CN115987745B - Low-complexity quadrature amplitude modulation cross constellation demapping method - Google Patents

Abstract

The present invention proposes a low-complexity orthogonal amplitude modulation cross constellation demapping method, which can be divided into the following steps: (1) constellation diagram segmentation: according to the 0/1 mapping distribution law of each bit in the constellation point, the constellation diagram is divided into multiple regions; (2) region selection: for the demodulation of each bit in the received modulation symbol, only the relevant region in the constellation diagram is selected and the real and imaginary values of the symbol are used to calculate the soft information, which greatly reduces the selection range of the demapping constellation point; (3) approximate fitting calculation of the log-likelihood ratio of each bit: in order to avoid the high complexity problem caused by the calculation of the Euclidean distance between the received symbol and the standard constellation point, the soft information of each bit is calculated by a linear function piecewise fitting method to ensure that the performance loss is acceptable. The present invention can effectively reduce the complexity of hardware implementation of high-order QAM soft demodulation.

Description

A low-complexity quadrature amplitude modulation cross constellation demapping method

Technical Field

The invention belongs to the technical field of communications and relates to a low-complexity demapping method for a quadrature amplitude modulation cross constellation diagram.

Background technique

High-performance communication systems need to achieve higher information transmission rates and lower power consumption. There are many ways to improve the performance of communication systems. Among them, digital modulation technology can use limited frequency band resources and lower power consumption to improve information transmission rates. Linear modulation methods are divided into amplitude keying (ASK), phase shift keying (PSK) and quadrature amplitude modulation (QAM) according to the changing elements of the transmission signal. Since QAM can use less bandwidth to achieve higher data transmission rates, high-order QAM is widely adopted by modern communication standards. The square QAM constellation diagram is used for even-order QAM modulation, with a total of 2 even-power constellation points. The cross QAM constellation diagram is used for odd-order QAM modulation, with a total of 2 odd-power constellation points. The cross QAM is obtained by partially rotating the rectangular QAM constellation diagram. It has lower peak and average power and can improve demodulation performance, but it brings an increase in computational complexity compared to square and rectangular QAM during demapping. When QAM uses higher-order modulation, it needs to cooperate with channel coding technology to reduce the impact of channel noise. Therefore, the output of demapping should be a soft information value (generally using log-likelihood ratio LLR) to represent the reliability metric of the transmitted bit, so it is called soft demodulation.

There are currently a variety of soft demodulation algorithms for QAM. The traditional approximate method based on Max-Log-MAP (reference [1]: Viterbi, AJ, "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, pp 260–264, Feb. 1998) replaces the e-exponential and logarithmic operations with the maximum function (max), but requires a high number of multiplication operations and has a complexity of O(2 ^m ). The boundary-based low-complexity demapping method for QAM (reference [2]: F. Tosato, P. Bisaglia. "Simplified soft-output demapper for binary interleaved COFDM with application to HIPERLAN/2". Proc. IEEE ICC, vol. 2, pp. 664-668, 2002) decomposes the constellation diagram into two subsets, the I path and the Q path. Within each subset, boundaries are drawn according to the values of the standard constellation points. The distance between the two-dimensional coordinate points is replaced by the distance between the one-dimensional coordinates. When calculating the LLR of each bit, the broken line approximation method is used according to the received symbol. The nonlinear operation in Max-Log-MAP is converted into a linear operation to reduce the overall complexity. However, this method is currently only applied to square QAM. The cross constellation QAM demapping algorithm suitable for G.HN (Reference [3]: Xu Juan, Yao Rugui, Nan Hua Ni, Gao Fanqi. Low-complexity demapping algorithm for cross constellation QAM in G.HN standard [J]. Journal of Harbin Institute of Technology, 2015, 47(05): 110-117.) uses contribution weights to measure the contribution of standard constellation points to demapping, narrows the demapping search range and reduces the implementation complexity.

The above [1] requires a large number of multiplication operations, which is not conducive to hardware circuit implementation based on field programmable gate array circuits (FPGA) or application-specific integrated circuits (ASIC). Although [2] greatly simplifies the number and complexity of calculations, there is no precedent for its use on a cross constellation diagram. [3] can achieve the same performance as [1], but it is necessary to select a suitable search range according to the channel noise conditions and perform multiplication operations multiple times, which is still difficult for low-complexity hardware implementation.

Summary of the invention

In view of the above problems, the present invention proposes a low-complexity algorithm that can be used for orthogonal amplitude modulation (QAM) cross constellation soft demodulation. The algorithm can be divided into the following main steps: (1) Constellation diagram segmentation: According to the 0/1 mapping distribution law of each bit in the constellation point, the constellation diagram is divided into multiple regions; (2) Region selection: For the demodulation of each bit in the received modulation symbol, only the relevant region in the constellation diagram is selected and the real and imaginary values of the symbol are used to calculate the soft information, which greatly reduces the selection range of the demapping constellation point; (3) Approximate fitting calculation of the log-likelihood ratio of each bit: In order to avoid the high complexity problem caused by the calculation of the Euclidean distance between the received symbol and the standard constellation point (more complex multiplication operations will be introduced in the hardware design), the soft information of each bit is calculated by using a linear function piecewise fitting method to ensure that the performance loss is acceptable. The present invention can effectively reduce the complexity of hardware implementation of high-order QAM soft demodulation.

The specific steps of the present invention are:

Step 1: Constellation diagram segmentation, that is, according to the distribution law of 0 and 1 in each bit of the constellation diagram, all constellation points are divided into multiple sub-areas, and the method for calculating the soft information value in each sub-area is the same.

The QAM modulation in which each symbol in the constellation diagram carries m bits of information is represented as 2 ^m -ary QAM. The scope of consideration of the present invention is the cross constellation diagram when m is an odd number. In order to increase the Hamming distance, the standard constellation diagram adopts Gray mapping to arrange the in-phase component (I path) and the orthogonal component (Q path) at equal intervals, and the distribution rules of 0 and 1 of each bit position in the standard constellation diagram can be obtained respectively.

A more accurate soft demodulation LLR calculation uses the MAP algorithm, and the definition of calculating the b _i- th bit soft information is:

Among them, σ ² is the channel noise variance, the coordinates of the received noisy symbol Z = x + jy in the complex plane are expressed as (x, y), the symbol point in the standard constellation diagram is s = s _x + js _y , and its coordinates on the complex plane are expressed as (s _x , _sy ), S ₀ and S ₁ represent the point sets whose current _bi bit position is 0 and 1 in the standard constellation diagram, respectively, that is, the symbol in set S ₀ is 0 at the _bi bit position, and the symbol in set S ₁ is 1 at the _bi bit position. The above formula finally shows that to calculate the soft information of the _bi position, it is only necessary to consider the Euclidean distance between the received symbol and the most adjacent 0 and 1 symbols, rather than all the constellation points in the standard constellation diagram.

Step 1.1: For the cross constellation mapping, we first need to find the boundaries between all bit positions 0 and 1 in the standard constellation.

Step 1.2: Find the nearest boundary to each bit position in the received symbol, and determine the relationship between the Euclidean distance from the received symbol to the nearest 0 and 1 symbol and the in-phase component or orthogonal component. The set of positions with the same relationship is divided into the same area, and the same operation is used to calculate the soft information value in the area.

Step 2: Region selection, that is, classifying the received noisy symbol Z into the sub-region of step 1 according to its position on the constellation diagram.

Since the received symbol coordinates (x, y) contain noise, they will have a certain offset relative to the coordinates of the points in the standard constellation diagram (s _x , s _y ), s _x ∈{±A,±3A,±5A,±7A,±9A,...}, and similarly s _y ∈{±A,±3A,±5A,±7A,±9A,...}, where A is the normalization factor. When the received symbol Z is soft-demodulated, (x, y) can uniquely determine and select the area in step 1 and perform the corresponding operation in step 3. The soft information calculation of most areas is only related to the in-phase component or the orthogonal component, and very few areas are related to both components.

Step 3: Approximate fitting is used to calculate the log-likelihood ratio of each bit, that is, based on the linear function piecewise fitting method, the LLR of each position in each sub-region is approximated, and the fitting value is used instead of the exact value.

Formula (1) provides a relatively accurate method for calculating LLR. However, it can be further simplified when the soft information of a certain bit is only related to the in-phase or orthogonal component. Here, the calculation of the in-phase component is taken as an example:

Where x is the in-phase component of the received symbol, _sx1 and _sx0 are the in-phase component values of the symbol closest to x in the sets _S1 and _S0 , respectively. The absolute value is an integer multiple of the normalization factor A. The coefficient after the last equal sign is Under the same constellation diagram and channel conditions, it is always a constant and has no effect on the soft demodulation performance, so it can be ignored. Because s _x1 and s _x0 also change when the region where x is located changes, a hardware-friendly method is needed to calculate the soft information of bit b _i according to the received x value by equation (2). Here, a method based on piecewise fitting of a linear function is used to approximate the precise LLR, that is, first, each point is uniformly selected in each region of step 2 to calculate the result of equation (2), and then a linear function is used for fitting instead, so that the complex multi-bit multiplication can be converted into addition and subtraction operations, which is conducive to hardware implementation.

The advantages and beneficial effects of the present invention are:

The present invention applies the approximate fitting method to the demodulation of the quadrature amplitude modulation (QAM) cross constellation, divides the standard constellation into regions according to the relationship between the soft information calculation of each bit position on the constellation diagram and the in-phase component or the orthogonal component, and uses the linear function piecewise fitting method to match the corresponding soft information operation, which greatly reduces the hardware complexity introduced by calculating the precise Euclidean distance and the large search range.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic diagram of a 128-QAM cross constellation diagram using Gray mapping.

FIG2 is a schematic diagram of the constellation diagram area division of the b ₀ bit (most significant bit) in the 128-QAM constellation.

FIG3 is a schematic diagram of the approximate fitting of b _0- bit soft information in a 128-QAM constellation.

FIG4 is a schematic diagram of the region division of the constellation diagram of b ₁ bit in the 128-QAM constellation.

Figure 5 is a schematic diagram of the approximate fitting of b _1- bit soft information in the 128-QAM constellation. (Area A)

FIG6 is a schematic diagram of the region division of the constellation diagram of b ₂ bits in the 128-QAM constellation.

FIG7 is a schematic diagram of a method for approximating the square term of soft information in the b _2- bit D region in a 128-QAM constellation.

FIG8 is a schematic diagram of the region division of the constellation diagram of b ₃ bits in the 128-QAM constellation.

FIG9 is a schematic diagram of the approximate fitting of b _3- bit soft information in a 128-QAM constellation.

FIG10 is a schematic diagram of the region division of the constellation diagram of b ₄ bits in the 128-QAM constellation.

FIG11 is a schematic diagram showing the approximate fitting of b _4- bit soft information in a 128-QAM constellation.

FIG12 is a schematic diagram showing the region division of the constellation diagram of b ₅ bits in the 128-QAM constellation.

Figure 13 is a schematic diagram of the approximate fitting of b _5- bit soft information in the 128-QAM constellation. (Area A)

FIG14 is a schematic diagram showing the region division of the constellation diagram of b ₆ bits (least significant bit) in the 128-QAM constellation.

FIG15 is a schematic diagram showing the approximate fitting of b _6- bit soft information in a 128-QAM constellation.

Detailed ways

The present invention is described in detail below by taking 128-QAM cross constellation modulation as an example in combination with the accompanying drawings and implementation examples.

FIG1 is a 128-QAM constellation diagram designed by the Gray mapping method adopted in this embodiment. There are 128 constellation points in total in the figure, each constellation point represents 7 bits of information {b ₀ , b ₁ , ..., b ₆ }, where b ₀ is the most significant bit (MSB), b ₆ is the least significant bit (LSB), and each constellation point is evenly arranged in a cross shape, and the distance between adjacent constellation points in the I-path direction and the Q-path direction is 2A. Based on the above steps 1 to 3, the constellation diagram area division method and the soft information approximate fitting calculation method for each bit position of b ₀ to b ₆ are analyzed in turn below.

Step 1: Constellation diagram segmentation. When only focusing on the 0 and 1 cases of _b0 , FIG2 is a schematic diagram of the constellation diagram area division of the _b0 bit position in the 128-QAM constellation. In the figure, except for the 4 vertices without constellation points, the dark area on the left side of the Q axis is _b0 = 1, and the light area on the right side of the Q axis is _b0 = 0.

Step 2: Region selection. It can be seen that when receiving the symbol (x, y), the soft information of the _b0 bit is only related to the in-phase component x. Substituting the received x value and the corresponding _sx1 and _sx0 into formula (2) can calculate the accurate LLR of the _b0 bit. However, in order to further simplify, the constellation diagram is further divided according to the type of approximate operation. As shown by the double solid lines in the figure, it is divided into two areas, Aarea and B area, and satisfies {Aarea:|y|≤8A∪|x|＞|y|} and {Barea:|y|＞8A∩|x|≤|y|}. The main difference between the two areas is that when |x|＞8A, the nearest _sx1 and _sx0 are selected in different ways. The specific selection of _sx1 and _sx0 in different x ranges and the LLR calculation values according to formula (2) are shown in Tables 1 and 2. However, too many segments will lead to the consumption of additional hardware selectors and comparators. Therefore, a linear fitting method is used here to obtain a unified calculation expression based on the relationship between the x value range and LLR.

Table 1 LLR calculation results for each segment of A area

x range interval s _{x1 x0} LLR (ignore 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 2 LLR calculation results for each segment of B area

x range interval s _{x1 x0} LLR (ignore 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: Approximate fitting to calculate the log-likelihood ratio of each bit. Figure 3 is a schematic diagram of the approximate fitting of each segment of soft information of the _b0 bit. The horizontal axis in the figure is the metric after the in-phase component x value of the received symbol is divided by the normalization factor A, and the vertical axis is the calculation result of the soft information LLR. The circle represents the LLR calculation result corresponding to Table 1 when x is located in area A, and the diamond represents the LLR calculation result corresponding to Table 2 when x is located in area B. The two are very close and overlap when |x| is small, so the same approximate formula can be considered to represent the LLR calculation of areas A and B, as shown by the dotted line in Figure 3. The approximate expression is:

LLR(b ₀ )＝-x(3)

Although there is still a certain gap between the fitting results and the actual calculation results when |x| is large, the simulation shows that there is no significant loss in demodulation performance.

The same steps 1 to 3 are used for constellation diagram division, region selection and fitting at the bit positions _b1 to _b6 . The following will not repeat the steps themselves, but will explain the diagram division and fitting results from the perspective of different bit positions:

FIG4 is a schematic diagram of the constellation region division at the _b1 bit position in the 128-QAM constellation. At this time, the middle 64 constellation points _b1 = 1, and the rest _b1 = 0. According to the same processing idea, according to the position of the received symbol (x, y), the relationship with the in-phase and orthogonal components when calculating LLR ( _b1 ) is determined, and the constellation is divided into region A and region B in the figure, where region A is divided into upper and lower parts to satisfy {Aarea:|x|≤|y|}, and the distance between the received symbol and the most adjacent _sy1 and _sy0 is only related to the orthogonal component y. Region B is divided into left and right parts to satisfy {Barea:|x|＞|y|}, and the distance between the received symbol and the most adjacent _sx1 and _sx0 is only related to the in-phase component x. Formula (2) can correspond to the LLR calculation method of region B. Replace x, _sx1 and _sx0 with y, _sy1 and _sy0 to calculate the LLR of region A. FIG5 is a schematic diagram of the approximate fitting of b _1- bit soft information in region A. The circles are the LLR calculation results of each segment in region A obtained according to the above method. After fitting, the piecewise function |y|-8A can be obtained as shown by the dotted line. Combined with the fitting calculation of the in-phase component in region B, the calculation method of b _1- bit soft information can be obtained as follows:

Figure 6 is a schematic diagram of the region division of the _b2- bit constellation diagram. Because the boundary between _b2 = 0 and _b2 = 1 does not run through the entire I axis or Q axis, the region division is relatively complex. It is divided into 5 regions from A to E, and the position distribution in each quadrant is the same. For the received symbol (x, y), the range of the central region A of the constellation diagram satisfies {Aarea: (|y|≤8A∩|y|≤(-|x|+12A))∪|y|≤4A}, the middle constellation point in the region is _b2 = 0, and the constellation points on the left and right sides are _b2 = 1, so the soft information in this region is only related to the in-phase component. Similar to the _b1- bit soft information calculation method, the soft information of the b2 _- bit region A can be approximated as

LLR(b ₂ _A)＝-|y|+4A (5)

Region B is symmetrically distributed about the I and Q axes, and its range satisfies {Barea:4A≤|x|≤8A∩|y|＞(-|x|+12A)}. The soft information is only related to the orthogonal component, so the soft information of b2 _- bit region B can be approximated as

LLR(b ₂ _B)＝|y|-8A (6)

Region C satisfies {Carea:|x|＞8A∩4A＜|y|≤8A}, and its characteristics are that the 4 points in each quadrant have b ₂ =1 and their most adjacent points with b ₂ =0 are in the diagonally opposite region B. Therefore, in order to reduce the error in calculating soft information, it is necessary to consider both the in-phase component and the orthogonal component. Region C is further divided into 4 cases, C1, C2, C3, and C4, which correspond to the regions where the 4 points with b ₂ =1 are located. Each region satisfies 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:|x|＞8A∩|x|≤10A∩|y|＞4A∩|y|≤6A} (7)

Their LLR calculation is expanded on the basis of formula (2). Here, the C1 area is taken as an example to illustrate the calculation method of LLR:

Omitting the same constant term yields:

LLR( _{b2_C1} )＝-2|x|+|y|+10A (9)

Similarly, the LLR calculation method for regions C2, C3, and C4 can be obtained, and the constant term is also omitted:

LLR( _{b2_C2} )＝-|x|+|y| (10)

LLR( _{b2_C3} )=-2|x|+2|y|+4A (11)

LLR( _{b2_C4} )＝-|x|+2|y|-6A (12)

Region D is located at the four corners of the constellation diagram and satisfies {Darea:|x|＞8A∩|y|＞8A}. There is no valid constellation point in the region. When the received symbol (x, y) is within this region, the nearest points ( _s1 and _s0 ) with _b2 ＝1 and _b2 ＝0 are in regions C and B respectively. Therefore, the actual soft information is related to both the in-phase component and the orthogonal component. However, in order to further simplify the computational complexity, the distance between (x, y) and _s1 is approximated as only related to the orthogonal component y, and the distance between (x, y) and _s0 is approximated as only related to the in-phase component x. The specific soft information calculation formula is:

The above formula contains the square terms of x and y, which is not very friendly to hardware implementation. Figure 7 is a schematic diagram of the square term approximation method in the b _2- bit D region, x∈[-12A,-8A]∪[8A,12A], the circle represents x ² , and the dotted line represents 3.0861*|x|-2.348, so a more accurate fitting is performed on the square term reduction. This conclusion is applied to formula (13), and the constant term is ignored to obtain:

Region E satisfies {Earea:|x|＜4A∩|y|＞8A}. Each quadrant contains 4 points with b ₂ =0 and their most adjacent points with b ₂ =1 are in the diagonally opposite region A. Its soft information value is related to both the in-phase and quadrature components. Similar to the processing method of region C, region E is further divided into 4 cases, E1, E2, E3, and E4, which correspond to the regions where the 4 points with b ₂ =0 are located. Each region satisfies the following conditions:

{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)

Referring to the derivation of formula (8), the LLR calculation method in 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)

FIG8 is a schematic diagram of the regional division of the constellation diagram of the b ₃ bit in the constellation. In the figure, the regions of b ₃ =1 and b ₃ =0 are alternately distributed in the I-axis direction. According to the position of the received symbol (x, y), the constellation diagram is divided into region A and region B in the figure, which is exactly the same as the division method of b ₀ bit. The main difference between regions A and B is that when |x|>8A and |y|>8A, the most adjacent constellation points of b ₃ =1 and b ₃ =0 are selected differently. For the convenience of hardware implementation, only the in-phase component x can be considered when calculating LLR (b ₃ ) and the orthogonal component y can be ignored.

FIG9 is a schematic diagram of the approximate fitting of each segment of the b _3- bit soft information. The circle represents the calculation result of formula (2) when x is located in region A, and the diamond represents the calculation result of formula (2) when x is located in region B. It can be seen that when |x|≤8A, the calculation results of the two regions completely overlap, while when |x|>8A, there is a large difference. Therefore, different approximate methods are used to fit the two regions. The dotted line and solid line in FIG9 represent the approximate fitting results of regions A and B respectively. The specific expression is:

FIG10 is a schematic diagram of the constellation diagram area division of _b4 bits in the constellation. In the figure, except for the four vertices without constellation points, the dark area below the I axis is _b4 = 1, and the light area above the I axis is _b4 = 0. The calculation of the soft information of _b0 bits is just the opposite. The soft information of _b4 bits is only related to the orthogonal component y. Therefore, similarly, it is divided into two areas A and B according to the figure to satisfy {Aarea:|x|≤8A∪|y|＞|x|} and {Barea:|x|＞8A∩|y|≤|x|}. The schematic diagram of the approximate fitting of the two areas is shown in FIG11. In the figure, the horizontal axis is the metric after the orthogonal component y value of the received symbol is divided by the normalization factor A, and the vertical axis is the calculation result of the soft information LLR. The circle and diamond legends represent the calculation results of area A and B using formula (2), respectively. The dotted line is the result of the approximate fitting. The fitting expression is:

LLR(b ₄ )＝y (21)

Figure 12 is a schematic diagram of the region division of the constellation diagram of b ₅ bits in the constellation. According to the position of the received symbol (x, y), the entire constellation diagram needs to be divided into three regions: A, B, and C. The three regions meet

{Aarea:|x|＜4A∩|y|≤-|x|+12A}

{Barea:|x|≥4A∩(|y|≤8A∪|x|＞|y|)}

{Carea:|x|≤|y|∩|y|＞-|x|+12A∩|y|＞8A} (22)

The soft information calculation of regions A and B is only related to the orthogonal component y, and the soft information calculation of region C is only related to the in-phase component x. Figure 13 is a schematic diagram of the approximate fitting of the soft information calculation of region A with ₅ bits. The horizontal axis is the metric of the orthogonal component y value of the received symbol divided by the normalization factor A, and the vertical axis is the calculation result of the soft information LLR. The circles represent the calculation results using formula (2), and the dotted line is the result of the approximate fitting. The approximate fitting expression in region A is:

LLR(b ₅ _A)＝-||y|-6A|+2A (23)

Similarly, omitting the proof, we can get the approximate fitting expression of regions B and C as follows:

LLR(b ₅ _B)＝|y|-4A (24)

LLR(b ₅ _C)＝|x|-4A (25)

FIG14 is a schematic diagram of the constellation region division of the _b6 bit (least significant bit) in the 128-QAM constellation. In the figure, the regions with _b6 = 1 and _b6 = 0 in the Q-axis direction are alternately distributed. According to the location of the received symbol (x, y), the constellation is divided into regions A and B in the figure to satisfy {Aarea:|x|≤8A∪|y|＞|x|} and {Barea:|x|＞8A∩|y|≤|x|}. When calculating soft information, only the value of the orthogonal component y needs to be considered. FIG15 is a schematic diagram of the approximate fitting of the _b6 bit soft information. The dotted line and the solid line respectively approximate the LLR calculation results of regions A and B. The specific expressions are:

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+js_y, the coordinates on the complex plane are expressed as (S _x,s_y),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,s_y) 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: