a memory so as to hold two outputs, and a configuration for obtaining a partial waveform.

  Next, the coding search metric will be described.

  First, in order to avoid selection of a symbol that may increase the peak power, a point where an infinite branch metric value is given will be described.

  QAM has a square or cross-shaped constellation, and is considered to have a higher peak power than a circular constellation. Therefore, before calculating a metric using a partial waveform, a setting is made so that symbols that may increase this peak power are not selected.

  In FIG. 9, in the QAM constellation, the appearance of symbols located at corners is suppressed to make it closer to a circle. For this purpose, the branch metric of the symbol located outside the circle of radius γs is set to infinity, and the appearance probability of the symbol at the corner is set to zero. The path in the trellis is always erased there, so the appearance of corners is completely suppressed.

  Next, when both the current symbol and the symbol before the temporary point are located inside the circle, a metric (transition metric) is given by the following process, and PAR is further reduced.

  Peak power is considered to be related to variations in instantaneous power. For example, constant envelope signals such as FSK and MSK have zero instantaneous power dispersion, and therefore PAR is also 0 [dB], and have excellent peak power characteristics.

  Therefore, the metric of the present invention uses a metric that minimizes the dispersion of instantaneous power. For this metric, a reference power Pref (referred to as reference power) is determined in advance, and a square moment (that is, instantaneous power) of the partial waveform described above and a statistical moment between Pref are obtained and used as a metric.

Given the unshaped bits ui, uj, the metric for the transition from state Si to state Sj is
It is defined as Here, β is the moment order, and Ns is the oversampling number. 1 / Ns of the coefficient is a factor for normalization, and there is no problem even if it is omitted in the actual calculation.

The complex signal Si, j (k) is the kth sampling point of the partial waveform generated by the transition from state Si to state Sj under ui, uj. If the impulse response of the filter is h (n),
Si, j (k) = Ai · h (k) + Aj · h (Ns−k)
k = 0, 1,..., Ns (15)
It can also be expressed as Here, Ai is a complex symbol point corresponding to Si, ui.

  Note that the calculation amount can be reduced by calculating the convolution calculation and the moment calculation in advance as in Expression (12) and Expression (14) and using a lookup table.

  Further, by adjusting Pref, not only PAR but also average power can be reduced.

  10A and 10B, the peak power is reduced by adjusting Pref to a predetermined value that does not exceed the maximum value of the signal. Note that the state shown in FIG. 9B shows a state in which the peak power is reduced by shaping from the state shown in FIG.

Further, when reducing the average power, for example, if β = 1 and Pref = 0 in the equation (14),
It becomes. This is equivalent to shaping the average power for the oversampled signal. 10C and 10D, the average power is reduced by adjusting Pref to zero. The state shown in FIG. 10D shows a state in which the average power is reduced by shaping from the state shown in FIG.

Also, if Pref is set to a sufficiently large value to exceed the maximum value of the signal,
Thus, only the peak power is shaped.

  10E and 10F, only the peak power is shaped by adjusting Pref to a value exceeding the maximum value of the signal. Note that the state shown in FIG. 10F shows a state that is shaped from the state shown in FIG.

  By increasing / decreasing Pref in this way, a trade-off between peak power and average power can be performed, and the relationship between both powers can be adjusted.

  The selection of the shaping code with the smallest transition metric can be performed by computer search. Since burst errors occur in the syndrome on the receiving side, if the suppression of peak power is the same, the corresponding syndrome is selected as simple as possible.

  Next, MAP decoding based on the Markov process will be described. By applying shaping, the transition probability of the symbol points becomes non-uniform and the information source becomes a Markov information source, so the occurrence probability of the current symbol depends on the symbol point before the temporary point.

  Therefore, the error rate can be improved by using MAP decoding using the occurrence probability of symbol points for decoding.

  MAP decoding is a decoding method in which when a complex reception point r is received, a symbol point sm that maximizes the posterior probability P (sm | r) is selected, and maxP (sm | r) is calculated for m.

Using Bayes' theorem, maxP (sm | r) is
maxP (sm | r) = maxP (r | sm) P (sm) (18)
In AWGN (white Gaussian noise), N ₀ is the noise power and maximization is obtained.
maxP (sm | r) = min [(r−sm) ² −N ₀ llnP (sm)] (19)
Is obtained.

Note that N ₀ needs to be estimated on the receiving side.

The occurrence probability P (sm) of the symbol sm is obtained from the posterior probability P ^(n-1) (sm | r) before the temporary point based on the Markov process as follows.

  Here, P (sm | si) is a transition probability from Si to Ssm, and can be obtained by computer simulation.

  In the above description, QAM is shown, but the present invention can also be applied to PSK. FIG. 11 is a diagram for explaining an example of a metric when applied to PSK.

In this case, the first metric uses a moment representing the variation in the power distribution as the metric based on the relationship between the peak power and the variation in the power distribution. FIG. 11A shows the variation in power distribution from the normalized value represented by 1. This metric is
metric≡ (p−1) β (21)
Defined by β is the moment order.

  The second metric is for the limiter model and minimizes the power lost in the limiter.

This metric is
metric≡p (p> pmax)
0 (others) (22)
It is represented by FIG. 11B shows the input / output relationship at this time, and FIG. 11C shows an example of a metric.

  Hereinafter, simulation results of the present invention by computer simulation will be described.

  PAR is defined by the ratio of peak power to average power and depends on the length T of the transmission sequence. Here, in order to perform the evaluation independent of T, a normalized distribution cumulative distribution function (CCDF: Complementary Cumulative Distribution Function) is used for the evaluation.

Normalized power is defined as the instantaneous value of power divided by the average power,
η (t) ≡ | s (t) | ² / Pav
Also, the cumulative distribution complementary function F (x) is a probability that η (t) exceeds a certain value,
F (x) = Prob [η (t)> x]
It is expressed.

  First, the normalized power characteristic will be described.

  Changes in characteristics due to changes in the reference power are shown in FIG. 12 with 64QAM as a representative. A cosine roll-off filter having a roll-off coefficient α = 0.4 is used. Hereinafter, 0.4 unless otherwise specified. The symbols and r shown in Table 1 are used. These codes are optimum for the constraint length K = 3.

  FIG. 12 shows that the average power increases as the reference power increases. It can also be seen that as the moment order β is increased, the change is more gradual where Pref is larger and smaller. When Pref is lower than the minimum value of the waveform, the waveform changes more rapidly as the order of the moment increases, and it is considered that the average power is increased in order to avoid a large peak caused by the waveform. The reverse is true when Pref is higher than the maximum value of the waveform.

  FIG. 13 shows the normalized power characteristics when the reference power is changed for β = 2. It can be seen that the normalized power generally decreases as Pref increases. As described above, the average power and the PAR can be traded off by increasing or decreasing the reference power. When using a power amplifier having relatively good characteristics, the characteristics can be easily set by increasing or decreasing this parameter, such as setting Pref low.

  FIG. 14 shows the change in the characteristic of the normalized power due to β under the condition of the average electric car constant. A, B, C, and D in FIG. 14 indicate A, B, C, and D in FIG. When the average power is low, such as at points A and B, the larger the β, the better the characteristics. In these two points, even if β = 6 or more, no further improvement is achieved. At point C, better characteristics than β = 6 can be obtained when β = 20. This is probably because the larger the β is, the more rapidly changing the waveform is seen, and the greater the effect of suppressing variations in amplitude. However, when the average power increases as at point D, the effect of β is not seen.

  Next, the best PAR will be described using β = 2 and the values shown in Table 2.

  As described above, the combination with TCM cannot be used in 16QAM, but the result of shaping all bits for comparison purposes is shown. In addition, rs is described as being normalized so that the average power of the QAM constellation is 1.

  In the following, an example of a baseband waveform is shown for the QAM of FIGS. 15 shows a 16QAM baseband waveform, FIG. 16 shows a 32QAM baseband waveform, FIG. 17 shows a 64QAM baseband waveform, FIG. 18 shows a 128QAM baseband waveform, and FIG. 19 shows 256QAM. This is a baseband waveform.

  In each figure, the left figure shows a conventional QAM, and the right figure shows a QAM according to the present invention. In each figure, it is observed that the vicinity of the corner of the QAM constellation is eliminated and the transition through the vicinity of the origin is greatly reduced.

  Next, normalized power characteristics will be described.

  FIG. 20 shows the normalized power cumulative distribution complement function of the case without shaping and the shape with shaping. As can be seen from the figure, by applying shaping, a gain of around 2.5 [dB] can be obtained in a 16, 64, 256 QAM square constellation. Further, in the 32,128QAM cross constellation, the gain as high as the square constellation is not seen. When evaluation is performed with the same information bits per symbol, the gain is 1.6 [dB] for 16QAM-64QAM, 1.1 [dB] for 32QAM-128QAM, and 2.0 [dB] for 64QAM-256QAM. Gain of.

  FIG. 21 shows changes in characteristics depending on the constraint length of the shaping code. From the figure, it is confirmed that the characteristics do not improve much even if the constraint length is increased.

  FIG. 22 shows characteristics when multi-dimensional shaping is performed in 64QAM. In multi-dimensional, since a plurality of symbols must be shaped at a time, the control ability is reduced, and if rs is used as it is, all paths on the trellis are cut. Therefore, it corresponds by changing rs as shown in Table 3.

  Instead of reducing the redundancy, it is observed that the characteristics deteriorate.

  Next, a trade-off between peak power and average power will be described. Table 1 shows a simulation result of the reduction amount of the peak power and the average power by adjusting the reference power. This example is an example of 64QAM.

  The simulation results in Table 1 show that a trade-off is possible between the reduction of average power and the reduction of peak power by adjusting the reference power Pref. The peak power in the table represents the normalized power x that satisfies F (x) = 10−6 in the above-described cumulative distribution complementary function F (x).

  In a region where Pref is small, the average power is remarkably reduced, whereas the peak power is larger than that without shaping. On the other hand, in the region where Pref is large, the peak power can be greatly reduced even though the average power is higher than 1. Further, in the vicinity of Pref = 0.7, both the average power and the peak power can be reduced.

  FIG. 23 shows the peak power with respect to the transmission rate (communication path capacity). According to FIG. 23, the amount of reduction in peak power with respect to the transmission rate (communication path capacity) is improved as compared with the prior art (indicated by “x” mark, “□” mark, “△” mark in the figure). It shows that.

  Next, addition of memory will be described. By adding two memories (three memories in total), a more accurate partial waveform can be obtained.

  FIG. 24 shows a change in characteristics when the number of memories is increased in 256QAM. When α = 0.4, the curve with a larger amount of memory is slightly steeper and inferior to near 3.6 [dB], but after that it is reversed and becomes better. Further, when α = 0, 1, it indicates that the rotation is reversed in the vicinity of 6.2 [dB].

  In addition, when a waveform obtained in consideration of two symbols before and after is used for 256QAM, peak power can be reduced as shown in Table 5.

  Next, the BER characteristic in the AWGN communication path will be described. FIG. 25 shows the BER characteristics in the AWGN communication path.

  As described above, when the set division is performed three times, 64QAM asymptotically falls below the error rate of 16QAM. On the other hand, when the encoder that outputs the first bit shown in FIG. 26 is used as it is, the set division is performed only twice. Therefore, this 64QAM has the same MSED as the conventional 16QAM. From the simulation results, it can be observed that the 64QAM of the present invention gradually approaches the conventional 16QAM. Even at an error rate of 10-5, 64QAM is slightly worse.

  This example is the case of the simulation using the simplest TCM, but it is also assumed that 16QAM is exceeded by using a TCM with a large number of states. Further, although the PAR characteristics are slightly deteriorated, the BER can be improved by increasing the MSED if the average power can be reduced by lowering the Pref.

  Next, a case where MAP decoding is used will be described.

FIG. 27 shows a BER characteristic obtained under the assumption that a state transition probability matrix is obtained by measurement by computer simulation, and that N ₀ can be accurately estimated on the receiving side. Although no significant improvement is observed, it is observed that the gain decreases as E _b / N ₀ increases. This is considered to be due to the fact that the dependence on P (sm) decreases as N ₀ decreases in equation (19). However, in the case of 64QAM, a gain of about 1 [dB] exists near 7 [dB]. In other words, if a strong code that greatly changes the characteristic curve at a low S / N ratio is used, it is expected that a gain of about 1 [dB] will eventually be generated.

It is a block diagram for demonstrating schematic structure of the single carrier modulation of this invention. It is a figure for demonstrating the setting of the metric value of this invention. It is a figure for demonstrating the structural example which combined the trellis shaping and TCM of this invention. It is a figure for demonstrating the structure of a trellis shaping. It is a figure for demonstrating the relationship between the trellis and symbol in the case of aiming at reduction of average electric power and peak electric power. It is a figure for demonstrating the partial waveform of this invention. It is a figure which shows the example of a circuit which acquires the present symbol and the symbol before a temporary point of this invention. It is a figure which shows the structure which obtains the convolutional code for shaping of this invention, and the structure which obtains a partial waveform. It is a figure for demonstrating a branch metric in the QAM constellation of this invention. It is a figure for demonstrating the electric power adjustment by adjustment of Pref of this invention. It is a figure for demonstrating the example of the metric when it applies to PSK of this invention. It is a figure for demonstrating the change of the characteristic by the change of reference electric power. It is a figure which shows the normalized power characteristic at the time of changing reference electric power. It is a figure which shows the change of the characteristic of the normalized electric power under the conditions of average electric car constant. It is a figure which shows an example of a baseband waveform about QAM. It is a figure which shows an example of a baseband waveform about QAM. It is a figure which shows an example of a baseband waveform about QAM. It is a figure which shows an example of a baseband waveform about QAM. It is a figure which shows an example of a baseband waveform about QAM. It is a figure which shows a normalized electric power cumulative distribution complement function. It is a figure which shows the change of the characteristic by the constraint length of a shaping code. It is a figure which shows the characteristic at the time of performing multi-dimensional shaping. It is a figure which shows the peak electric power with respect to a transmission rate (communication path capacity). It is a figure which shows the change of the characteristic when the number of memories is increased. It is a figure which shows the BER characteristic in an AWGN communication path. It is a figure which shows an encoder. It is a figure which shows the BER characteristic by computer simulation.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Generator 1a Partial waveform calculating part 1b Metric calculating part 1c Trace back part 1d Decoder 2 Inverse syndrome 3 Mapping unit 3A TCM-QAM mapping unit 11 Syndrome 13 Inverse mapping unit

Claims (24)

A single carrier modulation method for QAM modulating a single carrier by trellis shaping,
In QAM mapping, by setting a sufficiently large metric value to be regarded as infinite for symbols existing outside the set radius range from the center of the QAM constellation, and making the appearance probability of the symbol substantially zero A single carrier modulation method characterized by reducing peak power. A single carrier modulation method for QAM modulating a single carrier by trellis shaping,
A single carrier modulation method characterized in that a transition metric for a transition between symbols obtained by QAM mapping is determined by variation in instantaneous power. A single carrier modulation method for QAM modulating a single carrier by trellis shaping,
In QAM mapping, a sufficiently large metric value is set for a symbol existing outside the set radius range from the center of the QAM constellation to make the appearance probability of the symbol substantially zero,
A single carrier modulation method, wherein a transition metric for a transition between symbols is determined by a variation in instantaneous power in symbols existing within a set radius range obtained by QAM mapping. The transition metric determined by the variation in instantaneous power is:
A continuous signal is formed from discrete symbols, instantaneous power is calculated from the signal waveform of the continuous signal, a statistical moment with respect to the reference power of the instantaneous power is obtained, and the statistical moment is used as a transition metric. The single carrier modulation method according to claim 2 or 3.   The instantaneous power of the complex symbol point is calculated by squaring the sampling value of the complex symbol obtained by oversampling the signal waveform of the continuous signal, and the difference between the instantaneous power and the preset reference power is raised to the power of the moment. The single carrier modulation method according to claim 4, wherein a value obtained by accumulating the power value for the number of oversamplings is used as a transition metric.   6. The single power according to claim 4, wherein peak power is reduced by setting the reference power to be equal to or less than a maximum value of instantaneous power of complex symbol points existing within the range of the set radius. Carrier modulation method.   6. The single carrier modulation method according to claim 4, wherein the average power is reduced by performing trellis shaping so that a transition metric obtained by setting the reference power to 0 is minimized.   The reference power is increased or decreased between the maximum value of the instantaneous power of complex symbol points existing within the set radius and 0, and trellis shaping is performed so that the transition metric obtained by the reference power is minimized. The single carrier modulation method according to claim 4, wherein an increase / decrease between the peak power and the average power is adjusted. Trellis code modulation of at least some of the bits of the information code sequence that are not to be trellis shaped,
Trellis shaping at least a part of the bits of the information code string that are not subjected to trellis coding modulation;
9. The error rate is improved by mapping the trellis-coded modulated information and the trellis-shaped information with a TCM-QAM constellation by a mapper. Single carrier modulation method as described in one. In decoding the encoded information,
At the symbol point of the information, the occurrence probability of the symbol point is calculated from the posterior probability before the temporary point, and the symbol point having the maximum occurrence probability is selected, so that the single carrier symbol QAM modulated by the trellis shaping The single carrier modulation method according to claim 1, wherein MAP decoding is performed using a point occurrence probability.   6. The single carrier modulation method according to claim 4, wherein the transition metric is provided in a table form, and the transition metric is read from the table based on the continuous signal. A single carrier modulation method for multi-level PSK modulation of a single carrier by trellis shaping,
Set power as a metric value limiter. For power exceeding the set power, use the power value as the metric value. For power below the set power, use 0 as the metric value, and minimize the power lost by the limiter. A single carrier modulation method. It is a single carrier modulation device that QAM modulates a single carrier by trellis shaping,
An inverse syndrome that encodes bits for shaping an information sequence;
A generator for determining a codeword that minimizes a metric with a Viterbi algorithm based on the encoded bits and bits that are not subjected to shaping of the information sequence;
A mapper for mapping information obtained by adding the codeword to the encoded bits to complex symbol points;
The generator sets a metric value sufficiently large to be considered infinite for a symbol that exists outside the set radius range from the center of the QAM constellation, and sets the appearance probability of the symbol to substantially zero. A single carrier modulation device. It is a single carrier modulation device that QAM modulates a single carrier by trellis shaping,
An inverse syndrome that encodes bits for shaping an information sequence;
A generator for determining a codeword that minimizes a metric with a Viterbi algorithm based on the encoded bits and bits that are not subjected to shaping of the information sequence;
A mapper for mapping information obtained by adding the codeword to the encoded bits to complex symbol points;
The generator determines a transition metric for a transition between symbols obtained by QAM mapping based on variations in instantaneous power. It is a single carrier modulation device that QAM modulates a single carrier by trellis shaping,
An inverse syndrome that encodes bits for shaping an information sequence;
A generator for determining a codeword that minimizes a metric with a Viterbi algorithm based on the encoded bits and bits that are not subjected to shaping of the information sequence;
A mapper for mapping information obtained by adding the codeword to the encoded bits to complex symbol points;
The generator sets a metric value sufficiently large to be considered infinite for a symbol that is outside the set radius range from the center of the QAM constellation, and the appearance probability of the symbol is substantially zero.
A single carrier modulation device, characterized in that a transition metric for a transition between symbols obtained by QAM mapping is determined by variation in instantaneous power. The generator is
A partial waveform calculation unit that forms a continuous signal by convolution of a plurality of bits for shaping an information sequence;
Calculating a momentary power from the signal waveform of the continuous signal, obtaining a statistical moment with respect to the reference power of the instantaneous power, and a metric calculation unit using the statistical moment as a transition metric;
A traceback unit for obtaining a trellis that minimizes the transition metric;
16. The single carrier modulation device according to claim 14, further comprising a decoder that obtains a code word from the trellis. The metric calculation unit of the generator is
The instantaneous power of the complex symbol point is calculated by squaring the sampling value of the complex symbol obtained by oversampling the signal waveform of the continuous signal, and the difference between the instantaneous power and the preset reference power is raised to the power of the moment. The single carrier modulation device according to claim 16, wherein a value obtained by accumulating the power value for the number of oversamplings is used as a transition metric. The metric calculation unit of the generator is
18. The single power according to claim 16, wherein peak power is reduced by setting the reference power to be equal to or less than a maximum value of instantaneous power of complex symbol points existing within the range of the set radius. Carrier modulation device. The metric calculation unit of the generator is
18. The single carrier modulation device according to claim 16, wherein the average power is reduced by performing trellis shaping so that a transition metric obtained by setting the reference power to 0 is minimized. The metric calculation unit of the generator is
The reference power is increased or decreased between the maximum value of the instantaneous power of complex symbol points existing within the set radius and 0, and trellis shaping is performed so that the transition metric obtained by the reference power is minimized. The single carrier modulation device according to claim 16, wherein an increase / decrease between the peak power and the average power is adjusted by: A TCM coder that trellis-code modulates at least some of the bits of the information code string that are not trellis-shaped;
The TCM-QAM mapper which maps the information trellis-coded and modulated by the TCM coder and the information trellis-shaped by the inverse syndrome by TCM-QAM using a constellation. 21 to 20 The single carrier modulation device according to any one of the above.   A reverse mapper that decodes a symbol point from information output from the mapper, and the reverse mapper calculates a symbol point occurrence probability from a posterior probability before the temporary point, and a symbol that maximizes the occurrence probability The single point according to any one of claims 13 to 21, wherein by selecting a point, MAP decoding is performed using an occurrence probability of a symbol point of a single carrier that is QAM modulated by the trellis shaping. Carrier modulation device.   19. The single carrier modulation device according to claim 17, wherein the metric calculation unit of the generator includes the transition metric as a table, and reads the transition metric from the table based on the continuous signal. It is a single carrier modulation device that multi-level PSK modulates a single carrier by trellis shaping,
Set power as a metric value limiter. For power exceeding the set power, use the power value as the metric value. For power below the set power, use 0 as the metric value, and minimize the power lost by the limiter. A single carrier modulation device.