CN111756666B - Working method of equal gain combining system based on constellation rotation - Google Patents

Working method of equal gain combining system based on constellation rotation Download PDF

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CN111756666B
CN111756666B CN202010563960.4A CN202010563960A CN111756666B CN 111756666 B CN111756666 B CN 111756666B CN 202010563960 A CN202010563960 A CN 202010563960A CN 111756666 B CN111756666 B CN 111756666B
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朱雪梅
吴瑾瑜
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Shandong University
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Abstract

A working method of an equal gain combining system based on constellation rotation belongs to the technical field of wireless communication. Firstly, an equal gain combining and receiving method is used, and the equal gain combining and receiving method does not need to carry out self-adaptive adjustment on weighting coefficients according to signal-to-noise ratios of all paths, so that the equipment is simple, the complexity is low, and accurate channel estimation is not needed; secondly, constellation rotation is introduced, namely in-phase and quadrature components are obtained through rotation of a constellation diagram, and then the in-phase and quadrature components are respectively sent through different antennas to eliminate correlation between the two paths of components, so that the sent signals are independently transmitted on respective fading channels. The method provided by the invention has obvious improvement on the performance of a modulation system based on equal gain combination, does not sacrifice the bandwidth and power of a frequency band while obtaining modulation diversity gain due to the introduction of constellation rotation, does not need an interleaver and a deinterleaver due to the fact that a component interleaving mode is not used, and can reduce the complexity of system implementation.

Description

Working method of equal gain combining system based on constellation rotation
Technical Field
The invention relates to a working method of an equal gain combining system based on constellation rotation, and belongs to the technical field of wireless communication.
Background
Signal Space Diversity (SSD) is an effective improvement scheme for dealing with fading, has the advantages of high Diversity gain and no need of occupying additional time and frequency band resources, can effectively improve the performance impact caused by fading, and has been widely used in wireless communication. Constellation rotation in combination with component interleaving is a key technique for SSD. The minimum number of distinguishable components in the multi-dimensional symbol set is defined by the diversity order, and the constellation rotation can maximize the diversity order between any two constellation points, so that the performance is improved. The component interleaving can eliminate the correlation among the components, so that the transmitted signals are independently transmitted on fading channels, and therefore, even if one path of components is subjected to severe fading, a receiver can restore the signals by only one component.
As is well known, in mobile communication, Equal Gain Combining (EGC) and maximum-ratio Combining (MRC) reception techniques are two of the most commonly used diversity Combining techniques. The performance of combining Constellation rotation and Component interleaving in a maximal ratio combining system under the condition of single-input antenna and multiple-output antenna is studied by Sungho Jeon in an article, Component-Interleaved received MRC with Rotated Constellation configuration for Signal Space Diversity, published in 2009. However, MRC combines the multiple signals in-phase with weighting determined by the snr corresponding to each branch, and the output snr of MRC is equal to the sum of the snrs of each branch. The EGC does not need to weight signals, signals of all branches are added by equal gains, compared with maximum ratio combination, the EGC does not need channel estimation, calculation of weighted values is simplified, a circuit is simple, realization is easy, and performance is slightly inferior to that of the maximum ratio combination. Therefore, a working method of an equal gain combining system based on constellation rotation under the condition of multiple input antennas and multiple output antennas is provided to improve the performance of the EGC, and no research is made in the aspect of searching documents.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides the working method of the constellation rotation-based equal gain combining system under the condition of multiple input antennas and multiple output antennas, which can save hardware resources, reduce the complexity of system implementation and obtain more excellent anti-fading performance compared with the constellation non-rotation equal gain combining system.
The technical scheme of the invention is as follows:
a working method of an equal gain combination system based on constellation rotation comprises the following steps:
(1) firstly, input symbol stream is Gray mapped to complex frequency domain; let the transmitted signal vector be s ═ s0,s1,...,sn,...,sN-1]N is the length of the input symbol stream, where snRepresents the constellation point corresponding to the transmitted nth signal and has the value of sn＝sI,n+jsQ,nWherein s isI,nAnd sQ,nAre respectively snThe real and imaginary parts of (a) represent the in-phase and quadrature components of the constellation, respectively, and j represents the imaginary unit;
(2) rotating the signal constellation, and setting the transmitted signal vector after rotation as x ═ x0,x1,...,xn,...,xN-1]Wherein x isnIs the constellation point corresponding to the rotated nth signal, and its value is xn＝xI,n+jxQ,nLikewise, xI,nAnd xQ,nAre each xnThe real part and the imaginary part of (a) respectively represent the rotated in-phase component and quadrature component of the constellation diagram, and j represents an imaginary unit; and xI,nAnd xQ,nAvailable ofI,nAnd sQ,nIs represented by, i.e. xI,n＝sI,ncosθ+sQ,nsinθ,xQ,n＝-sI,nsinθ+sQ,ncos theta, theta is the rotation angle which makes the system error rate performance optimal, and the value range is [0, pi/2%]；
(3) To remove the correlation between the two components, the two components can be subjected to independent fading, i.e. the in-phase component x is transmitted separately through different antennasI＝[xI,0,xI,1,...,xI,n,...,xI,N-1]And an orthogonal component xQ＝[xQ,0,xQ,1,...,xQ,n,...,xQ,N-1](ii) a For a more concise representation, the transmission signals are represented here by a matrix of
Figure BDA0002547123400000021
The 1 st and 2 nd rows of the matrix represent two paths of sending signals, and obviously, the number of sending antennas is preferably 2;
(4) and a receiving end of the signal adopts a receiving mode of equal gain combination. When the system is applied to a flat fading channel, the number of receiving antennas is set to MREach antenna receives in-phase and quadrature parts, which can be regarded as a pair, MRAlso represents the number of diversity branches when the in-phase and quadrature components are respectively subjected to equal gain combination; the k-th pair of received signals may be represented as Yk＝Hk·X+NkWherein
Figure BDA0002547123400000022
Lines 1 and 2 of (a) respectively represent the kth pair of received signals,
Figure BDA0002547123400000023
lines 1 and 2 are independent identically distributed random variables under independent fading experienced by the kth pair of signals, respectively
Figure BDA0002547123400000024
Is the additive white gaussian noise added to the k-th signal, where "·" denotes the dot product of the matrix; calculating weighting coefficients of kth pair of signals
Figure BDA0002547123400000025
Where "+" denotes conjugation, the resulting normalized received signal vector is
Figure BDA0002547123400000031
Then, the output signal of the equal gain combiner can be obtained as
Figure BDA0002547123400000032
(5) Finally, the output signals of the equal gain combiner are combined
Figure BDA0002547123400000033
Using minimum ohmAnd (4) judging according to a formula distance criterion, and obtaining a final output symbol stream, namely the recovered input symbol stream after judgment.
Preferably, in step (1), s is used for QPSK modulation and 8PSK modulationI,nAnd sQ,nThe respective value ranges are respectively
Figure BDA0002547123400000034
And
Figure BDA0002547123400000035
preferably, in step (2), the optimum QPSK modulation rotation angle θ is equal to 30.3 °, and the optimum 8PSK modulation rotation angle θ is equal to 9.5 °.
Preferably, in step (4), the flat fading channel comprises a flat rayleigh fading channel.
Preferably, in step (5), the error rate can be obtained by comparing the final output symbol stream obtained after the decision with the input symbol stream, and the error rate at the optimal rotation angle θ should be lower than the error rate value when the symbol stream is not rotated.
Preferably, in step (5), the Euclidean distance is calculated by
Figure BDA0002547123400000036
rI,nAnd rQ,nFor the received nth rIAnd rQA signal wherein
Figure BDA0002547123400000037
hk,I,nAnd hk,Q,nRespectively represent the nth hk,IAnd hk,QValue of
Figure BDA0002547123400000038
And
Figure BDA0002547123400000039
respectively representing the horizontal and vertical coordinates of each constellation point after rotation.
The invention has the beneficial effects that:
the invention introduces constellation rotation in an equal gain combination system, namely in-phase (I path) and quadrature (Q path) components are obtained through rotation of a constellation diagram, and then the in-phase and quadrature components are respectively sent through different antennas to eliminate the correlation between the two paths of components, so that the sent signals are independently transmitted on respective fading channels. The method provided by the invention has obvious improvement on the performance of a modulation system based on equal gain combination, does not sacrifice the bandwidth and power of a frequency band while obtaining modulation diversity gain due to the introduction of constellation rotation, and does not need an interleaver and a deinterleaver because a component interleaving mode is not used for eliminating the correlation between two paths of components, thereby saving hardware resources and reducing the complexity of system realization. From the technical point of view, the invention has simple thought and easy implementation.
Drawings
Fig. 1 is a block diagram of an equal gain combining system based on constellation rotation according to the present invention.
Fig. 2 is a graph comparing bit error rates of gain combining systems such as QPSK modulation based on constellation rotation. In the 2 curves in fig. 2, from top to bottom, respectively, are the bit error rate curves of the QPSK modulation system in which (i) equal gain combining is adopted and the constellation is not rotated (θ ═ 0 °); and the error rate curve of the QPSK modulation system is combined by equal gain and constellation rotation (the optimal rotation angle theta is 30.3 degrees).
Fig. 3 is a graph comparing bit error rates of gain combining systems such as 8PSK modulation based on constellation rotation. In the 2 curves in fig. 3, from top to bottom, respectively, there are (i) error rate curves of an 8PSK modulation system that employs equal gain combining and constellation does not rotate (θ ═ 0 °); and the error rate curve of an 8PSK modulation system adopting equal gain combination and constellation rotation (the optimal rotation angle theta is 9.5 degrees).
Detailed Description
The present invention will be further described by way of examples, but not limited thereto, with reference to the accompanying drawings.
Example 1:
a working method of equal gain combination system based on constellation rotation uses the number of receiving end antennas as MRThe present invention is described by taking as an example a constellation rotation based equal gain combining system of 2.The system block diagram is shown in FIG. 1: firstly, an input data sequence is mapped to a complex frequency domain through Gray to obtain an in-phase component and an orthogonal component, namely sI,sQ(ii) a Then, constellation rotation is performed to obtain xI,xQTransmitting them through different antennas respectively; after passing through a flat Rayleigh fading channel, the signal r is obtained by equal gain combinationI,rQAnd finally, performing minimum Euclidean distance judgment to obtain an output sequence.
The method comprises the following specific steps:
(1) firstly, input symbol stream is Gray mapped to complex frequency domain; let the transmitted signal vector be s ═ s0,s1,...,sn,...,sN-1]N is the length of the input symbol stream, where snRepresents the constellation point corresponding to the transmitted nth signal and has the value of sn＝sI,n+jsQ,nWherein s isI,nAnd sQ,nAre respectively snThe real and imaginary parts of (a) represent the in-phase and quadrature components of the constellation, respectively, and j represents the imaginary unit; for QPSK modulation and 8PSK modulation, sI,nAnd sQ,nThe respective value ranges are respectively
Figure BDA0002547123400000041
And
Figure BDA0002547123400000042
(2) rotating the signal constellation, and setting the transmitted signal vector after rotation as x ═ x0,x1,...,xn,...,xN-1]Wherein x isnIs the constellation point corresponding to the rotated nth signal, and its value is xn＝xI,n+jxQ,nLikewise, xI,nAnd xQ,nAre each xnThe real part and the imaginary part of (a) respectively represent the rotated in-phase component and quadrature component of the constellation diagram, and j represents an imaginary unit; and xI,nAnd xQ,nAvailable ofI,nAnd sQ,nIs represented by, i.e. xI,n＝sI,ncosθ+sQ,nsinθ,xQ,n＝-sI,nsinθ+sQ,ncos θ, θ is such thatThe rotation angle with the optimal system error rate performance has the value range of [0, pi/2 ]](ii) a The optimum rotation angle θ of QPSK modulation is 30.3 °, and the optimum rotation angle θ of 8PSK modulation is 9.5 °.
(3) To remove the correlation between the two components, the two components can be subjected to independent fading, i.e. the in-phase component x is transmitted separately through different antennasI＝[xI,0,xI,1,...,xI,n,...,xI,N-1]And an orthogonal component xQ＝[xQ,0,xQ,1,...,xQ,n,...,xQ,N-1](ii) a For a more concise representation, the transmission signals are represented here by a matrix of
Figure BDA0002547123400000051
The 1 st and 2 nd rows of the matrix represent two paths of sending signals, and obviously, the number of the sending antennas is 2;
(4) and a receiving end of the signal adopts a receiving mode of equal gain combination. The system applies any flat fading channel in the same step, and the embodiment takes a flat rayleigh fading channel as an example. When the system is applied to a flat Rayleigh fading channel, the number of receiving antennas is set as MREach antenna receives in-phase and quadrature parts, which can be regarded as a pair, MRAlso represents the number of diversity branches when the in-phase and quadrature components are respectively subjected to equal gain combination; the k-th pair of received signals may be represented as Yk＝Hk·X+NkWherein
Figure BDA0002547123400000052
Lines 1 and 2 of (a) respectively represent the kth pair of received signals,
Figure BDA0002547123400000053
lines 1 and 2 of (a) are independent identically distributed random variables under independent Rayleigh fading experienced by the kth pair of signals, respectively
Figure BDA0002547123400000054
Is the additive white gaussian noise added to the k-th signal, where "·" denotes the dot product of the matrix; computing the kth creditWeighting coefficient of number
Figure BDA0002547123400000055
Where "+" denotes conjugation, the resulting normalized received signal vector is
Figure BDA0002547123400000056
Then, the output signal of the equal gain combiner can be obtained as
Figure BDA0002547123400000057
(5) Finally, the output signals of the equal gain combiner are combined
Figure BDA0002547123400000061
And judging by adopting a minimum Euclidean distance criterion, and obtaining a final output symbol stream, namely a recovered input symbol stream after judgment. And comparing the final output symbol stream obtained after judgment with the input symbol stream to obtain the error rate, wherein the error rate at the optimal rotation angle theta is lower than the error rate value when the symbol stream is not rotated.
The Euclidean distance calculation method comprises
Figure BDA0002547123400000062
rI,nAnd rQ,nFor the received nth rIAnd rQA signal wherein
Figure BDA0002547123400000063
hk,I,nAnd hk,Q,nRespectively represent the nth hk,IAnd hk,QValue of
Figure BDA0002547123400000064
And
Figure BDA0002547123400000065
respectively representing the horizontal and vertical coordinates of each constellation point after rotation.
The invention takes the bit error rate as an index for measuring the system performance, compares the method provided by the invention with a method without constellation rotation, and the comparison result is shown in figures 2 and 3.
In fig. 2 and 3, the number of antennas at the receiving end is 2, and it is obvious that, in QPSK modulation and 8PSK modulation, the performance of the obtained EGC system is better than that of the EGC system when the constellation is not rotated at the optimal rotation angle.

Claims (6)

1. A working method of an equal gain combination system based on constellation rotation is characterized by comprising the following steps:
(1) firstly, input symbol stream is Gray mapped to complex frequency domain; let the transmitted signal vector be s ═ s0,s1,...,sn,...,sN-1]N is the length of the input symbol stream, where snRepresents the constellation point corresponding to the transmitted nth signal and has the value of sn＝sI,n+jsQ,nWherein s isI,nAnd sQ,nAre respectively snThe real and imaginary parts of (a) represent the in-phase and quadrature components of the constellation, respectively, and j represents the imaginary unit;
(2) rotating the signal constellation, and setting the transmitted signal vector after rotation as x ═ x0,x1,...,xn,...,xN-1]Wherein x isnIs the constellation point corresponding to the rotated nth signal, and its value is xn＝xI,n+jxQ,nLikewise, xI,nAnd xQ,nAre each xnThe real part and the imaginary part of (a) respectively represent the rotated in-phase component and quadrature component of the constellation diagram, and j represents an imaginary unit; and xI,nAnd xQ,nAvailable ofI,nAnd sQ,nIs represented by, i.e. xI,n＝sI,ncosθ+sQ,nsinθ,xQ,n＝-sI,nsinθ+sQ,ncos theta, theta is the rotation angle which makes the system error rate performance optimal, and the value range is [0, pi/2%]；
(3) In order to eliminate the correlation between the two components, the two components are subjected to independent fading, i.e. the in-phase component x is transmitted separately via different antennasI＝[xI,0,xI,1,...,xI,n,...,xI,N-1]And an orthogonal component xQ＝[xQ,0,xQ,1,...,xQ,n,...,xQ,N-1](ii) a Representing the transmitted signal by a matrix of
Figure FDA0002995683400000011
The 1 st and 2 nd rows of the matrix represent two paths of sending signals, and the number of the sending antennas is 2;
(4) the receiving end of the signal adopts the equal gain combination receiving mode, when the system is applied to the flat fading channel, the number of the receiving antennas is set as MREach antenna receives in-phase and quadrature parts, which can be regarded as a pair, MRAlso represents the number of diversity branches when the in-phase and quadrature components are respectively subjected to equal gain combination; the k-th pair of received signals may be represented as Yk＝Hk·X+NkWherein
Figure FDA0002995683400000012
Lines 1 and 2 of (a) respectively represent the kth pair of received signals,
Figure FDA0002995683400000013
lines 1 and 2 are independent identically distributed random variables under independent fading experienced by the kth pair of signals, respectively
Figure FDA0002995683400000014
Is the additive white gaussian noise added to the k-th signal, where "·" denotes the dot product of the matrix; calculating weighting coefficients of kth pair of signals
Figure FDA0002995683400000021
Where "+" denotes conjugation, the resulting normalized received signal vector is
Figure FDA0002995683400000022
Then, the output signal of the equal gain combiner can be obtained as
Figure FDA0002995683400000023
(5) Finally, the output signals of the equal gain combiner are combined
Figure FDA0002995683400000024
And judging by adopting a minimum Euclidean distance criterion, and obtaining a final output symbol stream, namely a recovered input symbol stream after judgment.
2. The method of claim 1, wherein in step (1), s is used for QPSK modulation and 8PSK modulationI,nAnd sQ,nThe respective value ranges are respectively
Figure FDA0002995683400000025
And
Figure FDA0002995683400000026
3. the operating method of the constellation rotation-based equal gain combining system according to claim 1, wherein in step (2), the optimum rotation angle θ for QPSK modulation is 30.3 °, and the optimum rotation angle θ for 8PSK modulation is 9.5 °.
4. The method of claim 1, wherein in step (4), the flat fading channel comprises a flat rayleigh fading channel.
5. The method of claim 1, wherein in step (5), the error rate is obtained by comparing the final output symbol stream obtained after the decision with the input symbol stream, and the error rate at the optimal rotation angle θ is lower than the error rate without rotation.
6. Constellation rotation based equalization according to claim 1The working method of the Yihe combination system is characterized in that in the step (5), the calculation method of the Euclidean distance is that
Figure FDA0002995683400000027
rI,nAnd rQ,nFor the received nth rIAnd rQA signal wherein
Figure FDA0002995683400000028
hk,I,nAnd hk,Q,nRespectively represent the nth hk,IAnd hk,QValue of
Figure FDA0002995683400000029
And
Figure FDA00029956834000000210
respectively representing the horizontal and vertical coordinates of each constellation point after rotation.
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