CN105207751B - Keying method and its combined optimization method when sky based on multi-dimensional modulation - Google Patents

本发明涉及一种基于多维调制的空时键控方法，包括以下步骤：S1.信源每产生的B个比特经过串/并转换生成下支路的B₁个比特和上支路的B₂个比特，B＝B₁+B₂个比特生成一个N‑D STSK码字，记作第i个码字；S2.对于上支路，根据输入的B₂个比特从大小为的DMS中选择一个DM，表示为S3.对于下支路，根据输入的B₁个比特从大小为的N(N>2)维星座图中选择一个星座点Ω_l，并对星座点Ω_l进行多维调制，获得N‑D符号S4.将N‑D符号通过在空间和时间上离散，获得第i个N‑D STSK码字S⁽ⁱ⁾，其中表示Kronecker积；S5.将S⁽ⁱ⁾通过信道发射至接收端，接收端对发送端发射的符号信息进行解调。本发明提供的方法能够获得更好的误码率性能。

The present invention relates to a space-time keying method based on multi-dimensional modulation, comprising the following steps: S1. Each B bits generated by an information source are converted into B ₁ bits of the lower branch and B ₂ bits of the upper branch through serial/parallel conversion. bits, B=B ₁ +B ₂ bits generate an N-D STSK codeword, denoted as the i-th codeword; S2. For the upper branch, according to the input B ₂ bits from size to Select a DM in the DMS, expressed as S3. For the lower branch, according to the input B ₁ bits are from size to Select a constellation point Ω _l in the N(N>2)-dimensional constellation diagram of , and perform multi-dimensional modulation on the constellation point Ω _l to obtain N-D symbols S4. The N‑D symbol pass Discrete in space and time to obtain the i-th N‑D STSK codeword S ⁽ⁱ⁾ , in Represents the Kronecker product; S5. Transmit S ⁽ⁱ⁾ to the receiving end through the channel, and the receiving end demodulates the symbol information transmitted by the transmitting end. The method provided by the present invention can obtain better bit error rate performance.

Keying method and its combined optimization method when sky based on multi-dimensional modulation

Technical field

The present invention is towards wireless communication multi-antenna technology field, keyed system when proposing a kind of sky based on multi-dimensional modulation Scheme, and from a kind of multivariate joint probability optimization method of the angle design of improving performance.

Background technique

With multiple-input and multiple-output (Multiple Input Multiple Output, MIMO) technology appearance and answer With wireless communication system is greatly improved [1] in terms of capacity and reliability.Keying when proposed in recent years empty (Space-Time Shift Keying, STSK) [2] modulation scheme is a kind of novel MIMO technology, which can satisfy The requirement of high-speed radio transceiver reliable communication in dispersion fading channel.Existing relevant STSK (Coherent STSK, CSTSK shown in such as Fig. 1 of transmitter architecture) [1].B bit of input is divided into two parts by serioparallel exchange: a part It is the B of upper branch₂A bit, be used to fromOne of them is selected in a discrete matrix (Dispersion Matrix, DM) Discrete matrix A_q；Another part is the B of lower branch₁A bit, for being from sizeQAM/PSK planisphere in select One symbol s_l.Then s_lWith discrete matrix A_qIt is multiplied, discretization is realized on room and time, to obtain STSK code word S= s_lA_q, finally sent by space and time mapping device.

It since STSK takes full advantage of time domain and spatial domain, can be designed using more flexible system, be increased in space diversity A good trade-off [2] is obtained between benefit and spatial multiplexing gain the two.Since there is no mutual channel disturbance (Inter Channel Interference, ICI), the maximum likelihood (Maximum based on single data stream of low complex degree can be used in receiving end Likelihood, ML) rule codeword detection, this compared with the MIMO scheme (such as space division multiplexing) of multiple data stream, have compared with Low demodulated complex degree.In addition, STSK (Generalised STSK, G-STSK) scheme of broad sense expands to the concept of STSK One energy includes linear discrete code (Linear Dispersion Code, LDC), spatial modulation (Spatial Modulation, SM), dblast when (Bell Laboratories Layered Space-Time, BLAST) With the wider framework of the technologies such as orthogonal space time packet (Orthogonal Space Time Block Code, OSTBC), This makes STSK become the attractive technique direction that advanced MIMO is applied.

On the other hand, in a communications system, flat in identical normalization from the perspective of digital modulation planisphere In the case where equal power, the planisphere with bigger minimum euclidean distance (Minimum Euclidean Distance, MED) It can be obtained on additive white Gaussian noise channel (Additive Gaussian White Noise, AWGN) channel preferably Link robustness.Three-dimensional (Three-Dimensional, 3-D) planisphere is capable of providing than (including identical with same size The constellation point of quantity) the bigger MED of two dimension (Two-Dimensional, 2-D) planisphere, thus better chain can be provided Road performance.16 common point 3-D planispheres have 16CIC [3] and 16RCIC [4] etc..Multidimensional (Multi- is introduced in STSK Dimensional, M-D) planisphere, it is expected to the performance of STSK system can further be promoted.And realize a multidimensional signal Mode such as can be used time-division or frequency division multiplexing, using multiple independent transmissions or use polarization of ele there are many [5] Mode transmit various dimensions symbol.

Further, due to the performance of STSK system by planisphere and discrete matrix set (DM Set, DMS) two because The limitation of element, this combination may be uncoordinated due to the property of constellation graph structure and DMS, and limits the property of system entirety Energy.It is therefore desirable to introduce a kind of combined optimization algorithm, while considering planisphere and the optimization of DM, coordinates the two in system entirety Effect, it is ensured that system can give full play to multi-dimensional constellation diagram and the advantage of STSK, and then bring being obviously improved for system performance.Such as From another perspective, this combined optimization method in fact provides the method for a kind of co-design planisphere and DMS to fruit. Current existing combined optimization method [6] is only used for the STSK system using two dimensional constellation figure, and for using multi-dimensional constellation The STSK system of figure is there is not yet corresponding combined optimization method.

Summary of the invention

The present invention is to solve the defect of the above prior art, keying method when providing a kind of sky based on multi-dimensional modulation, Keying scheme when compared to traditional sky, keying method can obtain better bit error rate performance when the sky of multi-dimensional modulation, and As low as in medium sized signal-to-noise ratio (SNR) range, keying method can obtain higher spectrum efficiency when the sky of multi-dimensional modulation.

To realize the above goal of the invention, the technical solution adopted is that:

Keying method when a kind of sky based on multi-dimensional modulation, comprising the following steps:

S1. B bit of the every generation of information source generates the B of lower branch by serial/parallel conversion₁The B of a bit and upper branch₂It is a Bit, B=B₁+B₂A bit generates a N-D STSK code word, is denoted as i-th of code word；N-D indicates N-dimensional；

S2. for upper branch, according to the B of input₂A bit is from sizeDiscrete matrix set DMS in select One discrete matrix DM, is expressed as

S3. for lower branch, according to the B of input₁A bit is from sizeN (N > 2) dimension planisphere in select one A constellation point Ω_l, and to constellation point Ω_lMulti-dimensional modulation is carried out, N-D symbol is obtained

S4. by N-D symbolPass throughIt is discrete on room and time, obtain i-th of N-D STSK code word S⁽ⁱ⁾,WhereinIndicate Kronecker product；In l, q respectively indicate discrete matrix in discrete matrix Index in set；

S5. by S⁽ⁱ⁾Emitted by channel to receiving end, the symbolic information that receiving end emits transmitting terminal demodulates.

Preferably, it in step S3, is realized by time-multiplexed mode to constellation point Ω_lMulti-dimensional modulation, wherein Ω_l =(x_1l,x_2l,...,x_Nl)；Time division multiplexing mode includes two schemes:

(1) it directly extends in time, it is this to be achieved in that by a symbol period T_sInside it is uniformly distributed N number of seat Punctuate is to obtain a N-D symbol:

The slot time that each coordinate points occupy is T_p=T_s/ N, the sample rate needed are N times of 2-D STSK, occupancy Bandwidth is also N times of 2-D, so this kind of realize is referred to as " RN realization ".

(2) combinatorial coordinates are used, will indicate the coordinate of a N-D constellation point by way of same phase and orthogonal modulation two-by-two Combination, if N is even number, the N-D symbol of acquisition can be indicated are as follows:

If N is odd number, the N-D symbol obtained can be indicated are as follows:

In above scheme, the time that each time slot occupies can be expressed asWhereinExpression takes upwards It is whole.It is this kind of to realize that the sample rate needed is 2-D STSKTimes, the bandwidth of occupancy is also 2-D'sTimes, so will It is this kind of realize be referred to as "It realizes ".

Wherein, wherein k₁,k₂,...k_NFor normalizing the power of signal in each time slot, guarantee being averaged for each time slot Power is roughly the same, to reduce the range of linearity requirement to transmitter power amplifier.

Preferably, it is demodulated in receiving end using the symbolic information that ML demodulator emits transmitting terminal.

Preferably, the constellation point is expressed as Ω_l=(x_1l,x_2l,x_3l), then i-th of the N-D STSK code word generated can Equally write as:

Wherein

Assuming that transmitting terminal is sent symbolic information by frequency-flat rayleigh fading channel, then the received letter in receiving end Number indicate are as follows:

Y (i) [v]=H (i) [v] S (i) [v]+Z (i) [v], v=1,2,3, (1)

Wherein H (i) [v] indicates channel matrix, andIt is a N_rRow N_tThe complex matrix of column, N_rIt is to connect Receive antenna number, N_tIt is receiving antenna number, each single item in H (i) [v] obeys the multiple height that independent same distribution zero-mean variance is 1 This distribution CN (0,1), enables H (i) [v]=H (i) (v=1,2,3)；Each single item obeys CN (0, N in Z (i) [v]₀) distribution, wherein N₀ It is the noise power of each time slot；

The process that the symbolic information that then receiving end sends transmitting terminal is demodulated is specific as follows:

Vectorization is carried out using operator vec () to each single item in formula (1), is obtained:

Wherein

I is the unit matrix of T × T dimension, and T indicates the length of N-D STSK code word, ()_:,vIndicate the v of selection matrix Column, furthermoreIndicate N_rThe complex matrix set that T row 1 arranges,Indicate N_rT row N_tThe complex matrix set of T column,Indicate N_tThe complex matrix set of T row Q column；Meanwhile equivalently represented signal transmission matrix K (i) is defined as follows:

If Ω_l=(x_1l,x_2l,x_3l) be modulated by the way of directly extending in time,

Then

If Ω_l=(x_1l,x_2l,x_3l) be modulated by the way of combinatorial coordinates,

Then

Wherein []^TThe transposition of representing matrix；

Then receiving end can be expressed as follows using the process that ML demodulator demodulates acquisition information:

WhereinIndicate the N-D symbol of ML demodulator estimationIn constellation graph laplacian,Indicate ML demodulator estimation from Dissipate matrixLabel in DMS.

Meanwhile present invention is alternatively directed to the keying method when the sky of multi-dimensional modulation, a kind of multi-dimensional constellation diagram and DMS are provided Combined optimization method can give full play to the advantage of both multi-dimensional modulation and STSK using this method and effectively combine them, from And obtain being obviously improved for STSK system performance.

To realize the above goal of the invention, the technical solution adopted is that:

The combined optimization method of keying method when a kind of sky based on multi-dimensional modulation, comprising the following steps:

S1. N is generated at random_RDA N-D planisphere and DMS pairs, to each planisphere and DMS to calculating corresponding N-D STSK The discrete input of system continuously exports channel capacity, and therefrom finds out the planisphere for possessing maximum capacity and DMS as initial Planisphere Ω (1) and DMS χ (1), wherein DMS is indicated with matrix χ, and the q column element in matrix χ is A_qVectorization as a result, As following formula indicates:

χ:,_q=vec (A_q) (q=1 ... Q)

S2. to using discrete input of the STSK system of Ω (1) and χ (1) at a certain specific SNR γ continuously to export no note Recall channel DCMC capacity DCMC capacity C_DCMC(χ (1), Ω (1)) calculates it to the gradient value A (1,1) of χ and its to the gradient of Ω Value B (1,1), wherein B (1,1)=▽_ΩC_DCMC(χ (1), Ω (1)), A (1,1)=▽_χC_DCMC(χ (1), Ω (1)), A (1,1) and B There is ordinal number to respectively correspond DMS and constellation graph laplacian, ▽ to (1,1) in (1,1)_χAnd ▽_ΩIt respectively indicates to χ and ladder is asked to Ω The gradient operator of degree；；

S3. be arranged DMS initial search direction D (1)=A (1,1) and planisphere initial search direction G (1)=B (1, 1), step-size in search μ > 0, iteration ends value ε > 0 and sliding average window size L are set_c∈ Z+ is set initial change amount β (1) =| | A (1,1) | |+| | B (1,1) | | and i=1；

S4. DMS: χ new (i+1)=χ (i)+μ D (i) is obtained；

S5. new planisphere is obtained: if transmitting terminal by the way of directly extending to constellation point Ω in time_lIt is adjusted System,

Then

WhereinExpression takes real part to operate.

If transmitting terminal is by the way of combinatorial coordinates to constellation point Ω_lIt is adjusted and N is even number,

Then Ω (i+1)=Ω (i)+μ G (i)；

If N is odd number, new planisphere is obtained by formula (2)；

S6. the new DMS direction of search: D (i+1)=φ is calculated_iD (i)+A (i+1, i+1), in which:

S7. the new planisphere direction of search: G (i+1)=ψ is calculated_iG (i)+B (i+1, i+1), in which:

S8. calculate variable quantity β (i+1)=| | A (i+1, i+1) | |+| | B (i+1, i+1) | |；

S9.i=i+1, if i < 2L_c, then going to S4, otherwise enter S10；

S10. ifSo χ (i) and Ω (i) is exactly the DMS that final optimization pass is crossed With N-D planisphere, S4 is otherwise gone to.

Preferably, it in the step S4, calculates after obtaining new DMS, power normalization is carried out to new DMS, specifically such as Under:

It in the step S5, calculates after obtaining new planisphere, power normalization is carried out to new planisphere, specifically such as Under:

Compared with prior art, the beneficial effects of the present invention are:

Keying scheme when keying method is compared to traditional sky when the sky of multi-dimensional modulation provided by the invention, can obtain more Good bit error rate performance, and low in medium sized signal-to-noise ratio (SNR) range, keying method can when the sky of multi-dimensional modulation Obtain higher spectrum efficiency.By the combined optimization method provided through the invention, can give full play to multi-dimensional modulation and The advantage of both STSK simultaneously effectively combines them, to obtain being obviously improved for STSK system performance.

Detailed description of the invention

Fig. 1 is the transmitter architecture of traditional C/S TSK system.

The flow chart of keying method when Fig. 2 is the sky of multi-dimensional modulation.

Fig. 3 is the flow chart of MDJO method.

Fig. 4 is the transmitter architecture of 3-D STSK.

Fig. 5 is the space structure for two kinds of 16 common point 3-D planispheres that present invention experiment uses.

Fig. 6 is the comparison diagram of the frame error rate performance of 3-D STSK and 2-D STSK.

Fig. 7 is the comparison diagram of the effective spectrum efficiency performance of 3-D STSK and 2-D STSK.

Fig. 8 is the 3-D/4-D STSK using MDJO and the comparison of the frame error rate performance of the 3-D STSK using 16RCIC Figure.

The comparison diagram of the frame error rate performance of Fig. 9 the 3-D/4-D STSK using MDJO and the 3-D STSK using 16RCIC.

Specific embodiment

The attached figures are only used for illustrative purposes and cannot be understood as limitating the patent；

Below in conjunction with drawings and examples, the present invention is further elaborated.

Embodiment 1

The keying method when sky provided by the invention based on multi-dimensional modulation, as shown in Figure 2, comprising the following steps:

S1. B bit of the every generation of information source generates the B of lower branch by serial/parallel conversion₁The B of a bit and upper branch₂It is a Bit, B=B₁+B₂A bit generates a N-D STSK code word, is denoted as i-th of code word；

S2. for upper branch, according to the B of input₂A bit is from sizeDMS in select a DM, indicate For

S3. for lower branch, according to the B of input₁A bit is from sizeN (N > 2) dimension planisphere in select one A constellation point Ω_l, and to constellation point Ω_lMulti-dimensional modulation is carried out, N-D symbol is obtained

S4. by N-D symbolPass throughIt is discrete on room and time, obtain i-th of N-D STSK code word S⁽ⁱ⁾,WhereinIndicate Kronecker product；

S5. by S⁽ⁱ⁾Emitted by channel to receiving end, the symbolic information that receiving end emits transmitting terminal demodulates.

Wherein in step S3, realized by time-multiplexed mode to constellation point Ω_lMulti-dimensional modulation, wherein Ω_l= (x_1l,x_2l,...,x_Nl)；Time division multiplexing mode includes two schemes:

(1) it directly extends in time, it is this to be achieved in that by a symbol period T_sInside it is uniformly distributed N number of seat Punctuate is to obtain a N-D symbol:

The slot time that each coordinate points occupy is T_p=T_s/ N, the sample rate needed are N times of 2-D STSK, occupancy Bandwidth is also N times of 2-D, so this kind of realize is referred to as " RN realization ".

(2) combinatorial coordinates are used, will indicate the coordinate of a N-D constellation point by way of same phase and orthogonal modulation two-by-two Combination, if N is even number, the N-D symbol of acquisition can be indicated are as follows:

If N is odd number, the N-D symbol obtained can be indicated are as follows:

In above scheme, the time that each time slot occupies can be expressed asWhereinExpression takes upwards It is whole.It is this kind of to realize that the sample rate needed is 2-D STSKTimes, the bandwidth of occupancy is also 2-D'sTimes, so By it is this kind of realize be referred to as "It realizes ".

In the present embodiment, in order to which the superiority to method provided by the invention is adequately illustrated, also do further Experiment, experiment use 3-D STSK system, wherein the transmitter architecture of 3-D STSK system is as shown in Figure 4.In the present embodiment, With 3D-STSK (N_t,N_r, T, Q, R) and indicate a specific 3-D STSK system configuration, wherein N_tIt is transmission antenna number, N_rTo connect Antenna number is received, T is 3-D STSK code word size, and Q is the size of DMS, and R indicates specific multidimensional signal implementation, such as R=2 It indicates R2 3-D STSK scheme, i.e., carries out multi-dimensional modulation to constellation point using combinatorial coordinates；R=3 indicates R3 3-D The direct extension of STSK scheme, i.e. constellation point coordinate in time.Used in this example configuration include 3D-STSK (3,2,2, And 3D-STSK (3,2,2,16,2) 16,3).

To R=2 implementation, 3-D symbol is expressed asTo the realization side R=3 Formula, 3-D symbol are expressed as

The constellation that scheme uses is respectively two kinds of common 3-D planispheres, i.e., 16CIC and 16RCIC shown in fig. 5.System DMS used in test is generated at random previously according to order-determinant criterion [7].

I-th of 3-D STSK code word that Fig. 4 is generated is expressed as

For convenience of analysis, formula (2) can equally be write as

Wherein

Assuming that channel is frequency-flat rayleigh fading channel, and channel coherency time is that at least one 3-D STSK code word is long Degree, then the signal of receiving end can be expressed as:

Y (i) [v]=H (i) [v] S (i) [v]+Z (i) [v], v=1,2,3, (10)

WhereinIt is channel matrix, each single item obeys the multiple Gauss that independent same distribution zero-mean variance is 1 It is distributed CN (0,1), for the sake of simplicity, it is assumed here that H (i) [v]=H (i) (v=1,2,3), furthermoreEach single item Obey CN (0, N₀) distribution, wherein N₀It is the noise power of each time slot.Using the method for document [8], to each single item of formula (10) Vectorization is carried out using operator vec (), is obtained

Wherein

I is the unit matrix of T × T dimension, () in formula (11)_:,vIndicate the v column of selection matrix.In addition, K's (i) determines Justice is as follows:

[] in formula (16)^TThe transposition of representing matrix.In receiving end, it is assumed that ideal channel status letter can be obtained The acquisition of ML detector can be used in breath, the information that transmitting terminal is sent:

As R=3, for the demodulation of R3 3-D STSK, K (i) uses the definition of formula (16) formula；As R=2, it to be used for R2 The demodulation of 3-D STSK, K (i) use the definition of formula (17) formula.

The bandwidth as needed for R2 and R3 scheme is 2 times and 3 times of 2-D system respectively, for protrusion 3-D of the invention The advantage of STSK furthermore presents the measurement of effective spectrum efficiency (Effective Spectral Efficiency, ESE) Mode is defined as follows:

η_ESE=(1-e_FER)·(M/T/B)(bits/sec/Hz) (19)

Wherein e_FERIt is frame error ratio (Frame Error Ratio, FER), M is the bit number of every frame, and T is frame length, and B is System bandwidth.ESE measurement reflects system spectrum efficiency obtained by reality there are error code, it is forthright by error code It can connect, the relationship of the two can be embodied and influence each other with spectrum efficiency performance, so as to more intuitively characterize The actual performance of system.What is calculated in this example is the normalized ESE measurement of frame, and wherein frame length is set as 512 STSK code words Length, i.e. T=512T_s, B is normalized based on the bandwidth of 2-D STSK.For R23-D STSK, B=2；And for R33-D STSK, B=3.

The frame error rate (FER) of 3-D STSK and 2-D STSK and the performance comparison figure of ESE is set forth in Fig. 6 and Fig. 7.2- The antenna number of D STSK and the DMS used are identical with 3-D system, and 2-D system has used the 2-D planisphere of 16QAM.It can be with It as can be seen from Figure 6 is 10 in FER^-2When, 3-D STSK scheme is compared with corresponding 2-D system, there is the SNR gain of about 6-9dB.It obtains So significant performance boost is obtained, mainly since the 2-D planisphere with same size is compared, 3-D planisphere has bigger MED, thus there is higher link robustness.Fig. 7 show 3-D STSK scheme proposed by the invention SNR range be 0- When 16.5dB, the utilization rate ratio 2-D system of bandwidth is higher；But when SNR is promoted to more than 17.5dB, with ESE It measures, it using traditional 2-D STSK system of 16QAM will be advantageously.This imply that 3-D STSK is down to medium SNR range in have preferable application potential.

Embodiment 2

The combined optimization method of keying method when the present invention also provides a kind of for sky, as shown in figure 3, it is embodied Scheme is as follows:

S1. N is generated at random_RDA N-D planisphere and DMS pairs, to each planisphere and DMS to calculating corresponding N-D STSK The discrete input of system continuously exports channel capacity, and therefrom finds out the planisphere for possessing maximum capacity and DMS as initial Planisphere Ω (1) and DMS χ (1), wherein DMS is indicated with matrix χ, and the q column element in matrix χ is A_qVectorization as a result, As following formula indicates:

χ_:,q=vec (A_q) (q=1 ... Q)

S2. to using DCMC capacity C of the STSK system of Ω (1) and χ (1) at a certain specific SNR γ_DCMC(χ(1),Ω (1)) its gradient value A (1,1) to the χ and its gradient value B (1,1) to Ω, is calculated, wherein B (1,1)=▽_ΩC_DCMC(χ(1), Ω (1)), A (1,1)=▽_χC_DCMC(χ (1), Ω (1)) has ordinal number to respectively correspond DMS to (1,1) in A (1,1) and B (1,1) With constellation graph laplacian；

S3. be arranged DMS initial search direction D (1)=A (1,1) and planisphere initial search direction G (1)=B (1, 1), step-size in search μ > 0, iteration ends value ε > 0 and sliding average window size L are set_c∈Z⁺, set initial change amount β (1) =| | A (1,1) | |+| | B (1,1) | | and i=1；

S4. DMS: χ new (i+1)=χ (i)+μ D (i) is obtained；

S5. new planisphere is obtained: if transmitting terminal by the way of directly extending to constellation point Ω in time_lIt is adjusted System,

Then

If transmitting terminal is by the way of combinatorial coordinates to constellation point Ω_lIt is adjusted and N is even number,

Then Ω (i+1)=Ω (i)+μ G (i)；

If N is odd number, new planisphere is obtained by formula (2)；

S6. the new DMS direction of search: D (i+1)=φ is calculated_iD (i)+A (i+1, i+1), in which:

S7. the new planisphere direction of search: G (i+1)=ψ is calculated_iG (i)+B (i+1, i+1), in which:

S8. calculate variable quantity β (i+1)=| | A (i+1, i+1) | |+| | B (i+1, i+1) | |；

S9.i=i+1, if i < 2L_c, then going to S4, otherwise enter S10；

S10. ifSo χ (i) and Ω (i) is exactly the DMS that final optimization pass is crossed With N-D planisphere, S4 is otherwise gone to.

Wherein, it in step S4, calculates after obtaining new DMS, power normalization is carried out to new DMS, specific as follows:

It in the step S5, calculates after obtaining new planisphere, power normalization is carried out to new planisphere, specifically such as Under:

Simultaneously in order to which the superiority to method provided by the invention is adequately illustrated, further experiment has also been done, It is as follows to test concrete condition:

The present embodiment optimizes 3-D and 4-D system, i.e. R3 3-D STSK, R4 using MDJO algorithm (combined optimization method) 4-D STSK and R2 4-DSTSK, what is used is configured to 3D-STSK (3,2,2,16,3), 4D-STSK (3,2,2,16,4) and 4D- STSK(3,2,2,16,2).For R2 4-D STSK, to combinatorial coordinates (x₁+jx₂,x₃+jx₄) optimize.Meanwhile N is set_RD =100, μ=5, L_c=15, ε=0.001.In addition, to avoid falling into local optimum [6], φ_iAnd ψ_iValue every 10 times repeatedly 0 is reset to after generation.Gradient operator used in this optimization method is defined as: WhereinWithIt respectively indicates to the 1st column of matrix χ and to the 1st of matrix Ω Column derivation, above-mentioned gradient operator define in other formulas meaning and so on；It defines simultaneouslyAccording to document [6], ▽_mC_DCMCTheoretical value are as follows:

Desired operation, the intermediate quantity in formula (20) are asked in wherein E [] formula expressionIs defined as:

Wherein K_q,lAnd K_q',l'Indicate two different equivalent signal transmission matrixs, andIt can be calculated as described below:

Wherein []^HIndicate conjugate transposition.▽_kC_DCMCIt can similarly be calculated according to formula (20), the gradient in formula Theoretical value are as follows:

In formula (23), there is δ as k=l_k,l=1, there is δ as k ≠ l_k,l=0.Pay attention in formula (21)-(23), for R3 3-D STSK, there is R=3；For R4 4-D STSK, there is R=4；For R2 4-D STSK, R=2.Optimization calculates the SNR chosen It is set as 0dB.

Fig. 8 and Fig. 9 compares the 3-D STSK being not optimised when using 16RCIC and 3-D the and 4-D system that optimized The comparison of FER and ESE performance.It can be seen that the 3-D scheme optimized has than using 16RCIC's in the identical situation of R value The better bit error rate performance of 3-D scheme.In addition, increasing the dimension of planisphere under similar system configuration, such as increase from 3-D The improvement of performance can be obtained to 4-D, this point can be as can be seen from Figure 9.Specifically, the R4 4-D and R2 of MDJO have been used 4-D is got well than the performance of the R3 3-D and R2 3-D STSK optimized respectively.In addition, the ESE result of Fig. 9 and observing for Fig. 7 Be consistent, i.e., at low SNR, have higher effective spectrum efficiency than the scheme of low-dimensional using the scheme of higher-dimension planisphere.

Obviously, the above embodiment of the present invention be only to clearly illustrate example of the present invention, and not be pair The restriction of embodiments of the present invention.For those of ordinary skill in the art, may be used also on the basis of the above description To make other variations or changes in different ways.There is no necessity and possibility to exhaust all the enbodiments.It is all this Made any modifications, equivalent replacements, and improvements etc., should be included in the claims in the present invention within the spirit and principle of invention Protection scope within.

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