CN115987745B - Low-complexity quadrature amplitude modulation cross constellation demapping method - Google Patents
Low-complexity quadrature amplitude modulation cross constellation demapping method Download PDFInfo
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Abstract
The invention provides a low-complexity quadrature amplitude modulation cross constellation demapping method, which can be divided into the following steps: (1) constellation segmentation: dividing a constellation diagram into a plurality of areas according to a 0/1 mapping distribution rule of each bit in the constellation point; (2) region selection: for demodulation of each bit in a received modulation symbol, only selecting a relevant area in a constellation diagram and calculating soft information by using real and imaginary parts of the symbol, so that the selection range of demapping constellation points is greatly reduced; (3) approximate fitting to calculate log likelihood ratio of each bit: in order to avoid the problem of high complexity caused by calculation of Euclidean distance between a received symbol and a standard constellation point, soft information of each bit is calculated by adopting a linear function piecewise fitting mode, so that acceptable performance loss is ensured. The invention can effectively reduce the complexity of hardware for realizing high-order QAM soft demodulation.
Description
Technical Field
The invention belongs to the technical field of communication, and relates to a low-complexity demapping method of a quadrature amplitude modulation cross constellation.
Background
There are various ways in which high performance communication systems may be required to achieve higher information transfer rates and lower power consumption to improve communication system performance, wherein digital modulation techniques may use limited frequency band resources and lower power consumption to improve information transfer rates. The linear modulation mode is divided into Amplitude Shift Keying (ASK), phase Shift Keying (PSK) and Quadrature Amplitude Modulation (QAM) according to the variation factors of the transmission signal, and since QAM can use less bandwidth to achieve higher data transmission rate, high-order QAM is widely adopted by modern communication standards, square QAM constellation is used for even-order QAM modulation, and has 2 even-order constellation points, cross QAM constellation is used for odd-order QAM modulation, and has 2 odd-order constellation points, wherein cross QAM is obtained by partial rotation of rectangular QAM constellation, has lower peak value and average power, and can improve demodulation performance, but compared with square and rectangular QAM, the calculation complexity is improved in demapping. When QAM adopts higher order modulation, the influence of channel noise needs to be reduced in cooperation with channel coding and decoding technology, so the output of demapping should be a reliability measure that the soft information value (generally adopts log likelihood ratio LLR) represents the transmitted bit, so the output is called soft demodulation.
At present, there are various soft demodulation algorithms for QAM (literature [1]：Viterbi,A.J.,"An Intuitive Justification and a Simplified Implementation of the MAP Decoder for Convolutional Codes,"IEEE Journal on Selected Areas in Communications,vol.16,No.2,pp260–264,Feb.1998), although e index and logarithm operation are replaced by maximum value function (Max), the needed multiplication operation times are high and complexity is O (2 m). A low-complexity de-mapping method for boundary-based QAM (literature [2]：F.Tosato,P.Bisaglia."Simplified soft-output demapper for binaryinterleaved COFDM with application to HIPERLAN/2".Proc.IEEEICC,vol.2,pp.664-668,2002), a constellation diagram is decomposed into two subsets of I path and Q path, values of standard constellation points are respectively delimited in each subset, distances between one-dimensional coordinates are replaced by distances between two-dimensional coordinate points, and when LLR of each bit is calculated, nonlinear operation in Max-Log-MAP is converted into linear operation by adopting a method of broken line approximation according to received symbols, so that the complexity of the whole implementation is reduced, but the method is only applied to square QAM (literature [3]: xu Juan, yao Rugui, nanne, gao Fanqi, cross constellation QAM low-complexity de-mapping algorithm [ J ]. Haer industry university, 2015,47 ] is applied to cross constellation QAM low-complexity de-mapping algorithm in G.HN standard (literature [3 ]. A) and the complexity of the constellation point is reduced by using a method of broken line approximation, so that the complexity of the constellation point is reduced by using a reduced-contribution of the mapping algorithm to the search standard.
The above-mentioned [1] requires more multiplication operations, which is not beneficial to the implementation of hardware circuits based on Field Programmable Gate Array (FPGA) or Application Specific Integrated Circuit (ASIC), while [2] greatly simplifies the number of times and complexity of computation, but has no precedent adopted on cross constellation, and [3] can achieve the performance consistent with that of [1], but needs to select a suitable search range according to the channel noise condition to perform multiplication operations for multiple times, and has a certain difficulty for the implementation of hardware with low complexity.
Disclosure of Invention
The present invention proposes a low complexity algorithm for Quadrature Amplitude Modulation (QAM) cross constellation soft demodulation, which can be divided into the following main steps: (1) constellation segmentation: dividing a constellation diagram into a plurality of areas according to a 0/1 mapping distribution rule of each bit in the constellation point; (2) region selection: for demodulation of each bit in a received modulation symbol, only selecting a relevant area in a constellation diagram and calculating soft information by using real and imaginary parts of the symbol, so that the selection range of demapping constellation points is greatly reduced; (3) approximate fitting to calculate log likelihood ratio of each bit: in order to avoid the problem of high complexity caused by the calculation of Euclidean distance between a received symbol and a standard constellation point (more complex multiplication operations are introduced in hardware design), soft information of each bit is calculated by adopting a linear function piecewise fitting mode, so that acceptable performance loss is ensured. The invention can effectively reduce the complexity of hardware for realizing high-order QAM soft demodulation.
The method comprises the following specific steps:
step 1: the constellation diagram is divided, namely all constellation points are divided into a plurality of subareas according to the distribution rule of 0 and 1 of each bit in the constellation diagram, and the method for calculating the soft information value in each subarea is the same.
The QAM modulation of each symbol carrying m bit information in the constellation diagram is expressed as 2 m -ary QAM, the consideration scope of the invention is a cross constellation diagram when m is odd, in order to increase the Hamming distance, the standard constellation diagram is arranged on an in-phase component (I path) and a quadrature component (Q path) at equal intervals in a Gray (Gray) mapping mode, and the 0 and 1 distribution rules of each bit position in the standard constellation diagram can be respectively obtained.
The more accurate soft demodulation LLR calculation adopts MAP algorithm, and the definition of the soft information of the b i bit is calculated as follows:
Where σ 2 is the channel noise variance, the coordinates of the received noisy symbol z=x+jy on the complex plane are expressed as (x, y), the symbol point in the standard constellation is s=s x+jsy, the coordinates on the complex plane are expressed as (S x,sy),S0 and S 1 represent the point set where the current b i bit position is 0 and 1 in the standard constellation, respectively, i.e. the symbol in set S 0 where the symbol in the b i bit position is 0,S 1 is 1 in the b i bit position, and finally the above formula indicates that the soft information in the b i position is calculated by considering the euclidean distance between the received symbol and the nearest 0 and 1 symbol, instead of all constellation points in the standard constellation.
Step 1.1: for cross constellation mapping it is first necessary to find the demarcation between all bit positions 0 and 1 in the standard constellation.
Step 1.2: and respectively finding the boundary closest to each bit position in the received symbol, and judging the relation between Euclidean distance from the received symbol to the nearest 0 and 1 symbols and in-phase components or quadrature components. And dividing the position sets with the same relation into the same area, and calculating soft information values in the area by adopting the same operation.
Step 2: the region selection, i.e. classifying the received noisy symbols Z into sub-regions of step1, is based on their position on the constellation.
The received symbol coordinates (x, y) may be offset from the standard constellation midpoint coordinates (s x,sy) by inclusion of noise, s x e { ±a, ±3A, ±5A, ±7A, ±9A,..and the same as s y e { ±a, ±3A, ±5A, ±7A, ±9A,..and where a is a normalization factor. When soft demodulating the received symbol Z, (x, y) can uniquely determine and select the region in step 1 and perform the corresponding operation in step 3, the soft information calculation of most regions is related to only the in-phase component or the quadrature component, and few regions are related to both components.
Step 3: the approximate fitting calculates the log-likelihood ratio of each bit, namely, the LLR of each position of each sub-area is approximated based on a linear function piecewise fitting method, and the fitting value is used for replacing the accurate value.
Equation (1) provides a more accurate method of calculating the LLR, but can be further simplified when a bit of soft information is related to only the in-phase or quadrature components, here taking the operation of the in-phase component as an example:
Wherein x is the in-phase component of the received symbol, S x1 and S x0 are the in-phase component values of the symbols closest to x in the sets S 1 and S 0, respectively, the absolute value is an integer multiple of the normalization factor A, and the last coefficient after the equal sign Is constant under the same constellation and channel condition, has no influence on soft demodulation performance, and can be ignored. Because s x1 and s x0 change when the region where x is located changes, a hardware friendly method is needed to calculate soft information of bit b i from equation (2) according to the received x value, and a method based on linear function piecewise fitting is adopted to approximate accurate LLR, namely, firstly, the result of each point calculation equation (2) is uniformly selected in each region of step 2, and then linear function is used for fitting substitution, so that complex multi-bit multiplication can be converted into addition and subtraction operation, and hardware implementation is facilitated.
The invention has the advantages that:
the method applies the approximate fitting method to demodulation of Quadrature Amplitude Modulation (QAM) cross constellation, calculates the relation between the in-phase component or quadrature component according to soft information of each bit position on the constellation diagram, divides the standard constellation diagram into areas, and matches corresponding soft information operation by using the linear function piecewise fitting method, thereby greatly reducing hardware complexity introduced by calculating accurate Euclidean distance and larger searching range.
Drawings
Fig. 1 is a diagram of a 128-QAM cross constellation diagram employing gray mapping.
Fig. 2 is a schematic diagram of the constellation region division of b 0 bits (the most significant bits) in a 128-QAM constellation.
Fig. 3 is a schematic diagram of a approximate fit of b 0 bits of soft information in a 128-QAM constellation.
Fig. 4 is a schematic diagram of constellation region division of b 1 bits in a 128-QAM constellation.
Fig. 5 is a schematic diagram of approximate fitting of b 1 bits of soft information in a 128-QAM constellation. (area A)
Fig. 6 is a schematic diagram of constellation region division of b 2 bits in a 128-QAM constellation.
Fig. 7 is a schematic diagram of a method for approximating soft information square terms in the b 2 bit D region in a 128-QAM constellation.
Fig. 8 is a diagram of constellation region division of b 3 bits in a 128-QAM constellation.
Fig. 9 is a diagram of a approximate fit of b 3 bits of soft information in a 128-QAM constellation.
Fig. 10 is a schematic diagram of constellation region division of b 4 bits in a 128-QAM constellation.
Fig. 11 is a schematic diagram of approximate fitting of b 4 bits of soft information in a 128-QAM constellation.
Fig. 12 is a diagram illustrating the constellation region division of b 5 bits in a 128-QAM constellation.
Fig. 13 is a diagram of a approximate fit of b 5 bits of soft information in a 128-QAM constellation. (area A)
Fig. 14 is a diagram of the constellation region division of b 6 bits (least significant bits) in a 128-QAM constellation.
Fig. 15 is a diagram of a approximate fit of b 6 bits of soft information in a 128-QAM constellation.
Detailed Description
The invention will be described in detail below with reference to the accompanying drawings and examples of implementation using 128-QAM cross constellation modulation as an example.
Fig. 1 is a 128-QAM constellation diagram designed by using a gray mapping manner in this embodiment, in which 128 constellation points are total, each constellation point represents 7 bits of information { b 0,b1,…,b6 }, where b 0 is the Most Significant Bit (MSB), b 6 is the Least Significant Bit (LSB), the constellation points are uniformly arranged in a cross shape, and the distance between adjacent constellation points in the I-path direction and the Q-path direction is 2A. The constellation map region dividing method and the soft information approximate fitting calculation method of each bit position of b 0～b6 are analyzed sequentially based on the steps 1-3.
Step 1: constellation segmentation. Focusing on only the 0 and 1 cases of b 0, fig. 2 is a schematic diagram of the constellation region division of the b 0 bit position in the 128-QAM constellation, in which, except for 4 vertices without constellation points, the dark region b 0 =1 on the left side of the Q axis and the light region b 0 =0 on the right side of the Q axis.
Step 2: and (5) selecting a region. It can be seen that when receiving the symbol (x, y), B 0 bits of soft information is related to only the in-phase component x, the exact B 0 bits of LLR can be calculated by substituting the received x value and the corresponding s x1 and s x0 into formula (2), but for further simplification, the constellation is further divided according to the type of approximation operation, as shown by the double solid line in the figure, into two regions Aarea and B area and satisfying { Aarea: |y|8 a|x| > |y|and { Barea: |y| > 8 a|x|y| the main difference between the two regions is that the nearest s x1 and s x0 are selected when |x| > 8A, and the specific two regions are selected in the different x ranges and the LLR calculation values according to formula (2) are shown in tables 1 and 2. However, excessive segmentation causes additional hardware selector and comparator consumption, so that a unified calculation expression is obtained by adopting a linear fitting method according to the relation between the x value range interval and the LLR.
TABLE 1A area LLR calculation results for each segment
| X range interval | sx1 | sx0 | LLR (neglecting coefficient terms) |
| x<-10A | A | -11A | -6(x+5A) |
| -10A≤x<-8A | A | -9A | -5(x+4A) |
| -8A≤x<-6A | A | -7A | -4(x+3A) |
| -6A≤x<-4A | A | -5A | -3(x+2A) |
| -4A≤x<-2A | A | -3A | -2(x+A) |
| -2A≤x<0 | A | -A | -x |
| 0≤x<2A | A | -A | -x |
| 2A≤x<4A | 3A | -A | -2(x-A) |
| 4A≤x<6A | 5A | -A | -3(x-2A) |
| 6A≤x<8A | 7A | -A | -4(x-3A) |
| 8A≤x<10A | 9A | -A | -5(x-4A) |
| X≥10A | 11A | -A | -6(x-5A) |
TABLE 2B area LLR calculation results for each segment
| X range interval | sx1 | sx0 | LLR (neglecting coefficient terms) |
| x<-6A | A | -7A | -4(x+3A) |
| -6A≤x<-4A | A | -5A | -3(x+2A) |
| -4A≤x<-2A | A | -3A | -2(x+A) |
| -2A≤x<0 | A | -A | -x |
| 0≤x<2A | A | -A | -x |
| 2A≤x<4A | 3A | -A | -2(x-A) |
| 4A≤x<6A | 5A | -A | -3(x-2A) |
| X≥6A | 7A | -A | -4(x-3A) |
Step 3: the approximate fit computes the log-likelihood ratio for each bit. Fig. 3 is a schematic diagram of approximate fit of B 0 bits of soft information, in which the horizontal axis is a measure obtained by dividing the value of the in-phase component x of the received symbol by the normalization factor a, the vertical axis is the calculation result of the soft information LLR, the circle represents the calculation result of the LLR corresponding to table 1 when x is located in the region a, the diamond represents the calculation result of the LLR corresponding to table 2 when x is located in the region B, and the two are very close and overlap when |x| is small, so that the LLR calculation using the same approximation formula for both regions a and B can be considered, as shown by the dashed line in fig. 3, and the approximation expression is:
LLR(b0)＝-x(3)
Although the fitting result and the actual calculation result still have a certain difference when |x| is larger, simulation shows that demodulation performance is not greatly lost.
The bits of b 1～b6 are respectively subjected to constellation diagram division, region selection and fitting by adopting the same steps 1-3, and the steps are not repeated, but diagram division and fitting results are sequentially described from the angles of different bits:
Fig. 4 is a schematic diagram of constellation region division at b 1 bit positions in a 128-QAM constellation, where the middle 64 constellation points b 1 =1 and the rest b 1 =0. According to the same processing thought, according to the position of a received symbol (x, y), judging the relation between the received symbol and in-phase and quadrature components when calculating LLR (B 1), dividing a constellation diagram into a region A and a region B in the diagram, wherein the region A is divided into an upper part and a lower part, the distance between the received symbol and the nearest s y1 and s y0 is only related to the quadrature component y, the region B is divided into a left part and a right part, the distance between the received symbol and the nearest s x1 and s x0 is only related to the in-phase component x, and the LLR calculation method of the region B can be calculated by replacing x, s x1 and s x0 with y, s y1 and s y0. Fig. 5 is a schematic diagram of approximate fitting of B 1 bits of soft information in the region a, circles are calculated results of LLR of each segment in the region a according to the foregoing method, and after fitting, a piecewise function |y| -8A is shown as a dashed line, and in combination with fitting calculation of an in-phase component in the region B, a calculation manner of B 1 bits of soft information is as follows:
fig. 6 is a schematic diagram of a constellation region division of b 2 bits, and because the boundary of b 2 =0 and b 2 =1 does not extend through the whole I-axis or Q-axis, the division of the region is complex, divided into a-E5 regions and the position distribution in each quadrant is the same. For the received symbol (x, y), the range of the central area A of the constellation diagram satisfies { Aarea: (|y|. Ltoreq.8A|y|. Ltoreq (- |x|+12A)) |y|. Ltoreq.4A }, the middle constellation point in the area is b 2 =0, and the constellation points b 2 =1 on the left and right sides, so that the soft information in the area is only related to the in-phase component. Similar to the b 1 -bit soft information calculation method, the soft information of the b 2 -bit region a can be approximated as
LLR(b2_A)＝-|y|+4A (5)
The region B is distributed symmetrically about the I and Q axes in a range satisfying { Barea:4A.ltoreq.xIltoreq.8AΣ.ltoreq.yI > (- |xI|+ 12A) }, the soft information is related only to the orthogonal component, so the soft information of the B 2 -bit region B can be approximated as
LLR(b2_B)＝|y|-8A (6)
The area C satisfies { Carea } x| > 8A n 4A < |y|.ltoreq.8A }, and is characterized in that 4 points B 2 =1 in each quadrant and the points of the nearest neighbor B 2 =0 are in the diagonally opposite area B, so that the in-phase component and the quadrature component need to be considered simultaneously for reducing the error of soft information calculation, the area C is further divided into areas where 4 points corresponding to 4B 2 =1 in total, and the conditions are respectively satisfied:
{C1area:|x|＞10A∩|y|＞6A∩|y|≤8A}
{C2area:|x|＞8A∩|x|≤10A∩|y|＞6A∩|y|≤8A}
{C3area:|x|＞10A∩|y|＞4A∩|y|≤6A}
{C4area:|x|＞8A∩|x|≤10A∩|y|＞4A∩|y|≤6A} (7)
Their LLR calculation is extended based on equation (2), here the LLR calculation method is illustrated by the C1 region:
Omitting the same constant term may result in:
LLR(b2_C1)＝-2|x|+|y|+10A (9)
The method for calculating LLR of the available areas C2, C3 and C4 is omitted in the same way, and constant terms are omitted:
LLR(b2_C2)＝-|x|+|y| (10)
LLR(b2_C3)＝-2|x|+2|y|+4A (11)
LLR(b2_C4)＝-|x|+2|y|-6A (12)
The area D is located at four corners of the constellation diagram and satisfies { Darea: |x| > 8A |y| > 8A }, no valid constellation points are located in the area, and when the received symbol (x, y) is within the area, the points (s 1 and s 0) of B 2 =1 and B 2 =0, which are closest to each other, are respectively located in the area C and the area B, so that the actual soft information is related to both the in-phase component and the quadrature component, but in order to further simplify the computational complexity, the distance between (x, y) and s 1 is only approximately related to the quadrature component y, and the distance between (x, y) and s 0 is only approximately related to the in-phase component x, where the specific soft information calculation formula is:
The square terms of x and y are included in the above formula, which is not friendly to hardware implementation, fig. 7 is a schematic diagram of a square term approximation method in the b 2 bit D region, x e [ -12A, -8A ] [8A,12A ], a circle represents x 2, and a dotted line represents 3.0861 x|x| -2.348, so that the square term reduction is more accurately fitted, and the conclusion is applied to formula (13), and the constant term is ignored, so that the following results are obtained:
The area E satisfies { Earea |x| < 4 A|y| > 8A }, 4 points of b 2 =0 are contained in each quadrant, the points of the nearest neighboring b 2 =1 are in the diagonally opposite area A, the soft information value is related to in-phase and quadrature components, the processing mode of the area E is similar to that of the area C, the area E is further divided into areas where 4 points of b 2 =0 are respectively corresponding to 4 cases of E1, E2, E3 and E4, and the conditions are respectively satisfied:
{E1area:|x|＞2A∩|x|＜4∩A|y|＞10A}
{E2area:|x|＞2A∩|x|＜4A∩|y|＞8A∩|y|≤10A}
{E3area:|x|≤2A∩|y|＞10A}
{E4area:|x|≤2A∩|y|＞8A∩|y|≤10A} (15)
The derivation of equation (8) is referred to herein directly as the LLR calculation method in regions E1-E4:
LLR(b2_E1)＝-|x|+2|y|-14A (16)
LLR(b2_E2)＝-|x|+|y|-4A (17)
LLR(b2_E3)＝-2|x|+2|y|-12A (18)
LLR(b2_E4)＝-2|x|+|y|-2A (19)
Fig. 8 is a schematic diagram of dividing the constellation diagram of B 3 bits in the constellation diagram, in which the regions B 3 =1 and B 3 =0 are alternately distributed in the I-axis direction, and the constellation diagram is divided into a region a and a region B in the diagram according to the position of the received symbol (x, y), and the dividing manner of the regions a and B is exactly the same as that of the region B 0 bits, in which the constellation points of the nearest neighboring regions B 3 =1 and B 3 =0 are selected differently when |x| >8A and |y| >8A, and only the in-phase component x can be considered and the quadrature component y can be ignored when calculating the LLR (B 3) for the convenience of hardware implementation.
Fig. 9 is a schematic diagram of approximate fitting of B 3 bits of soft information, circles represent the calculation result of formula (2) when x is located in region a, diamonds represent the calculation result of formula (2) when x is located in region B, it can be seen that the calculation results of the two regions are completely coincident when |x|is less than or equal to 8A, and there is a large difference when |x| >8A, so that the two regions are fitted in different approximate manners, and the dotted line and the solid line in fig. 9 represent the approximate fitting results of regions a and B, respectively, with the specific expression:
Fig. 10 is a schematic diagram of constellation region division of b 4 bits in a constellation. In the figure, except that 4 vertexes have no constellation points, the dark area B 4 =1 below the I-axis, the light area B 4 =0 above the I-axis, and the opposite of the calculation of B 0 bits of soft information, B 4 bits of soft information are only related to the orthogonal component y, so that the two areas a and B are divided into the two areas a and B according to the figure, which satisfies { Aarea: the approximate fitting schematic diagram of the two areas is shown in figure 11, wherein the horizontal axis is the measurement of the y value of the orthogonal component of the received symbol divided by the normalization factor A, the vertical axis is the calculation result of the soft information LLR, the circle and the diamond legend respectively represent the calculation result of the areas A and B by using the formula (2), the dotted line is the approximate fitting result, and the fitting expression is as follows:
LLR(b4)＝y (21)
fig. 12 is a schematic diagram of constellation region division of b 5 bits in a constellation. According to the position of the received symbol (x, y), the whole constellation diagram needs to be divided into three areas A, B and C, and the three areas respectively meet the following requirements
{Aarea:|x|＜4A∩|y|≤-|x|+12A}
{Barea:|x|≥4A∩(|y|≤8A∪|x|＞|y|)}
{Carea:|x|≤|y|∩|y|＞-|x|+12A∩|y|＞8A} (22)
Wherein the soft information calculations for regions a and B are related only to the quadrature component y and the soft information calculations for region C are related only to the in-phase component x. Fig. 13 is a schematic diagram of approximate fitting of soft information calculation of b 5 bit region a, in which the horizontal axis is a metric obtained by dividing the y value of the orthogonal component of the received symbol by the normalization factor a, the vertical axis is the calculation result of soft information LLR, the circle represents the calculation result using formula (2), the dotted line is the result of approximate fitting, and the approximate fitting expression in region a is:
LLR(b5_A)＝-||y|-6A|+2A (23)
The omission of the same proves that the approximate fit expression for regions B and C can be obtained as:
LLR(b5_B)＝|y|-4A (24)
LLR(b5_C)＝|x|-4A (25)
Fig. 14 is a diagram of the constellation region division of b 6 bits (least significant bits) in a 128-QAM constellation. The areas B 6 =1 and B 6 =0 are alternately distributed in the Q axis direction in the figure, the constellation diagram is divided into an area A and an area B in the figure according to the positions of the received symbols (x, y), and the areas A and B meet the requirements that { Aarea: |x|is less than or equal to 8 A|y| > |x| } and { Barea: |x| > 8 A|y|is less than or equal to |x| } and only the value of the orthogonal component y needs to be considered when soft information is calculated. Fig. 15 is a schematic diagram of approximate fitting of B 6 bits of soft information, and the dotted line and the solid line approximate the LLR calculation results of the region a and the region B, respectively, with the specific expression:
Claims (7)
1. A128 quadrature amplitude modulation cross constellation demapping method is characterized by comprising the following specific steps:
Step 1: dividing the constellation diagram, namely dividing all constellation points into a plurality of subareas according to the distribution rule of 0 and 1 of each bit in the constellation diagram, wherein the method for calculating the soft information value in each subarea is the same;
step 2: region selection, namely classifying the received noisy symbols Z into the subregions of the step1 according to the positions of the noisy symbols Z on the constellation diagram;
Step 3: calculating soft information values of each bit by approximate fitting, namely, performing approximation on LLRs of each position of each sub-region based on a linear function piecewise fitting method, and replacing an accurate value by using a fitting value;
In step 1, the QAM modulation carried by m bits of information in each symbol in the constellation diagram is represented as 2 m -ary QAM, and when m is an odd number, the cross constellation diagram is used for increasing the hamming distance, the standard constellation diagram is arranged on the in-phase component I path and the quadrature component Q path at equal intervals in a Gray mapping mode, so as to obtain 0 and 1 distribution rules of each bit position in the standard constellation diagram;
The soft demodulation LLR calculation adopts MAP algorithm, and the definition of the soft information of the b i bit is calculated as follows:
Wherein σ 2 is the channel noise variance, the coordinates of the received noisy symbol z=x+jy on the complex plane are expressed as (x, y), the symbol points in the standard constellation are s=s x+jsy, the coordinates on the complex plane are expressed as (S x,sy),S0 and S 1 represent the point set of 0 and 1 in the standard constellation for the current b i bit position, respectively, i.e. the symbol in set S 0 is 0,S 1 at b i bit position and 1 at b i bit position, and the soft information at b i position is calculated by only considering the euclidean distance between the received symbol and the nearest 0 and 1 symbols, instead of all constellation points in the standard constellation;
In step 2, the received symbol coordinates (x, y) are offset by a certain amount from the coordinates (s x,sy) of the standard constellation points due to the noise, s x e { ±a, ±3A, ±5A, ±7A, ±9A,.+ -, and s y e { ±a, ±3A, ±5A, ±7A, ±9A,.} wherein a is a normalization factor; when the received symbol Z is in soft demodulation, (x, y) can uniquely determine and select the area in the step 1 and perform corresponding operation in the step 3, and soft information calculation of most areas is only related to in-phase components or quadrature components;
in step 3, when the soft information of a certain bit is related to only the in-phase or quadrature component, it is simplified as:
Wherein x is the in-phase component of the received symbol, S x1 and S x0 are the in-phase component values of the symbols closest to x in the sets S 1 and S 0, respectively, the absolute value is an integer multiple of the normalization factor A, and the last coefficient after the equal sign Constant is kept under the same constellation diagram and channel condition, and the soft demodulation performance is not influenced, so that the soft demodulation performance is ignored; because s x1 and s x0 also change when the area where x is located changes, soft information of bit b i needs to be calculated by equation (2) according to the received value of x, and a linear function piecewise fitting-based method is adopted to approximate accurate LLR, namely, firstly, the result of each point calculation equation (2) is uniformly selected in each area in step 2, then, linear function is used for approximate fitting substitution, complex multi-bit multiplication is converted into addition and subtraction operation, and hardware implementation is facilitated.
2. A 128 quadrature amplitude modulation cross constellation demapping method as in claim 1 wherein: the constellation region of b 1 bits is divided into: at this time, the middle 64 constellation points b 1 =1, and the rest b 1 =0; judging the relation between the received symbol (x, y) and the in-phase component and the quadrature component when calculating the LLR (B 1), dividing the constellation diagram into a region A and a region B, wherein the region A is divided into an upper part and a lower part to meet the requirements of { Aarea: |x|less than or equal to |y| } and the distance between the received symbol and the nearest s y1 and s y0 is only related to the quadrature component y, the region B is divided into a left part and a right part to meet the requirements of { Barea: |x| > |y| } and the distance between the received symbol and the nearest s x1 and s x0 is only related to the in-phase component x, and the LLR of the region A can be calculated by replacing x, s x1 and s x0 with y, s y1 and s y0; the segmentation function |y| -8A is obtained after approximate fitting, and the B 1 bit soft information is obtained by combining approximate fitting calculation of the in-phase component in the region B:
3. A 128 quadrature amplitude modulation cross constellation demapping method as in claim 1 wherein: the constellation region of b 2 bits is divided into: because the boundaries of b 2 =0 and b 2 =1 do not extend through the entire I-axis or Q-axis, the boundaries are divided into a to E total 5 areas and the position distribution in each quadrant is the same; for the received symbol (x, y), the range of the central area A of the constellation diagram satisfies { Aarea: (|y| is less than or equal to 8 A|y| is less than or equal to (- |x|+12A)) |y| is less than or equal to 4A }, the middle constellation point in the area is b 2 =0, the constellation points on the left and right sides are b 2 =1, so that the soft information in the area is only related to the in-phase component, and the soft information of the b 2 -bit area A is
LLR(b2_A)＝-|x|+4A (5)
The region B is symmetrically distributed about the I and Q axes in a range of { Barea:4A.ltoreq.IxIΣ8AΣ.ltoreq.yI > (- |xI + 12A) }, the soft information is related to the orthogonal component only, so the soft information of the B 2 -bit region B is
LLR(b2_B)＝|y|-8A (6)
The area C satisfies { Carea |x| > 8A n 4A < |y|.ltoreq.8A }, 4 points B 2 =1 in each quadrant and the points of the nearest neighbor B 2 =0 are in the diagonally opposite area B, the in-phase component and the quadrature component need to be considered simultaneously for reducing the error of calculating soft information, the area C is divided into areas where 4 points corresponding to 4B 2 =1 respectively in total 4 cases of C1, C2, C3 and C4 respectively satisfy the following conditions:
{C1area:|x|＞10A∩|y|＞6A∩|y|≤8A}
{C2area:|x|＞8A∩|x|≤10A∩|y|＞6A∩|y|≤8A}
{C3area:|x|＞10A∩|y|＞4A∩|y|≤6A}
{ C4area } (7) C1 region with |x| > 8 A|x|10 A|y| > 4 A|y|6A } (7) is:
Omitting the same constant term yields:
LLR(b2_C1)＝-2|x|+|y|+10A (9)
the method for calculating LLR of C2, C3 and C4 also omits constant terms:
LLR(b2_C2)＝-|x|+|y| (10)
LLR(b2_C3)＝-2|x|+2|y|+4A (11)
LLR(b2_C4)＝-|x|+2|y|-6A (12)
The area D is located at four corners of the constellation diagram and satisfies { Darea: |x| > 8A |y| > 8A }, no valid constellation points exist in the area, and when the received symbol (x, y) is within the area, the points (s 1 and s 0) of B 2 =1 and B 2 =0, which are closest to each other, are respectively in the area C and the area B, so that the actual soft information is related to both the in-phase component and the quadrature component, and in order to simplify the computational complexity, the distance between (x, y) and s 1 is only approximately related to the quadrature component y, and the distance between (x, y) and s 0 is only approximately related to the in-phase component x, and the specific soft information calculation formula is:
the square terms of x and y are contained in the formula, so that the method is not friendly to hardware implementation; fitting the square term reduction more accurately, applying the conclusion to the formula (13), and ignoring the constant term to obtain:
The area E satisfies { Earea |x| < 4A n|y| > 8A }, 4 points of b 2 =0 are contained in each quadrant, the points of the nearest neighboring b 2 =1 are in the diagonally opposite area A, the soft information value is related to in-phase and quadrature components, the area E is divided into areas where 4 points of b 2 =0 are respectively located in 4 cases of E1, E2, E3 and E4, and the conditions are respectively satisfied:
{E1area:|x|＞2A∩|x|＜4A∩|y|＞10A}
{E2area:|x|＞2A∩|x|＜4A∩|y|＞8A∩|y|≤10A}
{E3area:|x|≤2A∩|y|＞10A}
{E4area:|x|≤2A∩|y|＞8A∩|y|≤10A} (15)
referring to equation (8), the LLR calculation method in the regions E1 to E4 is directly given here:
LLR(b2_E1)＝-|x|+2|y|-14A (16)
LLR(b2_E2)＝-|x|+|y|-4A (17)
LLR(b2_E3)＝-2|x|+2|y|-12A (18)
LLR(b2_E4)＝-2|x|+|y|-2A (19)。
4. A 128 quadrature amplitude modulation cross constellation demapping method as in claim 1 wherein: the constellation region of b 3 bits is divided into: regions B 3 =1 and B 3 =0 in the I-axis direction are alternately distributed, a constellation diagram is divided into a region a and a region B according to the position of a received symbol (x, y), the division mode of the regions a and B is identical to that of the regions B 0 bits, the difference between the regions a and B is that when |x| >8A and |y| >8A, the constellation points of the nearest adjacent regions B 3 =1 and B 3 =0 are selected differently, and only the in-phase component x is considered and the quadrature component y is ignored when calculating an LLR (B 3) for hardware realization convenience;
when the value of the absolute value of x is less than or equal to 8A, the calculation results of the two areas are completely overlapped, and the difference of the absolute value of x is more than 8A, so that the two areas are fitted in different approximation modes, and the specific expression is as follows:
5. A 128 quadrature amplitude modulation cross constellation demapping method as in claim 1 wherein: the constellation region of b 4 bits is divided into: the region B 4 =1 below the I axis, the region B 4 =0 above the I axis, in contrast to the calculation of soft information of B 0 bits, the soft information of B 4 bits is related to the orthogonal component y only, and is divided into two regions A and B, which satisfy { Aarea: |x|less than or equal to 8 A|y| > |x| } and { Barea: |x| > 8 A|y|less than or equal to |x| } with the horizontal axis being the measurement of the division of the orthogonal component y value of the received symbol by the normalization factor A, and the vertical axis being the calculation result of the soft information LLR, the approximate fitting expression is:
LLR(b4)＝y (21)。
6. A 128 quadrature amplitude modulation cross constellation demapping method as in claim 1 wherein: the constellation region of b 5 bits is divided into: according to the position of the received symbol (x, y), the whole constellation diagram needs to be divided into three areas A, B and C, and the three areas respectively satisfy the following conditions:
{Aarea:|x|＜4A∩|y|≤-|x|+12A}
{Barea:|x|≥4A∩(|y|≤8A∪|x|＞|y|)}
{Carea:|x|≤|y|∩|y|＞-|x|+12A∩|y|＞8A} (22)
Wherein the soft information computation of regions a and B is related to quadrature component y only, and the soft information computation of region C is related to in-phase component x only; the horizontal axis is the metric of the received symbol orthogonal component y divided by the normalization factor a, the vertical axis is the calculation result of the soft information LLR, and the approximate fit expression in the region a is:
LLR(b5_A)＝-||y|-6A|+2A (23)
The approximate fit expression for regions B and C is:
LLR(b5_B)＝|y|-4A (24)
LLR(b5_C)＝|x|-4A (25)。
7. A 128 quadrature amplitude modulation cross constellation demapping method as in claim 1 wherein: the constellation region of b 6 bits is divided into: the regions B 6 =1 and B 6 =0 in the Q-axis direction are alternately distributed, and the constellation diagram is divided into the region a and the region B according to the position of the received symbol (x, y) so as to satisfy the following conditions
{ Aarea @ x @ is less than or equal to 8A @ y @ x @ and { Barea @ x @ is greater than 8A @ y @ x @ is less than or equal to 8A @ x @, the soft information is calculated by considering the value of the orthogonal component y; the specific expression of the LLR calculation result of the approximate region A and the region B is as follows:
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