CN112769727B - Improved partial transmission sequence design method for reducing PAPR in OFDM system - Google Patents
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Abstract
The invention relates to a method for designing an improved partial transmission sequence for reducing PAPR in an OFDM system, which comprises the following steps: s1, initializing a phase factor and calculating a PAPR value; s2, classifying the phase factors, and finding out the phase factor set C with Hamming distance i from the initial phase factor as reference i The Hamming distance is the number of different characters at the corresponding position between two character strings with equal length; s3 phase factor set C i Finding out the optimal solution PAPR by adopting a cuckoo search method; s4, changing the Hamming distance i, and judging whether the changed Hamming distance i is smaller than a preset maximum Hamming distance; if yes, go to step S2; if not, outputting an optimal phase factor, multiplying the optimal phase factor by the subsequences divided by the OFDM signals, and accumulating to obtain an improved partial transmission sequence; s6, the modified partial transmission sequence and the optimal phase factor as the sideband information are sent to free space. The invention is used for PAPR improvement of OFDM.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a method for improving a partial transmission sequence in an OFDM system to reduce PAPR.
Background
Orthogonal Frequency Division Multiplexing (OFDM) is a special frequency division multiplexing, and although there are many advantages to this technique, when the phases of the subcarriers are the same or close to each other, the superimposed signal is modulated by the same initial phase signal, so as to generate a larger instantaneous power peak, thereby further resulting in a higher peak-to-average power ratio (PAPR). Common treatment methods fall into two categories: predistortion technique, non-distortion technique.
The predistortion technology comprises the following steps: the basic idea is that before the signal is sent to the amplifier, the signal with larger peak power is pre-distorted through nonlinear processing, so that the signal does not exceed the dynamic change range of the amplifier, thereby avoiding the occurrence of larger PAPR.
Non-distortion technology: the main idea is to significantly reduce the occurrence probability of large peak power signals and make a linear change on the original frequency domain data vector, and common methods include a Selective Mapping (SLM) method and a Partial Transmit Sequence (PTS) method to optimize the statistical property of the peak average power ratio of OFDM signals, thereby achieving the purpose of reducing the PAPR of OFDM signals.
The above method requires the following mathematical methods, including the following:
1. IFFT method
The calculation method of Inverse Fast Fourier Transform (IFFT):
wherein x represents a time domain signal, x (k) is a frequency domain signal, N-1 represents the number of sampling points,
representing a parameter.
2. Linear congruence method
The linear congruence method is a pseudo-random number generation method widely applied at present, and the basic idea is that the next number is obtained by performing linear operation and modulus on the previous number, and the recursion formula is as follows:
x n+1 ＝(ax n +c)mod(m) (2)
y n+1 ＝x n+1 /m (3)
wherein the common divisor of c and m is only 1; the product of all prime factors of m can divide a-1; a, c, x 0 Are initial values which are all smaller than m, and a and c are positive integers.
3. Box method
Box is a generation method that produces a gaussian distribution, the basic form of which:
wherein, U 1 ，U 2 Are uniformly distributed random numbers.
The PTS algorithm in the OFDM system is promising, does not lose data transmission rate, power, and bit error probability (BER), and can significantly improve PAPR performance, and the specific method is:
dividing an input OFDM signal X into V non-overlapping subsequences which are also called sub-blocks, wherein vectors of each sub-block are equal in size;
wherein, X v Denotes the V-th subsequence, V-1, 2,3, …, V;
by phase factor b v Multiplying the V sub-blocks can obtain:
wherein, b v Representing the initial phase factor, X v Denotes the v-th subsequence of an equal-length division of OFDM symbols, Y is a complex number and denotes a phase factor b v And subsequence X v A scalar multiplied sequence;
obtaining a time domain signal through IFFT transformation:
wherein, b v Is the v-th element, x, of the set of phase factors v Is X v The IFFT value of (d);
it is then possible to select different phase factors b v Comparing PAPR to find out the minimum phase factor for PAPR of OFDM symbol
The mathematical equation can be expressed as:
wherein, argmin () represents the decision condition used when the function takes the minimum value.
Finally, the PTS sequence with the lowest peak is transmitted and the phase factor is sent as sideband information to free space.
However, the existing method needs a lot of calculation in finding the phase factor, and the performance of the traditional PTS iterative algorithm is far from the optimized algorithm because the traditional PTS iterative algorithm has no phase search optimization. Therefore, how to optimize the phase factor search and reduce the system computation amount is a problem to be solved in the field aiming at the defects of the prior art.
Disclosure of Invention
Aiming at the technical defects in the prior art, the invention provides a method for designing an improved partial transmission sequence for reducing the peak-to-average power ratio in an OFDM system; firstly, a randomly distributed bird nest set A is generated according to the set number of bird nests n N is 1,2,3 …, each bird nest A n Represents 1 group of phase factors, and takes the vector b with the length of M n,m ＝{b n,1 ；b n,2 ；…b n,m M is the number of sub-blocks divided into OFDM signals; when the algorithm is initialized, b nm ＝[1,1,…,1]M 1, setting phase factor b nm The Hamming distance of (C) is less than or equal to the phase factor set of i i At each iteration, at C i Finding out phase factor in the set, obtaining PAPR minimum value, comparing the PAPR of the former min Revising the PAPR in accordance with the revised PAPR size min 。
In order to achieve the above purpose, the invention adopts the following scheme:
a method for designing an improved partial transmission sequence for reducing PAPR in an OFDM system includes the following steps:
s1, initializing a phase factor, and calculating a PAPR value;
s2, classifying the phase factors, and finding out the phase factor set C with Hamming distance i from the initial phase factor as reference i The Hamming distance is the number of different characters at the corresponding position between two equal-length character strings;
s3 phase factor set C i Finding out the optimal solution PAPR by adopting a cuckoo search method;
s4, changing the Hamming distance i, and judging whether the changed Hamming distance i is smaller than a preset maximum Hamming distance; if yes, go to step S2; if not, outputting an optimal phase factor, multiplying the optimal phase factor by the subsequences divided by the OFDM signals, and accumulating to obtain an improved partial transmission sequence, namely an IPST sequence;
and S6, sending the IPST sequence and the optimal phase factor as sideband information to a free space.
Preferably, the step S1 includes:
s11, equally dividing the input OFDM signal X into V non-overlapping subsequences, wherein the vector size of each subsequence is equal;
wherein X v Denotes the V-th subsequence, V ═ 1,2,3, …, V;
s12, using the initial phase factor D 1 ＝[1,1,…,1]De-multiplying V subsequences and summing, represented as:
wherein，b v Representing the initial phase factor D 1 The v-th element in (1), Y represents a phase factor b v And subsequence X v Multiplying and accumulating the signal sequences;
s13, performing IFFT on the signal sequence Y to obtain a time domain signal after phase factor processing:
wherein x is v Is X v The IFFT value of (d);
s14, when the time domain signal y is processed, the PAPR value is calculated as follows:
wherein x is n Represents X n After IFFT conversion, OFDM time domain signal E is obtained after N times of sampling.]Representing a mathematical expectation.
Preferably, the step S2 includes:
statistics D 1 And phase factor B i The number of different characters at corresponding positions; wherein D is 1 Is the initial phase factor and B j Phase factor of unknown class, D 1 And B j Performing modulo two addition, counting the number of 1 after the modulo two addition, classifying the phase factors through the difference of the number of 1, and forming each phase factor set C i 。
Preferably, the step S3 includes:
s31, in the ith phase factor set C i Finding out 4 phase factors and recording as M ═ M 1 ,m 2 ,m 3 ,m 4 ]Calculating the PAPR value corresponding to each phase factor to obtain the optimal PAPR value, and setting the optimal PAPR value as the PAPR min Recording the phase factor;
s32, according to the discovery probability P a The phase factor to be found is selected at the element of M and then recalculated using the following adaptive step size methodPhase factor, updating M set;
wherein d is n Is phase factor, d' n For the purpose of the updated phase factor,
is a die two addition, A n Denotes the nth set of phase factors, A best Represents the currently optimal phase factor, d max The maximum Euclidean distance between the optimal solution and the rest solutions; s is min And s max Respectively representing a minimum step size and a maximum step size;
s33, changing the values of elements in the M set by adopting a disturbance method of a non-uniform mutation operator to the M set obtained in the step S32 to obtain the next group of phase factors;
b represents a pseudo-random number of Gaussian distribution generated by a Box method and a modulo-2 result of the pseudo-random number is calculated; a. the k Is the k-th set of phase factors; r is a pseudo random number uniformly distributed in (0, 1) generated by linear congruence method, T is searched set C i In B i Lambda is a system parameter of the heterogeneous system variation and is set to be 5; t is the number of cycles;
the maximum value and the minimum value of the kth phase factor are respectively;
s34, recalculating the PAPR of the phase factor obtained in the step S33, and selecting the current minimum PAPR new ；
S35, setting the initial valuePAPR min And PAPR new Comparing; if PAPR is min Greater than PAPR new Then the PAPR is adjusted new Assignment to PAPR min (ii) a Otherwise, returning to step S32;
s36 PAPR min And a preset PAPR 0 Comparing and judging whether the PAPR reaches the preset PAPR 0 (ii) a If yes, outputting a corresponding phase factor; if not, the process returns to step 32 for iteration.
Compared with the prior art, the invention has the following technical effects:
the invention optimizes grouping by constructing the phase factor set with fixed Hamming distance, and quickly searches the phase factor of the minimum PAPR by adopting a cuckoo search method, thereby reducing the system complexity and being applicable to the improvement of the PAPR under OFDM modulation.
Drawings
FIG. 1 is a Partial Transmission Sequence (PTS) schematic of the present invention;
FIG. 2 is a main flow chart of the IPTS algorithm of the present invention;
fig. 3 is a flow chart of an improved cuckoo search method.
Detailed Description
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
The invention relates to a method for reducing PAPR by IPTS, which classifies Hamming distances of phase factors first and then searches out the best phase factor by adopting an improved cuckoo search method, thereby reducing the peak-to-peak power of a system, simplifying the search computation complexity and improving the performance.
The method for designing the improved part of the transmission sequence for reducing the PAPR in the OFDM system comprises the following steps:
step 1, initializing a phase factor and calculating a PAPR value;
step 2, phase factor classification, using initial phase factor as reference to find out phase factor set C with Hamming distance i i The Hamming distance is the number of different characters at the corresponding position between two equal-length character strings;
step 3,In phase factor set C i The optimal solution PAPR is found out by adopting a cuckoo searching method;
step 4, changing the Hamming distance i, and judging whether the changed Hamming distance i is smaller than a preset maximum Hamming distance; if yes, go to step S2; if not, outputting an optimal phase factor, multiplying the optimal phase factor by the subsequences divided by the OFDM signals, and accumulating to obtain an improved partial transmission sequence, namely an IPST sequence;
and step 5, sending the IPST sequence and the optimal phase factor as sideband information to a free space.
Specifically, step 1 comprises the steps of:
step 1.1, an input OFDM symbol X is divided into V non-overlapping subsequences (also called sub-blocks), and the vector size of each sub-block is equal.
Wherein, X v (V-1, 2,3 … …, V) is a complex representation subsequence.
Step 1.2: by initialising the phase factor D 1 ＝[1,1,…,1]Multiplying the V sub-blocks can obtain:
wherein, b v Representing the initial phase factor D 1 The v element of (1), X v Denotes the v-th subsequence of an equal-length division of OFDM symbols, Y is a complex number and denotes a phase factor b v And subsequence X v Scalar multiplied sequence.
Step 1.3: through IFFT, a time domain signal is obtained:
wherein, b v Is the v-th element, x, of the set of phase factors v Is X v The IFFT value of (a).
Then, it is possible to select a different phase factor B v Comparing PAPR to find out the minimum phase factor for PAPR of OFDM symbol
The mathematical equation can be expressed as:
wherein, argmin () represents the decision condition used when the function takes the minimum value.
The IPTS method specifically comprises the following steps: generating a randomly distributed bird nest set A according to the set number of bird nests n N is 1,2,3 …, each bird nest A n Represents 1 group of phase factors, and takes the vector b with the length of M n,m ＝{b n,1 ；b n,2 ；…b n,m M is the number of sub-blocks divided into OFDM signals; calculating a set of phase factors B 1 ＝[1,1,…,1]As an initial value PAPR min 。
Wherein x is n Represents X n After IFFT conversion, OFDM time domain signal E is obtained after N times of sampling.]Representing a mathematical expectation.
The number of changes i of the correction phase factor is set.
In step 2, find out the phase factor D 1 Set of phase factors C with Hamming distance i i The method is characterized in that the phase factor sets are classified according to Hamming distance, so that the whole phase factor set is simplified.
In step 3, the phase factor set C i Searching set C by adopting improved cuckoo searching method i The medium optimal solution PAPR.
Further, step 3 specifically comprises: in set C i To find out 4 phase factors M ═[m 1 ,m 2 ,m 3 ,m 4 ]Finding out PAPR value of four phase factors, recording phase factors, and finding out probability P a And randomly screening the elements in the M, selecting the screened elements, and then recalculating the screened phase factors by adopting an adaptive step size formula.
Wherein d is n Is phase factor, d' n In order for the phase factor to be updated,
adding for two times, A n Denotes the nth set of phase factors, A best Representing the currently optimum phase factor, d max The maximum Euclidean distance between the optimal solution and the rest solutions; s is min And s max Representing the minimum step size and the maximum step size, respectively.
And obtaining a next group of phase factors by adopting a disturbance formula of the non-uniform mutation operator, and changing the values of the elements in the M set.
Wherein, B represents a result of generating a gaussian-distributed pseudo random number by the Box method described in the background art and calculating a modulo-2 thereof; a. the k Is the k-th set of phase factors; r is a pseudo-random number uniformly distributed in (0, 1) generated by the linear congruence method described in the background art, and T is the searched set C i In (B) i λ is a system parameter of the heterogeneous system variation, which can be generally set as 5, and t is the number of cycles;
respectively, the maximum and minimum values of the kth phase factor.
PAPR to PAPR min And PAPR new Comparing and judging PAPR min Whether greater than PAPR new If PAPR is min Greater than PAPR new Then the PAPR is adjusted new Assignment to PAPR min Otherwise, returning to the step 2;
determining PAPR min Whether the PAPR is larger than a preset value 0 If greater than PAPR 0 And returning to the step 2 for iteration, otherwise, outputting a corresponding phase factor.
In step 4, the Hamming distance is changed to obtain the next phase factor B i The hamming distance of (a) is a set of phase factors of i + 1;
and judging whether the Hamming distance i is greater than a threshold value, if so, outputting the current optimal phase factor, otherwise, returning to the step 2.
And outputting the optimal phase factor, and multiplying the phase factor into the signal to obtain the IPTS sequence.
In step 5, the optimal phase factor is sent as side information to free space along with the IPTS sequence.
According to the improved partial transmission sequence design method for reducing the PAPR in the OFDM system, the phase factor sets are classified according to different Hamming distances through the classification of the phase factor sets, so that the subsequent search of the phase factors is facilitated; searching the classified phase factor set by using an improved cuckoo searching method; the phase factor search is optimized, the search time is shortened, and the complexity of the system is simplified.
FIG. 1 is a Partial Transmit Sequence (PTS) diagram of the present invention:
the first step is as follows: the input OFDM symbol X is divided into V non-overlapping subsequences (also called sub-blocks), and each sub-block vector is equal in size.
Wherein: x v (V-1, 2,3 … …, V) is a complex representation subsequence.
The second step is that: by phase factor b v Multiplying the V sub-blocks gives:
wherein, b v Representing the initial phase factor B 1 The v element of (1), X v Denotes the v-th subsequence of an equal-length division of OFDM symbols, Y is a complex number and denotes a phase factor b v And subsequence X v Scalar multiplied sequence.
The third step: obtaining a time domain signal through IFFT transformation:
wherein, b v Is the v-th element, x, of the set of phase factors v Is X v The IFFT value of (a).
The fourth step: it is then possible to select a different phase factor b v Comparing PAPR to find out the minimum phase factor for PAPR of OFDM symbol
The mathematical equation can be expressed as:
wherein, argmin () represents the decision condition used when the function takes the minimum value.
FIG. 2 is a flowchart of the IIPTS design method of the present invention, including:
step 1, initializing a phase factor, calculating a PAPR value, and completing the steps as follows:
step 1.1, the input OFDM symbol X is divided into V non-overlapping subsequences, also called sub-blocks, each sub-block having equal vector size.
Wherein, X v (V ═ 1,2,3 … …, V) is a complex representation subsequence;
step 1.2, initialize the phase factor (or rotation factor) D 1 ＝[1,1,…1]Multiplying these V sub-blocks can be expressed as:
wherein, b v Representing the initial phase factor D 1 The v element of (1), X v Denotes the v-th subsequence of equal length division of OFDM symbols, Y is a complex number denotes the phase factor b v And subsequence X v Scalar multiplied sequence.
Step 1.3, performing IFFT on the Y signal obtained in step 1.2 to obtain a time domain signal:
wherein, b v Is the v-th element, x, of the set of phase factors v Is X v The IFFT value of (a).
Step 1.4, solving the PAPR value of the y signal obtained in step 1.3:
wherein x is n Represents X n After IFFT conversion, OFDM time domain signal E is obtained after N times of sampling.]Representing a mathematical expectation.
Step 2, taking the initial phase factor in the step 1.2 as a reference, and finding out a phase factor set C with the number i of different characters at the corresponding position between two equal-length character strings i 。
Step 3, mixingPhase factor set C obtained in step 2 i The optimal solution PAPR is found out by adopting an improved cuckoo search algorithm.
And 4, changing the Hamming distance in the step 2 to obtain a new phase factor set, and recalculating the optimal PAPR.
And 5, comparing the i value obtained in the step 1.2 with a preset maximum Hamming distance, if the i value is smaller than the preset maximum Hamming distance, executing the step 3, otherwise, outputting a phase factor with the minimum PAPR value, multiplying the phase factor by the sequence and accumulating to obtain an IPTS sequence.
And 6, adding the phase factor obtained in the step 5 into the signal sideband information, and sending the signal sideband information to the free space along with the IPTS sequence.
Fig. 3 is a flow chart of an improved cuckoo search method:
the first step is as follows: in phase factor set C i Finding out 4 phase factors as M ═ M 1 ,m 2 ,m 3 ,m 4 ]The PAPR values corresponding to the 4 sets of phase factors are obtained to obtain the optimum PAPR, and the optimum PAPR is set as the PAPR min The phase factor is recorded.
Wherein x is n Represents X n After IFFT conversion, OFDM time domain signal E is obtained after N times of sampling.]Representing a mathematical expectation.
The second step is that: according to the discovery probability P a And randomly selecting the discovered phase factor at the element of M, and then recalculating the discovered phase factor by adopting an adaptive step size formula.
Wherein d is n Is phase factor, d' n For the purpose of the updated phase factor,
is a die two addition, A n Denotes the nth set of phase factors, A best Representing the currently optimum phase factor, d max The maximum Euclidean distance between the optimal solution and the rest solutions; s min And s max Representing the minimum step size and the maximum step size, respectively.
The third step: and (4) changing the values of elements in the set by adopting a disturbance formula of a non-uniform mutation operator for the M set.
Wherein, B represents a result of generating a gaussian-distributed pseudo random number by the Box method described in the background art and calculating a modulo-2 thereof; a. the k Is the k-th set of phase factors; r is a pseudo random number uniformly distributed in (0, 1) generated by the linear congruence method described in the background art, T is the searched set C i In (B) i λ is a system parameter of the heterogeneous system variation, which can be generally set as 5, and t is the number of cycles;
respectively, the maximum and minimum values of the kth phase factor.
The fourth step: PAPR (Peak to average Power ratio) min And PAPR new Comparing and judging PAPR min Whether greater than PAPR new If PAPR is min Greater than PAPR new Then the PAPR is adjusted new Assignment to PAPR min Otherwise, the second step is returned.
The fifth step, determining PAPR min Whether the PAPR is larger than the preset value 0 If greater than PAPR 0 And returning to the second step of iteration, otherwise, outputting the corresponding phase factor.
The foregoing has outlined, rather broadly, the preferred embodiment and principles of the present invention in order that those skilled in the art may better understand the detailed description of the invention without departing from its broader aspects.
Claims (1)
1. A method for designing an improved partial transmission sequence for PAPR reduction in an OFDM system, comprising the steps of:
s1, initializing a phase factor and calculating a PAPR value;
s2, classifying the phase factors, and finding out the phase factor set C with Hamming distance i from the initial phase factor as reference i The Hamming distance is the number of different characters at the corresponding position between two character strings with equal length;
s3 phase factor set C i The optimal solution PAPR is found out by adopting a cuckoo searching method;
s4, changing the Hamming distance i, and judging whether the changed Hamming distance i is smaller than a preset maximum Hamming distance; if yes, go to step S2; if not, outputting an optimal phase factor, multiplying the optimal phase factor by the subsequences divided by the OFDM signals, and accumulating to obtain an improved partial transmission sequence, namely an IPST sequence;
s5, sending the IPST sequence and the optimal phase factor as sideband information to a free space;
the step S1 includes:
s11, equally dividing the input OFDM signal X into V subsequences which are not overlapped with each other, wherein the vector size of each subsequence is equal;
wherein, X v Denotes the V-th subsequence, V ═ 1,2,3, …, V;
s12, using the initial phase factor D 1 ＝[1,1,…,1]De-multiplying V subsequences and summing, represented as:
wherein, b v Representing the initial phase factor D 1 Y denotes a phase factor b v And subsequence X v Multiplying and accumulating the signal sequences;
s13, performing IFFT on the signal sequence Y to obtain a time domain signal after phase factor processing:
wherein x is v Is X v The IFFT value of (d);
s14, when the time domain signal y is processed, the PAPR value is calculated as follows:
wherein x is n Represents X n After IFFT conversion, OFDM time domain signal E is obtained after N times of sampling.]Represents a mathematical expectation;
the step S2 includes:
statistics D 1 And phase factor B i The number of different characters at corresponding positions; wherein D is 1 Is the initial phase factor and B i Phase factor of unknown class, D 1 And B i Modulo two is added, the number of 1 after modulo two is added is counted, the phase factors are classified through the difference of the number of 1, and each phase factor set C is formed i ；
The step S3 includes:
s31, in the ith phase factor set C i Finding out 4 phase factors and recording as M ═ M 1 ,m 2 ,m 3 ,m 4 ]Calculating the PAPR value corresponding to each phase factor to obtain the optimal PAPR value, and setting the value as the PAPR min Recording the phase factor;
s32, according to the discovery probability P a The phase factor to be found is selected at the element of M and the phase to be found is recalculated using the following adaptive step size methodBit factors, updating the M set;
d′ n ＝d n ⊕(s min +(s max -s min )d n ) (6)
wherein d is n Is phase factor, d' n For the updated phase factor, "#" is modulo two plus, A n Denotes the nth set of phase factors, A best Representing the currently optimum phase factor, d max The maximum Euclidean distance between the optimal solution and the rest solutions; s is min And s max Respectively representing a minimum step size and a maximum step size;
s33, changing the values of elements in the M set by adopting a disturbance method of a non-uniform mutation operator to the M set obtained in the step S32 to obtain the next group of phase factors;
b represents a pseudo-random number of Gaussian distribution generated by a Box method and a modulo-2 result of the pseudo-random number is calculated; a. the k Is the k-th set of phase factors; r is a pseudo random number uniformly distributed in (0, 1) generated by linear congruence method, T is searched set C i In (B) i λ is a system parameter of the heterogeneous system variation, and is set to be 5; t is the number of cycles;
maximum and minimum values of the kth phase factor respectively;
s34, recalculating the PAPR of the phase factor obtained in the step S33, and selecting the current minimum PAPR new ；
S35, PAPR initial value min And PAPR new Comparing; if PAPR is min Greater than PAPR new Then the PAPR is adjusted new Assignment to PAPR min (ii) a Otherwise, returning to the step S32;
s36 PAPR min And a preset PAPR 0 Comparing and judging whether the PAPR reaches the preset PAPR 0 (ii) a If yes, outputting a corresponding phase factor; if not, the process returns to step 32 for iteration.
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