CN114337751A - A power allocation method for time-reversed OFDM multi-user communication system - Google Patents

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

A power allocation method for time-reversed OFDM multi-user communication system

technical field

The invention relates to the field of information communication, in particular to a method for allocating user signal transmission power in a time-reversed OFDM multi-user communication system.

Background technique

Time Reversal (TR) can take advantage of the rich multipath radio propagation environment to generate space-time resonance effects, the so-called focusing effects, thereby increasing received signal strength while reducing interference. In the TR communication process, the receiving end first sends pilot pulses to the transmitting end, and the receiving end estimates the channel impulse response (CIR) according to the received signal; then the transmitting end performs time inversion on the estimated channel impulse response. The time-reversed waveform is obtained by the sum conjugation process, and finally it is convolved with the transmitted signal and sent to the receiving end through the channel. According to the channel reciprocity, TR essentially uses the multipath channel as a matched filter. The literature [Wang Beibei, Wu Yongle, HanFeng, et al. Green wireless communications: a time-reversal paradigm [J]. IEEE Journal on Selected Areas in Communications , 2011, 29(8):1698-1710.doi:10.1109/JSAC.2011.110918.] proved that due to the inherent characteristics of CIR, after multipath transmission, the energy of the signal is focused on a specific time domain and space domain, that is, TR can use Multipath propagation harvests the energy of a signal from the surrounding environment with very low complexity.

In a wireless communication system, Inter Symbol Interference (ISI) and Inter User Interference (IUI) degrade the Quality of Service (QoS) of each user. Since TR has a time-focusing characteristic, which reduces the energy leakage between symbols, the influence of ISI can be significantly reduced, which makes the receiver structure simple and does not require a high-complexity equalizer. In addition, the suppression of the spatial focusing effect 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. Literature [Emami M, Vu M, Hansen J, et al. Matched filtering with rate back-off for low complexity communications invery large delay spread channels [C] // Conference Record of the Thirty-Eighth Asilomar Conference on Signals, Systems and Computers, 2004 .Pacific Grove,CA,USA:IEEE Press 2004:218-222.doi:10.1109/ACSSC.2004.1399123.] It is proved that in the TR system, the received signal can be improved by increasing the Rate Back-off Factor (BOF). Signal to Interference plus Noise Ratio (SINR), BOF is defined as the ratio of the sampling rate to the symbol rate. Here, the sampling rate is the sampling rate of the discrete signal, and the symbol rate is the transmission rate of the symbols carrying information on the channel. The maximum sample rate is determined by the Nyquist criterion, usually one sample corresponds to one symbol, and the symbol rate is the same as the sample rate. If each sample does not correspond to a symbol, the symbol rate is lower than the sample rate, ie the BOF is greater than 1. When the BOF is greater than 1, the symbol rate is lower than the maximum rate under the bandwidth limitation, and the frequency band utilization rate is reduced, but the inter-symbol interference can be alleviated.

The literature [Lei Weijia, Yao Li. Performance analysis of time reversalcommunication systems [J]. IEEE Communications Letters, 2019, 23(4): 680-683.] deduces the signal-to-noise ratio (Signal-to-noise ratio) of the receiver in the TR system. ratio, SNR), analyze the ergodic capacity, outage probability and bit error rate under BPSK modulation, and show that the ISI decreases with the increase of the upsampling factor. The literature [Viteri-Mera C A, Teixeira F L. Equalized time reversal beamforming for frequency-selective indoor MISO channels[J]. IEEE Access, 2017, 5:3944-3957.doi:10.1109/ACCESS.2017.2682160.] derived time reversal The approximate closed-form expression of the ISI power in the system, the spatial focusing characteristics and time compression performance of the time-reversal beamforming technology are analyzed, and the simulation results show that the system can obtain a better bit error rate by using the balanced time-reversal technology to eliminate ISI performance. In a multi-user system, due to the different path and channel characteristics of different users, time reversal transmission can use multipath as a way to distinguish different users, and then time reversal can be introduced into the multiple access system. Literature [Han F, Yang Y, Wang B, et al. Time-reversaldivision multiple access over multipath channels [J]. IEEE Transactions on Communications, 2012, 60(7): 1953-1965. doi: 10.1109/TCOMM.2012.051012.110531 .] studied the multi-user communication system based on time reversal, and proposed a new wireless channel access method, namely Time Reversal Division Multiple Access (TRDMA), which expands the channel in large delay. The TR structure is used in the multi-user downlink system under the following conditions. The signals of different users are distinguished by multi-path. Through the time reversal technology, the multi-path channel is used to realize the downlink multi-user transmission, which can reduce the ISI and IUI and improve the SINR. The TRDMA system is also studied. SINR, achievable system rate, and achievable interrupt rate. The literature [Nguyen H T, Kovcs I Z, EggersP 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.] passed the actual measurement The performance of the multi-user time-reversal communication system is evaluated by the method. The experimental results show that the spatial focusing effect of time-reversal transmission can reduce the BER of the system and reduce the requirement for signal transmission power. Literature [Chen Y, Yang Y, Han F, et al. Time-reversal wideband communications [J]. IEEE Signal Processing Letters, 2013, 20(12): 1219-1222. doi: 10.1109/LSP.2013.2285467.] studied The achievable rate and computational complexity of the TRDMA system, the results show that when the bandwidth is large enough, the TRDMA system can obtain a higher achievable rate than the OFDM system, and the computational complexity is lower. Literature [Han Y, Chen Y, Wang B, et, al. Time-reversal massive multipath effect: a single-antenna “massive MIMO” solution [J]. IEEE Transactions on Communications, 2016, 64(8): 3382-3394 .doi:10.1109/TCOMM.2016.2584051.] Further research on the TRDMA system shows that the time reversal technology can be used to convert the multipath components in the wireless channel into virtual transmit antennas, so that only a single antenna is equipped at the transmit end. In this case, properties similar to MIMO transmission are obtained. Literature [Yang Y H, Wang B, Lin, etal.Near-optimal waveform design for sum rate optimization in time-reversalmultiuser downlink systems[J].IEEE Transactions on Communications,2013,12(1):346-357.doi:10.1109 /TWC.2012.120312.120572.] studied the optimization problem of power allocation and waveform design for maximum sum rate in time-domain TR multi-user downlink system, and jointly optimized the transmission waveform and power allocation to obtain better system performance. Literature [Yang Y H, Liu K J R.Waveform design with interference pre-cancellation beyond time-reversal systems[J].IEEE Transactions on WirelessCommunications,2016,15(5):3643-3654.doi:10.1109/TWC.2016.2524526.] The optimization problem of power waveform design to minimize the total root mean square error of the received signal in the time-domain TR multi-user downlink system is studied, and a waveform design with interference pre-cancellation is proposed. The simulation results show that this method is better than the traditional waveform design method. There are significant performance improvements.

TR transmission can be implemented in the time domain or in the frequency domain. Most of the current research on TR is aimed at TR systems implemented in the time domain. Literature [Dubois T, Helard M, Crussiere M, et al.Performance of time reversal precoding technique for MISO-OFDM systems[J].Eurasip Journal onWireless Communications&Networking,2013,2013(1):1-16.doi:10.1109/VTCSpring. 2015.7146002.] demonstrated that by preprocessing the signal in the frequency domain, the same effect as TR preprocessing in the time domain can also be achieved. Orthogonal Frequency Division Multiplexing (OFDM) is the key technology in the 4th and 5th generation mobile communication systems, and will also be the key technology in the new generation of mobile communication. clear practical significance, while TR preprocessing in the frequency domain is more suitable for OFDM systems. The frequency domain TR preprocessing process is the product of the conjugate of each subchannel transmission signal and the subchannel frequency response, and the computational complexity is low. According to the Fourier transform properties, this preprocessing is the same as the time domain. Convolution of the impulse response of the filter is equivalent. Literature [Nguyen T, Monfared S, Determe J, et al.Performance analysis of frequency domain precoding time-reversal MISO OFDM systems[J].IEEECommunications Letters,2019,24(1):48-51.doi:10.1109/LCOMM.2019.2949556 .] The closed-form expression of the root mean square error of the received signal of the frequency domain TR preprocessing system is derived, and the change of the root mean square error when the BOF changes is analyzed. The theoretical analysis and simulation results show that it is similar to the time domain TR system. , increasing the BOF can also reduce the root mean square error of the signal and improve the signal to noise ratio (Signal to Noise Ratio, SNR) of the system. Literature [Golstein S, Nguyen T, Horlin F, et al. Physical layer security in frequency-domain time-reversal SISOOFDM communication [C]//2020 International Conference on Computing, Networking and Communications (ICNC), Big Island, HI, USA: IEEE Press 2020:222-227.doi:10.1109/ICNC47757.2020.9049811.] studied the physical layer security in the frequency domain TR precoding system, and designed an artificial noise suitable for this system in order to make the security rate of the system larger , the results show 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 improve the SINR of the desired receiver and reduce the signal leakage at the undesired receiver, so the TR-OFDM can be better used in the multi-user system. Advantage. In the frequency domain TR multi-user system, the power of each signal of the user can be allocated by the method of average allocation, but the average power allocation often cannot obtain the best system performance, so the power allocation of the user signals can be optimized to obtain better performance. system performance.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a time-reversed OFDM multi-user communication system, under the condition of satisfying the total transmission power constraints of each user, to enhance the system and rate performance. power to maximize system and speed.

In order to achieve the above object, the present invention adopts the following technical scheme: on the basis of a conventional time reversal (Time Reversal, TR) OFDM multi-user communication system, the system and rate formulas are deduced, and a plurality of system and rate formulas are constructed to maximize the system and rate Then use the KKT condition to obtain the solution of the user's power allocation, and finally use the iterative algorithm to jointly optimize the transmit power of all users.

(1) Analyze the transmission process of the signal, build a communication system model, and obtain the signal-to-interference-to-noise ratio received by the user according to the built system model, and then obtain the system and rate; the communication system model is reversed in the regular time OFDM multi-user communication system On the basis of , the transmitting end and the receiving end are equipped with a single antenna, and the signals sent by the transmitting end to multiple users first pass through the TR precoding matrix, and then are allocated to the OFDM sub-channel for transmission.

(2) Taking the maximization of sum rate as the optimization objective, a mathematical model of joint power allocation of multiple users under the constraint of total transmit power is given.

The received signal-to-interference-to-noise ratio is:

为信道的噪声方差，H _k,m为对角矩阵H _k的第m个对角元素，H _k为频域信道矩阵，表示为where K is the number of users, p _k,m is the power of the symbol m allocated to user k by the transmitter, D is the rate backoff factor,

is the noise variance of the channel, H _k,m is the mth diagonal element of the diagonal matrix H _k , H _k is the frequency domain channel matrix, expressed as

h_k,l为用户k的多径信道的第l径的系数，l＝1,2,...,L，这里L为信道脉冲响应的长度；Among them, Q is the number of sub-carriers in the OFDM system, and the diagonal elements H _k,q , q=1,2,...,Q are the channel coefficients in the frequency domain, which are expressed as

h _k,l is the coefficient of the first path of the multipath channel of user k, l=1,2,...,L, where L is the length of the channel impulse response;

为H _k的共轭形式，即matrix

is the conjugated form of H _k , that is

The system and rate are:

In the formula, M represents the number of symbols sent to each user.

(3) Use the Karush-Kuhn-Tucker (KKT) condition to obtain the solution of the user's power allocation.

(4) Using an iterative algorithm to jointly optimize the transmit power of all users.

The present invention allocates power according to the channel state information of the channel in the process of optimally allocating the transmission power of the user signal. Since only user signal transmission power allocation is optimized, the optimization complexity of the present invention is low. And simulation experiments show that the method provided by the present invention can obviously obtain a higher system and rate than the average power distribution method. The present invention improves the sum rate performance of the system under lower optimization complexity.

Description of drawings

Fig. 1 is the communication system model of the present invention;

2 is a schematic diagram of subcarrier utilization of user k;

Fig. 3 is the equivalent communication system model of the present invention;

Figure 4 is a system and rate comparison of the present invention with average power distribution and traditional iterative water injection methods;

Fig. 5 is the relationship between the system and the rate of the present invention and the traditional iterative water injection method and the number of iterations;

Figure 6 shows the impact of the rate backoff factor on the system and rate;

Figure 7 shows the impact of the number of users on the system and rate.

Detailed ways

The symbols involved in the present invention have the following notes: letters with underlines represent frequency domain symbols, and those without underlines represent time domain symbols; lowercase bold letters represent vectors, and uppercase bold letters represent matrices; white letters represent scalars; |· |, ||·||, (·) ^* , and (·) ^H represent absolute or modulus value, 2-norm, conjugate and conjugate transpose, respectively.

这是为了避免将相同的数据符号分配到不同OFDM子载波上，从而造成高峰均功率比，并保证加扩过程不改变信号功率，即S ^H S＝I _M，I _M表示M×M的单位阵。S表示为The model of the TR-OFDM multi-user communication system is shown in Figure 1. The system has K users, and both the transmitter and the receiver are equipped with a single antenna. The sender sends mutually independent data vectors to K users at the same time, wherein the data vector sent to user k is denoted as x _k , k=1,2,...,K. x _k consists of M data symbols x _k,m , where m=1,2,...,M, ie x _k =[ x _k,1 , x _k,2 ,..., x _k,M ]. First, the data symbols are spread by a spreading matrix S with a size of Q×M. The purpose of the spreading is to allocate the data symbols to the OFDM subcarriers. Q is the number of subcarriers in the OFDM system, and Q=DM. After adding and spreading, each data symbol is allocated to D different subcarriers at an interval of M, where D is the rate backoff factor, which is equivalent to the upsampling factor in the time-domain TR system. S is formed by concatenating D M×M diagonal matrices, and its diagonal elements take equal values.

This is to avoid allocating the same data symbols to different OFDM subcarriers, resulting in a peak-to-average power ratio, and to ensure that the signal power does not change during the augmentation and spreading process, that is, S ^H S = _IM , IM represents the unit of _M ×M array. S is represented as

其中h_k,l为第l径的系数，也就是脉冲响应中的l个脉冲的强度，l＝0,1,...,L-1，这里L为信道脉冲响应的长度，也就是多径信道的路径数。接收机对接收信号进行FFT变换，得到频域符号。可以将IFFT、多径信道、FFT合在一起，等效为Q个频域并行信道，信道系数为

信道输出的频域符号为发送的频域符号与对角矩阵H _k相乘。H _k的第q个对角元素为H _k,q，即In the TR-OFDM system, the spreading matrix S is added, which is equivalent to the up-sampling in the time-domain TR system. After adding and spreading, a schematic diagram of subcarrier utilization of user k is shown in FIG. 2 . The added and spread symbols need to be multiplied by a precoding matrix for precoding before transmission, which is equivalent to prefiltering in the time-domain TR system. The precoded symbol obtains a time-domain signal through an inverse fast Fourier transform (Inverse Fast Fourier Transform, IFFT), and is sent out after adding a cyclic prefix. Fast Fourier Transform (FFT) is performed at the receiving end and then converted into a frequency domain signal. The multipath channel between the transmitter and user k is a linear system, and the impulse response in the medium-term discrete domain can be expressed as

Where h _k,l is the coefficient of the first path, that is, the intensity of l pulses in the impulse response, l=0,1,...,L-1, where L is the length of the channel impulse response, that is, the number of The number of paths in the path channel. The receiver performs FFT transformation on the received signal to obtain frequency domain symbols. IFFT, multipath channel, and FFT can be combined together, which is equivalent to Q parallel channels in frequency domain, and the channel coefficient is

The frequency domain symbol output by the channel is the multiplication of the transmitted frequency domain symbol by the diagonal matrix H _k . The q-th diagonal element of H _k is H _k,q , that is,

时域TR系统中的预滤波器为信道脉冲响应的共轭反转，发送信号经过该预滤波器对应频域中为频域符号与预编码矩阵

相乘。

为Correspondingly, the system model can be equivalent to Figure 3. where v _k =[ v _k (1), v _k (2),..., v _k (Q)] is the frequency domain Additive White Gaussian Noise (AWGN) sequence, which is the time domain AWGN noise Fourier transform of the sequence v _k , where the elements of v _k and v _k have the same variance

The pre-filter in the time-domain TR system is the conjugate inversion of the channel impulse response. The transmitted signal passes through the pre-filter and corresponds to the frequency-domain symbol and precoding matrix in the frequency domain.

Multiply.

for

The sequence received by the user needs to be multiplied by SH for ^despreading , and the despread signal of user k is

The received SINR of user k is the ratio of the useful signal power received by the user to the sum of the inter-user interference power and the channel noise power, namely

为信道的噪声方差，H _k,m为对角矩阵H _k的第m个对角元素。和速率是评价系统传输性能常用的指标，本发明以最大化系统和速率为目标对信号功率分配进行优化。系统和速率为where p _k,m is the power of the symbol m allocated to user k by the transmitter, D is the rate backoff factor,

is the noise variance of the channel, and H _k,m is the mth diagonal element of the diagonal matrix H _k . The sum rate is a commonly used index for evaluating the transmission performance of the system, and the present invention optimizes the signal power distribution with the goal of maximizing the system sum rate. The system and rate are

In the optimization process of power allocation, it should be ensured that the sum of the power of each signal allocated to the user is less than or equal to the total transmission power of the user, that is,

where P _k is the total transmit power of user k. The optimization problem is structured as

The above-mentioned multi-objective joint optimization is a non-convex optimization, but for user k, if the power distribution of the remaining users is fixed at this time, the optimal solution of the power distribution of user k satisfies the KKT condition. Construct the Lagrangian function as

Among them, λ=[λ ₁ ,λ ₂ ,...,λ _K ] ^T is a non-negative Lagrangian multiplier vector. Let Λ(p,λ) be derived from p _k,m and equal to 0, then the most The optimal p and λ satisfy the following equations

Among them, t _k,m includes the interference caused by user k to other users, which is defined as

The power allocation of user k is solved as

In the formula, [x] ⁺ means to take the maximum value between 0 and x, and x is the content in the brackets in the above formula. And because the power constraints are met, there are

make

The transmitter allocates higher power to the signal on the sub-channel with better channel conditions, and when causing excessive interference to other users, tk _,m will reduce the power allocated to the signal. λ _k can be found by the bisection method. When λ _k is non-positive to satisfy the power constraint equation, then λ _k is 0. An iterative algorithm is used to solve the power allocation for all users. Assign an initial power value to each signal of each user. Based on the assigned initial value, t can be obtained, where t is the set of t _k,m , that is, t={t _k,m }, k=1,2,...,K , m=1,2,...,M. First, start with user 1. Since the power distribution of t and other users is fixed, the power distribution of user 1 can be obtained; then the power distribution of user 2 is optimized, and the updated p _1,1 , p ₁ are used for the solution. _,2 ,...,p _1,M values, while t and the power allocation starting from user 3 are still the previous values; the power allocations of the remaining users are also updated similarly, and the updated p is obtained, where p is p A set of _k,m , ie p={p _k,m }, k=1,2,...,K, m=1,2,...,M. After p is updated, update t, repeat the above process, and iteratively update the power allocation of each user until the relative difference of the power allocation obtained by two consecutive iterations is smaller than the preset value or reaches the predetermined number of iterations, and finally each user is obtained. The optimal solution p ^* for the power distribution of each signal of the user. The specific iterative algorithm is shown in Table 1, where n represents the number of iterations, and τ ₁ is the relative difference that controls the end of the iteration, that is, the convergence factor.

Table 1 Iterative Algorithms

其中σ_T＝10/B为路径的均方根延迟，T_s＝1/B为采样周期。η_k＝η₀(d_k/d₀)^-c为信道的大尺度衰落系数。其中，c＝4为路径损耗指数，η₀为参考距离处的传输损耗，d₀＝10m为参考距离，d_k为发送端与用户k的距离，假设d_k是随机的，在100m到2000m之间。设定η₀＝10^-5，信道的噪声功率设为1×10^-11W。求解功率分配的迭代算法中最大迭代次数设为100，收敛因子τ₁＝1×10^-5。系统总发送功率为P，每个用户的发送总功率P_k＝P/K。The present invention will be further described in detail below with reference to the accompanying drawings. The simulation results for the systems and rates given in each figure are averages over 10,000 channel implementations. Unless otherwise specified, the parameters in the simulation are set as follows: a SISO OFDM system is used, and the number of subcarriers Q=1024. The channel is a Rayleigh fading channel, the total channel bandwidth is B=15.36MHz, the number of channels that can be resolved is L=10, and the channel impulse response coefficient obeys a complex Gaussian random distribution with zero mean. The variance of the channel is

where σ _T =10/B is the root mean square delay of the path, and T _s =1/B is the sampling period. η _k =η ₀ (d _k /d ₀ ) ^-c is the large-scale fading coefficient of the channel. Among them, c=4 is the path loss index, η ₀ is the transmission loss at the reference distance, d ₀ =10m is the reference distance, d _k is the distance between the sender and user k, assuming that d _k is random, between 100m and 2000m between. Set η ₀ =10 ⁻⁵ , and the noise power of the channel is set to 1×10 ⁻¹¹ W. In the iterative algorithm for solving the power distribution, the maximum number of iterations is set to 100, and the convergence factor τ ₁ =1×10 ^-5 . The total transmission power of the system is P, and the total transmission power of each user is P _k =P/K.

Fig. 4 is the simulation result of the change of the system sum rate with the increase of transmit power when the number of users K=4, the number of BOF D=1, and the number of paths L=10. The result of the improved iterative water-filling algorithm in the figure is the result of the optimal allocation method of user signal transmission power provided by the present invention, and the simulation results of the traditional iterative water-filling power allocation method and the system and rate of average power allocation are given. The difference between the traditional iterative water-filling algorithm is that t _k,m is 0, that is, when each signal allocates power regardless of the interference to other users, it only needs to maximize its own rate, while the average power allocation is for all users regardless of channel conditions. The signals are assigned the same power, ie p _k,m =P _k /M,m=1,2,...,M. The sum rate in the graph is the average of the instantaneous sum rate for all channel states. As can be seen from the figure, as the transmit power increases, the system sum rate increases, and then gradually tends to an upper limit. This is because when the transmit power is small, the interference power is small relative to the channel noise power, the total transmit power increases, and the sum rate increases accordingly. When the transmit power increases to a certain extent, the interference power will be significantly higher than the channel noise power. Since the signal power and the interference power increase synchronously with the transmit power, at this time, the transmit power and rate no longer increase significantly. It can be seen from the figure that the system and rate of average power allocation is the lowest, because when average power allocation is used, the power allocated to all signals is the same, and different signals are allocated to different subcarriers, After different sub-channel gains, if the same power is allocated to the signal on the sub-channel with low channel gain and the sub-channel with high channel gain, the system performance will definitely not be the best. However, when using the traditional iterative water-filling algorithm, when each user optimizes its signal power allocation, it only considers the highest rate of its own, while ignoring the interference to other users, so it often causes greater interference to other users. , and therefore also cannot achieve the best sum rate performance. The improved iterative water-filling power allocation algorithm provided by the present invention maximizes its own rate, and at the same time, the existence of _tk,m reduces the interference to other users, so the system and rate can be improved most effectively. As shown in the simulation results, the sum rate under the traditional iterative water injection algorithm can only be increased by 8%, while the sum rate of the improved iterative water injection algorithm is increased by 13.8%, which proves that the improved iterative water injection algorithm provided by the present invention has better performance.

5 shows the relationship between the system and rate of the power allocation algorithm and the traditional iterative water-filling algorithm provided by the present invention and the number of iterations when the number of users K=4, the number of BOF D=1, the number of paths L=10, and the transmit power is 30dBm. The convergence of the two algorithms can be seen from the figure, and the improved iterative water-filling algorithm provided by the present invention has a faster convergence speed and has a better solution when converging. The traditional iterative water-filling algorithm can only converge when the number of iterations reaches 6, while the iterative water-filling algorithm converges when the number of iterations reaches 4 or 5, which proves that the improved iterative water-filling algorithm has better convergence, so it is not necessary to wait for complete convergence in practical applications. , just iterate 4-6 times.

Fig. 6 is the simulation result of the system and rate under different BOFs when the number of users is K=4 and the number of paths is L=10, as the transmit power increases. The simulation results show that with the increase of BOF, the sum rate of the system decreases. This is because the increase of BOF can reduce the IUI, but at the same time, the increase of BOF reduces the number of data symbols that can be transmitted, which leads to the reduction of symbols. The rate is reduced, and the reduction in IUI is not enough to compensate for the large reduction in symbol rate, so the system and rate are reduced. Figures 7(a) and (b) are BOF D=1 and the number of paths L is 10 and 20 respectively, with the increase of transmit power, the system and rate under different numbers of users. It can be seen that when the transmit power is small, with the increase of the number of users, the system and rate increase, which shows that the frequency domain TR precoding technology can significantly reduce the IUI in the multi-user system, but when the transmit power is large, the noise power It is relatively small and can be ignored. The interference power increases synchronously with the transmission power, and the interference power of more users will be larger, so the SINR of multi-users will be smaller, and the system and rate will be lower. That is, as shown in the figure, as the transmit power increases, the curves of K=2 and K=4 will intersect, and the sum rate of the number of users will exceed that of the number of users. Moreover, it can be seen from Fig. 7(a) and (b) that, with the increase of the number of paths, the system sum rate will increase, which shows that the frequency domain TR is suitable for the rich multipath environment and can effectively improve the multipath environment. The performance of the communication system, and the greater the number of paths, the greater the focusing gain obtained.

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, p_k,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

h_k,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 P_kTotal 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,...,λ_K]^TNon-negative Lagrange multiplier vector, let Λ (p, λ) to p_k,mDerivative and equal to 0, then the optimal p and λ satisfy the following equations

Wherein, t_k,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 solving_1,1,p_1,2,...,p_1,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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