CN117395119A - FP-OFDM system prototype filter optimal design method facing system error symbol rate improvement requirement - Google Patents
FP-OFDM system prototype filter optimal design method facing system error symbol rate improvement requirement Download PDFInfo
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Abstract
According to the system error symbol rate improvement demand oriented FP-OFDM system prototype filter coefficient optimization design method, as shown in figure 2, the method establishes an optimization mathematical model of the FP-OFDM system by taking an SER expression as an objective function, prototype filter coefficients as optimization variables and prototype filter performance indexes as constraint conditions, solves the optimization model to obtain a prototype filter with good performance, and can be used for the FP-OFDM system to effectively improve the communication reliability of the FP-OFDM system. According to the method, firstly, according to the signal processing process of the FP-OFDM system, a signal interference mathematical relation expression on a receiving terminal carrier is obtained, and SINR expressions on different subcarriers are continuously obtained on the basis of the mathematical relation expression, and then the SINR expressions are converted into SER expressions. And then establishing an optimized mathematical model which takes the SER expression as an objective function, prototype filter coefficients as optimization variables and prototype filter performance indexes as constraint conditions, and determining constraint threshold values in the mathematical model according to the system performance requirements in practical application. And then solving the optimization model by using a non-convex optimization algorithm to obtain a prototype filter with better performance. And finally, the designed prototype filter coefficient is used for the FP-OFDM system to reduce the SER and improve the reliability of the system.
Description
Technical Field
The invention relates to the technical field of mobile communication, is suitable for a Filtered prefix orthogonal frequency division multiplexing (FP-OFDM) system, and is a prototype filter coefficient optimization method for improving the performance of the error symbol rate (Symbol Error Rate, SER) of the FP-OFDM system. According to the method, the subband average symbol error rate is used as an objective function, an optimization model of prototype filter design is fused, the prototype filter coefficient of the FP-OFDM system is optimally designed, the optimized prototype filter coefficient is obtained, and the optimization model is used for the FP-OFDM system, so that the SER of the system can be effectively reduced, and the communication reliability is improved.
Background
With the continuous development of modern communication systems, the application of the filtering orthogonal frequency division multiplexing (filtered Orthogonal Frequency Division Multiplexing, OFDM) technology is also becoming more and more widespread, and is applied to the fields of various wireless communication systems. Nowadays, the 6G era is advanced, and the 6G is emphasized in various scenes such as intelligent interaction, super-energy traffic, indoor positioning and the like by the characteristics of super-high transmission rate, wide development coverage, high reliability, high time delay performance index and the like. However, 6G puts higher demands on the mobile communication technology, and if f-OFDM technology is continuously adopted to meet these demands, the implementation complexity of the communication system will be great. Therefore, to reduce the complexity of the system, a learner has proposed FP-OFDM based on the prior art.
Years 2019 was a researcher in Swedish research center, renaud-Alexandre Pitaval et al further proposed an FP-O FDM system with low complexity and low delay that can reduce in-band distortion on the basis of f-O FDM (literature one: pitaval R A,B M.Filtered-prefix OFDM[J]IEEE Co mmunications Letters,2018,23 (1): 28-31, i.e. Pitaval R A, -)>B M filtering prefix OF DM [ J ]]IEEE communication flash, 2018,23 (1): 28-31.). Although FP-OFDM increases out-of-band leakage over f-OFDM, out-of-band leakage is still significantly reduced over conventional orthogonal frequency division multiplexing techniques. The scheme considers that when the filter length is smaller than the Cyclic prefix length, the time domain filtering can be divided into two parts, namely, CP filtering and subcarrier weighting of the Cyclic Prefix (CP) part. This converts the convolution operation of the time-domain filtering into two low-complexity operations: filtering operation of CP section, multiplication of frequency domain signal and weighting matrixAnd (5) performing product operation. Through the conversion operation, the FP-OFDM reduces the complexity of the filtering operation and also reduces the complexity of system realization. FP-OFDM reduces in-band distortion compared to conventional f-OFDM schemes, while system delay and system complexity are further reduced due to the use of shorter finite length impulse response filters (Finite Impulse Response, FIR).
Renaud-Alexandre Pitaval et al do not continue to delve into the optimal solution of the FP-OFDM prototype filter coefficients, but only give a set of possible solutions. In order to meet the requirements of better performance of the symbol error rate of 6G and the like, an optimization mathematical model is established by taking an SER expression as an objective function, prototype filter coefficients as optimization variables and filter performance indexes as constraint conditions of an FP-OFDM system, and the prototype filter coefficients with better performance are obtained by solving the optimization model.
Disclosure of Invention
The FP-OFDM system is based on f-OFDM, and its system structure block diagram is similar to that of the f-OFDM system, as shown in fig. 1 (document one). The first document shows that the difference between the two is that f-OFDM time domain filtering operation is divided into two steps of CP filtering and subcarrier weighting when the signal processing is carried out at a transmitting end. By CP filtering and subcarrier weighting, the FP-OFDM system implementation complexity is greatly reduced compared to f-OFDM. Renaud-Alexandre Pitaval et al only gives one possible solution and does not continue to study the optimal solution of the FP-OFDM prototype filter coefficients in depth.
In order to solve the problem that the communication reliability of the system is lower due to the insufficient design of a prototype filter of an FP-OFDM system, the invention refers to a method in the literature II (Chen H, hua J, wen J, et al, unlink interference analysis of F-OFDM systems under non-ideal synchronization [ J ]. IEEE Transactions on Vehicular Technology,2020,69 (12): 15500-15517, namely Chen H, hua J, wen J, et al, under non-ideal synchronization, F-OFDM system uplink interference analysis [ J ]. IEEE vehicle technical journal, 2020,69 (12): 15500-15517), and further obtains a signal interference expression and a signal interference noise ratio (Signal to Interference plus Noise Ratio, SINR) expression on a carrier wave of a receiving terminal according to the signal processing flow of the FP-OFDM system. And then establishing an optimized mathematical model taking the SER expression as an objective function, prototype filter coefficients as optimized variables and prototype filter performance indexes as constraint conditions. A constraint threshold value in a mathematical model is determined according to the system performance requirement in practical application, a non-convex optimization algorithm is used for solving the optimization model to obtain a prototype filter with better performance, and a successive convex approximation algorithm (Successive Convex Approximation, SCA) is selected to be used for solving the optimization model without losing generality (thirdly, yang Y, pesavento M.A unified successive pseudoconvex approximation framework [ J ]. IEEE Transactions on Signal Processing,2017,65 (13): 3313-3328, namely Yang Y, pesavento M, a unified successive pseudo convex approximation framework [ J ], IEEE signal processing journal, 2017,65 (13): 3313-3328). And finally, the designed prototype filter coefficient is used for the FP-OFDM system to reduce the SER and improve the system performance. The method can also be called as an FP-OFDM system prototype filter optimization design method facing the system symbol error rate improvement requirement.
The technical scheme adopted for solving the technical problems is as follows:
the method comprises the steps of firstly establishing an optimization mathematical model of an FP-OFDM system, which takes an SER expression as an objective function, prototype filter coefficients as an optimization variable and prototype filter performance indexes as constraint conditions, and solving the optimization model to obtain a prototype filter with better performance, wherein the prototype filter is used for the FP-OFDM system. FIG. 2 is a flow chart of the implementation of the present invention, comprising the steps of:
1) According to the signal processing process of the FP-OFDM system, a signal interference mathematical relation expression on a receiving terminal carrier is obtained, SINR expressions on different subcarriers are continuously obtained on the basis, and then the SINR expressions are converted into SER expressions, so that a cost function is obtained. Without loss of generality, the subbands considered by the invention are the ith and the jth subbands with unequal subcarrier intervals, and two adjacent subbands can be selected in practical application, because the interference power between the adjacent subbands accounts for the majority of the interference power between all the subbands. More subbands can be expanded on the basis of the method if more subbands are to be considered;
2) And establishing an optimization mathematical model of the FP-OFDM system taking the SER expression as an objective function, prototype filter coefficients as optimization variables and prototype filter performance indexes as constraint conditions. Determining an optimized mathematical model constraint condition threshold value according to the system performance of practical application;
3) Solving the optimization model established in the step 2), wherein a nonlinear optimization method is needed to solve because the SER expression is a nonlinear function relative to the function expression of the filter coefficient. Without losing generality, the case of the invention adopts SCA algorithm to solve;
4) Substituting the prototype filter coefficient obtained by the optimal design into the FP-OFDM system, and observing the improvement of the system performance.
Further in said step 1), fig. 1 shows a block diagram of an FP-OFDM system model, where a subband refers to a set of subcarriers consisting of subcarriers allocated to a user. Without loss of generality, the following deduction of the present invention assumes two adjacent subbands with different subcarrier spacing, which is the most severe case of FP-OFDM system interference. Taking subband i as an example, the FP-OFDM system firstly obtains a time domain signal by inverse discrete Fourier transform (In verse Discrete Fourier Transform, IDFT) of a frequency domain signal at a transmitting end and then extracts a CP (CP length g) i ，N i The scale is transformed for IDFT. Secondly, the last frame signal CP and the current frame signal CP are connected in series and then are connected with a matrix T formed by the filter coefficients cp Multiplying to obtain CP filtered signal with length g i Wherein G is g i ×(g i -L i +1) dimension zero vector, < >>G is g i ×(g i +L i -1) a toeplitz matrix of order [ f ] i (L i -1),0,…,0] T For the first column, [ f ] i (L i -1),…,f i (1),f i (0),0,…,0]For the first row, f i (l),l∈[0,L i -1]Representing the i-th subband filter coefficients, L i Is the filter length. Subband filter coefficients may be obtained by frequency shifting prototype filter coefficients, i.e. prototype filter coefficients of FP-OFDM system with +.>Corresponding multiplication, where l.epsilon.0, L i -1]，/>I Si And I Ei Indicating the initial and cut-off sequence numbers of the subcarriers in subband i. Then the frequency domain signal and the weighting matrix are subjected to dot multiplication and then are converted into a time domain signal through IDFT, and the signal length is N i . The two parts of signals are connected in series to obtain a complete time domain transmitting signal with the signal length of N i +g i . After receiving the signal, the receiving end removes the CP and then makes N i Point DFT demodulates the received frequency signal, and a more detailed system receiving and transmitting process flow is described in document one. According to the above procedure and literature, the transmission end c-th frame subband i nth symbol time domain transmission signal is represented as follows:
wherein t is c,i,cp Representing the transmitted signal CP, t c,i,n Represents the data part of the transmitted signal, which is specifically represented by the formula (6) and has
In the formula (2), the amino acid sequence of the compound,the CP part of the nth symbol of the sub-band i of the c-th frame is provided with
Wherein X is c,i,n (u) is the nth symbol nth subcarrier of the c-frame subband i of the frequency domain signal of the transmitting end.
The scalar of the time domain signal after CP removal of the nth symbol of the c-th frame sub-band i at the receiving end is expressed as follows:
where ε represents the carrier frequency offset, z (k) represents the additive white Gaussian noise (Additive White Gaussian Noise, AWGN), t c,i,n (k) Representing the time domain signal after the carrier weighting and IDFT of the transmitting terminal, and has
Wherein,weighting coefficients for the corresponding subcarriers.
According to the signal processing procedure of fig. 1 and the above formula, the frequency domain received signal obtained when only the dual sub-bands are considered is as follows:
wherein the first term Signal represents the useful Signal, the second term INBI represents the in-band interference, the third term ITBI represents the out-of-band interference, the source of which comprises CP and data of subband j, and the ITBI expression will be given later.Is a frequency domain representation of additive white gaussian noise, S i Representing a set of sub-carriers for sub-band i, and having
Because the subcarrier spacing of two adjacent subbands is inconsistent, the subcarrier spacing of the subband i is 2 times that of the subcarrier spacing of the subband j, namely, the number of subcarriers of each symbol of the subband i is half that of the subcarriers of each symbol of the subband j under the condition of consistent analog domain width of the subbands, when the symbols of the subbands are aligned, the symbols of the two subbands i correspond to the symbol of one subband j, namely, the 2n-1 and the 2n symbol of the subband i correspond to the n symbol of the subband j in time, so that the out-of-band interference born by the two subbands is different. Researches show that when the sub-band i is taken as a target sub-band, the types of interference suffered by the 2n-1 th symbol and the 2 n-th symbol of the sub-band i are different, the 2n-1 th symbol can be interfered by the CP part and the data part of the n-th symbol of the sub-band j, and the 2 n-th symbol can only be interfered by the data part of the n-th symbol of the sub-band j. However, the research and calculation of the present invention show that the interference suffered by the 2n-1 nd and 2n th symbols of the subband i has the same variation trend relative to the prototype filter, and the interference values are approximately equal, as shown in fig. 3. Prototype filter optimization may be performed only for the 2n-1 symbol of subband i, with the result being equally valid for the 2n symbol. When the subband j is the target subband, the interference experienced by each symbol of subband j is the same. Thus, only the nth symbol of subband j needs to be prototype filter optimized.
The partial interference expression for the nth symbol of subband j for the 2n-1 symbol of subband i can be written as follows, according to equation (7).Representing the interference of the CP portion of the nth symbol of subband j to the 2n-1 symbol of subband i,
wherein,
in the formula (10), f j (l),l∈[0,L j -1]The sub-band j filter coefficients, which can be transformed by the prototype filter of the system.
Order theInterference of the data portion representing the nth symbol of subband j with the 2n-1 symbol of subband i may be obtained
Wherein,
according to equations (7) (9) (12), the SINR expression on the m-th subcarrier of the 2n-1 th symbol of subband i can be further deduced as follows,
wherein P is Noise (m) represents noise power, P i Signal (m) and P i INBI (m) is the useful signal power on the mth subcarrier of subband i and the in-band interference power,
the CP portion of subband j represents the interference power for subband i,
the data portion representing subband j interferes with the power of subband i,
by and P i SINR (m) the same derivation procedure, the SINR expression on the mth subcarrier of the nth symbol of subband j can be obtainedAnd will not be described in detail here.
For V-dimensional quadrature amplitude modulation (V Quadrature Amplitude Modulation, VQAM) (V is the QAM order), the average bit error rate in an AWGN environment is formulated as follows:
wherein E is av To average signal variance, N 0 In order to be a noise power spectral density,the signal-to-noise ratio SNR of the system is obtained, and Q (x) is the complementary cumulative distribution function of the standard normal distribution. Since SINR and SNR parameters are similar, SINR may be used instead of SNR to calculate SER, and substituting SINR on the mth subcarrier into equation (15) may result in the bit error rate on the mth subcarrier being expressed as:
therefore, under the condition of the known SINR, the SER on each subcarrier of the subband can be solved according to the above equation. The average SER for a dual subband can thus be expressed as follows:
wherein S is j Representing the set of subcarriers of the nth symbol of subband j, M i And M j The number of subcarriers in the subcarrier sets for subband i and subband j, respectively. In the invention, the optimization model objective function only considers the average SER of the double sub-bands, and if more sub-bands need to be considered, the method can be referred to for expansion.
The cost function can be made according to equation (21) to be:
when the cost function J C At minimum, there is a minimum for the subband average SER.
In the step 2), an optimization constraint model is established by taking a subband average SER expression as an objective function, taking a prototype filter coefficient as an optimization variable and taking a prototype filter performance index as a constraint condition, wherein the objective function is the formula (22) in the step 1). Meanwhile, constraint is added to the prototype filter, and the main constraint adding conditions are passband ripple constraint and stopband ripple constraint. The final constructed optimized mathematical model is as follows:
wherein delta p Representing passband ripple, delta s Representing stop band fluctuations, ω p Represents the passband cut-off frequency point omega s Represents the stop band cut-off frequency point, and H (ω) represents the amplitude-frequency response of the prototype filter coefficients. Without loss of generality, it is assumed that an I-type linear phase FIR filter is employed, whose amplitude-frequency response can be expressed as,
wherein,
determining constraint threshold values in an optimization model of formula (23) according to system performance requirements in practical application, wherein the constraint threshold values comprise delta p 、δ s 、ω p And omega s 。
In the step 3), the optimization mathematical model determined in the step 2) is solved, and a nonlinear optimization method is needed to be adopted for solving because the function expression of the SER about the prototype filter coefficient is a nonlinear function. Without loss of generality, the test sample of the invention is solved by adopting the SCA method.
In the step 4), the prototype filter coefficient obtained by the optimization solution in the step 3) is substituted into the FP-OFDM system, and the degree of performance improvement of the system is observed.
The technical conception of the invention is as follows: in order to improve the performance of an FP-OFDM system and reduce the transmission symbol error rate, the invention establishes an optimized mathematical model which takes an SER expression as an objective function, prototype filter coefficients as an optimized variable and prototype filter performance indexes as constraint conditions, solves to obtain prototype filter coefficients with better performance, substitutes the prototype filter coefficients into the FP-OFDM system, and observes the improvement of the system performance.
The beneficial effects of the invention are mainly shown in the following steps: the prototype filter coefficient obtained by solving the optimized mathematical model is used for the FP-OFDM system, so that the SER of the system can be effectively improved, and the communication reliability of the system is further improved.
Drawings
Fig. 1 is a block diagram of an FP-OFDM system model structure.
Fig. 2 is a flow chart of a prototype filter design method of FP-OFDM system.
Fig. 3 is a diagram of out-of-band interference power versus parity symbols on subband i.
Fig. 4 is a graph of the frequency response of the prototype filter before and after optimization.
Fig. 5 is a graph comparing SER curves before and after prototype filter optimization.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
Referring to fig. 3 to 5, without loss of generality, the FP-OFDM system parameter set for simulation is shown in table 1, two subbands are adjacent in frequency, constraint threshold parameters selected for optimization design are shown in table 2, and for convenience of description, constraint threshold value R in dB form is used p And A s Representing delta p And delta s . Wherein, the system input signal adopts 16QAM modulation.
TABLE 1FP-OFDM System simulation parameters
Table 2 optimization design constraint threshold
TABLE 3 comparison of metrics before and after optimization of prototype filters
Table 3 shows the comparison of the indexes of the prototype filter before and after optimization, fig. 4 shows the frequency response diagram of the prototype filter, and the coefficients of the prototype filter can obtain the coefficients of different sub-band filters through frequency shift. As can be seen from table 3, the optimized prototype filter passband ripple Rp, the transition band and passband error energy Ep are all greater, while the stopband attenuation As and stopband error energy Es are improved. The method is equivalent to reducing the stop band error energy at the cost of increasing the pass band error energy and the transition band under the condition that the length of the prototype filter is unchanged, thereby reducing the out-of-band leakage. As can be seen from fig. 4, the prototype filter designed by the method generates the equiripple phenomenon in the stop band portion, and has certain advantages in the stop band fluctuation index compared with the filter before optimization.
Fig. 5 is a diagram of a comparison of FP-OFDM system demodulation SER using different prototype filters. In fig. 5, the curve { cheb, SER } represents the system demodulation SER curve generated by an uneptimized equiripple prototype filter, the curve { huawei, SER } represents the system demodulation SER curve generated by a prototype filter proposed in literature Filtered-prefix OFDM, and the curve { opti, SER } represents the system demodulation SER curve after optimizing the prototype filter using the present method. It can be seen from fig. 5 that as the SNR of the system increases, the performance of the optimized prototype filter on the system increases more significantly, i.e. the SER curve is always under the curves { cheb, SER } and { huawei, SER }. This shows that the method optimizes the prototype filter coefficient, can realize the purpose of reducing the SER of the system and improves the reliability of the system.
The embodiments described in this specification are merely illustrative of the manner in which the inventive concepts may be implemented. The scope of the present invention should not be construed as being limited to the specific forms set forth in the embodiments, but the scope of the present invention and the equivalents thereof as would occur to one skilled in the art based on the inventive concept.
Claims (5)
1. The FP-OFDM system filter coefficient optimization design method facing the system error symbol rate improvement requirement is characterized by comprising the following steps of: the method comprises the following steps:
1) According to the signal processing process of the FP-OFDM system, a signal interference mathematical relation expression on a receiving terminal carrier is obtained, SINR expressions on different subcarriers are continuously obtained on the basis, and then the SINR expressions are converted into SER expressions, so that a cost function is obtained. Without loss of generality, the subbands considered by the invention are the ith and the jth subbands with unequal subcarrier intervals, and two adjacent subbands can be selected in practical application, because the interference power between the adjacent subbands accounts for the majority of the interference power between all the subbands. More subbands can be expanded on the basis of the method if more subbands are to be considered;
2) And establishing an optimization mathematical model of the FP-OFDM system taking the SER expression as an objective function, prototype filter coefficients as optimization variables and prototype filter performance indexes as constraint conditions. Determining an optimized mathematical model constraint condition threshold value according to the system performance of practical application;
3) Solving the optimization model established in the step 2), wherein a nonlinear optimization method is needed to solve because the function expression of the SER expression about the filter coefficient is a nonlinear function. Without losing generality, the case of the invention adopts SCA algorithm to solve;
4) Substituting the prototype filter coefficient obtained by the optimal design into the FP-OFDM system, and observing the improvement of the system performance.
2. The FP-OFDM system filter coefficient optimization design method for system symbol error rate improvement requirements as claimed in claim 1, wherein: in said step 1), fig. 1 of the specification shows a block diagram of an FP-OFDM system model, where a subband refers to a set of subcarriers consisting of subcarriers allocated to a user. Without loss of generality, the following deduction of the present invention assumes two adjacent subbands with different subcarrier spacing, which is the most severe case of FP-OFDM system interference. Taking subband i as an example, the FP-OFDM system firstly obtains a time domain signal by inverse discrete Fourier transform (Inverse Discrete Fourier Transform, IDFT) of a frequency domain signal at a transmitting end and then extracts a CP (CP length g) i ，N i The scale is transformed for IDFT. Secondly, the last frame signal CP and the current frame signal CP are connected in series and then are connected with a matrix T formed by the filter coefficients cp Multiplying to obtain CP filtered signal with length g i WhereinG is g i ×(g i -L i +1) zero vector, T gi G is g i ×(g i +L i -1) a toeplitz matrix of order [ f ] i (L i -1),0,…,0] T For the first column, [ f ] i (L i -1),…,f i (1),f i (0),0,…,0]For the first row, f i (l),l∈[0,L i -1]Representing the i-th subband filter coefficients, L i Is the filter length. Subband filter coefficients may be obtained by frequency shifting prototype filter coefficients, i.e. prototype filter coefficients of FP-OFDM system with +.>Corresponding multiplication, where l.epsilon.0, L i -1]，/>I Si And I Ei Indicating the initial and cut-off sequence numbers of the subcarriers in subband i. Then the frequency domain signal and the weighting matrix are subjected to dot multiplication and then are converted into a time domain signal through IDFT, and the signal length is N i . The two parts of signals are connected in series to obtain a complete time domain transmitting signal with the signal length of N i +g i . After receiving the signal, the receiving end removes the CP and then makes N i Point DFT, demodulating the received frequency signal, and more detailed system-on-transmit processing flow is described in literature one (Pitaval R A,)>B M.Filtered-pre fix OFDM[J]IEEE Communications Letters,2018,23 (1): 28-31, i.e. Pitaval R A, -)>BM filtering prefix OFDM [ J ]]IEEE communication flash, 2018,23 (1): 28-31.). According to the above procedure and literature, the transmission end c-th frame subband i nth symbol time domain transmission signal is represented as follows:
wherein t is c,i,cp Representing the transmitted signal CP, t c,i,n Represents the data part of the transmitted signal, which is specifically represented by the formula (6) and has
In the formula (2), the amino acid sequence of the compound,the CP part of the nth symbol of the sub-band i of the c-th frame is provided with
Wherein X is c,i,n (u) is the nth symbol nth subcarrier of the c-frame subband i of the frequency domain signal of the transmitting end.
The scalar of the time domain signal after CP removal of the nth symbol of the c-th frame sub-band i at the receiving end is expressed as follows:
where ε represents the carrier frequency offset, z (k) represents the additive white Gaussian noise (Additive White Gaussian Noise, AWGN), t c,i,n (k) Representing the time domain signal after the carrier weighting and IDFT of the transmitting terminal, and has
Wherein,weighting coefficients for the corresponding subcarriers.
According to the signal processing procedure of fig. 1 and the above formula, the frequency domain received signal obtained when only the dual sub-bands are considered is as follows:
wherein the first term Signal represents the useful Signal, the second term INBI represents the in-band interference, the third term ITBI represents the out-of-band interference, the source of which comprises CP and data of subband j, and the ITBI expression will be given later.
Is a frequency domain representation of additive white gaussian noise, S i Representing a set of sub-carriers for sub-band i, and having
Because the subcarrier spacing of two adjacent subbands is inconsistent, the subcarrier spacing of the subband i is 2 times that of the subcarrier spacing of the subband j, namely, the number of subcarriers of each symbol of the subband i is half that of the subcarriers of each symbol of the subband j under the condition of consistent analog domain width of the subbands, when the symbols of the subbands are aligned, the symbols of the two subbands i correspond to the symbol of one subband j, namely, the 2n-1 and the 2n symbol of the subband i correspond to the n symbol of the subband j in time, so that the out-of-band interference born by the two subbands is different. Researches show that when the sub-band i is taken as a target sub-band, the types of interference suffered by the 2n-1 th symbol and the 2 n-th symbol of the sub-band i are different, the 2n-1 th symbol can be interfered by the CP part and the data part of the n-th symbol of the sub-band j, and the 2 n-th symbol can only be interfered by the data part of the n-th symbol of the sub-band j. However, the research and calculation of the present invention show that the interference suffered by the 2n-1 nd and 2n th symbols of the subband i has the same variation trend relative to the prototype filter, and the interference values are approximately equal, as shown in fig. 3. Prototype filter optimization may be performed only for the 2n-1 symbol of subband i, with the result being equally valid for the 2n symbol. When the subband j is the target subband, the interference experienced by each symbol of subband j is the same. Thus, only the nth symbol of subband j needs to be prototype filter optimized.
The partial interference expression for the nth symbol of subband j for the 2n-1 symbol of subband i can be written as follows, according to equation (7).Representing the interference of the CP portion of the nth symbol of subband j to the 2n-1 symbol of subband i,
wherein,
in the formula (10), f j (l),l∈[0,L j -1]The sub-band j filter coefficients, which can be transformed by the prototype filter of the system.
Order theInterference of the data portion representing the nth symbol of subband j with the 2n-1 symbol of subband i may be obtained
Wherein,
according to equations (7) (9) (12), the SINR expression on the m-th subcarrier of the 2n-1 th symbol of subband i can be further deduced as follows,
wherein P is Noise (m) represents noise power, P i Signal (m) and P i INBI (m) is the useful signal power on the mth subcarrier of subband i and the in-band interference power,
the CP portion of subband j represents the interference power for subband i,
the data portion representing subband j interferes with the power of subband i,
by and P i SINR (m) the same derivation procedure, the SINR expression on the mth subcarrier of the nth symbol of subband j can be obtainedAnd will not be described in detail here.
For V-dimensional quadrature amplitude modulation (V Quadrature Amplitude Modulation, VQAM) (V is the QAM order), the average bit error rate in an AWGN environment is formulated as follows:
wherein E is av To average signal variance, N 0 In order to be a noise power spectral density,the signal-to-noise ratio SNR of the system is obtained, and Q (x) is the complementary cumulative distribution function of the standard normal distribution. Since SINR and SNR parameters are similar, SINR may be used instead of SNR to calculate SER, and substituting SINR on the mth subcarrier into equation (15) may result in the bit error rate on the mth subcarrier being expressed as:
therefore, under the condition of the known SINR, the SER on each subcarrier of the subband can be solved according to the above equation. The average SER for a dual subband can thus be expressed as follows:
wherein S is j Representing the set of subcarriers of the nth symbol of subband j, M i And M j The number of subcarriers in the subcarrier sets for subband i and subband j, respectively. In the invention, the optimization model objective function only considers the average SER of the double sub-bands, and if more sub-bands need to be considered, the method can be referred to for expansion.
The cost function can be made according to equation (21) to be:
when the cost function J C At minimum, there is a minimum for the subband average SER.
3. The FP-OFDM system filter coefficient optimization design method for system symbol error rate improvement requirements of claim 1, wherein: in the step 2), an optimization constraint model is established by taking a subband average SER expression as an objective function, taking a prototype filter coefficient as an optimization variable and taking a prototype filter performance index as a constraint condition, wherein the objective function is the formula (22) in the step 1). Meanwhile, constraint is added to the prototype filter, and the main constraint adding conditions are passband ripple constraint and stopband ripple constraint. The final constructed optimized mathematical model is as follows:
wherein delta p Representing passband ripple, delta s Representing stop band fluctuations, ω p Represents the passband cut-off frequency point omega s Represents the stop band cut-off frequency point, and H (ω) represents the amplitude-frequency response of the prototype filter coefficients. Without loss of generality, it is assumed that an I-type linear phase FIR filter is employed, whose amplitude-frequency response can be expressed as,
wherein,
determining constraint threshold values in an optimization model of formula (23) according to system performance requirements in practical application, wherein the constraint threshold values comprise delta p 、δ s 、ω p And omega s 。
4. The FP-OFDM system filter coefficient optimization design method for system symbol error rate improvement requirements of claim 1, wherein: in the step 3), the optimization mathematical model determined in the step 2) is solved, and a nonlinear optimization method is needed to be adopted for solving because the function expression of the SER about the prototype filter coefficient is a nonlinear function. Without loss of generality, the test sample of the invention is solved by adopting the SCA method.
5. The FP-OFDM system filter coefficient optimization design method for system symbol error rate improvement requirements of claim 1, wherein: in the step 4), the prototype filter coefficient obtained by the optimization solution in the step 3) is substituted into the FP-OFDM system, and the degree of performance improvement of the system is observed.
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