CN114337751A - Power distribution method of time reversal OFDM multi-user communication system - Google Patents
Power distribution method of time reversal OFDM multi-user communication system Download PDFInfo
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Abstract
The invention discloses a power distribution method of a time reversal OFDM multi-user communication system. Aiming at a computing system and a speed of a time reversal OFDM multi-user communication system, the optimal distribution method of the user signal transmission power is carried out with the goal of maximizing the system and the speed. Firstly, a mathematical model of the joint distribution of the power of a plurality of users under the constraint condition of the total transmission power is given, the multi-objective joint optimization in the model is non-convex optimization, and then an improved iterative water-filling power distribution algorithm is given to jointly optimize the transmission power of all the users. Compared with an average power distribution method, the method provided by the invention can obtain a higher system and rate.
Description
Technical Field
The invention relates to the field of information communication, in particular to a method for distributing user signal transmission power in a time reversal OFDM multi-user communication system.
Background
Time Reversal (TR) can utilize a rich multipath radio propagation environment to generate a space-Time resonance effect, so-called focusing effect, thereby improving received signal strength while reducing interference. In the TR communication process, a receiving end firstly sends a pilot frequency pulse to a sending end, and the receiving end estimates the pulse Response (CIR) of a Channel according to a received signal; and then the sending end performs time reversal and conjugation processing on the estimated channel impulse response to obtain a time reversal waveform, and finally the time reversal waveform is convoluted with the sending signal and then sent to the receiving end through a channel. Based on the channel reciprocity, TR essentially uses multipath channel as a matched filter, and the document [ Wang beibeibeibeibeibei, Wu Yongle, Han Feng, et al green wireless Communications: a time-reversed parallel [ J ]. IEEE Journal on Selected Areas in Communications,2011,29(8):1698-1710.doi:10.1109/jsac.2011.110918 ] proves that the energy of the signal after multipath transmission focuses on a specific time domain and space domain due to the inherent characteristics of CIR, i.e. TR can collect the energy of the signal from the surrounding environment with extremely low complexity by using multipath propagation.
In a wireless communication system, Inter Symbol Interference (ISI) and Inter User Interference (IUI) deteriorate Quality of Service (QoS) of each User. Due to the time focusing characteristic of TR, the energy leakage between symbols is reduced, and thus the ISI effect can be significantly reduced, which makes the receiver simple in structure and does not require a high complexity equalizer. In addition to this, the spatial focusing effect suppression of TR focuses most of the Signal energy at the intended user, which means that the Signal to Interference plus Noise Ratio (SINR) of the receiver can be improved. The document [ Emami M, Vu M, Handen J, et al. matched filtering with Rate Back-off for low complexity communication in large delay channels [ C ]// Conference Record of the third-Eighth amplitude satellite Conference Signal, Systems and Computers,2004.Pacific Grove, CA, USA: IEEE Press 2004:218-222.doi:10.1109/ACSSC.2004.1399123 ] demonstrates that in a TR system, the SINR can be improved by increasing the Rate Back-off Factor (BOF), BOF is defined as the Ratio of the sampling Rate to the symbol Rate. Where the sample rate is the sample rate of the discrete signal and the symbol rate is the transmission rate of the symbols carrying the information over the channel. The maximum sample rate is determined by the nyquist criterion, and typically a sample corresponds to a symbol, when the symbol rate is the same as the sample rate. If not every sample corresponds to a symbol, the symbol rate is lower than the sample rate, i.e. the case where the BOF is greater than 1. When the BOF is larger than 1, the symbol rate is lower than the highest rate under the bandwidth limitation, the frequency band utilization rate is reduced, but the intersymbol interference can be reduced.
The document Lei Weijia, Yao Li, Performance analysis of time reversal communication systems [ J ]. IEEE Communications Letters,2019,23(4):680-683 ] deduces the probability density function and the cumulative distribution function of the Signal-to-noise ratio (SNR) of the receiving end in the TR system, analyzes the traversal capacity, the interruption probability and the bit error rate under BPSK modulation, and explains that ISI is reduced along with the increase of the up-sampling factor. The approximate closed expression of ISI power in a time reversal system is deduced in a document [ Viteri-Mera C A, Teixeira F L. equalized time reversed sample channels for frequency-selective index MISO channels [ J ]. IEEE Access,2017,5:3944-3957.doi:10.1109/ACCESS.2017.2682160 ], the space focusing characteristic and the time compression performance of the time reversal beam forming technology are analyzed, and a simulation result shows that ISI is eliminated by the equalized time reversal technology, so that the system can obtain better bit error rate performance. In a multi-user system, due to different path channel characteristics of different users, time reversal transmission can utilize multipath as a way of distinguishing different users, and further time reversal can be introduced into a multiple access system. The document [ Han F, Yang Y, Wang B, et al.time-reverse Division Multiple Access [ J ]. IEEE Transactions on Communications,2012,60(7):1953-1965.doi:10.1109/tcomm.2012.051012.110531.] studies a multi-user communication system based on Time Reversal, proposes a new radio channel Access method, i.e. Time-reverse Division Multiple Access (TRDMA), which uses a TR structure in a multi-user downlink system under a large delay spread channel, signals of different users are distinguished by multipath, and downlink multi-user transmission is realized by using a multipath channel through a Time Reversal technique, so that ISI and IUI can be reduced, improvement is achieved, and system performance indexes such as SINR, achievable system rate, interrupt rate and the like of the TRDMA system are studied. The performance of a multi-user time reversal communication system is evaluated by a practical measurement mode in a document [ Nguyen H T, Kovcs I Z, Eggers P C F.A time reversal transmission approach for multiuser UWB communications [ J ]. IEEE Transactions on Antennas and Propagation,2006,54:3216-3224.doi:10.1109/TAP.2006.883959 ], and experimental results show that the spatial focusing effect of time reversal transmission can reduce the BER of the system and reduce the requirement on signal transmission power. The document [ Chen Y, Yang Y, Han F, et al, time-reverse wireless communications [ J ]. IEEE Signal Processing Letters,2013,20(12):1219-1222.doi:10.1109/LSP.2013.2285467 ] studies the achievable rate and computational complexity of TRDMA systems, and the results show that when the bandwidth is large enough, the TRDMA system can obtain a higher achievable rate and lower computational complexity than the OFDM system. Further research on TRDMA systems is carried out in the literature [ Han Y, Chen Y, Wang B, et, al.Time-retransmission large multi-path effect: a single-antenna "massive MIMO" solution [ J ]. IEEE Transactions on Communications,2016,64(8):3382-3394.doi:10.1109/TCOMM.2016.2584051 ], and the results show that the time reversal technique can be used to convert the multipath components in the wireless channel into virtual transmitting antennas, so that the characteristics similar to MIMO transmission can be obtained in the case that the transmitting end is only provided with a single antenna. The document [ Yang Y H, Wang B, Lin, et al, near-optimal waveform design for time-reversal multi-user downlink systems [ J ]. IEEE Transactions on Communications,2013,12(1):346-357.doi:10.1109/TWC.2012.120312.120572 ] researches the power allocation and waveform design optimization problem for maximizing the sum rate in the time domain TR multi-user downlink system, jointly optimizes the transmission waveform and power allocation, and can obtain better system performance. The problem of optimizing the design of a power waveform which enables the total root mean square error of a received signal to be minimum in a time domain TR multi-user downlink system is researched by a document [ Yang Y H, Liu K J R.wave form design with interference pre-cancellation and time-conversion systems [ J ]. IEEE Transactions on Wireless Communications,2016,15(5):3643-3654.doi:10.1109/TWC.2016.2524526 ], and a waveform design with interference pre-cancellation is provided, and simulation results show that the method has obvious performance improvement compared with the traditional waveform design method.
The TR transmission can be implemented in the time domain and also in the frequency domain, and most of the current research on TR is directed to a TR system implemented in the time domain. The document Dubois T, Helard M, Crussiere M, et al. Performance of time inverting technique for MISO-OFDM systems [ J ]. Eurasip Journal on Wireless Communications & network, 2013(1):1-16.doi:10.1109/VTCSpring.2015.7146002 ] demonstrates that the same effect as the time domain TR preprocessing can also be achieved by preprocessing the signal in the frequency domain. Orthogonal Frequency Division Multiplexing (OFDM) is a key technology in 4 th and 5 th generation mobile communication systems, and will also be a key technology of new generation mobile communication, and applying TR technology to OFDM system has clear practical meaning, and TR preprocessing in Frequency domain is more suitable for OFDM system. The frequency domain TR pre-processing procedure is the product of each sub-channel transmission signal and the conjugate of the sub-channel frequency response, the computational complexity is low, and this pre-processing is equivalent to convolving the transmission signal with the impulse response of the TR pre-processing filter in the time domain according to the fourier transform property. According to the literature [ Nguyen T, Monfared S, Determe J, et al. Performance analysis of frequency domain preceding time-conversion MISO OFDM systems [ J ]. IEEE Communications Letters,2019,24(1):48-51.doi:10.1109/LCOMM.2019.2949556 ], a closed expression of the root mean square error of a received Signal of a frequency domain TR preprocessing system is deduced, and the change condition of the root mean square error when the BOF changes is analyzed, theoretical analysis and simulation results show that similar to the time domain TR system, the increase of the BOF can also reduce the root mean square error of the Signal and improve the Signal-to-Noise Ratio (SNR) of the system. The document Golstein S, Nguyen T, Horlin F, et al, physical layer security in frequency-domain time-reverse SISO OFDM communication [ C ]//2020International Conference on Computing, Networking and Communications (ICNC), Big Island, HI, USA, IEEE Press 2020:222-227.doi:10.1109/ICNC47757.2020.9049811 ] researches the physical layer security in frequency domain TR precoding system, in order to make the security rate of the system larger, an artificial noise suitable for the system is designed, the result shows that the proposed scheme can improve the physical layer security. For the TR-OFDM system, when the BOF is greater than 1, the focusing effect of TR can increase SINR of a desired receiver, reduce signal leakage at an undesired receiver, and thus can better exert the advantages of TR-OFDM in a multi-user system. In a frequency domain TR multi-user system, an average distribution method can be adopted to distribute power to each signal of a user, but the average power distribution cannot obtain the best system performance, so that the power distribution of the user signals can be optimized, and the better system performance is obtained.
Disclosure of Invention
The invention aims to provide a user signal transmission power optimal distribution method for enhancing system and rate performance under the condition of meeting the total transmission power constraint of each user in a time reversal OFDM multi-user communication system.
In order to achieve the purpose, the invention adopts the following technical scheme: on the basis of a conventional Time Reversal (TR) OFDM multi-user communication system, a system and a rate formula are deduced, an optimization problem of multi-user power joint distribution with the aim of maximizing the system and the rate is constructed, then a solution of the power distribution of users is obtained by utilizing a KKT condition, and finally the transmission power of all users is jointly optimized by utilizing an iterative algorithm.
(1) Analyzing the transmission process of the signals, constructing a communication system model, and obtaining a user receiving signal-to-interference-and-noise ratio according to the constructed system model so as to obtain a system and a rate; the communication system model is based on a conventional time reversal OFDM multi-user communication system, a sending end and a receiving end are both provided with a single antenna, and signals sent to a plurality of users by the sending end pass through a TR pre-coding matrix and then are distributed to OFDM sub-channels for transmission.
(2) And taking the sum rate maximization as an optimization target, and giving a mathematical model of the joint distribution of the power of the multiple users under the constraint condition of the total transmission power.
The received signal-to-interference-and-noise ratio is:
where K is the number of users, pk,mThe power of symbol m, allocated to user k by the transmitting end, D is the rate backoff factor,
is the variance of the noise of the channel,H k,mas a diagonal matrixH kThe m-th diagonal element of (a),H kis a frequency domain channel matrix expressed as
Wherein Q is the subcarrier number and diagonal element of OFDM systemH k,qQ is a frequency domain channel coefficient, denoted as Q1, 2
hk,lIs the coefficient of the L-th path of the multipath channel of user k, where L is the length of the channel impulse response;
matrix array
Is composed ofH kIn conjugated form, i.e.
The system and rate are:
in the formula, M represents the number of symbols transmitted to each user.
(3) And obtaining a solution of the power allocation of the user by using a Karush-Kuhn-Tucker (KKT) condition.
(4) An iterative algorithm is used to jointly optimize the transmit power of all users.
In the process of optimally distributing the user signal transmission power, the invention distributes the power according to the channel state information of the channel. The invention has lower optimization complexity because only the user signal transmission power distribution is optimized. And simulation experiments show that the method provided by the invention can obviously obtain a system and a rate higher than that of an average power distribution method. The invention improves the sum rate performance of the system under the condition of lower optimization complexity.
Drawings
FIG. 1 is a communication system model of the present invention;
fig. 2 is a schematic diagram of subcarrier utilization for user k;
FIG. 3 is an equivalent communication system model of the present invention;
FIG. 4 is a comparison of the system and rate of the present invention with average power distribution and a conventional iterative waterflooding method;
FIG. 5 is a system and rate versus iteration number for the present invention and a conventional iterative waterflooding method;
FIG. 6 is a graph of the effect of a rate backoff factor on the system and rate;
fig. 7 shows the effect of the number of users on the system and rate.
Detailed Description
The symbols involved in the present invention are annotated as follows: underlined letters denote frequency domain symbols, and not underlined time domain symbols; lower case bold letters represent vectors, upper case bold letters represent matrices; white letters represent scalars; | -, | | - |, (-))*And (·)HRespectively, absolute or modulus, 2 norm, conjugate, and conjugate transpose.
The model of the TR-OFDM multi-user communication system is shown in fig. 1, where the system has K users, and both the transmitting end and the receiving end are equipped with a single antenna. The sending end sends mutually independent data vectors to K users simultaneously, wherein the data vectors sent to the users K are recorded asx k，k＝1,2,...,K。x kBy M data symbolsx k,mComposition, M ═ 1, 2., M,namely, it isx k＝[x k,1,x k,2,...,x k,M]. First, a spreading matrix in which data symbols are sized QxMSAnd spreading, wherein the purpose of spreading is to distribute the data symbols to the OFDM subcarriers. Q is the number of OFDM system subcarriers, and Q is DM. After spreading, each data symbol is allocated to D different subcarriers at an interval M, where D is a rate back-off factor, which corresponds to an upsampling factor in the time domain TR system.SIs formed by connecting D M diagonal matrixes in series, and the diagonal elements of the diagonal matrixes have equivalent values
This is to avoid allocating the same data symbols to different OFDM sub-carriers, which results in a high peak-to-average power ratio, and to ensure that the spreading process does not change the signal power, i.e. the signal power is not changedS H S＝I M，I MRepresenting an M × M unit matrix.SIs shown as
By spreading the matrix in a TR-OFDM systemSThe spreading is equivalent to upsampling in the time domain TR system. The subcarrier utilization diagram for user k after spreading is shown in fig. 2. The symbols after spreading need to be multiplied by a precoding matrix for precoding before transmission, which is equivalent to pre-filtering in a time domain TR system. The precoded symbols are subjected to Inverse Fast Fourier Transform (IFFT) to obtain time domain signals, and cyclic prefixes are added to the time domain signals to transmit the time domain signals. Fast Fourier Transform (FFT) is performed at the receiving end and then converted into a frequency domain signal. The multipath channel between the transmitting end and the user k is a linear system, and the period impulse response can be expressed as
Wherein h isk,lIs the coefficient of the L-th path, i.e. the strength of the L pulses in the impulse response, L-0, 1The number of paths of the channel. The receiver performs FFT on the received signal to obtain a frequency domain symbol. IFFT, multipath channel and FFT can be combined together to be equivalent to Q frequency domain parallel channels, and the channel coefficient is
The frequency domain symbol output by the channel is the frequency domain symbol and the diagonal matrix which are sentH kMultiplication.H kThe qth diagonal element ofH k,qI.e. by
Accordingly, the system model may be equivalent to fig. 3. Whereinv k＝[v k(1),v k(2),...,v k(Q)]Is an Additive White Gaussian Noise (AWGN) sequence in frequency domain and an AWGN Noise sequence v in time domainkThe fourier transform of (a) the signal,v kand vkHave the same variance
The pre-filter in time domain TR system is the conjugate inversion of channel impulse response, and the transmitted signal passes through the pre-filter and is frequency domain symbol and pre-coding matrix in the corresponding frequency domain
Multiplication.
Is composed of
The sequence received by the user needs to be compared withS HMultiplying and de-spreading, wherein the de-spread signal of user k is
The received SINR of user k is the ratio of the power of the useful signal received by the user to the sum of the power of the interference between users and the power of the channel noise, i.e.
Wherein p isk,mThe power of symbol m allocated to user k for the transmitting end, D is the size of the rate backoff factor,
is the variance of the noise of the channel,H k,mas a diagonal matrixH kThe mth diagonal element of (1). And the sum rate is a commonly used index for evaluating the transmission performance of the system, and the invention optimizes the signal power distribution by taking the maximization of the system and the rate as targets. System and rate of
In the optimization process of power allocation, the sum of the powers allocated to the signals of the users is ensured to be less than or equal to the total transmission power of the users, that is to say
In the formula PkIs the total transmit power of user k. The optimization problem is constructed as
The multi-objective joint optimization is non-convex optimization, but for the user k, if the power allocation of the other users at the moment is fixed, the optimal solution of the power allocation of the user k meets the KKT condition. Construct a Lagrangian function of
Wherein λ ═ λ1,λ2,...,λK]TNon-negative Lagrange multiplier vector, let Λ (p, λ) to pk,mDerivative and equal to 0, then the optimal p and λ satisfy the following equations
Wherein, tk,mIncludes the interference caused by the user k to other users, and is defined as
Solve the power allocation of user k as
Wherein [ x ]]+The expression is taken to be the maximum value of both 0 and x, and x is the content in parentheses in the above formula. And because the power constraint condition is satisfied, the method comprises
Order to
The transmitting end distributes signals on sub-channels with better channel conditionsHigh power, when causing excessive interference to other users, tk,mThe power allocated to the signal is reduced. Lambda [ alpha ]kCan be found by bisection when λ of the power constraint equation is satisfiedkWhen it is not positive, then λkIs 0. And solving the power distribution of all users by adopting an iterative algorithm. Allocating an initial power value for each signal of each user, and obtaining t based on the assigned initial value, wherein t is tk,mI.e. t ═ tk,mK1, 2, …, K, M1, 2, …, M. Starting from user 1, since t and the power allocations of other users are fixed, the power allocation of user 1 can be obtained; then optimizing the power allocation of user 2, and using the updated p in solving1,1,p1,2,...,p1,MThe value, while t and the power allocation from user 3 are still the previous values; the power distribution of other users is updated similarly to obtain updated p, where p is pk,mI.e. p ═ pk,mK1, 2, …, K, M1, 2, …, M. After updating p, updating t, repeating the above process, iteratively updating the power distribution of each user until the relative difference of the power distribution obtained by two successive iterations is less than a preset value or reaches a preset iteration number, and finally obtaining the optimal solution p of the power distribution of each signal of each user*. A specific iterative algorithm is shown in Table 1, where n denotes the number of iterations, τ1To control the relative difference at the end of the iteration, i.e. the convergence factor.
TABLE 1 iterative Algorithm
The present invention will be described in further detail below with reference to the accompanying drawings. The simulation results for the system and rate given in each figure are the average for a 1-ten thousand channel realization. Unless otherwise indicated, the parameter settings in the simulation are as follows: a SISO OFDM system is used with a sub-carrier number Q1024. The channel is Rayleigh fading channel, the total bandwidth B of the channel is 15.36MHz, the channel resolvable path number L is 10, the impulse response coefficient of the channel is zero by following the average valueIs randomly distributed. The variance of the channel is
Wherein sigma T10/B is the root mean square delay of the path, T s1/B is the sampling period. Etak＝η0(dk/d0)-cIs the large scale fading coefficient of the channel. Where c is 4, η is the path loss exponent0For transmission losses at a reference distance, d010m is a reference distance, dkFor the distance of the sender from user k, let dkIs random and is between 100m and 2000 m. Setting eta0＝10-5Noise power of the channel is set to 1 × 10-11W is added. The maximum iteration number in the iterative algorithm for solving the power distribution is set as 100, and the convergence factor tau1＝1×10-5. Total transmission power of system is P, total transmission power of each user is Pk＝P/K。
Fig. 4 shows simulation results of the change of the system and rate with the increase of the transmission power when the number of users K is 4, BOF D is 1, and the number of paths L is 10. The result of improving the iterative water filling algorithm in the figure is the result of the optimal allocation method of the user signal transmission power provided by the invention, and simultaneously, the simulation results of the traditional iterative water filling power allocation method and the system and rate of average power allocation are provided. The difference of the traditional iteration water filling algorithm is tk,mTo assign a power to 0, i.e. each signal only needs to maximize its rate regardless of interference to other users, while the average power assignment assigns the same power, i.e. p, to all signals of all users regardless of channel conditionsk,m＝PkM, M ═ 1, 2. The sum rate in the figure is an average value of instantaneous sum rates in all channel states. As can be seen from the figure, as the transmission power increases, the system and rate increase and then gradually approach an upper limit. This is because when the transmission power is small, the interference power is small relative to the channel noise power, the total transmission power increases, and the rate increases accordingly. When the transmit power is increased to a certain extent, the interference power will be significantly higher than the channel noise power. Since signal power and interference power are synchronized with transmission powerAnd at this point there is no longer a significant increase in transmit power and rate. As can be seen from the figure, the system and rate of the average power allocation are the lowest because when the average power allocation is adopted, all signals are allocated with the same power, while different signals are allocated to different subcarriers and experience different subchannel gains, and if the same power is allocated to the signals on the subchannels with low channel gains and high channel gains, the system performance is definitely not the best. When the traditional iterative water filling algorithm is adopted, each user only considers that the own rate is the highest when optimizing the signal power distribution of the user, and ignores the interference brought to other users, so that the larger interference is often caused to other users, and the best rate performance cannot be realized. The improved iterative water injection power distribution algorithm provided by the invention not only maximizes the speed of the algorithm, but also maximizes the tk,mThe presence of (a) reduces interference to other users and thus most efficiently increases system and rate. As shown by simulation results, the sum rate of the traditional iteration water filling algorithm can only be improved by 8%, and the sum rate of the improved iteration water filling algorithm is improved by 13.8%, so that the improved iteration water filling algorithm provided by the invention is proved to have better performance.
Fig. 5 shows the relationship between the system and the rate of the power allocation algorithm and the conventional iterative water filling algorithm and the number of iterations when the number of users K is 4, BOF D is 1, the number of paths L is 10, and the transmission power is 30 dBm. The convergence of the two algorithms can be seen from the graph, and the improved iterative water-filling algorithm provided by the invention has higher convergence speed and better solution when converging. The traditional iteration water filling algorithm can be converged when the iteration times reach 6, and the iteration water filling algorithm is converged when the iteration times reach 4 and 5, which proves that the improved iteration water filling algorithm has better convergence, so that the iteration time is only 4-6 without waiting for complete convergence in practical application.
Fig. 6 shows simulation results of the system and rate under different BOFs as the transmission power increases when the number of users K is 4 and the number of paths L is 10. Simulation results show that as the BOF increases, the sum rate of the system decreases, because increasing the BOF can reduce the IUI, but at the same time, the increase of the BOF reduces the number of data symbols that can be transmitted, which also results in a decrease in the symbol rate, and the decrease of the IUI is not enough to compensate for the large decrease of the symbol rate, so the sum rate of the system decreases. Fig. 7(a) and (b) show the system and rate for different numbers of users as the transmission power increases when the BOF D is 1 and the number of paths L is 10 and 20, respectively. It can be seen that when the transmission power is smaller, as the number of users increases, the system and the rate increase, which indicates that the frequency domain TR precoding technique can significantly reduce the IUI in the multi-user system, but when the transmission power is larger, the noise power is relatively small and can be ignored, the interference power increases in synchronization with the transmission power, the interference power of more users is larger, therefore, the SINR of multiple users is smaller, and the system and the rate are also lower. That is, as the transmission power increases, the curves of K2 and K4 intersect, and the sum rate of the number of users exceeds the number of users. And, as can be seen from fig. 7(a) and (b), the number of paths increases, and the system and the rate increase, which shows that the frequency domain TR is suitable for a rich multipath environment, and can effectively improve the performance of the communication system in the multipath environment, and the larger the number of paths, the larger the obtained focusing gain.
Claims (7)
1. A power distribution method of a time reversal OFDM multi-user communication system is characterized in that: the method comprises the following steps:
(1) constructing a communication system model, and obtaining a user receiving signal-to-interference-and-noise ratio according to the constructed system model so as to obtain a system and a rate;
(2) taking the sum rate maximization as an optimization target, and giving a mathematical model of the joint distribution of the power of a plurality of users under the constraint condition of the total transmission power;
(3) obtaining a solution of power allocation of a user by using a KKT condition;
(4) an iterative algorithm is used to jointly optimize the transmit power of all users.
2. The power allocation method of the time-reversal OFDM multi-user communication system according to claim 1, wherein: the communication system model is based on a conventional time reversal OFDM multi-user communication system, a sending end and a receiving end are both provided with a single antenna, and signals sent to a plurality of users by the sending end pass through a TR pre-coding matrix and then are distributed to OFDM sub-channels for transmission.
3. The power allocation method of the time-reversal OFDM multi-user communication system according to claim 1 or 2, wherein: the user receiving signal-to-interference-and-noise ratio and the system and rate are respectively as follows:
the received signal-to-interference-and-noise ratio is:
where K is the number of users, pk,mThe power of symbol m, allocated to user k by the transmitting end, D is the rate backoff factor,
is the variance of the noise of the channel,H k,mas a diagonal matrixH kThe m-th diagonal element of (a),H kis a frequency domain channel matrix expressed as
Wherein Q is the subcarrier number and diagonal element of OFDM systemH k,qQ is a frequency domain channel coefficient, denoted as Q1, 2
hk,lIs the coefficient of the L-th path of the multipath channel of user k, where L is the length of the channel impulse response;
matrix array
Is composed ofH kIn conjugated form, i.e.
The system and rate are:
in the formula, M represents the number of symbols transmitted to each user.
4. The power allocation method of the time-reversal OFDM multi-user communication system according to claim 3, wherein: the mathematical model in step (2) takes the sum of powers of all signals allocated to the user less than or equal to the total power of the user's transmission as a constraint condition, and takes the system and the rate as an optimization target, specifically:
the transmit power constraints are:
in the formula PkTotal transmit power for user k;
the optimization problem is structured as follows:
5. the power allocation method of the time-reversal OFDM multi-user communication system according to claim 4, wherein: the obtaining of the solution of the power allocation of the given user by using the KKT condition in step (3) specifically includes: when optimizing the power distribution of user k, the power distribution of user k meets the KKT condition because the power distribution of other users is fixed, and the lagrangian function of the optimization problem meeting the power constraint is constructed as
Wherein λ ═ λ1,λ2,...,λK]TNon-negative Lagrange multiplier vector, let Λ (p, λ) to pk,mDerivative and equal to 0, then the optimal p and λ satisfy the following equations
Wherein, tk,mIncludes the interference caused by the user k to other users, and is defined as
The power allocation is solved into
Wherein [ x ]]+Representing taking the maximum of both 0 and x.
6. The power allocation method of the time-reversal OFDM multi-user communication system according to claim 1, wherein: the iterative algorithm in the step (4) is specifically as follows: allocating an initial power value to each signal of each user, and based on the assigned initial value, obtaining t, starting from user 1, and obtaining the power allocation of user 1 because t and the power allocation of other users are fixed; then optimizing the power allocation of user 2, and using the updated p in solving1,1,p1,2,...,p1,MThe value, while t and the power allocation from user 3 are still the previous values; the power distribution of other users is updated similarly, after updating p, t is updated, the process is repeated, the power distribution of each user is updated iteratively until the power distribution obtained by two iterations has a small difference or reaches a preset iteration number, and finally the optimal solution p of the power distribution of each signal of each user is obtained*。
7. A computer-readable storage medium storing a computer program, characterized in that: the computer program, when executed, may implement the power distribution method of any of claims 1-6.
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