CN106911622A - ACO ofdm system channel estimation methods based on compressed sensing - Google Patents

Abstract

The present invention is claimed a kind of ACO OFDM radio optical communication system channel estimation methods based on compressed sensing, belongs to intensity modulated optical communication field.The channel estimation methods are that frequency pilot sign causes the problem of bandwidth availability ratio reduction in order to solve to be based in the channel estimation of pilot tone.With ACO ofdm systems be combined channel estimation technique based on compressed sensing by the present invention, making pilot tone first has Hermitian symmetry, by minimizing DFT sub-matrix column cross-correlation quadratic sums come optimizing pilot allocative decision, and propose a kind of ACO ofdm systems pilot tone distribution optimized algorithm；Then channel response is estimated by a kind of improved variable step degree of rarefication Adaptive matching tracing algorithm, the innovatory algorithm can improve estimated accuracy and calculating speed, and further improve estimated accuracy using a kind of iterated revision algorithm finally.The method can effectively reduce frequency pilot sign number compared to channel estimation methods of the tradition based on pilot tone, improve system bandwidth utilization rate.

Description

ACO-OFDM system channel estimation methods based on compressed sensing

Technical field

The invention belongs to intensity modulated optical communication field, specially a kind of ACO-OFDM wireless opticals based on compressed sensing are led to Letter system channel estimation method.

Background technology

Wireless light communication has a free frequency spectrum resource, great available bandwidth, and system equipment is simple, small volume, secrecy Property it is good and by advantages such as electromagnetic interferences.Capacity and bandwidth demand more and more higher for communication system, wireless light communication show Go out its application value in a communications system, see document：“Boucouvalas A,Chatzimisios P,Ghassemlooy Z,et al.Standards for indoor Optical Wireless Communications[J].IEEE Communications Magazine,2015,53(3):24-31. " is described.Document " Gonzalez O, Perez-Jimenez R,Rodriguez S,et al.OFDM over indoor wireless optical channel[J].IEE Proceedings-Optoelectronics,2005,152(4):The wireless optical OFDM that 199-204. " is proposed (OFDM) technology, can effectively improve message transmission rate, be the important development direction of following wireless light communication technology.

Simple intensity modulated/direct detection (IM/DD) technology of equipment being used current wireless optical ofdm communication system more, it It is the luminous intensity that the electric signal of transmission is modulated to optical carrier, it is desirable to which electric signal is necessary for nonnegative real number.Common intensity is adjusted Light OFDM technology processed is document " Armstrong J, Lowery A J.Power efficient optical OFDM [J] .Electronics Letters,2006,42(6):The asymmetric amplitude limit light OFDM (ACO-OFDM) proposed in 370-372. ". Its signal to transmitting terminal carries out Hermitian and converts and carry out inverse fast Fourier transform after being assigned to odd subcarriers (IFFT) non-negative real signal then, is obtained by null value amplitude limit.

Optical signal may be caused error in communication process by channel effect, it is therefore desirable to carry out channel estimation then right Impacted optical signal is compensated.Channel estimation technique based on pilot tone is the wide variety of channel estimation side of OFDM technology Formula；Document Hashemi S K, Ghassemlooy Z, Chao L, et al.Channel estimation for indoor diffuse optical OFDM wireless communications[C].International Conference on Broadband Communications,Networks and Systems,2008.Broadnets.IEEE,2008:431- 434. propose using the ACO-OFDM system pilot channels methods of estimation of least square (LS) algorithm, but LS algorithms estimate essence Degree is not enough, and excessive frequency pilot sign will seriously reduce system subcarrier utilization rate, be unfavorable for high speed data transfer.

Channel estimation methods based on compressive sensing theory can effectively reduce pilot tone while estimated accuracy is ensured Number, improves system subcarrier utilization rate.Document " Bajwa W U, Haupt J, Sayeed A M, et al.Compressed Channel Sensing:A New Approach to Estimating Sparse Multipath Channels[J] .Proceedings of the IEEE,2010,98(6):1058-1076. " proposes the sparse multipath letter based on compressed sensing Road estimation theory, document " Qi C, Wu L.A Study of Deterministic Pilot Allocation for Sparse Channel Estimation in OFDM Systems[J].IEEE Communications Letters, 2012,16(5):742-744. " proposes OFDM channel estimation method and pilot tone the distribution optimization method based on compressed sensing.

Domestic and foreign scholars have certain achievement to the OFDM channel estimation method research based on compressed sensing, but for pressure The research that contracting perception theory is applied in ACO-OFDM channel estimations is still insufficient.Due to ACO-OFDM and conventional OFDM systems It is different, it is adaptable to which that the compressed sensing channel estimation methods of conventional OFDM systems can not be directly applied in ACO-OFDM systems.Base In above mentioned problem, set forth herein a kind of ACO-OFDM system channel estimation methods based on compressed sensing, asked for pilot tone distribution Topic, proposes a kind of pilot tone allocation algorithm, and propose that a kind of follow-on degree of rarefication Adaptive matching is followed the trail of (SAMP) algorithm and carried out Channel estimation.

The content of the invention

Present invention solves the technical problem that being：Because ACO-OFDM system frequency-region signals have Hermitian symmetry, no Conventional OFDM systems are same as, it is necessary to solve the pilot tone assignment problem of ACO-OFDM systems, and can restructing algorithm quick and precisely Recover the performance that channel response also contributes to compressed sensing channel estimation in ground.Proposed for problem above a kind of suitable for ACO- The pilot tone distribution optimization method of OFMD systems simultaneously improves SAMP algorithms and improves estimated accuracy and computational efficiency.

The technical solution adopted in the present invention is：A kind of pilot tone distribution optimization method of ACO-OFDM systems is improved with a kind of SAMP restructing algorithms.In the channel estimation based on compressed sensing, calculation matrix is by frequency pilot sign and the corresponding DFT of pilot tone index The row composition of matrix.Pilot tone distribution optimization can regard the construction of compressed sensing calculation matrix as, and it needs to meet RIP properties.But RIP Nature comparisons are abstract, realize that difficulty is larger in actual applications, and this programme is proposed using minimum DFT rectangular array cross-correlation The method of quadratic sum optimizes the pilot allocation scheme of ACO-OFDM systems.First to meet ACO-OFDM system requirements, order is inserted The pilot tone for entering has Hermitian symmetry, and calculation matrix, pilot bit are constituted by the corresponding DFT row matrixs of frequency pilot sign The selection put is obtained by minimum rectangular array cross-correlation quadratic sum, i.e., the row composition submatrix being adapted to is chosen from DFT matrixes, and Make the matrix column cross-correlation quadratic sum minimum, selected row has corresponded to the insertion position of pilot tone.The method is verified compared to RIP More directly perceived, easily application.In this theoretical foundation, ACO-OFDM system pilots are drawn with reference to the Hermitian symmetry of pilot tone Distribution optimized algorithm.

In channel estimation, restructing algorithm generally needs to ensure reconstruction accuracy and arithmetic speed.SAMP algorithms can be disobeyed Channel degree of rarefication priori conditions reconstruct channel response is relied often to apply in practice.Further to improve restructing algorithm arithmetic speed, Propose a kind of variable step SAMP algorithms.Indoor wireless optical channel generally have it is openness and with fading characteristics, in channel estimation Element during reconstruct with higher value would generally be reconstructed in initial iterations；As reconstruction signal is closer to actual signal Degree of rarefication, the change of its reconstruction signal energy is also tended to steadily.In addition SAMP arithmetic accuracies are relevant with step-length selection, and big step-length can To reduce iterations but precision is relatively low；Small step-length has preferable reconstruction accuracy, but also results in amount of calculation increase.Variable step SAMP algorithms are gradually reduced step-length according to iterations, and beginning goes out the channel response coefficient of higher value with big step-length quick reconfiguration, The method for gradually approaching channel degree of rarefication with small step-length takes into account computational efficiency and reconstruction accuracy.Precision of channel estimation is removed and calculated with reconstruct Method phase is outside the Pass, also relevant with calculation matrix performance.Although being divided using rectangular array cross-correlation quadratic sum method optimizing pilot is minimized With scheme, but still evaluated error can be caused due to calculation matrix performance.So after variable step SAMP algorithms carry out channel estimation, The evaluated error that calculation matrix is caused is reduced by a kind of iterated revision algorithm.

Brief description of the drawings

Fig. 1 ACO-OFDM systematic schematic diagrams；

The ACO-OFDM system channels that Fig. 2 is based on compressed sensing estimate flow chart；

Method proposed by the present invention compares with conventional channel method of estimation estimated accuracy under Fig. 3 same pilot numbers；

Method proposed by the present invention compares with conventional channel method of estimation error rate of system under Fig. 4 same pilot numbers；

Specific embodiment

Below in conjunction with accompanying drawing, implementation of the invention is further described.

ACO-OFDM systematic schematic diagrams are as shown in Figure 1.The present invention uses Comb Pilot, will in order to meet ACO-OFDM systems Ask, frequency pilot sign there need to be Hermitian symmetry and be inserted in odd subcarriers, with following relation：

Wherein N_PIt is pilot tone number ()^*Represent conjugation.

Calculation matrix during ACO-OFDM system channels are estimated is by frequency pilot sign and DFT submatrixsComposition, i.e.,：

WhereinIt is according to corresponding to pilot frequency locations N × NDFT row matrixs and preceding L row constitute, L is channel length.It is pilot frequency locations index, it is necessary to note Meaning be odd subcarriers it is corresponding be even number line in DFT matrixes because carrier number is calculated and DFT matrixes since 0 Row is calculated since 1, thereforeIt is even number.

According to compressive sensing theory, calculation matrix needs to meet RIP conditions, and the present invention is using minimum DFT matrixes The method of row cross-correlation number total sum of squares is come optimizing pilot position and is selected instead of RIP conditions, and the summation of its row cross-correlation square is determined Justice is：

Because pilot tone has Hermitian symmetry, pilot tone index has's Relation, may certify that and obtain：

Wherein(4) formula shows ACO-OFDM system pilots Distribution optimization can be by minimizingMode is obtained.That is only need fromDFT squares Chosen in battle arrayIndividual even number line constitutes submatrix W and calculates C_W, select C_WThe indexed set during minimum value for takingThen basis FormulaRelation obtain final pilot allocation scheme.

ACO-OFDM pilot tones distribution optimized algorithm is specially：

Definition：DFT submatrixs are It is i ＆ lt loop computation occasional pilot indexed set,It is i-th The pilot tone distribution index collection of secondary loop computation, N_pIt is the total number of pilots of insertion.

(1) initializeHere k be any even number andI=i+1.

(2) byIt is middle to add an even element to set up ith iteration calculatingIt is individual alternative Indexed set,DFT is obtained according to alternative indexed set MatrixAnd calculate

(3) selectThe indexed set that alternative indexed set when obtaining minimum value is obtained as ith iteration, i.e.,

(4) ifReturn (2), otherwise carry out (5).

(5) indexed set obtained according to the 4th stepAnd formulaIt is calculated final needs Pilot tone distribution index collection P.

ACO-OFDM system pilot indexed sets are obtained by above-mentioned algorithm to be designated asChannel Shock response sequence is denoted as h=[h (1) h (2) ... h (L)]^T, it can be expressed from the next：

Wherein L represents channel length, and less than circulating prefix-length, t_sIt it is the OFDM time-domain sampling cycles, τ represents every road The time delay in footpath, the numerical value depends on the average reflectance on room-size and surface.Assuming that all frequency pilot signs are equal, it is right to constitute Angular moment battle arrayPilot tone is remembered by the pilot tone received after channel ForRelation so between them has：

Y_P=Wh+ η (6)

Wherein η=[η (1) η (2) ... η (N_p)]^TIt is white Gaussian noise,

Condition of sparse channel response h in formula (6) can be reconstructed by SAMP algorithms and drawn.The reconstruction accuracy of SAMP algorithms and step Selection long is relevant, and big step-length can accelerate algorithm the convergence speed but cause reconstruction accuracy poor；When step-length is smaller reconstruction accuracy compared with It is good, but convergence rate is slower, and operation efficiency is relatively low.There is the characteristic of similar exponential damping due to wireless optical channel, with larger The response coefficient of numerical value can be reconstructed at the algorithm initial stage, as iterations increases, the larger unit of numerical value in channel response coefficient Plain number is also reduced therewith.Therefore the present invention estimates channel response using a kind of variable step SAMP algorithms.

Specify in the algorithm：I represents iterations, r_iResidual error is represented, s is step-length, and L represents supported collection size, B_iRepresent The indexed set that i iteration is obtained, C_iRepresent candidate's supported collection, F_iRepresent final supported collection, h_iRepresent that the channel that i ＆ lt is obtained rings Answer coefficient vector.Variable step SAMP algorithms are concretely comprised the following steps：

(0) initialize：I=1, r₀=Y_p,L=s, h₀=[0 0 ... 0]^T。

(1) calculate | | W^Hr_i-1| |, choose W matrix columns index corresponding to L maximum value and be stored in B_i, obtain candidate's support Collection C_i=F_i-1∪B_i。

(2) according to candidate's supported collection C_iSubmatrix is chosen from W matrixes, and is calculatedChoose L maximum value Corresponding column index is stored in F_i。

(3) according to final supported collection F_iSubmatrix is chosen from W matrixes, the channel response system that i ＆ lt is obtained is calculated Number vectorAnd update residual error

(4) judge whether to meet stop condition, if meet exiting circulation, return to h_i, otherwise into step 5.

(5) judge whether to meet | | r_new||≥||r_i-1| |, if meet entering (6), if being unsatisfactory for entering (8).

(6) judge whether to meet | | h_i||-||h_i-1||≤γ₁, if it is satisfied, s=β₁S, L=L+s, r_i=r_i-1, h_i-1 =h_i, i=i+1, return (1) continuation iteration.If being unsatisfactory for entering (7).

(7) s=s- β₂, L=L+s, r_i=r_i-1, h_i-1=h_i, i=i+1, return (1) continuation iteration.

(8) residual error r is updated_i=r_new, update supported collection F_i-1=F_i, i=i+1 simultaneously return (1) continue iteration.

Stop condition is：||r_new| | ＜ ε or | | h_i||-||h_i-1||≤γ₂。

SAMP algorithms estimated accuracy is relevant with computational efficiency and step-length setting, variable step SAMP algorithms by change step-length come Optimized algorithm efficiency and precision, the signal energy difference reconstructed by adjacent iterations is come given threshold.When algorithm starts Step-length can be set to bigger numerical, numerical value is larger in so can reconstructing channel response coefficient by a small amount of iterations Element, i.e., by big step-length Fast Convergent.As iterations increases, the element that numerical value is larger in channel response coefficient is reduced, step It is long to be reduced so as to steady convergence degree of rarefication, i.e. step (7) by linear.Set when the signal energy difference that adjacent iterative reconstruction goes out is less than When determining threshold value, show that reconstruction signal has tended towards stability, step-length multiple reduces to reach the step in best estimate precision, i.e. algorithm Suddenly (6).By setting constant beta in step (6) and step (7)₁And β₁To control step-length to restrain.ε can generally be set in stop condition Noise energy, | | h_i||-||h_i-1||≤γ₂Show the channel response coefficient stabilization estimated, higher value has reconstructed completion can stop Only iteration.The algorithm can take into account computational efficiency and reconstruction accuracy.

The present invention optimizes ACO-OFDM system pilots using the method for minimizing DFT rectangular array cross-correlation number totals sum of squares Distribution, and channel response is reconstructed by variable step SAMP, but the evaluated error brought by calculation matrix performance is difficult to avoid that, to enter One-step optimization estimated accuracy, estimated accuracy is further improved using a kind of iterated revision algorithm.Obtained by variable step SAMP algorithms Channel time domain response coefficient be designated as h₀, frequency domain is H₀, calculation matrix is W, and h is real channel response coefficient, then had：

WhereinSo (7) formula can be obtained：

G_WIt is the Gram matrixes of calculation matrix W, it is clear that if orthogonal between any two row of matrix W, then matrix G_WIt is right Angular moment battle array, precision of channel estimation will not be influenceed by matrix W.But if coefficient correlation is larger between matrix W row, then channel is estimated Meter precision will decline, to mitigate the influence using following iterated revision algorithm：

Iterations is designated as k, and λ is coefficient of relaxation, and iterative algorithm is specially：

h_k=λ (h₀-G_Wh_k-1)+h_k-1 (9)

Because intensity-modulated light OFDM channel responses have Decay Rate and response coefficient is arithmetic number, and combine variable step The final supported collection size L that SAMP algorithms are obtained, choose in the channel response coefficient that obtains of iterative algorithm preceding L maximum and Minus coefficient zero is obtained into final channel estimation results.

The ACO-OFDM radio optical communication system channel estimation methods based on compressed sensing proposed by the present invention are entered above Detailed description is gone, its flow chart is as shown in Figure 2.The method can effectively be reduced compared to traditional pilot channel estimation methods and led Frequency symbol number, improves bandwidth availability ratio and estimated accuracy.In the case of same pilot number, channel proposed by the invention is estimated Meter method is contrasted respectively as shown in Figures 3 and 4 with the estimated accuracy and error rate of system of channel estimation methods of the tradition based on pilot tone. It may be seen that when pilot tone number is identical, ACO-OFDM system channels proposed by the present invention estimate that performance is substantially better than traditional letter Channel estimation method.

Claims (5)

1. a kind of ACO-OFDM radio optical communication system channel estimation methods based on compressed sensing, its step is：First have to Derivation frequency symbol has Hermitian symmetry and is inserted in odd subcarriers, and using minimum DFT rectangular array cross-correlation The method of number total sum of squares carrys out optimizing pilot allocative decision, proposes ACO-OFDM system pilots distribution optimized algorithm, and using should The pilot allocation scheme insertion pilot tone that algorithm is obtained, channel response estimation is carried out in receiving terminal using variable step SAMP algorithms, is become Step-length SAMP algorithms are by changing constant beta₁And β₁To control step-length convergence rate, efficiency of algorithm and estimated accuracy are improved, finally will The channel response that variable step SAMP algorithms are obtained further improves estimation by iterated revision algorithm combining wireless optical channel feature Precision.

2. frequency pilot sign according to claim 1 has Hermitian symmetry and is inserted in odd subcarriers, and adopts Selected come optimizing pilot position with the method for minimizing DFT rectangular array cross-correlation number totals sum of squares, it is characterised in that：ACO-OFDM There is N in N number of subcarrier of symbol_PIndividual frequency pilot sign, be with Hermitian symmetry：

And selected come optimizing pilot position by minimizing DFT rectangular arrays cross-correlation number total sum of squares, row cross-correlation square Summation is defined as：

$C_W=\underset{\begin{array}{c}m,n=1\\ m<n\end{array}}{\overset{L}{\&Sigma;}}|\underset{i=1}{\overset{N_p}{\&Sigma;}}W(i,m)\stackrel{\&OverBar;}{W(i,n)}{|}^2.$

3. ACO-OFDM system pilots distribution optimized algorithm according to claim 1, and the pilot tone obtained using the algorithm Allocative decision inserts pilot tone, it is characterised in that：ACO-OFDM system pilots distribution optimized algorithm is specially：

(1) initializeHere k be any even number andI=i+1；

(2) byIt is middle to add an even element to set up ith iteration calculatingIndividual alternative index Collection,DFT submatrixs are obtained according to alternative indexed setAnd calculate

(3) selectThe indexed set that alternative indexed set when obtaining minimum value is obtained as ith iteration, i.e.,

(4) ifReturn (2), otherwise carry out (5)；

(5) indexed set obtained according to the 4th stepAnd formulaIt is calculated the pilot tone of final needs Distribution index collection P.

4. a kind of variable step SAMP algorithms according to claim 1 carry out channel estimation, it is characterised in that：In SAMP algorithms In by setting constant beta₁And β₁To control step-size change, specific algorithm is：

(0) initialize：I=1, r₀=Y_p,L=s, h₀=[0 0 ... 0]^T；(1) calculate ||W^Hr_i-1| |, choose W matrix columns index corresponding to L maximum value and be stored in B_i, obtain candidate's supported collection C_i=F_i-1∪B_i；

(2) according to candidate's supported collection C_iSubmatrix is chosen from W matrixes, and is calculatedChoose L maximum value corresponding Column index be stored in F_i；

(3) according to final supported collection F_iSubmatrix is chosen from W matrixes, the channel response coefficient vector that i ＆ lt is obtained is calculatedAnd update residual error

(4) judge whether to meet stop condition, if meet exiting circulation, return to h_i, otherwise into (5)；

(5) judge whether to meet | | r_new||≥||r_i-1| |, if meet entering (6), if being unsatisfactory for entering (8)；

(6) judge whether to meet | | h_i||-||h_i-1||≤γ₁, if it is satisfied, s=β₁S, L=L+s, r_i=r_i-1, h_i-1=h_i, i =i+1, returns to (1) and continues iteration.If being unsatisfactory for entering (7)；

(7) s=s- β₂, L=L+s, r_i=r_i-1, h_i-1=h_i, i=i+1, return (1) continuation iteration；

(8) residual error r is updated_i=r_new, update supported collection F_i-1=F_i, i=i+1 simultaneously return (1) continue iteration；

Stop condition is：||r_new| | ＜ ε or | | h_i||-h_i-1||≤γ₂。

5. a kind of iterated revision algorithm according to claim 1, it is characterised in that：Iterated revision algorithm is specially：Iteration Number of times is designated as k, and λ is coefficient of relaxation, and iterative step is：

h_k=λ (h₀-G_Wh_k-1)+h_k-1,

The final supported collection size L obtained by variable step SAMP algorithms, chooses h_kIn preceding L maximum and by minus system Number zero obtains final channel estimation.