阅读说明：本技术 一种空间相关信道下协作空间调制系统中功率分配方法 (Power distribution method in cooperative space modulation system under space correlation channel ) 是由 虞湘宾 潘青 胡亚平 李祺亦舒 王光英 黎宁 于 2019-03-14 设计创作，主要内容包括：本发明提供了一种空间相关信道下协作空间调制系统中功率分配方法。针对协作空间调制系统,考虑发送端和接收端天线之间存在相关性,利用相关信道下有效信噪比的矩生成函数,推导了平均误比特率的近似闭式表达式。根据该误比特率和高信噪比下的渐近表达式,提出了一种次优自适应功率分配方法。经仿真验证,本发明所提出的功率分配方法相比于通常的等功率分配方法,可有效降低系统误比特率,获得好的系统性能。(The invention provides a power distribution method in a cooperative space modulation system under a space correlation channel. For a cooperative spatial modulation system, the correlation between antennas of a sending end and a receiving end is considered, and an approximate closed expression of an average bit error rate is deduced by utilizing a moment generating function of an effective signal-to-noise ratio under a relevant channel. According to the bit error rate and the asymptotic expression under high signal-to-noise ratio, a suboptimal adaptive power allocation method is provided. Through simulation verification, compared with the common equal power distribution method, the power distribution method provided by the invention can effectively reduce the bit error rate of the system and obtain good system performance.)

1. A power distribution method in a cooperative space modulation system under a space correlation channel is characterized in that: the method comprises the following steps:

(1) considering a wireless cooperative spatial modulation system using spatial modulation, the system consists of N_tSource node of root transmitting antenna, relay node comprising single antenna and relay node comprising N_rThe source node only activates one antenna to send signals in each time slot, and the other antennas do not send signals;

(2) based on the correlation between the antennae of the source end and the destination end, a paired error probability expression is given by utilizing a moment generating function of an effective signal-to-noise ratio under a space correlation Rayleigh channel, so that a bit error rate approximate expression and an asymptotic expression under a high signal-to-noise ratio are obtained according to a unified upper bound formula;

(3) utilizing the bit error rate asymptotic expression obtained in the step (2) to obtain a power distribution coefficient r of the source node₁Derivation is performed to obtain a power distribution coefficient that minimizes the approximate bit error rate based on the derivative.

2. The method according to claim 1, wherein the power allocation method based on the cooperative spatial modulation system under the spatial correlation channel comprises:

(1) the step (2) comprises a self-adaptive power distribution method based on a cooperative spatial modulation system, and a calculation method of a power distribution coefficient is given according to the number of different receiving antennas;

(2) when N is present_rWhen the bit error rate is 1, the power distribution coefficient r of the source node is approximated and expressed₁The derivative of (2) is obtained by using a gradient descent method to obtain a suboptimal power distribution coefficient which enables a bit error rate approximate value to be minimum;

(3) when N is present_rAnd when the power distribution is more than or equal to 2, solving a quadratic equation to obtain a closed expression of the suboptimal power distribution scheme of the system.

The technical field is as follows:

the invention belongs to the field of mobile communication, relates to a resource allocation method of a mobile communication system, and particularly relates to a power allocation method in a wireless relay cooperative network based on spatial modulation.

Background art:

cooperative communication is one of research hotspots in the field of wireless communication in recent years, and by using antennas of other users in a wireless communication network as transmission of cooperative signals of relay nodes, the problem that multiple antennas cannot be placed in a mobile terminal in a traditional multiple-input multiple-output (MIMO) system due to volume and power limitations is solved, and a large amount of cost brought by a base station is effectively lowered while the frequency spectrum utilization rate is improved. According to different processing modes of the relay node for receiving signals, different cooperation protocols can be divided. An Amplify-and-Forward (AF) cooperative protocol is simpler and easier to implement than other protocols, and therefore is widely applied to cooperative systems. The basic idea is that the relay node directly amplifies the received signal and forwards the signal to the destination. The Spatial Modulation (SM) technology can realize single-link transceiving design by only activating one antenna to transmit symbols in each time slot, and effectively solves the problems of inter-channel interference and synchronization; meanwhile, the information is transmitted invisibly by utilizing the mapping of the serial numbers of the transmitting antennas and the bits of the transmitted information, so that the speed is high and the capacity is large. The SM technology is combined with cooperative communication, so that the advantages of the SM technology can be embodied, the defects in a cooperative communication system are effectively avoided, and the cooperative relay node can be used for helping the source node to transmit information to embody the advantages of the cooperative communication.

The spatial correlation depends on several physical parameters including the antenna spacing, the antenna arrangement and the surrounding scatterer distribution. In the actual communication process, due to the non-ideal of these physical parameters, the antenna correlation will reduce the spectrum efficiency and increase the detection error probability. Therefore, it is of practical significance to provide an adaptive power allocation scheme for system performance analysis under spatially correlated channels. Document 1(M.D. Renzo, H.Haas.space shift keying (SSK-) A Performance analysis and a new method for transmission-diversity [ J ]. IEEE Transactions on Communications, 2011, 59 (1): 116) A bit error rate formula is derived for a multiple-input multiple-output SSK system under the associated Rice channel. Meanwhile, because the traditional SM-MIMO can only obtain the receiving diversity, the SM-MIMO scheme designed based on the time orthogonal signal is also provided, the basic idea is to optimize the signal form sent by the antenna, so that the signal meets the orthogonality on the time dimension, and the scheme can obtain the receiving diversity and the sending diversity at the same time. Document 2(h.liu, j.p.zheng, y.li.combining modulation and VBLAST/STBC for corrected Rayleigh scaling channels: capacity and performance analysis [ C ]. International Conference on wireless communication and Signal Processing, 2013: 1-5.) combines SM with Space-Time Block Coding (STBC) and VBLAST, respectively, analyzes the system capacity under the spatially correlated Rayleigh channel, derives the bit error rate upper bound formula, and demonstrates that the proposed SM-STBC and SM-VBLAST schemes can obtain transmit diversity gain and higher spectral efficiency, with better robustness to transmit antenna correlation than conventional SM systems. Document 3(n.varshney, a.goel, a.k.jaganatham. cooperative communication in a spatially modulated MIMO systems [ C ]. IEEE Wireless Communications and network connectivity, 2016: 1-6.) combines an STBC and a cooperative DF spatial modulation system, analyzes the bit error rate performance of the system under spatially correlated channels, and gives a system diversity factor and an optimal power allocation scheme according to the approximate bit error rate under high signal-to-noise ratio. Therefore, in order to improve the performance of the cooperative spatial modulation system under the spatial correlation channel, it is necessary to research an adaptive power allocation scheme based on the system.

The invention content is as follows:

considering the correlation between the transmitting end antenna and the receiving end antenna, the invention provides a power distribution method of a cooperative spatial modulation system based on a spatial correlation channel by deducing an approximate closed expression of average bit error rate under high signal-to-noise ratio.

The technical scheme adopted by the invention is as follows: a power distribution method based on a cooperative spatial modulation system under a spatial correlation channel comprises the following steps:

(1) a cooperative spatial modulation system with a spatial modulation adopted at a source end considers the correlation between antennas at the source end and a destination end, and gives a pairwise error probability expression by utilizing a moment generating function of an effective signal-to-noise ratio under a spatial correlation channel, so that a bit error rate approximate expression is obtained according to a unified upper bound formula. And simultaneously, an approximate expression of the Bessel function is utilized to obtain an asymptotic expression of the bit error rate under the high signal-to-noise ratio.

(2) Utilizing the bit error rate asymptotic expression obtained in the step (1) to obtain a power distribution coefficient r of a source node₁Derivation is performed to obtain a power distribution coefficient that minimizes the approximate bit error rate based on the derivative.

(3) When N is present_rWhen the bit error rate is 1, the power distribution coefficient r of the source node is approximated and expressed₁The derivative of (2) is obtained by using a gradient descent method to obtain a suboptimal power distribution coefficient which enables a bit error rate approximate value to be minimum; when N is present_rAnd when the power distribution is more than or equal to 2, solving a quadratic equation to obtain a closed expression of the suboptimal power distribution scheme of the system.

The invention has the following beneficial effects: the invention provides a performance analysis scheme of a collaborative spatial modulation system under a spatial correlation channel, provides a bit error rate theoretical expression, and obtains a suboptimal power distribution scheme according to the theoretical expression. Compared with the equal power distribution scheme, the distribution scheme can effectively improve the system performance.

Description of the drawings:

fig. 1 is a diagram illustrating steps of a power allocation method for a cooperative spatial modulation system based on spatially correlated channels according to the present invention.

Fig. 2 is a schematic block diagram of a cooperative spatial modulation system in an embodiment of the present invention.

Fig. 3 shows average bit error rates of the cooperative spatial modulation system according to the embodiment of the present invention under different modulation modes.

Fig. 4 shows the average bit error rate of the cooperative spatial modulation system under different correlation coefficients according to an embodiment of the present invention.

Fig. 5 shows an average bit error rate when the cooperative spatial modulation system of the embodiment of the invention adopts different power allocation schemes.

The specific implementation mode is as follows:

the invention will be further described with reference to the accompanying drawings.

The model of the cooperative spatial modulation system involved in the invention is shown in FIG. 2, and the system comprises N_tSource node of root transmitting antenna, relay node comprising single antenna and relay node comprising N_rThe target node of the root receiving antenna is formed, and the relay node adopts an AF protocol. The source node only activates one antenna to transmit signals in each time slot, and the other antennas do not transmit signals. The total number of bits transmitted per slot is log₂(N_tM) where log₂N_tThe bits are used to determine the activated transmit antenna sequence number i, i ∈ [1, N_t]，log₂M bits are used for constellation symbol modulation of M-QAM, then the transmitted symbol vector can be represented as x_iq＝[0 0…x_q…0]^TWherein x is_qIs x_jqRepresents the qth symbol in the constellation diagram. The signal transmission process of the cooperative system is divided into two stages, in the first stage, a source node sends signals to a relay and a target, and the signals received by the relay and the target are respectively expressed as

In the second stage, according to the AF protocol, the relay node amplifies the signal received in the first stage and forwards the signal to the target. The signal received for the purpose in stage two is represented as

Wherein h is_sr，H_sdAnd h_rdSource to relay, source to destination and relay to destination channel matrices respectively,are respectively H_sdAnd h_srThe ith column and the ith element. n is_sr，n_sdAnd n_rdIs a mean of 0 and a variance of N₀Complex gaussian noise. A is the amplification factor of the signal to be amplified,P_sand P_rTransmitting power, P, of source and relay respectively_s+P_r＝P_t，P_tFor total transmitted power, the average signal-to-noise ratio SNR is expressed as

Assuming that the correlation exists between the antennas of the source end and the destination end, the channel vectors and the matrixes of the source-to-relay, the relay-to-destination and the source-to-destination are respectively expressed as a Kronecker correlation channel model

Andsatisfy independent same distribution, elements thereof respectively obey mean value of 0 and variance of

Andcomplex gaussian distribution.

m，n∈{s，r，d}，d_mnDistance between m-terminal and n-terminal, α is the path loss factor R_tAnd R_dAre respectively N_t×N_tTransmit correlation matrix and N of dimension_r×N_rReceiving correlation matrix of dimension, its elements definingIs composed of

ρ_tAnd ρ_rRespectively representing transmit correlation coefficients and receive correlation coefficients. The noise n ═ Ah was obtained from formula (3)_rdn_sr+n_rdHas a covariance matrix ofWhitening the obtained extract to obtain

WhereinThe destination adopts a demodulation algorithm of

Wherein

Andthe antenna sequence number and the estimated value of the constellation symbol, respectively.

1) The invention aims at the performance analysis of a cooperative spatial modulation system under a spatial correlation channel

1.1) theoretical closed expression

Based on the demodulation algorithm in equation (5), assume that the antenna serial number activated by the source end is i, and the transmission symbol is x_qThen D is_jm，iqCan be expressed as

WhereinFrom this it is possible to obtain a conditional PEP denoted by

Wherein

The moment generating functions of (8), (9) and (10) are respectively

Wherein: lambda [ alpha ]_k，k＝1，2，...，N_rIs R_dIs determined by the characteristic value of (a), derived from inverse Laplace transform

Probability density function ofIs expressed as a cumulative distribution function of

Thereby obtaining

CDF of

Wherein: k_v(. cndot.) is a Bessel function of the second kind of order v. Thereby the device is provided withIs expressed as

Wherein: w_λ，μ(z) is the Whitaker function. According to conditional Pairwise error probability (PEP, Pairwise ErrorProbasic) formula (7), andand

the moment of (2) is generated as a function, and the average PEP can be obtained

Wherein: phi is a_u＝cos((2u-1)π/(2N_p))，N_pIs the order of the chebyshev polynomial. The average bit error rate can be obtained by substituting the above formula into the uniform upper bound

Wherein N (x)_iq→x_jm) In order to send the difference between the actual value and the estimated value of the bit, the bit error rate theoretical value calculated by the formula (16) can keep better consistent with the simulated value under different receiving antenna numbers, and the correctness of the deduced theoretical expression is proved.

1.2) progressive approximation expression

When the signal-to-noise ratio tends to infinity, it can be obtainedApproximate expression of moment generating function

Approximation expression according to Bessel function

Can be approximated as

At the high signal-to-noise ratio,

wherein

Thereby obtaining an approximate expression of the moment generating function

By substituting equations (17) and (19) into (15), the average PEP can be approximated as

Let P_s＝r₁P_t，P_r＝r₂P_t，P_tIs the sum of the total powers of the source and the relay, the power distribution coefficient satisfies r₁+r₂＝1，r₁，r₂∈ (0, 1). The result isBased on this, when N is_rWhen the bit error rate is 1, the formula (20) is simplified and substituted into the bit error rate uniform upper bound

When N is present_rWhen the average BER is more than or equal to 2, a gradual approximate expression of the average BER can be obtained

Thus, N_r1 and N_rA gradual approximation of the average bit error rate at ≧ 2 can be obtained by equations (21) and (22), respectively. Fig. 3 compares average bit error rates of the cooperative AF-SM system when different modulation schemes are adopted in the relevant channels. The modulation modes respectively adopt 4QAM, 8QAM and 16QAM, and the correlation coefficient rho_t＝ρ_r0.4. The theoretical value of the average BER in the graph is calculated by equation (16). It can be seen from the figure that the simulated BER value and the theoretical BER value can be better matched under different modulation modes, and the correctness of the derived theoretical expression is illustrated. By comparison, it can be concluded that the BER of 4QAM is the lowest and the BER of 16QAM is the highest, because as the modulation order increases, the distance between constellation points becomes smaller, resulting in an increased probability of detection error. Fig. 4 shows the average bit error rate of the cooperative AF-SM system at different correlation coefficients. The modulation mode adopts 4QAM and the number of receiving antennas is N_r2, correlation coefficient ρ_t＝ρ_rRho and rho 0, 0.4, 0.8, d_sd∶d_sr∶d_rd1: 0.5. It can be seen from the figure thatThe theoretical value of the average BER can be consistent with the simulation value, and the deduced theoretical expression can accurately describe the BER performance under different correlation coefficients.

2) The invention provides a power distribution method based on an approximate expression of average bit error rate.

When N is present_rWhen the bit error rate is 1, the bit error rate progressive approximation expression (21) is related to the power distribution coefficient r of the source end₁Derived from the result of the derivation

Wherein

By gradient descent

Can be atThe power allocation coefficient that minimizes the approximate BER is found within the interval.

When N is present_rWhen r is not less than 2, the value of r in the pair of formula (22)₁Obtaining a first guide

Wherein

Gamma (r)₁) When the equation is 0, solving a quadratic equation of one element can obtain

WhereinTherefore, a closed expression of the suboptimal power allocation scheme of the AF-SM system under the relevant channel is obtained. Further, the theoretical expression of the average BER obtained from the expression (16) is based. FIG. 5 compares d_sd∶d_sr∶d_rdAnd when the ratio is 1: 0.75: 0.25, the cooperative AF-SM system has the average bit error rate of the equal power distribution scheme, the suboptimal power distribution scheme and the optimal power distribution scheme under different antenna numbers. The modulation mode is 4QAM, the number of receiving antennas is N_r1 and 2, correlation coefficient ρ_t＝ρ_r0.4. The coefficient of the equal power distribution scheme is r₁＝r₂＝0.5，N_r1 and N_rThe optimal power distribution scheme coefficient which is more than 1 is obtained by calculation through a gradient descent method and closed expressions (25) to (26), and is given by traversing and searching the minimum value of the theoretical expression of the average BER obtained by the expression (16) through an fminbnd function in Matlab. In the figure N_r1 and N_rThe BER asymptotic approximation curve > 1 is calculated by equations (21) and (22), respectively. It can be seen from the figure that the theoretical value of the mean BER coincides with the simulation value, and the asymptotic approximation value also tends to coincide with the simulation value at high signal-to-noise ratio. Thereby proving the correctness of the given theoretical expression and the progressive approximation expression. In addition, the average BER of the suboptimal power distribution scheme is obviously lower than that of the equal power distribution scheme, and compared with the optimal power distribution scheme, the suboptimal power scheme can obtain approximate performance and has lower calculation complexity. The above results show that the proposed suboptimal power allocation scheme can effectively improve the system performance.

In summary, the power allocation method provided by the present invention has better performance than the equal power allocation scheme, and can obtain performance gain similar to the optimal power allocation scheme, but has lower complexity. The effectiveness of the power allocation method in the wireless relay cooperative network based on the spatial modulation provided by the invention is fully demonstrated.

The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the foregoing description only for the purpose of illustrating the principles of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the invention as defined by the appended claims, specification, and equivalents thereof.

The foregoing is only a preferred embodiment of this invention and it should be noted that modifications can be made by those skilled in the art without departing from the principle of the invention and these modifications should also be considered as the protection scope of the invention.