Method for retrieving sequences of minimum papr in an OFDM communication system

Method for recovering sequence with minimum peak-to-average power ratio in OFDM communication system

Technical field

The present invention relates to a method for reducing PAPR (peak-to-average power ratio) to prevent performance degradation in an OFDM (orthogonal frequency division multiplexing) communication system, and more particularly to a method for quickly and effectively recovering a sequence with the smallest PAPR.

Background technique

Generally, in an OFDM (Orthogonal Frequency Division Multiplexing) system, which is one of multi-carrier transmission systems, information is simultaneously transmitted through uniformly distributed carrier frequencies. Therefore, in OFDM, a high data transmission rate can be obtained. Because in data transmission, data is distributed across the entire transmission bandwidth, even in the case of frequency selective fading and narrow-band interference, the OFDM system is stable. The OFDM method has good performance in multipath and mobile communication environments. Therefore, the OFDM method can be used in various communication systems, such as local area networks, digital audio broadcasting (DAB), digital video broadcasting (DVB), wireless ATM (asynchronous transfer mode) ), the Internet and IMT-2000 UMTS (Global System for Mobile Communications).

However, despite these advantages, the OFDM communication system also has the problem of high PAPR (peak-to-average power ratio). Generally speaking, in an OFDM communication system, the peak envelope power of a multi-carrier signal increases as the number of carriers increases. For example, in an OFDM system, when N signals overlap with the same phase, the maximum power of the multi-carrier signal is increased to N times the average power. Therefore, the PAPR, which is defined as the ratio of the maximum power of the multi-carrier to the average power, is also increased. When the PAPR is large, the OFDM communication system requires an amplifier with a wide dynamic range. In addition, a complex AD converter (analog-to-digital) and DA converter (digital-to-analog) are required to meet the requirements. Even in an OFDM communication system using an amplifier with a wide dynamic range, because the signal amplitude varies greatly, the amplifier may work in a non-linear range, the signal will be distorted, and the performance of the amplifier will decrease.

Therefore, in order to solve the above-mentioned problems caused by high PAPR in the OFDM communication system, various methods have been studied.

One of the methods is to limit the maximum amplitude of the signal by using clipping, so that it does not exceed a specified value to reduce PAPR. However, in this clipping method, by multiplying the OFDM signal with a rectangular window to limit the maximum amplitude, signal distortion will occur, the bit error rate will increase, and the out-of-band frequency performance will drop sharply.

Another way to reduce PAPR is to use error correction codes. In the method using error correction codes, in order to reduce the total PAPR, an OFDM signal is generated by selecting only codewords with a lower maximum power based on the block coding method. However, in the method using error correction codes, in order to select a code word with a lower PAPR, since all possible code words must be restored, a lot of restoration time is required.

Another method to reduce PAPR is a structural method used to define a binary Golay complementary sequence and generate this sequence. The Golay complementary sequence is a pair of sequences in which the sum of all offset aperiodic autocorrelation functions is zero. In the case of generating the OFDM signal by using the Golay complementary sequence, the PAPR does not exceed 3dB, and the autocorrelation characteristic of the Golay complementary sequence can be used for detection. In addition, the Golay complementary sequence can be extended to a multi-phase sequence suitable for multi-level phase modulation. However, in the Golay complementary sequence generation method, in order to use polyphase sequences, an attritional restoration process for restoring all polyphase sequences must be performed. In addition, in order to perform encoding and decoding, a memory for storing code words is required, which is complicated.

In order to solve the above problems, Davis and Jedwab proposed a structural method that can reduce PAPR in an OFDM system with fewer carriers, and at the same time by using Golay complementary sequence and RM (reed muller) code The correlation between maintains a certain coding rate and error correction performance. However, in this method, as the number of carriers increases, the coding rate is significantly reduced.

In addition, in terms of probability, among methods for reducing PAPR in a multi-carrier OFDM communication system, there are SLM (Selected Mapping) method and PTS (Partial Transmission Sequence) method.

The SLM method generates M sequences to represent the same information through a specific method, and selects the sequence with the smallest PAPR among these sequences and sends it. Since the SLM method selectively transmits the sequence with the smallest PAPR among the M sequences, the general characteristics of PAPR can be improved. However, in the SLM method, the receiving end needs additional information for restoring the original signal. Here, the additional information may have an important impact on system performance.

The PTS method divides the input sequence into several independent parts, adds the phase for reducing PAPR to each part and sends it. In the PTS method, the general characteristics of PAPR can be improved by selectively sending the sequence with the smallest PAPR among several sequences using different phases. However, in the PTS method, similar to the SLM method, in order to restore the original signal, additional information is required.

As mentioned above, in order to solve the problems caused by high PAPR in the OFDM communication system, a variety of methods for reducing PAPR are given, but each of them still has certain problems.

Therefore, in order to solve the problem caused by the high PAPR, it is necessary to accurately grasp the PAPR allocation of the input sequence in the OFDM communication system.

Summary of the invention

In order to solve the above-mentioned problems, the object of the present invention is to provide a method for realizing in an OFDM (Orthogonal Frequency Division Multiplexing) communication system by using the characteristic of dividing a sequence into congruential sequences with the same PAPR Quickly and efficiently restore the sequence with the lowest PAPR (peak-to-average power ratio).

Another object of the present invention is to provide a method for quickly and effectively grasping the PAPR allocation of an input sequence in an OFDM communication system.

Another object of the present invention is to provide a method for designing a device based on a sequence-based PAPR allocation state in an OFDM communication system to have a lower PAPR.

In order to achieve the above purpose, the method for recovering the sequence with the lowest PAPR (peak-to-average power ratio) in an OFDM (Orthogonal Frequency Division Multiplexing) communication system includes: dividing all input sequences into congruential sequences with the same PAPR ; Restore the sequence with two items as the specified value in advance; detect the sequence with the smallest PAPR in the restored sequence; select the congruence class sequence containing the detected sequence; and extract the sequences contained in the selected congruence class sequence respectively .

The prescribed value is "0".

In the classification step, the sequences generated by shifting the conversion for a predetermined time on the time axis and the conversion by multiplying by a random phase are assigned to the same congruence class sequence.

When the number of carriers is N and the M-PSK modulation method is used, the sequence a(φ) and the sequence a(m) are assigned to the same one in the classification step based on the sequence a=(a0, a1, .., aN-1) Congruence class sequence, where a(φ)=(a0+φ, a1+φ,...,aN-1+φ), φ=0,1,...M-1, a(m)=( a(m)0, a(m)1,...,a(m)N-1), m=0,1,2,...,M-1, and the i-th sequence a(m) The sequence is a(m)i=ai+im(mod M), i=0, 1,..., N-1.

When the number of carriers is N and the M-PSK modulation method is used, the sequence a=(0,0,a2,a3,...,aN-1), ai=0,1,2,...M-1 Was restored in the restoration step.

The restoration step includes several sub-steps: calculating the PAPR of the restored sequence; selecting the smallest PAPR among the calculated PAPR; and detecting the sequence with the smallest PAPR among all the restored sequences.

The method further includes: calculating the PAPR of a sequence in which two starting terms are fixed to a prescribed value; and calculating the PAPR by the number of sequences assigned to congruence class sequences including a sequence in which two starting terms are fixed to a prescribed value , Analyze the PAPR distribution of all input sequences.

The PAPR distribution state obtained by the analysis is used to determine the dynamic range required by the equipment of the OFDM communication system.

A method for recovering the sequence with the lowest PAPR (peak-to-average power ratio) in an OFDM (Orthogonal Frequency Division Multiplexing) communication system, including: recovering a sequence whose two starting terms are fixed to "0"; Calculate the PAPR of the recovered sequence; select the smallest PAPR among the calculated PAPR; and detect the sequence with the smallest PAPR; select the congruence class sequence that includes the detected sequence; and respectively generate the congruences contained in the selected congruence The sequence in the class sequence.

The two sequences whose starting terms are fixed to "0" are included in different congruence class sequences, and the sequences included in one congruence class sequence have the same PAPR characteristics.

When the number of carriers is N and the M-PSK modulation method is used, the sequence a=(0,0,a2,a3,...,aN-1), where ai=0,1,2,...M- 1, and i=2, 3,..., N-1 is restored in the restoration step.

In the generation step, a sequence with the same PAPR characteristics is generated by multiplying the detected sequence by a first conversion of a specified phase and by shifting the detected sequence on the time axis by a second conversion for a specified time. , Where the PAPR characteristic has the PAPR of the detected sequence.

The sequence generated by the first conversion is

a(φ)=(a0+φ,a1+φ,...,aN-1+φ), φ=0,1,...M-1, and the sequence generated by the second conversion is a(m) =(a(m)0, a(m)1,...,a(m)N-1), m=0,1,2,...,M-1 When the number of carriers is N and M- In the PSK modulation mode, the i-th sequence in the sequence a(m) is a(m)i=ai+im(mod M), i=0,1,...,N-1.

Description of the drawings

The accompanying drawings are incorporated in this specification and constitute a part of this specification to provide a further understanding of the present invention. They illustrate embodiments of the present invention, and the accompanying drawings and the description are used to explain the principle of the present invention.

In the drawings: FIG. 1 shows the structure of a general OFDM (Orthogonal Frequency Division Multiplexing) communication system; FIG. 2 is a flowchart of a method for recovering a sequence with the lowest PAPR in an OFDM communication system according to the present invention; And Figure 3 shows an example of a congruence class sequence according to the present invention.

detailed description

Fig. 1 shows the structure of a general OFDM (Orthogonal Frequency Division Multiplexing) communication system.

As shown in Figure 1, a general OFDM communication system includes a transmitting unit and a receiving unit. The transmitting unit includes: a first serial-to-parallel converter 2 for converting a serial input digital signal into a parallel signal; a first signal mapper 4 for converting a digital signal output from the first serial-to-parallel converter 2 into QPSK (Quadrature Phase Shift Keying) signal; modulator 6, for modulating each signal output in parallel from the first signal mapper 4 by IDFT (Inverse Discrete Fourier Transform); first parallel-to-serial converter 8, For converting the signal output in parallel from the modulator 6 into a serial signal; a guard interval inserter for inserting a guard interval into the signal output from the first parallel-serial converter 8; and a digital-to-analog converter 12 , Is used to convert the digital signal output from the guard interval inserter 10 into an analog signal, thereby eliminating the noise of the digital signal and transmitting the analog signal through the channel. The receiving unit includes: an analog-to-digital converter 14 for removing the noise of the signal received through the channel and converting the signal into a digital signal; a guard interval remover 16 for removing the signal output from the analog-to-digital converter 14 Guard interval; second serial-to-parallel converter 18, used to convert the signal output from the guard interval remover 16 into a parallel signal; demodulator 20, used to demodulate the second serial-to-parallel conversion by discrete Fourier transform respectively The second signal mapper 22 is used to convert the QPSK signal from the demodulator 20 into a digital signal; and the second parallel-to-serial converter 24 is used to parallel the second signal mapper 22 The output signal is converted into a serial signal.

Generally, in the transmission of an OFDM signal, an amplifier is required, but it is not shown in FIG. 1.

The operation of the general OFDM communication system is described below.

The first serial-to-parallel converter 2 converts the received serial digital signal into a parallel signal, the first signal mapper 4 performs mapping of the parallel signal to convert it into a QPSK signal, the modulator 6 converts the QPSK signal by the IDFT method, and A parallel-serial converter 8 converts the modulated IDFT signal into a serial signal. The guard interval inserter 10 inserts a guard interval into the serial signal in order to prevent interference from occurring, and the digital-to-analog converter 12 converts the serial digital signal into an analog signal, filters out the noise through a low-pass filter, and transmits the serial signal through the assigned channel. Analog signal.

When a signal is received through the allocated channel, the analog-to-digital converter 14 eliminates the noise of the received analog signal and converts the analog signal into a digital signal, the guard interval remover 16 removes the guard interval in the digital signal, and The second serial-to-parallel converter 18 converts the digital signal into a parallel signal. The demodulator 20 demodulates the parallel signal by DFT, the second signal mapper 22 maps the demodulated parallel signal into a digital signal, and the second parallel-serial converter 24 converts the parallel digital signal into a serial digital signal.

In the present invention, what will be described below is to obtain the PAPR distribution of all sequences and quickly recover the PAPR with the smallest PAPR by using the feature that all sequences available in the general OFDM communication system are classified into congruential sequences with the same PAPR. Sequence method.

Fig. 2 is a flowchart of a method for recovering a sequence with the lowest PAPR in an OFDM communication system according to the present invention.

In the present invention, by using a certain characteristic, all input sequences are divided into congruential sequences with the same PAPR, as shown in step S11. The sequence in which the first two items have a value of "0" is restored, as shown in step S13, and the PAPR of the restored sequence is calculated respectively. In the present invention, the smallest PAPR is selected among the calculated PAPRs, and the sequence with the smallest PAPR is selected, as shown in step S15. The check includes the congruence class sequence with the smallest PAPR sequence, as shown in step S17, and the sequence of the detected congruence class sequence is extracted as the sequence with the smallest PAPR, as shown in step S17.

This will be described in detail below.

First, the PAPR (Peak to Average Power Ratio) of an OFDM (Orthogonal Frequency Division Multiplexing) signal will be described.

In an OFDM system using N carriers, the modulated signal assigned to the k-th carrier in a given symbol area [0, T] is Ak (k=0, 1, .. N-1), and the OFDM signal s ( t) can be described as: s(t)=Σk=0N-1Akej2πkt/T]]> Formula 1 In Formula 1, Ak is one of the symbols of the signal constellation according to the modulation method.

The PAPR of the OFDM signal corresponding to Equation 1 is the ratio of the maximum instantaneous power to the average power, which can be described as Equation 2 below.

PAPR=max0t<T|S(t)|2E[|S(t)|2]]]> Formula 2 Here, E is an average operator.

Next, the PAPR characteristics of the OFDM signal using the M-PSK modulation method are described.

In an OFDM communication system using the M-PSK modulation method, the PAPR of the generated OFDM signal has certain characteristics. In the description of the two characteristics, for the first characteristic (A), even if the predetermined phase is multiplied by the OFDM signal, the PAPR characteristic of the OFDM signal is unchanged. For the second characteristic (B), although the OFDM signal is shifted on the time axis for a predetermined time, the PAPR characteristic of the OFDM signal is unchanged.

(A) The first characteristic: When ξ=exp(2πj/M), the i-th term Ai can be described as Ai=ξai,ai{0,1,...,M-1},]]> sequence A corresponds to the sequence a=(a0, a1, .., aN-1), therefore, the signal s(t) in formula 1 can be described as formula 3 below.

s(t)=Σk=0N-1ξakWkt]]> Formula 3 here, W=exp(j2π/T).

Even if a certain phase ξφ is multiplied by the OFDM signal s(t), the PAPR characteristic of the signal s(t) does not change, and M sequences a(φ)=(a0+φ,a1+φ,...,aN- 1+φ), φ=0, 1,...M-1 has the same PAPR as sequence a. Here, the addition operation is performed in the FM (Field) domain (the addition operation ends in the modulo M domain).

In more detail, when the signal obtained by multiplying the signal s(t) by a certain phase ξφ is s'(t), s'(t)=s(t)·ξφ

The PAPR of s'(t) can be calculated by Equation 2.

PAPR{s(t)}=max0t<T|s(t)|2E[|s(t)|2]=max0t<Ts(t)·s(t)*E [s(t)·s(t)*]]]>=max0t<Ts(t)ξφ·s(t)*ξ-φE[s(t)&xi ;φ·s(t)*ξ-φ]=max0t<Ts(t)·s(t)*E[s(t)·s(t)*]]]>= max0t<T|s(t)|2E[|s(t)|2]]]>Equation 4 Therefore, the PAPR of the signal s'(t) is the same as the PAPR of the signal s(t).

(B) The second characteristic is when the sequence a(m)=(a(m)0, a(m)1,... , The i-th term a(m)I of a(m)N-1) is defined as a(m)i=ai+im(mod M), i=0,1,...,N-1 , The PAPR of M sequences a(m) is the same as the PAPR of sequence a.

In more detail, the OFDM signal s(m)(t) corresponding to a(m) can be described as s(m)(t)=ξa0+ξa1+mWt+ξa2+2mW2t+... +ξaN-1+(N-1)mW(N-1)t]]>When τ=mT/M, it can be described as s(m)(t)=ξa0+ξa1Wt+ τm+ξa2W2(t+τm)+...+ξaN-1W(N-1)(t+τm)]]>In more detail, s(m)(t )=s(t+τm), it can be seen that s(m)(t) is a signal shifted by τm on the time axis. The OFDM signal is a periodic signal with a period of T, and a(m) and a generate an OFDM signal with the same PAPR performance.

When the first characteristic (A) and the second characteristic (B) are integrated, there are two conversions that do not change the PAPR performance of the signal, and M2 sequences can generate signals with the same PAPR performance. When the number of carriers is N and the M-PSK modulation method is adopted, the number of OFDM signals that can be generated is MN, and the PAPR restorer according to the present invention divides MN OFDM signals into congruence classes composed of M2 sequences with the same PAPR sequence. Therefore, the number of congruence class sequences is MN/M2=MN-2.

For example, in QPSK modulation, when N=4 and M=4, the number of sequences is MN=44=256. According to the conversion of the first characteristic (A) and the conversion of the second characteristic (B), there are M2=42=16 sequences with the same PAPR. Therefore, in the PAPR restorer according to the present invention, according to the conversion of the first characteristic (A) and the conversion of the second characteristic (B), a total of 256 sequences are divided into MN-2=44-2=16 congruence classes The sequence is shown in step S11.

Figure 3 shows one of these 16 congruence class sequences.

More specifically, in the PAPR restorer, by converting the sequence a(0,0,0,0) using the first and second characteristics (A) and (B), a sequence with and (0,0,0) is generated. , 0) 15 sequences of the same PAPR. The PAPR restorer assigns (0, 0, 0, 0) and the generated 15 sequences to a congruence class sequence. Therefore, these 16 sequences are assigned to a congruence class sequence with the same PAPR. With reference to Formula 1, the OFDM signal of (0,0,0,0) has a maximum PAPR value of N, and the sequences allocated to the congruence class sequence where the (0,0,0,0) sequence is located have the same PAPR characteristics . As described above, the PAPR restorer divides a total of 256 sequences into 16 congruence class sequences.

As a reference, it is well known that input sequences with the same PAPR are generated through a certain rule. Generally, a congruential sequence containing the sequence a(0,0,0,0) can be generated using linear block coding. For example, the congruence sequence of the sequence (0, 0, 0, 0) is regarded as a block code with 16 codewords. The generation matrix can be described as follows, where the operation of linear block coding is determined by F4 (modulo 4 field) definition.

G=11110123]]>

At the same time, in an OFDM system where the number of carriers is N and the M-PSK modulation method is adopted, in order to recover the input sequence with the smallest PAPR, it is considered that the two items at the beginning of the input sequence are fixed to "0" and only the remaining items are The sequence of changes. In more detail, only the following types of sequences are considered.

a=(0,0,a2,a3,...,ai,...,aN-1), ai=0,1,2,...M-1 Finally, by considering only the total MN inputs MN/M2 in the sequence = MN-2 sequences (included in this type), the input sequence with the smallest PAPR can be recovered.

In more detail, in this example, the Gaussian elimination method can be applied to the generation matrix in F4. After the Gaussian elimination method is applied, the generation matrix can be described as follows.

G=10320123=I2P]]> The code review matrix can be expressed as follows.

P=-PtIn-k=12102101]]>In the check matrix, the congruence class sequence containing the sequence (0,0,0,0), that is, the codeword that satisfies the check matrix has the characteristic code (syndrome)(0,0) ).

When the block codes contain different feature codes, they have the characteristics contained in different congruence class sequences. In more detail, the sequences with the same signature generated by the review matrix have the same PAPR. Generally, the code review matrix can be described as:-Pt is a two-column matrix. When the two starting items of the sequence are fixed to "0", a feature code is generated from the items other than the two items. In addition, when the input sequence is a=(0,0,a2,a3,...,aN-1), the feature code is generated by In-2, and the form of the feature code (S) is S=(a2,a3,. .., aN-1).

In more detail, a sequence of the form a=(0,0,a2,a3,...,aN-1) is included in different congruence class sequences, and the items of each congruence class sequence have the same Sequence composition of PAPR.

Therefore, in the PAPR restorer according to the present invention, in order to restore the input sequence with the smallest PAPR, the input sequence with a=(0,0,a2,a3,...,aN included in different congruence class sequences respectively -1) The sequence of the form, that is, the sequence in which the two start items are fixed to "0" is restored, as shown in step S13.

In the PAPR restorer, the PAPR of two sequences whose starting terms are fixed to "0" are calculated respectively, the smallest PAPR is selected from the calculated PAPR, and the two starting terms are fixed to "0" sequences are detected as having options The sequence of the minimum PAPR is shown in step S15.

In the PAPR restorer, the congruence class sequence containing the detected sequence is selected, as shown in step S17, and the sequence included in the congruence class sequence is selected as the sequence with the smallest PAPR, as shown in step S19. Therefore, in the PAPR restorer, without calculating the PAPR of all sequences of length N, by separately calculating the PAPR of the two sequences whose starting terms are fixed to "0", the calculated PAPR is selected to have The sequence with the smallest PAPR, and the congruence sequence containing the selected sequence is selected, so that the sequence with the smallest PAPR can be quickly and effectively restored.

In an OFDM system where the number of carriers is N and the M-PSK modulation method is adopted, in order to recover the input sequence with the smallest PAPR, only MN-2 sequences need to be considered, thus the complexity is reduced by M2.

At the same time, in order to analyze the PAPR distribution of all the sequences used in the OFDM system, the PAPR restorer divides all the sequences into the same PAPR characteristics by using the conversion for multiplying the sequence by a certain phase and the conversion for shifting the specified time The sequence of congruence classes. After that, since the PAPRs of the two sequences whose starting terms are fixed to "0" are contained in different congruence-type sequences, the PAPR restorer calculates the PAPR of the sequences whose two starting terms are fixed to "0". The PAPR restorer judges the sequence of the congruence class sequence that has the same PAPR as a sequence whose two starting terms are fixed to "0", and the PAPR and related homology of the sequence whose two starting terms are fixed to "0" Calculate the PAPR distribution of all sequences on the basis of the number of remainder sequences. Therefore, in the PAPR restorer, the PAPR distribution of all the sequences can be effectively obtained by calculating the PAPR of the two sequences whose starting terms are fixed to "0" instead of calculating the PAPR of all the sequences.

In an OFDM system with N carriers using the M-PSK modulation method, in order to analyze the PAPR distribution of all sequences, only MN-2 sequences need to be considered in a total of MN input sequences.

As mentioned above, when analyzing the PAPR distribution of all sequences, referring to the analyzed PAPR distribution, the system designer can select the sequence that can be used in the OFDM system to have good BER (bit error rate) and not too high PAPR, In addition, system designers can also design some equipment, such as amplifiers, AD converters, or DA converters, so as to construct the OFDM system as a device with a lower dynamic range.

As described above, in the present invention, by dividing all input sequences into congruence class sequences with the same PAPR and using the feature that two sequences whose starting terms are fixed to "0" are included in different congruence class sequences, The PAPR based on the sequence with two start terms fixed to "0" can quickly and effectively restore the sequence with the smallest PAPR.

In the present invention, by dividing all input sequences into congruence series with the same PAPR and using the feature that two sequences whose starting terms are fixed to "0" are included in different congruence series, based on the characteristics of having two congruence series The PAPR of the sequence whose starting term is fixed to "0" can quickly and effectively restore the PAPR distribution of all sequences. Therefore, in an OFDM system where the number of carriers is N and the M-PSK modulation method is adopted, when recovering the sequence with the smallest PAPR, it is not necessary to calculate the PAPR of all MN input sequences, only the PAPR of MN-2 sequences can be calculated. Reduce the complexity of recovery. In addition, the larger the size M of the constellation used, the more significant the reduction in recovery complexity.

In the present invention, according to the PAPR distribution state of all sequences available in the OFDM system, it is possible to design an OFDM system device with good BER and low PAPR. In addition, in the present invention, the OFDM system can be constructed as a device with a lower dynamic range.