CN113746776B - Signal receiving method based on constellation point sequencing and dynamic tree search - Google Patents
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Abstract
The invention belongs to the technical field of wireless communication, and particularly relates to a signal receiving method based on constellation point sequencing and dynamic tree search. The key point of the method is to pre-sequence the constellation points, and avoid the calculation complexity generated by calculating the Euclidean distance. And after the QRM-MLD search is finished, the dynamic tree search is carried out again, the discarded constellation points are searched for the second time, and the accuracy of signal recovery is improved. The method has the beneficial effect that the calculation complexity can be effectively reduced under the condition of meeting the system performance.
Description
Technical Field
The invention belongs to the technical field of wireless communication, and particularly relates to a signal receiving method based on constellation point sequencing and dynamic tree search.
Background
In massive MIMO, with a large increase in the number of antennas, the system capacity also grows linearly. In order to meet the requirement of high-speed communication, the MIMO system fully utilizes space resources, multipath effect and frequency selectivity bring serious interference between symbols, and the performance of the system is directly affected by the quality of a signal detection algorithm. And the computational complexity of signal detection increases exponentially with the number of antennas, so that the key of the MIMO technology is to introduce a low-complexity and high-efficiency detection algorithm capable of accurately recovering the transmitted signals.
Currently, maximum Likelihood (MLD) receivers have been widely studied to achieve better performance than linear receivers. But is too complex to be acceptable in engineering terms as it requires a one-by-one detection of all possible transmitted signals. For the challenge of extremely high complexity of the MLD algorithm, the QR decomposition-based maximum likelihood receiver (QRM-MLD) algorithm achieves performance close to MLD with much lower complexity than the MLD receiver and is easier to implement in engineering. The QRM-MLD algorithm carries out QR decomposition on a channel at a receiving end, converts a channel matrix into a triangular matrix, and can search layer by layer during searching detection to ensure that a useful signal is not influenced by other interference signals. Firstly, searching layer by layer from the last signal, and secondly, combining the candidate set of the searched signals to search the candidate set of the next signal. The traditional QRM-MLD algorithm combines QR decomposition and M algorithm to reduce the algorithm detection complexity of the traditional MLD, but the QRM-MLD algorithm is gradually close to the traditional MLD algorithm, the value of M is gradually increased, and the QRM-MLD calculation complexity is greatly increased along with the improvement of the number of layers and the modulation mode.
To make the performance of the QRM-MLD algorithm approach the MLD algorithm gradually, M should approach C as much as possible, so the problem of how to compromise the system performance and the computational complexity arises.
Disclosure of Invention
The invention aims at the problem of how to compromise the computation complexity and the system performance, and provides a signal receiving method based on the combination of constellation point pre-sequencing and dynamic tree search based on the traditional QRM-MLD algorithm.
The technical scheme adopted by the invention is as follows, and the key point is to pre-sequence the constellation points and avoid the calculation complexity generated by calculating the Euclidean distance. And after QRM-MLD searching is finished, dynamic tree searching is carried out again, and secondary searching is carried out on discarded constellation points, so that the correctness of signal recovery is improved.
The specific scheme of constellation point pre-ordering is as follows, assuming that the number of transmit-receive antennas is 2, the modulation mode is 16QAM, where M is the number of candidate constellation point sets, M =8, each constellation point is composed of a fixed real part and an imaginary part, and a signal sent by a transmitting end is represented in the following form:
wherein x is 1 、x 2 Representing two transmitted symbols, respectively, the signal received at the receiving end representingIn the form:
wherein y is 1 、y 2 Respectively representing two received symbols, after QR decomposition is carried out on a channel matrix H at a receiving end, the signal matrix H is converted into an upper triangular matrix, and then the MLD measurement is represented as the following form:
wherein r is 11 Representing the elements of the first row and the first column of the R matrix, R 12 Representing the elements of the first row and second column of the R matrix, R 22 Representing the elements of the second row and the second column of the R matrix, y m1 、y m2 Respectively representing the received symbols after QR decomposition, then x 2 When the detection is carried out, the influence of other interference signals is avoided, and firstly, x is detected 2 Pre-estimation is performed, namely:
wherein x is p2 The method is characterized in that a pre-estimation point is represented, the Euclidean distance between the pre-estimation point and each constellation point needs to be calculated in the traditional QRM-MLD, the complexity is high, and the algorithm only needs to calculate the difference value between the real part and the imaginary part of the pre-estimation point and each constellation point for sequencing. The specific process is as follows, calculating the difference value between the pre-estimated point and the real part of each constellation point:
diff_r k ＝|r-r k |,k＝1,2,...,16 (5)
wherein r is k The value of the real part representing the kth constellation point, diff _ r k And the absolute value of the difference between the real part of the kth constellation point and the real part of the pre-estimation point is represented. Since the modulation mode is 16QAM, i.e. the signal has 16 sampling points, and each 4-bit binary number represents one sampling point, the real part of the constellation point has 4 values, i.e. diff _ r k Has 4 values for itAnd sequencing from small to large, and sequencing the real parts of the constellation points in sequence according to the sequence numbers.
Similarly, the difference between the pre-estimation point and the imaginary part of each constellation point is calculated:
diff_i k ＝|i-i k |,k＝1,2,...,16 (6)
wherein i k Denotes the imaginary value of the kth constellation point, diffi k Representing the absolute value of the difference between the imaginary part of the kth constellation point and the imaginary part of the pre-estimation point. Similarly, the imaginary part of the constellation point has 4 values, i.e. diff _ i k 4 values are arranged, the values are sorted from small to large, and the imaginary parts of the constellation points are sequentially sorted according to the sequence numbers;
and performing coordinate representation on the constellation points according to the sorting values of the real parts and the imaginary parts of the constellation points: (a, b), wherein a represents the real part ordering value of the constellation points, and b represents the imaginary part ordering value of the constellation points.
And pre-storing a sorted list before the algorithm is carried out, wherein the sorted list is used for determining the distance sorting value of each constellation point and a pre-estimated point according to the coordinate sorting value of each constellation point. The specific sorting operation is as follows: constellation point coordinates: (1, 1), then corresponding to the constellation point sorting value: 1; the coordinates of the constellation points are as follows: (1, 2), then corresponding to the constellation point ranking value: 2; constellation point coordinates: (2, 1), then corresponding to the constellation point ranking value: 3; constellation point coordinates: (2, 2), the corresponding constellation point ordering value: 4; constellation point coordinates: (3, 1), corresponding to the constellation point sorting value: 5; constellation point coordinates: (1, 3), the corresponding constellation point ordering value: 6; constellation point coordinates: (3, 2), then corresponding to the constellation point ranking value: 7; constellation point coordinates: (2, 3), the corresponding constellation point ordering value: 8; the coordinates of the constellation points are as follows: (3, 3), the corresponding constellation point ordering value: 9; the coordinates of the constellation points are as follows: (1, 4), the corresponding constellation point ordering value: 10; constellation point coordinates: (4, 1), the corresponding constellation point ordering value: 11; the coordinates of the constellation points are as follows: (2, 4), then corresponding to the constellation point ranking value: 12; constellation point coordinates: (4, 2), the corresponding constellation point ordering value: 13; constellation point coordinates: (3, 4), the corresponding constellation point ordering value: 14; the coordinates of the constellation points are as follows: (4, 3), then corresponding to the constellation point ranking value: 15; constellation point coordinates: (4, 4), then the corresponding constellation point ranking value: and 16, finally obtaining the sequence of all constellation points, and selecting M candidate vector sets with the minimum distance from the sequence.
The specific scheme of dynamic tree search is as follows, the configuration of the transmitting terminal is as shown above, and x is obtained by using the constellation point pre-ordering scheme 2 Candidate constellation point set of (1):
x 2 _candidate＝{c 1 ,c 2 ,...,c M } (7)
according to the candidate constellation point set, the discarded non-candidate constellation points are 16-M:
x 2 _discarded＝{c M+1 ,c M+2 ,...,c 16 } (8)
computing LLRs using a set of known candidate constellation points can be approximated as:
wherein σ 2 The power representing noise, when the number of candidate vector sets is small, the MLD solution is likely to be discarded in advance, and therefore, the metric values are recalculated by using the non-candidate vector sets
And
and if the metric value calculated by using the non-candidate vector set is smaller than the minimum metric value calculated by using the candidate vector set, updating the minimum metric value, and recalculating the LLR soft information by using the updated minimum metric value.
The method has the beneficial effect that the calculation complexity can be effectively reduced under the condition of meeting the system performance.
Drawings
Fig. 1 is a simulation comparison diagram of the method of the present invention and the conventional method when M =4, (a) is a throughput simulation diagram, and (b) is a throughput simulation diagram;
fig. 2 is a simulation comparison diagram of the method of the present invention and the conventional method when M =16, where (a) is a throughput simulation diagram, and (b) is a throughput simulation diagram.
Detailed Description
Having described the invention in detail in the summary of the invention, the following description, taken in conjunction with the accompanying drawings and simulation examples, illustrates the utility of the invention.
In the invention, the real number multiplication times of each emission vector are used as parameters for measuring complexity, and the complexity difference of the traditional QRM-MLD algorithm and the QRM-MLD algorithm with constellation point pre-ordering is compared.
For the conventional QRM-MLD algorithm, according to the formula (1-2), the weight calculation formula of each layer can be expressed as:
for any constellation point in the constellation diagram, the above formula is calculated, and then: calculating r i,i x i 2 real multiplications are required; computing
Requires 4 × (N) t -i) a real multiplication; calculating the complex square requires 2 real multiplications. Therefore, the number of real multiplications required for the weight calculation of each layer is represented as:
num_i＝4×(N t -i)+4 (12)
s for each layer i ×2 bps All nodes need to be multiplied in real time, and finally the real multiplication times of the traditional QRM-MLD algorithm are expressed as follows:
wherein s is i Representing the number of surviving candidate constellation point sets calculated by the upper layer, 2 bps Indicating the number of all constellation points, where bps represents the binary number of QAM quadrature amplitude modulation.
For the QRM-MLD algorithm of the constellation point pre-sequencing, according to the formula (1-2), the weight calculation formula of each layer of the constellation point pre-sequencing can also be expressed as the formula (1-15), but only the central node needs to be calculated:
and traversing all constellation points to calculate the central node, solving the equation: calculating r i,i x i 2 real multiplications are required; computing
Requires 4 × (N) t -i) a real multiplication; without calculating the complex square. Therefore, the real multiplication times required by the weight calculation of each layer are expressed as follows:
num_i 1 ＝4×(N t -i)+2 (15)
after the central node is obtained, the positions of the horizontal and vertical coordinates of all the constellation points from the central node are calculated, namely | (x-x) i ) r |、|(x-x i ) i And I, performing coordinate representation on the constellation points, wherein the real multiplication times required in the process are as follows:
num_i 2 ＝2×bps (16)
the bps represents the system number of QAM quadrature amplitude modulation, and the horizontal and vertical coordinate numbers of all constellation points are determined by the QAM system number. For each layer, only s needs to be calculated i The real multiplication of the survived candidate constellation points is only needed, and the real multiplication times of the QRM-MLD algorithm of the final constellation point pre-sequencing are as follows:
comparing the equation (13) with the equation (17), it can be seen that the complexity of the constellation point pre-ordering algorithm is significantly reduced compared with the conventional QRM-MLD algorithm. Along with the gradual increase of the number of the transmitting antennas, the complexity of the constellation point pre-ordering algorithm is obviously reduced, while the complexity of the traditional QRM-MLD algorithm is exponentially increased, so that the advantages of the constellation point pre-ordering algorithm are obvious under the condition of large-scale antenna number.
The invention simplifies the calculation of the weight of each layer through the pre-stored sorting table, thereby achieving the purpose of reducing the calculation complexity. As can be seen from the simulation result shown in fig. 1, when M =4 is set, the performance of the conventional QRM-MLD algorithm is greatly reduced compared with the throughput of the MLD algorithm, which is because the dynamic tree search algorithm finds a solution that may be discarded, and the complexity of the conventional QRM-MLD algorithm is reduced by the constellation point pre-ordering, so that the performance and the complexity of the algorithm of the present invention are well balanced; as can be seen from fig. 2, when M =8 is set, the performance of the algorithm of the present invention is not greatly different from that of the conventional QRM-MLD algorithm, because the performance of the conventional QRM-MLD algorithm gradually approaches to that of the MLD algorithm with the gradual increase of M, and from the simulation result, the performance of the algorithm of the present invention is better than that of the conventional QRM-MLD algorithm.
Claims (1)
1. A signal receiving method based on constellation point sequencing and dynamic tree search is characterized in that the number of transmitting and receiving antennas in a communication system is 2, the modulation mode is 16QAM, each constellation point is composed of a fixed real part and an imaginary part, and a signal sent by a transmitting end is represented in the following form:
wherein x is 1 、x 2 Representing two transmitted symbols, respectively, characterized in that said receiving method comprises:
the signals received by the receiving end are:
wherein y is 1 、y 2 Respectively representing two received symbols, carrying out QR decomposition on a channel matrix H at a receiving end, converting the signal matrix H into an upper triangular matrix, and obtaining an MLD metric expression as follows:
wherein r is 11 Representing the elements of the first row and the first column of the R matrix, R 12 Represents the first in the R matrixOne row and a second column of elements, r 22 Representing the elements of the second row and second column of the R matrix, y m1 、y m2 Respectively representing the received symbols after QR decomposition, first, for x 2 Performing pre-estimation:
wherein x is p2 Representing the pre-estimation points, and calculating the difference value between the pre-estimation points and the real part of each constellation point:
diff_r k ＝|r-r k |,k＝1,2,...,16
wherein r is k The value of the real part representing the kth constellation point, diff _ r k The absolute value of the difference between the real part of the kth constellation point and the real part of the pre-estimated point is represented, the 16QAM modulation mode corresponds to 16 sampling points, each 4-bit binary number represents one sampling point, and therefore the real part of the constellation point is 4, namely diff _ r k 4 values are provided, the values are sorted from small to large, and the real parts of the constellation points are sequentially sorted according to the serial numbers;
calculating the difference value between the pre-estimation point and the imaginary part of each constellation point:
diff_i k ＝|i-i k |,k＝1,2,...,16
wherein i k Denotes the imaginary value of the kth constellation point, diffi k Representing the absolute value of the difference between the imaginary part of the kth constellation point and the imaginary part of the pre-estimation point, and similarly, the imaginary part of the constellation point has 4 values, i.e. diff _ i k 4 values are arranged, the values are sorted from small to large, and the imaginary parts of the constellation points are sequentially sorted according to the sequence numbers;
and according to the sorting values of the real part and the imaginary part of the constellation points, performing coordinate representation on the constellation points: (a, b), wherein a represents the real part ordering value of the constellation points, b represents the imaginary part ordering value of the constellation points, and the ordering rule is as follows: the coordinates of the constellation points are as follows: (1, 1), then corresponding to the constellation point ranking value: 1; constellation point coordinates: (1, 2), the corresponding constellation point ordering value: 2; the coordinates of the constellation points are as follows: (2, 1), then corresponding to the constellation point ranking value: 3; constellation point coordinates: (2, 2), the corresponding constellation point ordering value: 4; the coordinates of the constellation points are as follows: (3, 1), corresponding to the constellation point sorting value: 5; the coordinates of the constellation points are as follows: (1, 3), the corresponding constellation point ordering value: 6; constellation point coordinates: (3, 2), then corresponding to the constellation point ranking value: 7; the coordinates of the constellation points are as follows: (2, 3), the corresponding constellation point ordering value: 8; the coordinates of the constellation points are as follows: (3, 3), then corresponding to the constellation point ranking value: 9; constellation point coordinates: (1, 4), the corresponding constellation point ordering value: 10; constellation point coordinates: (4, 1), then corresponding to the constellation point ranking value: 11; the coordinates of the constellation points are as follows: (2, 4), the corresponding constellation point ordering value: 12; the coordinates of the constellation points are as follows: (4, 2), the corresponding constellation point ordering value: 13; the coordinates of the constellation points are as follows: (3, 4), the corresponding constellation point ordering value: 14; constellation point coordinates: (4, 3), then corresponding to the constellation point ranking value: 15; the coordinates of the constellation points are as follows: (4, 4), the corresponding constellation point ordering value: 16, finally obtaining the sequence of all constellation points, and then selecting M candidate vectors with the minimum distance;
after a candidate constellation point set is obtained according to constellation point pre-sorting, a signal is recovered based on dynamic tree searching, which specifically comprises the following steps:
obtaining x by constellation point pre-sorting 2 The set of candidate constellation points is:
x 2 _candidate＝{c 1 ,c 2 ,...,c M }
according to the candidate constellation point set, the discarded non-candidate constellation points are 16-M:
x 2 _discarded＝{c M+1 ,c M+2 ,...,c 16 }
the LLR is calculated using the set of known candidate constellation points as:
wherein sigma 2 Representing the power of the noise, B represents the set of candidate vectors of the MLD algorithm,
and
respectively representing the direction of the ith symbol with the l bit value of 1 and 0Quantity set, recalculating metric values using non-candidate vector set
And
and if the metric value calculated by using the non-candidate vector set is smaller than the minimum metric value calculated by using the candidate vector set, updating the minimum metric value, and recalculating the LLR soft information by using the updated minimum metric value.
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