Dual-index modulation radio frequency division multiplexing (AFDM) imitated AFDM communication method

Abstract

The invention discloses a double-index modulation simulated radio frequency division multiplexing (AFDM) communication method. The method comprises the following steps: step 1, a transmitting end performs serial-parallel change; step 2, obtaining a transmission signal according to the index position of the joint selection AFDM activation subcarrier in the mapping table, the modulation bit mapping and the pre-chirp parameter of the activation subcarrier; step 3, obtaining a time domain signal; 4, performing parallel-serial conversion on the time domain signal; step 5, performing propagation transmission through a time-varying channel based on the time domain signal; step 6, constructing a time domain channel matrix, and performing serial-to-parallel conversion on the time domain receiving signal to obtain a receiving signal; step 7, performing channel estimation on the chirp parameter equivalent channel matrix; step 8, detecting an activated subcarrier position, an activated subcarrier modulation bit and an activated subcarrier pre-chirp parameter based on the chirp parameter equivalent channel matrix, and performing pre-chirp parameter transformation; and step 9, recovering the bit stream through parallel-serial change. The spectrum efficiency of the AFDM system is further improved, and the bit error rate is reduced.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of affine frequency division multiplexing in wireless communication technology, and particularly relates to an affine frequency division multiplexing AFDM communication method with double index modulation.

BACKGROUND

[0002] In the existing wireless communication system, the orthogonal frequency division multiplexing (OFDM) is widely applied in the 4G and 5G systems due to its high frequency spectrum efficiency and anti-multipath interference capability. However, the OFDM cannot effectively process the Doppler frequency shift under the time-frequency double-selected channel, resulting in that the orthogonality between the OFDM subcarriers is seriously destroyed. In order to solve this problem, the affine frequency division multiplexing (AFDM) is proposed, and the AFDM converts the effective channel in the AFDM system into a sparse quasi-static channel through the discrete affine Fourier transform and the inverse discrete affine Fourier transform, and realizes the complete diversity in the double dispersion channel.

[0003] In the prior art, the index modulation technology has the advantages of significantly improving the frequency spectrum efficiency and improving the data transmission rate, and therefore, in order to improve the frequency spectrum efficiency of the AFDM system, the research team of the Nanyang Technological University of Singapore and the South China University of Technology jointly proposes the AFDM-IM system "Affine Frequency Division Multiplexing With Index Modulation" which activates the subcarrier position. However, the AFDM-IM only transmits information through the activation state of the subcarrier, and although the frequency spectrum efficiency is improved, the available index combination is limited, which limits the further improvement of the frequency spectrum efficiency. The AFDM-PIM transmits information through the pre-chirp parameters of the subcarrier, but does not fully utilize the active subcarrier position of the traditional index modulation, which limits the further improvement of the frequency spectrum efficiency.

SUMMARY

[0004] The application aims to provide an affine frequency division multiplexing AFDM communication method with double index modulation, which further improves the frequency spectrum efficiency of the AFDM system and reduces the bit error rate.

[0005] The application adopts the following technical scheme: an affine frequency division multiplexing AFDM communication method with double index modulation, comprising the following steps:

[0006] Step 1, at the transmitting end, performing serial-parallel conversion;

[0007] Step 2, jointly selecting the index position of the AFDM active subcarrier, the modulation bit mapping and the pre-chirp parameter c2 of the active subcarrier from the pre-defined mapping table according to the input bit stream, obtaining the mapping symbol u according to the index position of the mapping active subcarrier and the modulation bit based on the invented double-index modulation mapping criterion, and obtaining the transmission signal x by performing the pre-chirp parameter inverse transformation according to the selected pre-chirp parameter;

[0008] Step 3, performing the inverse chirp Fourier transformation on the transmission signal x to obtain the time domain signal s;

[0009] Step 4, inserting the chirp period prefix into the time domain signal s and performing the parallel-serial conversion;

[0010] Step 5, propagating and transmitting the time domain signal generated based on the above steps through the time-varying channel;

[0011] Step 6, constructing the time domain channel matrix, performing the serial-parallel conversion on the received time domain received signal, removing the chirp period prefix to obtain the time domain received signal r without the prefix, and then performing the chirp Fourier transformation on r to obtain the received signal z;

[0012] Step 7, constructing the chirp parameter equivalent channel matrix and performing the channel estimation thereon;

[0013] Step 8, based on the estimated chirp parameter equivalent channel matrix, using the low-complexity minimum mean square error-maximum likelihood signal detection method or the maximum likelihood joint signal detection method to detect the active subcarrier position, the active subcarrier modulation bit, the active subcarrier pre-chirp parameter, and performing the pre-chirp parameter transformation;

[0014] Step 9, recovering the bit stream through the serial-parallel conversion.

[0015] Further, in Step 2, the input bit stream b is divided into g groups, and the total number of subcarriers N is divided into g groups, and the number of subcarriers in each group is n=N / g, and the mapping table is defined as O={a, d, p}, wherein the mapping table includes the active position a of the subcarriers, the modulation data bit d, and the pre-chirp parameter p;

[0016] The active position a represents all possible combinations of selecting m active subcarriers from n subcarrier indexes; the modulation data bit d is all possible M mod order modulation symbols; and the pre-chirp parameter p is all possible ordered combinations of selecting m active subcarrier pre-chirp parameters from n pre-chirp parameters; taking the i-th (i=1, …, g) group as an example, the pre-chirp parameter of the active subcarrier, the active subcarrier state and the data bit are jointly selected from the pre-defined mapping table according to the input b i bit stream.

[0017] Further, in step 2, the calculation formula of the input bit stream is:

[0018]

[0019] Wherein: represents the floor operation, M mod is the M-ary PSK, g represents the number of groups, m represents the number of active subcarriers, n represents the number of subcarriers per group, C(n,m) represents combination, i.e. randomly selecting m elements from n elements, and m! represents the factorial of m.

[0020] Further, in step 2, according to the selected pre-chirp parameters, the pre-chirp parameter inverse transformation is performed to obtain the transmission signal x, and the formula is:

[0021]

[0022] Wherein is the pre-chirp matrix:

[0023]

[0024] c 2,k represents the subcarrier pre-chirp parameter value of the kth subcarrier.

[0025] Further, in step 3, the transmission signal x is subjected to inverse chirp Fourier transform to obtain the time domain signal s, and the formula is:

[0026]

[0027] Wherein, represents the post-chirp matrix:

[0028]

[0029] Wherein c1 is the post-chirp parameter;

[0030] F represents the discrete Fourier transform matrix:

[0031]

[0032] Further, in step 6, the chirp Fourier transform is performed on the time domain signal r to obtain the received signal z, which can be represented as:

[0033]

[0034] Wherein w is a complex additive Gaussian noise, P represents the number of multiple paths, h i , f i , and l i respectively represent the channel gain, Doppler shift, and integer delay of the ith path.i ∈ [0, 1 max ], where l max is the maximum delay.

[0035] Further, in step 8,

[0036] The equivalent channel matrix of the chirp parameters can be expressed as:

[0037] where the permutation matrix is Π:

[0038]

[0039] Δ fi is an N x N diagonal matrix;

[0040]

[0041] is an N x N diagonal matrix:

[0042]

[0043] where h i , f i , l i represent the channel gain, Doppler shift, and integer delay of the i-th path, respectively; when 2Nc1 is an integer and N is even,

[0044] where the channel gain of the incomplete channel is expressed as:

[0045]

[0046] where φop are independent, and ε is the channel error value, ε ∈ [0, 1], and when ε = 0, it is a perfect channel gain;

[0047] represents the post-chirp matrix:

[0048]

[0049] where c1 is the post-chirp parameter;

[0050] F is expressed as a discrete Fourier transform matrix:

[0051]

[0052] Further, in step 8, the low-complexity minimum mean square error-maximum likelihood signal detection step is:

[0053] 1) Obtain the received signal x by minimum mean square error-detector p :

[0054]

[0055] where, denotes the average signal-to-noise ratio, I N is an N x N unit matrix;

[0056] 2) Based on the estimated signal power |x p | 2 , the active subcarrier index position is detected by a greedy algorithm:

[0057]

[0058] 3) Based on the index position of all detected active subcarriers, the maximum likelihood signal detection method is used to retrieve the active subcarrier modulation bits and pre-chirp parameters:

[0059]

[0060] where d represents all possible values of the modulation bits, and p represents all possible values of the pre-chirp parameters.

[0061] Further, in step 8, the maximum likelihood joint signal detection method is:

[0062]

[0063] where d represents all possible values of the modulation data bits, p represents all possible values of the pre-chirp parameters, and a represents all possible active subcarrier positions.

[0064] The beneficial effects of the present application are: at the sending end, the method of the present application uses the active state and the pre-chirp parameter to jointly transmit information bits, so that the system can carry more information bits under the same spectrum resource condition, thereby improving the spectrum efficiency. The method of the present application also constructs a chirp parameter equivalent channel matrix, and at the receiving end, based on the estimated chirp parameter equivalent channel matrix, a low-complexity minimum mean square error-maximum likelihood signal detection algorithm is proposed. Compared with the maximum likelihood joint signal detection, the algorithm optimizes the detection process, significantly reduces the computational complexity, and only introduces marginal performance loss of the bit error rate, effectively achieving a good trade-off between the bit error rate and the complexity. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 is a modulation and demodulation block diagram of an affine frequency division multiplexing AFDM communication method of the present application;

[0066] Figure 2is a spectrum efficiency comparison chart of AFDM, AFDM-IM, AFDM-PIM communication in different active subcarrier numbers in the embodiment of the application;

[0067] Figure 3 is a spectrum efficiency comparison chart of AFDM, AFDM-IM, AFDM-PIM communication in different subcarrier numbers per group in the embodiment of the application;

[0068] Figure 4 is a BER comparison chart of simulation and theory of AFDM-DIM system under different channel conditions in the embodiment of the application;

[0069] Figure 5 is a BER comparison chart of AFDM-DIM and AFDM under different path numbers in the embodiment of the application under perfect channel;

[0070] Figure 6 is a BER comparison chart of AFDM-DIM and AFDM-IM, AFDM-PIM in the embodiment of the application under perfect channel;

[0071] Figure 7 is a theoretical and simulation BER comparison chart of AFDM-DIM and AFDM-IM, AFDM-PIM in the embodiment of the application under imperfect channel;

[0072] Figure 8 is a BER comparison chart of MMSE-ML and ML joint signal detection in the AFDM-DIM system in the embodiment of the application.

CONCRETE IMPLEMENTATION

[0073] The application will be described in detail below in combination with the drawings and specific embodiments.

[0074] The application discloses a double-index modulation affine frequency division multiplexing AFDM communication method, referred to as AFDM-DIM. A pre-chirp parameter is introduced to form a double-index parameter, which improves the transmission rate relative to the conventional index modulation AFDM system. A low-complexity signal detection method is also disclosed, which reduces the signal detection complexity while only having marginal loss in the bit error rate.

[0075] The method comprises the following steps of: at a transmitting end: firstly, performing serial-parallel conversion; jointly selecting an index position of an AFDM active subcarrier, a modulation bit of the active subcarrier and a pre-chirp parameter of the active subcarrier according to a predefined mapping table, then obtaining a mapping symbol according to the index position and the modulation bit of the mapping active subcarrier based on the invented double-index modulation mapping criterion, and further obtaining a transmission signal by performing inverse pre-chirp parameter conversion according to the selected pre-chirp parameter; then, performing chirp inverse Fourier transformation on the transmission signal to obtain a time domain signal; then, inserting a chirp cycle prefix and performing parallel-serial conversion; finally, transmitting the processed AFDM time domain signal through a time-varying channel. At a receiving end: performing serial-parallel conversion on a received time domain received signal and removing the chirp cycle prefix to obtain a time domain received signal without a prefix; then, performing chirp Fourier transformation to obtain a signal z; inventing a chirp parameter equivalent channel matrix and performing channel estimation on the chirp parameter equivalent channel matrix; detecting the active subcarrier position, the active subcarrier modulation bit and the active subcarrier pre-chirp parameter by using the invented low-complexity minimum mean square error-maximum likelihood signal detection or maximum likelihood joint signal detection method based on the estimated chirp parameter equivalent channel matrix, and performing pre-chirp parameter conversion; and finally, recovering a bit stream through parallel-serial conversion.

[0076] Embodiment:

[0077] 1. An input bit stream b is divided into g groups, and the total number of subcarriers N is divided into g groups, and the number of subcarriers in each group is n=N / g, and the mapping table is defined as O={a,d,p}, wherein the mapping table contains the active position a of the subcarrier, the modulation data bit d, and the pre-chirp parameter p;

[0078] The active position a represents all possible combinations of selecting m active subcarriers from n subcarrier indexes; the modulation data bit d is all possible M mod order modulation symbols; and the pre-chirp parameter p is all possible ordered combinations of selecting m active subcarrier pre-chirp parameters from n pre-chirp parameters; taking the i(th) (i=1,…,g) group as an example, the pre-chirp parameter of the active subcarrier, the active subcarrier state and the data bit are jointly selected from the predefined mapping table according to the input b i bit.

[0079] 2. The calculation formula of the system for each frame input bit stream is:

[0080]

[0081] Wherein: represents a down rounding operation, M mod is an M-ary PSK, g represents the number of groups, m represents the number of active subcarriers, n represents the number of subcarriers in each group, C(n,m) represents combination, that is, randomly selecting m elements from n elements, and m! represents the factorial of m.

[0082] 3. The mapping symbol u is pre-chirped according to the selected pre-chirp parameters to obtain the transmission signal x, which is expressed as:

[0083]

[0084] wherein is the pre-chirp matrix:

[0085]

[0086] c 2,k represents the sub-carrier pre-chirp parameter value of the kth sub-carrier.

[0087] 4. The transmission signal x is inverse chirp-Fourier transformed to obtain the time-domain signal s, which is expressed as:

[0088]

[0089] wherein represents the post-chirp matrix:

[0090]

[0091] wherein c1 is the post-chirp parameter.

[0092] F represents the discrete Fourier transform matrix:

[0093]

[0094] 5. The time-domain signal s is inserted with a chirp period prefix, which is expressed as: wherein L cp is the chirp period prefix length and is subjected to parallel-serial conversion.

[0095] 6. Assuming that the channel is known, the time-domain channel matrix can be modeled as:

[0096]

[0097] wherein the permutation matrix is Π:

[0098]

[0099] is an N x N diagonal matrix:

[0100]

[0101] is an N x N diagonal matrix:

[0102]

[0103] where h i , f i , l i represent the channel gain, Doppler shift, integer delay of the i-th path, respectively. When 2Nc1 is an integer and N is even,

[0104] where the channel gain of the incomplete channel is represented as:

[0105]

[0106] where, φpair are independent, and ε is the channel error value, ε ∈ [0, 1], when ε = 0, it is a perfect channel gain.

[0107] 7. At the receiving end, the received signal is subjected to serial-parallel conversion and removal of the chirp period prefix operation to obtain the time-domain received signal r, and then subjected to chirp Fourier transform to obtain the received signal z, which can be represented as:

[0108]

[0109] where w is a complex additive Gaussian noise, P represents the number of multipaths, f i , l i represent the Doppler shift, integer delay of the i-th path, respectively. l i ∈ [0, l max ], where l max is the maximum delay.

[0110] 8. The chirp parameter equivalent channel matrix can be represented as:

[0111]

[0112] where the permutation matrix is Π:

[0113]

[0114] is an N × N diagonal matrix:

[0115]

[0116] is an N × N diagonal matrix:

[0117]

[0118] where h i , f i , l irespectively represent the channel gain, Doppler shift, and integer delay of the ith path; and

[0119] where the channel gain of the incomplete channel is represented as:

[0120]

[0121] where φ is independent of is the channel error value, and ε ∈ [0, 1], where ε = 0 is a perfect channel gain;

[0122] represents the post-chirp matrix:

[0123]

[0124] where c1is the post-chirp parameter.

[0125] F is represented as a discrete Fourier transform matrix:

[0126]

[0127] 9. Based on the estimated equivalent channel matrix of the chirp parameters, a low complexity minimum mean square error-maximum likelihood signal detection step is shown as follows:

[0128] 1) Obtain the received signal x by a minimum mean square error (MMSE) detector p :

[0129]

[0130] where represents the average signal-to-noise ratio, I N is an N x N identity matrix.

[0131] 2) Based on the estimated signal power |x p | 2 , detect the active subcarrier index position by a greedy algorithm:

[0132]

[0133] 3) Based on the detected index position of all active subcarriers, perform a maximum likelihood signal detection method decision to retrieve the active subcarrier modulation bits and pre-chirp parameters:

[0134]

[0135] where d represents all possible values of the modulation bits, and p represents all possible values of the pre-chirp parameters.

[0136] 10. The maximum likelihood joint signal detection method of the invention is as follows:

[0137]

[0138] where d represents all possible values of the modulated bits, p represents the pre-chirp parameters of all possible values, and a represents all possible active subcarrier positions.

[0139] After the signal detection, the asymptotically tight upper bound of the average bit error rate of the maximum likelihood joint signal detection method is given, and the specific method is as follows:

[0140] 1) The received signal z can be rewritten as:

[0141]

[0142] where and

[0143] 2) In the presence of channel estimation error, the conditional pairwise error probability (CPEP) between the transmitted symbol x i and its estimated value x j can be expressed as:

[0144]

[0145] 3) where Therefore, it can be simplified as:

[0146]

[0147] where Q(x) can be approximated as:

[0148] 4) The unconditional pairwise error probability of the AFDM-DIM scheme can be expressed as:

[0149]

[0150] where and defined Therefore, the probability density function of can be expressed as:

[0151]

[0152] 5) Without loss of generality, it is assumed that the proposed AFDM-DIM scheme satisfies the complete diversity condition, making the rank The further unconditional PEP can be expressed as:

[0153]

[0154] where, T is the eigenvalue of the matrix T.

[0155] 6) Based on the obtained unconditional PEP, the upper bound of the ABEP of the proposed AFDM-DIM scheme under the incomplete CSI condition can be calculated:

[0156]

[0157] where e(x i ,x j ) represents the number of error bits when x i is estimated as x j .

[0158] 11. The spectral efficiency (SE) of the proposed AFDM-DIM scheme of the present application can be represented as:

[0159]

[0160] In addition, the SE of the classical AFDM, AFDM-IM and AFDM-PIM is represented as:

[0161] η AFDM = log2(M mod )

[0162]

[0163] The spectral efficiency of different AFDM systems is compared by using the simulation conditions in Table 1 below:

[0164] Table 1

[0165]

[0166] The simulation results are shown in Figure 2 , which gives the spectral efficiency comparison chart of the detection method AFDM-DIM of the present application and the existing detection methods AFDM, AFDM-IM and AFDM-PIM under different active subcarriers. As Figure 2As shown, with 16 subcarriers per group, it can be observed that the spectral efficiency of AFDM-DIM improves as the number of active subcarriers increases from 12 to 14. When the number of active subcarriers is 14, the spectral efficiency of AFDM-DIM is improved by 0.25 bits / s / Hz, 0.75 bits / s / Hz, and 1 bit / s / Hz, respectively, compared to AFDM, AFDM-IM, and AFDM-PIM. The results indicate that AFDM-DIM has a higher spectral efficiency than AFDM, AFDM-IM, and AFDM-PIM.

[0167] Using the simulation conditions in Table 2 below, the spectral efficiency of different AFDM systems is compared:

[0168] Table 2

[0169]

[0170] Simulation results are as follows Figure 3 As shown, a comparison chart of the spectral efficiency of AFDM-DIM with AFDM, AFDM-IM, and AFDM-PIM under different numbers of subcarriers per group is presented. The number of subcarriers per group is taken as a base-2 exponent, and the active subcarrier is taken as the number of subcarriers per group minus 1. When the number of subcarriers per group is 4, the spectral efficiency of AFDM-DIM is improved by 0.25 bits / s / Hz, 1 bit / s / Hz, and 1.25 bits / s / Hz, respectively, compared to AFDM, AFDM-IM, and AFDM-PIM. The results show that, under different numbers of subcarriers per group, the spectral efficiency of AFDM-DIM is improved compared to that of AFDM, AFDM-IM, and AFDM-PIM.

[0171] Using the simulation conditions in Table 3 below, the bit error rate performance of AFDM-DIM systems with different channel estimation errors is compared:

[0172] Table 3

[0173]

[0174] Simulation results are as follows Figure 4 As shown, the theoretical and simulated bit error rates (BER) of the AFDM-DIM scheme using maximum likelihood joint signal detection (ML) under different channel estimation errors are presented. It can be observed that under perfect channel state CSI (ε = 0), both the theoretical and simulated curves fit well in the high signal-to-noise ratio (SNR) region. However, as the channel estimation error (i.e., ε) increases, the BER performance of the proposed AFDM-DIM scheme deteriorates, and an error layer appears. The results demonstrate the effectiveness of the theoretical derivation.

[0175] The simulation conditions in Table 4 below are used to compare the bit error rate performance between AFDM-DIM and classical AFDM:

[0176] Table 4

[0177]

[0178] The simulation results, as shown in Figure 5 , demonstrate the bit error rate performance comparison between AFDM-DIM and classical AFDM with maximum likelihood joint signal detection (ML). It can be observed that when BPSK is used in both AFDM-DIM and AFDM, the proposed AFDM-DIM scheme outperforms the AFDM scheme in terms of bit error rate (BER) when considering the multipath effect. The AFDM-DIM scheme achieves about 10 dB gain when the path number is 2 at a BER of 10 -3 -3. The performance enhancement of the proposed AFDM-DIM increases with the increase of the path number. In the AFDM-DIM scheme, the path number of 3 achieves about 2.5 dB gain compared to the path number of 2 at a BER of 10 -3 -3. This is because as the path number increases, AFDM-DIM can obtain diversity gain from more independent paths, thereby significantly reducing the bit error rate (BER) and improving the overall performance of the system.

[0179] The simulation conditions in Table 5 below are used to compare the bit error rate performance of different AFDM systems:

[0180] Table 5

[0181]

[0182] The simulation results, as shown in Figure 6 , demonstrate the BER performance comparison of different AFDM systems with maximum likelihood joint signal detection (ML). Among them, AFDM-PIM transmits additional bits through pre-chirp parameters, and AFDM-IM transmits additional bits through the activation state of subcarriers. In order to ensure fairness in comparison, both AFDM-DIM and AFDM-PIM use BPSK modulation, and AFDM-IM uses QPSK. It can be observed that when the BER is 10 -2 -3, AFDM-DIM achieves about 2 dB gain compared to AFDM-PIM. The experimental results show that the performance of the AFDM-DIM scheme is better than that of the AFDM-PIM and AFDM-IM schemes.

[0183] The simulation conditions in Table 6 below are used to compare the bit error rate performance of the theoretical and simulated AFDM-DIM scheme and other benchmark schemes under imperfect channels:

[0184] Table 6

[0185]

[0186]

[0187] Simulation results are as follows Figure 7 As shown, the bit error rate (BER) performance of the AFDM-DIM scheme employing maximum likelihood joint signal detection (ML) and other benchmark schemes under theoretical and simulated conditions in imperfect channels is illustrated. To ensure fairness in the comparison, AFDM-DIM and AFDM-PIM both use BPSK modulation, while AFDM-IM uses QPSK. It can be seen that, both theoretically and in simulations, the AFDM-DIM scheme exhibits better BER performance than the AFDM-IM and AFDM-PIM schemes. For example, in the simulated curves, at a BER of 10... -3 At that time, AFDM-DIM achieved a signal-to-noise ratio gain of approximately 0.5 dB and 1 dB compared to AFDM-PIM and AFDM-IM, respectively. Under theoretical curves, AFDM-DIM achieved a signal-to-noise ratio gain of 1.2 and 2.5 dB under similar conditions. Experimental results show that, under imperfect channel conditions, the performance of the AFDM-DIM scheme proposed in this invention is still superior to the AFDM-PIM and AFDM-IM schemes.

[0188] Using the simulation conditions in Table 7 below, the bit error rate performance of the proposed low-complexity minimum mean square error-maximum likelihood signal detection (MMSE-ML) and maximum likelihood joint signal detection (ML) is compared:

[0189] Table 7

[0190]

[0191] Simulation results are as follows Figure 8 As shown, this invention proposes a low-complexity minimum mean square error-maximum likelihood signal (MMSE-ML) method. It can be observed that, in order to maintain good performance while reducing complexity, compared to maximum likelihood joint signal detection (ML), at a BER of 10... -4 The marginal performance loss is approximately 2 dB. The complexity of maximum likelihood joint signal detection (ML) is calculated to be... The complexity of low-complexity minimum mean square error-maximum likelihood signal (MMSE-ML) detection is... Where m is the number of active subcarriers. It is the length of the pre-chirped parameter set.

[0192] The application provides an AFDM transmission structure based on double index modulation (DIM).

[0193] Compared with the existing AFDM-IM scheme, only the activation state of the subcarrier is used for information expansion, and the pre-chirp parameter specific to AFDM is not involved; and the AFDM-PIM scheme uses the pre-chirp parameter to transmit information, but does not fully exert the information bearing potential of the activated subcarrier position in the traditional index modulation.

[0194] On the basis of the existing research, the application invents a system that jointly uses the activated subcarrier position and the pre-chirp parameter, so that the activated subcarrier position and the pre-chirp parameter can be fully utilized, thereby significantly improving the spectral efficiency. In addition, the input-output relationship of the system is redesigned for the invented system, and a chirp parameter equivalent channel matrix model is proposed. Based on the model, a maximum likelihood joint signal detection method is designed, which considers the activated subcarrier position combination, the corresponding modulation symbol and the pre-chirp parameter in the search space at the same time, and finds the most possible bit sequence from the global optimal point of view. A low-complexity minimum mean square error-maximum likelihood signal detection algorithm is further proposed, which can significantly reduce the complexity under the premise of ensuring the performance, and improve the practical realizability of the system. The experimental results show that: ① under the same system parameter setting, compared with the AFDM-IM and AFDM-PIM schemes, the AFDM-IM system proposed in the application has better spectral efficiency. ② under the same spectral efficiency condition, compared with the AFDM-IM and AFDM-PIM schemes, the system proposed in the application can be implemented by using a lower-order modulation mode and a smaller number of activated subcarriers, so the application has better bit error rate performance.

Claims

1. A dual-index modulation analog radio frequency division multiplexing (AFDM) communication method, characterized in that, Includes the following steps: Step 1: At the transmitting end, perform serial-to-parallel conversion; Step 2: Based on the input bit stream, jointly select the index position of the AFDM active subcarrier, the modulation bit mapping, and the pre-chirp parameter c2 of the active subcarrier from the predefined mapping table. Based on the invention's dual-index modulation mapping criterion, obtain the mapping symbol u according to the index position of the mapped active subcarrier and the modulation bit, and perform the inverse transformation of the pre-chirp parameter according to the selected pre-chirp parameter to obtain the transmission signal x. Step 3: Perform a chirped inverse Fourier transform on the transmitted signal x to obtain the time-domain signal s; Step 4: Insert a chirped periodic prefix into the time-domain signal s and perform a parallel-to-serial conversion; Step 5: The time-domain signal generated based on the above steps is propagated and transmitted through a time-varying channel; Step 6: Construct the time-domain channel matrix, perform serial-to-parallel transformation on the received time-domain signal, and remove the chirped periodic prefix to obtain the unprefixed time-domain received signal r. Then, perform a chirped Fourier transform on r to obtain the received signal z. Step 7: Construct the chirp parameter equivalent channel matrix and perform channel estimation on it; Step 8: Based on the estimated chirp parameter equivalent channel matrix, use the low-complexity minimum mean square error-maximum likelihood signal detection method or maximum likelihood joint signal detection method to detect the active subcarrier position, active subcarrier modulation bit, and active subcarrier pre-chirp parameter, and perform pre-chirp parameter transformation. Step 9: Recover the bit stream through parallel-to-serial conversion.

2. The dual-index modulation analog AFDM communication method according to claim 1, characterized in that, In step 2, the input bit stream b is divided into g groups, and the total number of subcarriers N is divided into g groups. The number of subcarriers in each group is n = N / g. The mapping table is defined as O = {a, d, p}, where the mapping table contains the active position a of the subcarrier, the modulation data bit d, and the pre-chirp parameter p. The activation position 'a' represents all possible combinations of selecting m active subcarriers from n subcarrier indices; the modulation data bit 'd' includes all possible M... mod The modulation symbol is of order; and the pre-chirp parameter p is all possible ordered combinations of m active subcarrier pre-chirp parameters selected from n pre-chirp parameters; taking the i-th (i = 1, ..., g) group as an example, according to the input b i The bits jointly select the pre-chirp parameters, activation subcarrier state, and data bits from a predefined mapping table.

3. The dual-index modulation analog AFDM communication method according to claim 1, characterized in that, In step 2, the formula for calculating the input bit stream is: in: M represents the floor operation. mod It is an M-ary PSK, where g represents the number of groups, m represents the number of active subcarriers, n represents the number of subcarriers in each group, C(n,m) represents the combination, that is, randomly selecting m elements from n elements, and m! represents the factorial of m.

4. The dual-index modulation analog AFDM communication method according to claim 1, characterized in that, In step 2, the transmitted signal x is obtained by performing an inverse transformation of the selected pre-chirp parameters, as follows: in For the pre-chirp matrix: c 2,k This represents the subcarrier prechirp parameter value for the k-th subcarrier.

5. The dual-index modulation analog AFDM communication method according to claim 1, characterized in that, In step 3, the transmitted signal x undergoes a chirped inverse Fourier transform to obtain the time-domain signal s using the following formula: in, Representing the post-chirp matrix: Where c1 is the post-chirp parameter; F is represented as the discrete Fourier transform matrix:

6. The dual-index modulation analog AFDM communication method according to claim 1, characterized in that, In step 6, the received signal z obtained by performing a chirped Fourier transform on the time-domain signal r can be expressed as: in w represents additive Gaussian noise, P represents the number of multipaths, and h i f i l i Let l represent the channel gain, Doppler shift, and integer delay of the i-th path, respectively; i ∈[0,l max ], where l max This represents the maximum delay.

7. The dual-index modulation analog AFDM communication method according to claim 1, characterized in that, In step 8: The chirp parameter equivalent channel matrix can be expressed as: The permutation matrix is ​​Π: It is an N×N diagonal matrix; It is an N×N diagonal matrix: Where, h i f i l i Let represent the channel gain, Doppler shift, and integer delay of the i-th path, respectively; when 2Nc1 is an integer and N is even, The channel gain of the incomplete channel is expressed as: in φ pair It is independent, ε is the channel error value, ε∈[0,1], and when ε=0 is the perfect channel gain; Representing the post-chirp matrix: Where c1 is the post-chirp parameter; F is represented as the discrete Fourier transform matrix:

8. The dual-index modulation analog AFDM communication method according to claim 1, characterized in that, In step 8, the low-complexity minimum mean square error-maximum likelihood signal detection step is as follows: 1) Obtain the received signal x using a minimum mean square error detector. p : in, I represents the average signal-to-noise ratio. N It is an N×N identity matrix; 2) Based on the estimated signal power |x p | 2 The active subcarrier index position is detected using a greedy algorithm: 3) Based on the index positions of all detected active subcarriers, a maximum likelihood signal detection method is used to determine the active subcarrier modulation bits and pre-chirp parameters: Where d represents all possible values ​​of the modulation bit, and p represents the pre-chirp parameter for all possible values.

9. The dual-index modulation analog AFDM communication method according to claim 1, characterized in that, In step 8, the maximum likelihood joint signal detection method is as follows: Where d represents all possible values ​​of the modulated data bits, p represents all possible values ​​of the pre-chirp parameter, and a represents all possible positions of the activated subcarrier.

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