CN101562464B - Method for detecting spherical decode based on depth-first search - Google Patents

Abstract

The invention provides a method for detecting spherical decode based on depth-first search, which comprises the following steps: A, performing QR deposition on a channel matrix; B, multiplying a conjugate transpose and a received signal of a Q matrix to obtain an equalizing signal rho; C, setting an initial search radius; D, executing the depth-first search according to the initial search radius, an R matrix and the rho, and updating the search radius; E, setting an upper limit value M of the search total node number and an upper limit value Ki of the ith layer search node number; F, executing the depth-first search according to the current search radius, the R matrix and the rho, and when the search gets to the ith layer, judging whether the searched node number on the ith layer is equal to Ki or not, otherwise, executing the search on the ith layer, and if so, getting to search the i+1th layer; and G, repeating the step F until the searched total node number is equal to M or all the layers cannot be searched any more, and outputting a decoding result. The method can effectively reduce the operation complexity of the sphere decoding, and is easy to achieve through hardware.

Description

A kind of method for detecting spherical decode based on depth-first search

Technical field

The invention belongs to wireless communication field; Be particularly related to a kind of method for detecting spherical decode based on depth-first search that is used for multiple-input and multiple-output (MIMO) system, the present invention also can be applied in OFDM (OFDM) and the mimo system detection to the MIMO signal.

Background technology

MIMO maximum likelihood (ML) detects and can make system obtain best bit error rate performance; But the search of traversal formula is because of its nondeterministic polynomial (Non-deterministic polynomial; NP) computational complexity often is difficult to real-time implementation and maybe can not realizes in real system, the MIMO-ML of low complex degree and always be mimo system problem to be solved near the signal detection algorithm of ML.

Viterbo etc. have proposed a kind of detection algorithm that is called as globular decoding (sphere decoding) to the source signal with lattice-shaped planisphere on the research basis of Pohst etc.Globular decoding comes down to be configured to MIMO-ML detection problem the problem of an optimal path of search on a source signal constellation point tree, and in search procedure, constantly strengthens constraints.The operation principle of globular decoding is: in receiving signal space, presetting one earlier is the ball in the center of circle with the received signal points; Be mapped as an ellipsoid in the space that transmits to this ball again; And possible the transmitting a little of search in ellipsoid; In case find one to transmit a little, promptly the mapping point with this signaling point is that radius shrinks preset ball with the distance that receives signal, thereby makes follow-up search be able in littler scope, carry out.

After initial globular decoding algorithm occurs, because computational complexity is still very high, therefore a lot of improvement have appearred.The globular decoding algorithm of propositions such as Viterbo all starts anew to search for after dwindling the radius of a ball at every turn, thereby has comprised repeat search; Chan etc. have done improvement to it, the search after at every turn dwindling the radius of a ball below continue the source signal point position that searches, thus eliminated repeat search, further reduced the complexity of search.Traditional globular decoding algorithm is not generally considered the influence of channel estimation errors, and Xu etc. have proposed to combine the size of average channel estimation error to calculate the algorithm of the radius of a ball in a source signal point back that searches at every turn.The tree search of globular decoding has reached the purpose that reduces computational complexity through constantly dwindling the hunting zone.The research of Hassibi and Vikalo shows that globular decoding has the multinomial operation complexity.

However, the globular decoding algorithm still has many deficiencies, has influence on the practical application of this algorithm.At first, the selection of initial radium is most important for globular decoding, and excessive initial radium can cause excessive computational complexity, and the mapping point that transmits does not all have and make to search for failure in the ball and too small initial radium can cause.Then; Grid point quantity is a stochastic variable in the globular decoding; Receive the influence of channel condition, noise and initial radium, thus the quantitative analysis detection complexity with postpone very difficulty, pointed as Jalden etc.; The computational complexity of globular decoding remains NP's under worst condition, this is very disadvantageous in the real time high-speed rate is used; In addition, the uncertain hardware of globular decoding that also makes is realized acquiring a certain degree of difficulty.

Summary of the invention

Technical problem to be solved by this invention provides a kind of method for detecting spherical decode based on depth-first search, with the computational complexity of reduction globular decoding, and is easy to realize through hardware.

For solving the problems of the technologies described above, the present invention provides technical scheme following:

A kind of method for detecting spherical decode based on depth-first search comprises the steps:

A, channel matrix H is carried out QR decompose, obtain Q matrix and R matrix;

B, with the conjugate transpose of Q matrix with receive signal y and multiply each other, obtain receiving the equalizing signal rho of signal;

C, the initialization search radius is set;

D, carry out depth-first search, and the current search radius is updated to the weights of the bottom node that searches according to said initialization search radius, R matrix and ρ;

The higher limit K of E, the upper limit value M that the search total node number is set and i layer search node number _i, i=1,2 ..., N _T, N _TBe number of transmit antennas;

F, carry out depth-first search, when search enters into the i layer, judge whether the node number that the i layer was searched for equals K according to current search radius, R matrix and ρ _i, if not, carry out the search of i layer, if, the search that gets into the i+1 layer;

G, repeated execution of steps F, when total node number of search equals M or all layers and all can not continue to carry out search, the output decode results.

Above-mentioned method for detecting spherical decode, in the steps A, the QR that said QR is decomposed into ordering decomposes, and makes the mould value of i element on the diagonal of R matrix be not more than the mould value of i+1 element.

Above-mentioned method for detecting spherical decode in the step e, is provided with the higher limit K of said i layer search node number according to modulation system, target bit and channel condition information _i

Above-mentioned method for detecting spherical decode, in the step e, the higher limit K of set i layer search node number _iBe not less than the higher limit K of i+1 layer search node number _I+1

Above-mentioned method for detecting spherical decode, in the step F, the search of carrying out the i layer comprises:

Whether the weights of judging the present node correspondence if not, cut down present node and all branch thereof less than the current search radius; If; Judge whether present node is bottom node; If present node is not a bottom node, then the child node of present node is carried out table-looking-up sequencing according to the sphere decoding expression of being confirmed by R matrix and ρ, and calculate the search that gets into the i+1 layer behind the weights of said child node; If present node is a bottom node, then upgrade the weights that the current search radius is a present node.

Above-mentioned method for detecting spherical decode, step C specifically comprises:

C1, the current condition number of channel of calculating and signal to noise ratio;

C2, according to said conditional number and snr computation one associating weights;

C3, calculate a threshold values according to modulation system and target bit;

C4, whether judge said associating weights, if then calculate the initialization search radius based on the interchannel noise variance greater than said threshold values; Otherwise, separate calculating initialization search radius based on receiving the signal Minimum Mean Square Error.

The present invention is in the globular decoding testing process based on depth-first search, and the node number of every layer of search and total search node number limit, and have reduced the computational complexity of globular decoding, and have made algorithm have controllability and robustness.The QR that the present invention also further sorts to channel matrix decomposes, and, adopt lookup table mode to carry out the intranodal ordering, further reduced the computational complexity of globular decoding, and be easy to realize through VLSI hardware.

Description of drawings

Fig. 1 is basic mimo system illustraton of model;

Fig. 2 is the method for detecting spherical decode flow chart based on depth-first search of the embodiment of the invention;

Fig. 3 is the flow chart that is provided with of initialization search radius in the embodiment of the invention;

Fig. 4 compares sketch map for the algorithm complex of the globular decoding of the traditional spheroidal decoding and the embodiment of the invention.

Embodiment

For making the object of the invention, technical scheme and advantage clearer, describe the present invention below in conjunction with accompanying drawing and specific embodiment.

Mimo system model for basic is as shown in Figure 1, supposes that number of transmit antennas is N _t, the reception antenna number is N _R, its channel is a falt fading channel, then this system can use shown in the following formula:

y＝H·s+n (1)

Wherein y is N _R* 1 received signal vector, s are N _t* 1 emission signal vector, n is N _R* 1 noise vector, its average are 0, and variance is N ₀/ 2, H is N _R* N _tThe channel model vector (channel matrix) of dimension.

Adopt the maximal possibility estimation algorithm, expression formula is following:

$\underset{s\∈\mathrm{\Ω}}{\min }{\left|\right|n\left|\right|}^2=\underset{s\∈\mathrm{\Ω}}{\min }{\left|\right|y-\mathrm{Hs}\left|\right|}^2---\left(2\right)$

Wherein, Ω is effective modulation signal point.In order to reduce the maximum likelihood algorithm complexity; In the globular decoding algorithm, proposed to reduce the method for search volume; Its core concept is exactly to select the radius of a suitable initial radium as the globular decoding region of search, and the target of globular decoding is exactly square to satisfy the grid point of following expression formula (3) for removal search in the diameter of Spherical Volume of C at initial radium.

$E=\underset{s\∈\mathrm{\Ω}}{\min }{\left|\right|y-\mathrm{Hs}\left|\right|}^2---\left(3\right)$

H is carried out the QR decomposition can obtain unitary matrice Q and upper triangular matrix R.Therefore, expression formula (3) is continued to decompose can obtain following expression formula (4):

Because R is a upper triangular matrix, therefore can utilize the method for iteration, obtain following expression formula (5):

Wherein, $\mathrm{\ρ}=Q^{H}y={({\mathrm{\ρ}}_1,{\mathrm{\ρ}}_2,{\mathrm{\ρ}}_3,...,{\mathrm{\ρ}}_{N_R})}^T,$ r _{I, j}The capable element that is listed as with j of representing matrix R i, () ^HExpression is asked conjugate transpose to (), Be the demodulation vector,

For J element of vector.Because (5) second is a constant in the expression formula, can not influence follow-up judgement to globular decoding, therefore can it be ignored usually.

Order ${\mathrm{\β}}_k=({\mathrm{\ρ}}_k-\underset{j=k+1}{\overset{N_t}{\mathrm{\Σ}}}{r}_{k,j}{\hat{s}}_j)/r_{k,k}$ With

Wherein, k=1,2 ..., N _tSo, can obtain following expression formula (6):

Can be write as following statement formula (7):

and

substitution following formula, can obtain following expression formula (8)

Can find out from above-mentioned formula, find the solution the emission vector in fact from N _tDimension (globular decoding the 1st layer) beginning, several modulation signal points that satisfy boundary condition are found out in setting according to radius

And then according to known N _tThe signal of dimension, and known N _tDimension present node and N _tThe boundary condition of-1 dimension is obtained N _tThe current point that satisfies condition of-1 dimension.Carrying out recursion like this goes down; Obtain the point

of first dimension (bottom of globular decoding) at last and form a hypersphere body by the candidate point of these dimensions, the point of hypersphere body wherein is exactly the grid point of the required acquisition of globular decoding.

In addition, in the present invention, for describing conveniently, with the e in the above formula _iThe Euclidean distance that is called node, E _iThe weights that are called node.

With reference to Fig. 2, the method for detecting spherical decode based on depth-first search of the embodiment of the invention mainly comprises the steps:

Step 201: channel matrix H is carried out QR decompose, obtain Q matrix and R matrix;

Preferably, the QR that said QR is decomposed into ordering decomposes, and obtains Q matrix, R matrix and P matrix (ordering switching matrix).QR through ordering decomposes, and makes the mould value of i element on the diagonal of R matrix be not more than the mould value of i+1 element, that is, the diagonal entry of said R matrix from the upper left corner to the lower right corner according to mould value sequence arrangement from small to large.The QR of ordering decomposes, and is equivalent to search tree is carried out the interlayer ordering.Through said interlayer ordering; Make that the Euclidean distance of upper level node is relatively large, the node number of every layer of search is set, can reduce the probability that correct constellation point is not searched in conjunction with self adaptation in the subsequent step; Thereby the raising search speed, the computational complexity of reduction globular decoding.

Step 202: the conjugate transpose and the reception signal y of Q matrix are multiplied each other, obtain receiving the equalizing signal rho of signal, that is, and ρ=Q ^HY;

In the present invention, be with the reception signal of ρ as equivalence, with the channel matrix of R matrix, and make up search tree based on R matrix and ρ and carry out globular decoding as equivalence.

Step 203: the initialization search radius is set;

Initial radium setting to globular decoding is the key factor that influences globular decoding algorithm complex and performance, and therefore, the present invention is optimized the initialized radius of traditional spheroidal decoding algorithm.With reference to Fig. 3, the said initialization search radius that is provided with specifically comprises the steps:

Step 301: calculate current condition number of channel and signal to noise ratio;

Step 302: according to said conditional number and snr computation one associating weights;

The computing formula of associating weights is: ψ=-(1-β) * CN+ β * SNR, wherein, ψ is the associating weights, and β is a weight coefficient, and CN is a conditional number, and SNR is a signal to noise ratio.

Step 303: calculate a threshold values according to modulation system and target bit;

Step 304～306: whether judge said associating weights greater than said threshold values, if then calculate the initialization search radius based on the interchannel noise variance; Otherwise, separate calculating initialization search radius based on receiving the signal Minimum Mean Square Error.

The computing formula of calculating the initialization search radius based on the interchannel noise variance is:

d ²=α N _Tσ ², wherein, d is the initialization search radius, α is the initial radium coefficient, σ ²Be noise variance.

Separating calculating initialization search radius based on reception signal Minimum Mean Square Error is specially:

Calculating the Minimum Mean Square Error that receives signal separates

$\hat{x}={(H^{H}H+I{\mathrm{\σ}}^2)}^{-1}{H}^{H}y,$ Wherein, I is a unit matrix, σ ²Be noise variance;

carried out hard decision obtain corresponding grid point, and utilize channel H to carry out reconstruct to obtain

Calculate initialization search radius d: $d=\left|\right|y-\hat{y}\left|\right|.$

Through the calculating of above-mentioned initialization search radius, can guarantee to have a grid point in the initial radium ball at least, thereby avoid the possibility of repeat search.

Step 204: carry out depth-first search according to said initialization search radius, R matrix and ρ, and the current search radius is updated to the weights of the bottom node that searches;

In this step, be to carry out a depth-first search according to sphere decoding expression (8).Through the current search radius being updated to the weights of the bottom node that searches, can so that the search of subsequent step in littler ball, carry out, thereby reduce the computational complexity of globular decoding.

Step 205: the upper limit value M of search total node number and the higher limit K of i layer search node number are set _i, i=1,2 ..., NT;

In traditional globular decoding algorithm; For every layer of search tree; The node number of search is at random, and the resource that therefore consumes also is at random, particularly under the bad situation of channel quality; Its algorithm complex might reach the complexity of ML algorithm, causes algorithm not have robustness and controllability like this.To this situation, every layer of node number of being searched for that the present invention proposes for search tree is adaptive, and whole globular decoding altogether the search node number be restricted principle.Like this, solved on the one hand that the globular decoding algorithm do not have a robustness with the potential risk problem that might get into endless loop (if channel matrix H is an ill-condition matrix), what is more important reduces the computation complexity of globular decoding greatly.

The higher limit K of said i layer search node number can be set according to modulation system, target bit and channel condition information (CSI) particularly, _i(this makes that every layer of node number of being searched for is adaptive).The higher limit K of i layer search node number preferably, can also be set _iBe not less than the higher limit K of i+1 layer search node number _I+1, that is, the node number of high-rise search is more relatively.The node number of high-rise search is more relatively, can reduce the probability that correct constellation point is not searched.

Step 206: carry out depth-first search according to current search radius, R matrix and ρ, when search enters into the i layer, judge whether the node number that the i layer was searched for equals K _i, if not, carry out the search of i layer, if, the search that gets into the i+1 layer;

Particularly, the search of carrying out the i layer comprises: whether the weights of judging the present node correspondence if not, cut down present node and all branch thereof less than the current search radius; If; Judge whether present node is bottom node; If not, the child node of present node is carried out table-looking-up sequencing according to the sphere decoding expression of being confirmed by R matrix and ρ, and calculate the search that gets into the i+1 layer behind the weights of said child node; If upgrading the current search radius is the weights of present node.

Child node for a node sorts, and conventional method is to calculate the Euclidean distance of each child node earlier, and the size according to Euclidean distance sorts then, sorts as adopting methods such as bubbling, insertion, and algorithm complex is high.In the present invention, do not need to calculate earlier the Euclidean distance of each child node, but directly carry out table-looking-up sequencing, thereby reach the purpose that reduces algorithm complex and elevator system performance according to the sphere decoding expression of confirming by R matrix and ρ (4).

So-called table-looking-up sequencing is meant: carry out iterative according to sphere decoding expression (4); Obtain the component of demodulation vector

definite

vector in current layer, and the position of this component in the source signal planisphere of current layer; Relative size according to the distance (Euclidean distance) between the position of each constellation point (node) of current layer source signal planisphere and said component sorts to said node.Because constellation point is regular distribution in the planisphere, therefore, after confirming said position, need not calculate Euclidean distance, just can directly confirm the relative size of the Euclidean distance between all constellation point and this position according to this regularity of distribution.

Step 207: whether total node number of judging search equals M, if, get into step 209, otherwise, step 208 got into;

Total node number through to search limits, and makes that the complexity of algorithm is controlled, and can avoid algorithm to get into endless loop.

Step 208: judge whether that all layers all can not continue to carry out search, if, get into step 209, otherwise, step 206 returned;

For the i layer, if there is not the node of also not searching in this layer, perhaps, the node number that this layer searched for has reached K _i, then this layer can not continue to carry out search.

Step 209: output decode results.

In this step, the constellation point mapping value in the path that the bottom node that final weights are minimum is corresponding consists of the globular decoding result.Need to prove that what in step 201, carry out is under the QR of the ordering situation of decomposing, also need sort to said constellation point mapping value that the sequence that ordering is obtained is as final decode results according to said P matrix.

Fig. 4 compares sketch map for the algorithm complex of the globular decoding of the traditional spheroidal decoding and the embodiment of the invention.Its simulated conditions is as shown in the table.

Send and reception antenna	4×4
		Modulation system	16QAM
Channel condition	Flat fading (flat fading)
		Chnnel coding	There is not chnnel coding
The emulation symbolic number	4×100

As can beappreciated from fig. 4, the algorithm complex of the embodiment of the invention is lower than the algorithm complex of traditional spheroidal decoding.

Should be noted that at last; Above embodiment is only unrestricted in order to technical scheme of the present invention to be described; Those of ordinary skill in the art is to be understood that; Can make amendment or be equal to replacement technical scheme of the present invention, and not break away from the spirit of technical scheme of the present invention, it all should be encompassed in the middle of the claim scope of the present invention.

Claims (9)

1. the method for detecting spherical decode based on depth-first search is characterized in that, comprises the steps:

A, channel matrix H is carried out QR decompose, obtain Q matrix and R matrix;

B, with the conjugate transpose of Q matrix with receive signal y and multiply each other, obtain receiving the equalizing signal rho of signal;

C, the initialization search radius is set;

D, carry out depth-first search, and the current search radius is updated to the weights of the bottom node that searches according to said initialization search radius, R matrix and ρ;

The higher limit K of E, the upper limit value M that the search total node number is set and i layer search node number _i, i=1,2 ..., N _T, N _TBe number of transmit antennas;

F, carry out depth-first search, when search enters into the i layer, judge whether the node number that the i layer was searched for equals K according to current search radius, R matrix and ρ _i, if not, carry out the search of i layer, if, the search that gets into the i+1 layer;

G, repeated execution of steps F, when total node number of search equals M or all layers and all can not continue to carry out search, the output decode results.

2. method for detecting spherical decode as claimed in claim 1 is characterized in that:

In the steps A, the QR that said QR is decomposed into ordering decomposes, and makes the mould value of i element on the diagonal of R matrix be not more than the mould value of i+1 element.

3. method for detecting spherical decode as claimed in claim 1 is characterized in that:

In the step e, the higher limit K of said i layer search node number is set according to modulation system, target bit and channel condition information _i

4. method for detecting spherical decode as claimed in claim 1 is characterized in that:

In the step e, the higher limit K of set i layer search node number _iBe not less than the higher limit K of i+1 layer search node number _I+1

5. method for detecting spherical decode as claimed in claim 1 is characterized in that, in the step F, the search of carrying out the i layer comprises:

Whether the weights of judging the present node correspondence if not, cut down present node and all branch thereof less than the current search radius; If; Judge whether present node is bottom node; If present node is not a bottom node, then the child node of present node is carried out table-looking-up sequencing according to the sphere decoding expression of being confirmed by R matrix and ρ, and calculate the search that gets into the i+1 layer behind the weights of said child node; If present node is a bottom node, then upgrade the weights that the current search radius is a present node.

6. method for detecting spherical decode as claimed in claim 1 is characterized in that step C specifically comprises:

C1, the current condition number of channel of calculating and signal to noise ratio;

C2, according to said conditional number and snr computation one associating weights;

C3, calculate a threshold values according to modulation system and target bit;

C4, whether judge said associating weights, if then calculate the initialization search radius based on the interchannel noise variance greater than said threshold values; Otherwise, separate calculating initialization search radius based on receiving the signal Minimum Mean Square Error.

7. method for detecting spherical decode as claimed in claim 6 is characterized in that, among the step C2, the computing formula of associating weights is:

ψ=-(1-β) * CN+ β * SNR, wherein, ψ is the associating weights, and β is a weight coefficient, and CN is a conditional number, and SNR is a signal to noise ratio.

8. method for detecting spherical decode as claimed in claim 7 is characterized in that, among the step C4, the computing formula of calculating the initialization search radius based on the interchannel noise variance is:

d ²=α N _Tσ ², wherein, d is the initialization search radius, α is the initial radium coefficient, σ ²Be noise variance.

9. method for detecting spherical decode as claimed in claim 7 is characterized in that, among the step C4, separates calculating initialization search radius based on reception signal Minimum Mean Square Error and is specially:

Calculating the Minimum Mean Square Error that receives signal separates

$\hat{x}={(H^{H}H+{\mathrm{I\σ}}^2)}^{-1}{H}^{H}y,$ Wherein, I is a unit matrix, σ ²Be noise variance;

carried out hard decision obtain corresponding grid point, and utilize channel H to carry out reconstruct to obtain

Calculate initialization search radius d: $d=\left|\right|y-\hat{y}\left|\right|.$

Images