CN102694765A - Design method of non-2 integer power order QAM (quadrature amplitude modulation) - Google Patents

Abstract

The invention discloses a design method of non-2 integer power order QAM (quadrature amplitude modulation) and belongs to the field of communication. In the method disclosed by the invention, a new modulation mode is built by five steps of setting a bit rate, selecting a modulation order, arranging constellation point positions, selecting a constellation point grouping mode and setting a sign bit mapping relation. According to the new modulation mode designed by the method, the bit rate and the bit error ratio capability may be between two traditional modulation modes adjacent to the modulation order. Selection of the modulation mode in an adaptive communication system can be increased, and the performance interval between the modulation modes can be reduced. By the design method disclosed by the invention, the limitation of the modulation order to the modulation mode can be broken through; the selection of the bit rate is no longer an integer and the M-QAM modulation system is greatly enriched.

Description

The QAM modulation design method on a kind of non-2 integer power rank

Technical field

The invention belongs to the communications field, be specifically related to the qam mode method for designing on a kind of non-2 integer power rank.

Background technology

Adaptive Modulation is a kind ofly to select the technology of digital modulation mode flexibly according to channel condition, in order under the unsettled situation of communication environment, to select optimum communication mode.Suitable modulation system can be selected to the requirement of communication quality according to communication channel condition and system by system, under the good situation of channel condition, sends more information, under the bad situation of channel condition, sends less information to guarantee communication quality.Adaptive Modulation can increase the availability of frequency spectrum and the data transmission rate of system; In the various systems that occur in recent years---OFDM (Orthogonal Frequency Division Multiplexing especially; OFDM) (multiple input multiple output has obtained application more and more widely in MIMO) for system and multi-input multi-output system.

According to the characteristics of adaptive modulation system, require to exist in the communication system the less modulation system in multiple performance each other interval, communication system balance communication channel condition and receiving terminal are selected suitable modulation system to the requirement of communication quality.For three kinds of traditional modulation systems---MPSK (M-ary Phase Shift Keying; MPSK), multiple frequency shift keying (M-ary Frequency Shift Keying; MFSK), multi-system amplitude keying (M-ary Amplitude Shift Keying; MASK) exist the not good problem of performance after order of modulation increases, this is because the characteristics of its unitary variant modulation determine, so it does not satisfy the requirement of adaptive modulation system.(Quadrature Amplitude Modulation QAM), under identical channel condition, is 2 in order to make order of modulation for bivariant quadrature amplitude modulation ⁿWith order of modulation be 2 ^N+1Modulating system reach the identical error rate, its desired signal interference ratio (Signal Interference Ratio, difference SIR) is about 3dB, this performance is at interval for adaptive modulation system and Yan Taida.How to dwindle the interval of the performance between the various modulation systems in the adaptive modulation system, just become an important research project.

Recent years; In the face of the excessive at interval problem of various communication mode performances; In practical application, mainly form the smaller at interval code modulation system of performance through the chnnel coding that modulation system is combined various parameters; Integral body is considered modulation and chnnel coding part, and how the characteristics according to chnnel coding well have been combined into important research direction with modulation technique and its.Document " Wu Yiling, Li Hongbin, Zhao Yuping. a kind of new 2 ²ⁿ⁺¹Rank qam constellation figure design " in, the author has proposed a kind of new qam constellation figure method for designing to the characteristics of chnnel coding, has obtained performance better, has embodied the theory of chnnel coding with the modulation combination.Though the performance that the chnnel coding kind is many and modulation system can reduce various communication systems after combining greatly at interval, various coded system applicable elements still can't solve the bigger problem in adaptive modulation system performance interval fully with the restriction that parameter is selected.

In document " Anh Tuan Le and Kiyomichi Araki, A group of modulation schemes for adaptive modulation ", it is 3 * 2 that the author has proposed a kind of exponent number ^N-1QAM modulation, this modulating system is 2 between exponent number to the requirement of SIR all with reaching transmission code speed under specific bit error rate ⁿWith exponent number be 2 ^N+1QAM modulation between, can dwindle between the modulation system performance at interval.Its implementation procedure is with 3 * 2 ^N-1Individual constellation point is divided into that to count be 2 ⁿWith 2 ^N-1Two parts, when the symbol of first transmission is that to count be 2 ^N-1During one of that group constellation point, it is 2 that the symbol of second transmission is counted exactly ⁿPoint in the middle of that group is if the symbol of first transmission is 2 for counting ⁿDuring point in the middle of that group, the symbol of second transmission is in the planisphere whole 3 * 2 ^N-1One of individual point, thus realize 2 through the Continuous Selection constellation point ²ⁿ⁺¹Plant the constellation point combination; 0,1 sequence that length is 2n+1 of every kind of constellation point combination mapping; Promptly represent the information of 2n+1 bit through sending two continuous symbols; The combination that realizes continuous two constellation point is corresponding one by one with a bit sequence, and its modulation code check be (n+0.5) bit/symbol, through analyzing and emulation can show that all its performance of BER is 2 between exponent number ⁿWith exponent number be 2 ^N+1QAM modulation between.Exponent number is 3 * 2 ^N-1QAM modulation replenished adaptive modulation system effectively.However, also just to have designed order of modulation be 3 * 2 in this design ^N-1QAM modulation, the performance between the various modulation systems still has about 1.5dB at interval.

In sum; In the face of the excessive at interval problem of various modulation system performances in the adaptive modulation system; Wherein a part of researcher combines through modulating with chnnel coding; Obtain the communication system of various performances through the parameter that changes chnnel coding, but because the restriction of chnnel coding characteristic and parameter, and can't solve the excessive problem in performance interval completely; Another part researcher is through making up constellation point cleverly, breaks through order of modulation and be the restriction of 2 integer power, and designing order of modulation is 3 * 2 ^N-1QAM modulation, select from modulation system is abundant, but these two kinds of methods are subject to chnnel coding characteristics and bit rate restriction, still can't satisfy the requirement of Adaptive Modulation to modulation classification completely.

Summary of the invention

To the at interval excessive problem of performance between each modulation system in the adaptive modulation system; The present invention has provided a kind of new modulation method for designing; Can design the QAM modulation of the integer power of order of modulation non-2 in this way; Its performance is dwindled the performance interval between the various modulation systems between existing adjacent two kinds of modulation systems.

The present invention proposes the method for designing of the QAM modulation on a kind of non-2 integer power rank, is divided into following five steps substantially:

Step 1: the bit rate of setting modulation system to be designed:

Design a kind of new qam mode and will select the bit rate of modulation system to be designed earlier; Select specific bit rate based on dwindling modulation system performance demand at interval; Here the bit rate of setting adopts the form k/n bit/symbol of mark, and denominator is the precision n of bit rate; If the order of modulation of two kinds of adjacent modulation systems is W and 2 * W, then sets the bit rate interval and be:

${\log }_{2}W<\frac{k}{n}<{\log }_2(2\&times;W)$

Step 2: according to the selected order of modulation of selected bit rate; The selected of described order of modulation M should be with reference to following two conditions:

(1) $\sqrt[n]{2^k}=2^{\frac{k}{n}}\&le;M,$

(2) under the situation that the constellation point ceiling capacity is confirmed, select maximum order of modulation.

Wherein, (1) individual condition is a necessary condition.

Step 3: selected constellation point packet mode:

According to the value of selected order of modulation M, exhaustive computations goes out possible packet mode, and one group of parameter selecting implementation complexity minimum (parameter all is that the integer power parameter of even number and 2 is maximum) therein is as the constellation point packet mode;

Step 4: the constellation point of arranging position:

Set the position of constellation point according to order of modulation M and arrange, promptly set the planisphere of new QAM modulation, the packet mode that should combine to select and the restriction of modulation system signal peak-to-average ratio carried out of arranging;

Step 5: set symbol bit sequence mapping relations:

This step is set up the packet design scheme according to constellation point position and packet mode earlier, sets up the mapping relations of constellation point combination and bit sequence then according to the modulation parameter (comprising bit rate, order of modulation, packet mode, constellation point position) of packet design scheme and setting before.Consider implementation complexity; Mapping relations are preferentially according to single sign map one bit section, and each sign map relation is separate, and the constellation point combination that has more is filled a vacancy and shone upon; Consider the modulation performance of BER, mapping is as far as possible according to gray mappings or approximate gray mappings;

Through after these five steps, the mapping relations of symbol and bit sequence are established.Original bit sequence that will be to be modulated in the modulated process is mapped as constellation point according to mapping relations, will be mapped as bit sequence according to the constellation point that rule rules out in the demodulating process.

For the performance to newly-designed qam mode is verified; Use for reference traditional QAM modulation bit error rate formula; The QAM method for designing that the present invention is directed to new proposition has proposed a kind of Bit Error Rate Computation method; The performance of BER of the qam mode newly designed is derived being used for, verify its practicality.

The present invention provides a kind of method for designing of QAM modulation; Through continuous n symbol integral body is mapped to bit sequence; Realize the QAM modulation of multiple bit rate, multiple order of modulation, between the adjacent conventional modulated mode of two kinds of performances, create a kind of new modulation system, the performance of dwindling both at interval; Enriched modulation system, for adaptive modulation system provides more selection.

Description of drawings

Fig. 1 is a method for designing flow chart provided by the invention;

Fig. 2 is modulation grouping sketch map among the present invention;

Fig. 3 is a packet mode exhaust algorithm sketch map involved in the present invention;

Fig. 4 sets the corresponding sketch map of sign bit in the sign bit mapping relations step for the present invention;

Fig. 5 is a selected order of modulation step medium energy constellation point sketch map in the embodiment of the invention one;

Fig. 6 is a packet mode exhaust algorithm sketch map in the embodiment of the invention one;

Fig. 7 is constellation point arrangement mode and each constellation point numbering sketch map selected in the embodiment of the invention one;

Fig. 8 is the 16QAM that mentions among the present invention sign bit mapping relations according to gray mappings;

Fig. 9 is the embodiment of the invention one a 24QAM sign bit mapping relations sketch map (first symbol number is 1-16);

Figure 10 is the embodiment of the invention one a 24QAM sign bit mapping relations sketch map (first symbol number is 17-24);

Figure 11 is the 24QAM bit error rate simulation result among the embodiment one;

Figure 12 is a packet mode exhaust algorithm sketch map in the embodiment of the invention two;

The 32QAM cross constellation point arrangement mode of Figure 13 for mentioning in the embodiment of the invention two;

Figure 14 is constellation point arrangement mode and each constellation point numbering sketch map selected in the embodiment of the invention two;

Figure 15 is the embodiment of the invention two 28QAM sign bit mapping relations sketch mapes (first symbol number is 1-16, and second symbol number is 1-28, and the 3rd symbol number is 1-28);

Figure 16 is the embodiment of the invention two 28QAM sign bit mapping relations sketch mapes (first symbol number is 21-28, and second symbol number is 1-16, and the 3rd symbol number is 1-16);

Figure 17 is the embodiment of the invention two 28QAM sign bit mapping relations sketch mapes (first symbol number is 21-28, and second symbol number is 17-20, and the 3rd symbol number is 1-16);

Figure 18 is the embodiment of the invention two 28QAM sign bit mapping relations sketch mapes (first symbol number is 17-20, and second symbol number is 1-20, and the 3rd symbol number is 1-16);

Figure 19 is the simulation result of 28QAM bit error rate among the embodiment two.

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is elaborated.

The core concept of modulation design is to realize 2 through certain constellation point selection scheme ⁿPlant the constellation point selection mode, each constellation point is selected the sequence of a n bit of mapping, thereby realizes the modulation of n Bit data.For example the 16QAM modulation is in 16 constellation point, to select 1 transmission, and obviously this selection has 16 kinds of possibilities, can realize the transmission of 4 Bit datas, and its bit rate is 4 bit/symbol.For traditional qam mode, each symbol is demodulated into bit sequence separately, and this just requires order of modulation is 2 integral number power, and its modulation code speed is restricted to integer.

The present invention proposes the method for designing of the QAM modulation on a kind of non-2 integer power rank; Through the whole demodulation of continuous a plurality of symbols is realized the non-integral modulation system of bit rate; This method is divided into following five steps substantially, and flow chart of steps is as shown in Figure 1, and concrete steps realize as follows:

Step 1: the bit rate of setting modulation system to be designed:

If the bit rate of modulation system to be designed is the k/n bit/symbol; Promptly transmit the data of k bit with continuous n symbol, consider the complexity of subsequent step, its bit rate precision n tries not, and (suggestion surpasses 4 too greatly; Be preferably 2 or 3 among the present invention); Bit rate is waited to dwindle between the bit rate of performance two kinds of adjacent modulation systems at interval between needs, and the order of modulation of establishing two kinds of adjacent modulation systems is respectively W and 2 * W, then sets the bit rate interval to be:

${\log }_{2}W<\frac{k}{n}<{\log }_2(2\&times;W)$

Step 2: selected order of modulation:

Following two requirements when being selected, order of modulation are arranged:

(1) order of modulation must be enough big to satisfy the requirement of bit rate.According to the bit rate k/n bit/symbol of setting, promptly transmit the data of k bit with continuous n symbol, establishing order of modulation is M, n the maximum possible number of combinations of symbol are M continuously ⁿ, and be 2 in order to form the number of combinations of shining upon minimum needs one by one with the data of k bit ^k, its theoretical lowest modulation exponent number M need satisfy following condition:

$\sqrt[n]{2^k}=2^{\frac{k}{n}}\&le;M$

This condition is for realizing that bit rate is the necessary condition of the M-QAM modulation of k/n bit/symbol.

(2) selection of order of modulation should be easy to subsequent design as far as possible.Consider the selection and the definite mapping relations of simplification of enriching packet mode, order of modulation should be chosen as the even number of some greatly; But consider from another point of view, the size of suitable again control order of modulation, excessive and bring the excessive problem of peak-to-average force ratio to avoid in the signal ceiling capacity signal energy.In view of these two reasons; Order of modulation often is chosen in maximum order of modulation under the definite situation of constellation point ceiling capacity; Different with (1) individual requirement; This requirement (2) is not the necessary condition that realizes modulation, just can the simplified design step according to this condition, and the performance of optimal design; If in the practical application under the situation that the constellation point ceiling capacity is confirmed maximum order of modulation too big (reaching the order of modulation of the modulation system adjacent) with its performance, also can in scope, select than its slightly smaller even number as order of modulation.

(1) individual condition is a necessary condition in above-mentioned two conditions, must satisfy, and (2) individual condition is not a necessary condition, considers according to actual conditions.

Step 3: selected constellation point packet mode:

This step is according to two steps in front selected bit rate, order of modulation, and exhaustive computations goes out possible packet mode, selects wherein relatively to be easy to a packet mode of realizing then.

If the bit rate that preceding two steps are confirmed is the kn bit/symbol, establishing order of modulation in addition is M, and the modulation layering number of plies is m, and modulation system is chosen continuous n constellation point mapping k bit from M constellation point, be the group technology sketch map like Fig. 2, wherein packet parameters M among the figure _Sw(s=1,2 ..., n, w=1,2 ..., m) should satisfy following two rules:

$\underset{w=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{s=1}{\overset{n}{\mathrm{\&Pi;}}}{M}_{\mathrm{sw}}=2^k---\left(1\right)$

$\underset{w=1}{\overset{m}{\mathrm{\&Sigma;}}}{M}_{1w}=M---\left(2\right)$

M constellation point is divided into the m group, and for the corresponding constellation point group of first symbol, wherein every group of constellation point number is M _1w(w=1,2 ..., m), the constellation point that each group comprises does not repeat, when the corresponding constellation point of first symbol S1 that sends is in the w group, and s the symbol S that sends subsequently _s(s=2 ..., n) be specific M _SwIn the individual constellation point one, the constellation point in the constellation point group that wherein non-first symbol of each layer is corresponding allows identical.Like this, select the possible combination of a continuous n constellation point total

Kind, be the possible permutation and combination several 2 of the bit sequence of k as long as make itself and length ^kEquate, set up mapping relations one by one, just can be through sending n constellation point transmission k Bit data continuously.

For confirming the suitable constellation point number M of respectively organizing _Sw, confirm modulation layering number of stories m (m is set at 2 usually, and bigger its design complexities of the value of m is high more) earlier.After confirming the value of m, the present invention uses the method for exhaustion to seek possible group technology, the sketch map of exhaust algorithm such as Fig. 3.This exhaust algorithm is confirmed one group of M according to the constraint of formula (2) earlier _1w(w=1,2 ..., m), attempt all possible M then _Sw(s=2,3 ..., n; W=1,2 ..., m; M _Sw≤M), calculate to judge whether formula (1) is set up, set up the parameter M that then writes down its establishment of ordering when formula (1) _Sw(s=1,2 ..., n; W=1,2 ..., m); Conversion M then _1w(w=1,2 ..., m) carry out again, until whole M _1w(w=1,2 ..., the traversal that possibly make up m) is accomplished, and experiment finishes.

The exhaustive packet mode that goes out generally has a variety of, selects than the carrying out that is easier to realize according to following rule:

(1) in possible packet mode, selection constellation point number is 2 the maximum or approaching the most the more pairing packet mode of packet parameters of integer power.The situation of the integral number power of existence 2 in packet mode; Can directly use the gray mappings or the approximate gray mappings of moulding in follow-up sign bit mapping relations part; So not only can abbreviation sign bit mapping relations, and can obtain better performance of BER.

(2) numeral of odd number or too small (for example 2,4,6) does not appear in the packet parameters in the selected packet mode.Cause modulation efficiency to cross low and because the non-homogeneous other problems that brings of constellation point for fear of I (real part of corresponding complex plane), Q (imaginary part of corresponding complex plane) two-way signal of communication average power difference; And in packet parameters, occur under the situation of odd number; Can complicated greatly follow-up sign bit mapping relations confirm part (step 5), the packet parameters in the selected packet mode should satisfy as far as possible: packet parameters is the parameter of enough big or maximum (the requiring more than or equal to 8 among the embodiment) of even number entirely.

According to above-mentioned packet mode, if the packet mode that meets the demands is arranged, then change step 4, if do not have, then return step 2, selected again order of modulation.

Step 4: the constellation point of arranging position:

This step is according to order of modulation selected in the step 2, and the constellation point of arranging position obtains the QAM modulation constellation.The design of planisphere accordings to traditional qam constellation figure design, the preferential constellation point of selecting to use energy less (promptly more near the planisphere initial point), and traditional qam constellation figure designs referring to list of references: Cao Zhigang, Qian Yasheng, " Principles of Modern Communication " P295.

Step 5: confirm the sign bit mapping relations:

This step is a most essential steps of the present invention, according to bit rate, order of modulation, packet mode, the constellation point position set before, sets up the packet design scheme, sets the sign bit mapping relations.

The packet design scheme is promptly set according to constellation point position of arranging and packet mode.Packet design to first symbol; Consider performance; The preferential constellation point that energy is little is distributed to and is selected maximum d layers, and wherein d is for making (w=1,2; ..., the m) value of maximum s; Reduce the subsequent design complexity if pay the utmost attention to, preferentially select the constellation point that energy is little to distribute to the layer that first parameter is 2 integer power.Follow-up symbol (non-first symbol) because and do not require that the constellation point of each layer selection is different; So just consider to performance; If the preferential average energy of using the little constellation point of constellation point energy then can make modulation signal descends, under specific signal to noise ratio, can obtain better performance of BER; If the preferential big constellation point of constellation point energy of using can make the average energy quantitative change of modulation signal big, the peak-to-average force ratio of modulation signal can be smaller.

Confirming of sign bit mapping relations according to following rule:

(1) make in the mapping relations the some bit section in the bit sequence only relevant with a certain special symbol.Modulation system provided by the invention is intended to continuous a plurality of symbols and bit sequence are set up mapping relations realization modulation; If certain bit section is relevant with a plurality of symbols, under the bad situation of channel condition, the some symbols in continuous a plurality of symbols are misjudged; What bit section was just wrong probably like this goes against accepted conventions very much; In order to obtain good modulating performance, the influence of avoiding chain mistake to bring, specific bit should be relevant with few symbol of trying one's best.

(2) make the Hamming distance between the bit sequence that adjacent constellation point is shone upon in the sign bit mapping relations minimum.In the communication signal transmission process; Because the interference and the characteristic of channel that receive; Can make the signal of signal that receiving terminal receives and transmission different, adjudicating the constellation point that demodulates so just might be different with the original mappings constellation point, receives very big influence for fear of bit sequence owing to the erroneous judgement of constellation point; Should make the Hamming distance between the bit sequence that adjacent constellation point is shone upon in the sign bit mapping relations little as far as possible, reduce the influence of symbol error bit sequence.

Definite cardinal principle of sign bit mapping relations can be according to following steps:

(1) substantially corresponding relation is set up in bit sequence segmentation and symbol according to the packet mode of selecting.The maximum d layer of constellation point combination selection is paid the utmost attention in the foundation of this corresponding relation; Wherein d is for making

(w=1; 2; ..., the m) value of maximum s.As shown in Figure 4, f before the 1st the symbol correspondence ₁Individual bit (b ₁b ₂B _F1), the corresponding f of the 2nd symbol ₁+ 1 to f ₂Individual bit, integral body have been set up the mapping relations of symbol and bit section.

(2) all constellation point of d layer are arranged combination according to segmentation corresponding relation and bit sequence foundation mapping.Can carry out according to the gray mappings criterion, its implementation procedure ratio is easier to here.

(3) will except that the constellation point of other layers the d layer arrange the combination with bit sequence set up mapping relations.It can regard as with the constellation point of other layer arrange combination with not have with the d layer in have the bit sequence of the mapping relations set up to set up one-to-one relationship, the more layer of preferential constellation point permutation and combination makes the corresponding bit sequence Hamming distance minimum of adjacent constellation point.

Through after these five steps; Setting up a continuous n symbol and length is the mapping relations of the bit sequence of k; According to these mapping relations bit sequence to be sent being mapped as a continuous n symbol during modulation normally sends then and gets final product; Need in the demodulation signal that receives is adjudicated, according to packet mode and mapping relations signal is demodulated into bit sequence again and gets final product.

If the above-mentioned modulation system performance that obtains meets the requirements then finishes this design,, then return step 2 and confirm that again order of modulation designs if undesirable.

In order to verify the practicality of newly-designed qam mode, use for reference traditional QAM modulation bit error rate formula, the QAM modulation design method that the present invention is directed to new proposition has proposed a kind of Bit Error Rate Computation method, following two formulas (3) and formula (4).Through type (3) calculates the mistake symbol probability P of j symbol of i layer _s(M), the mean value of different bit numbers in the bit group of adjacent constellation point mapping in the expression planisphere, N _AdjThe number of representing the adjacent constellation point of each constellation point,

For half of constellation point distance after the adjacent power normalization multiply by

Square root; To go into formula (4) by each layer mistake symbol probability band that formula (3) calculate, can calculate theoretical bit error rate P _b(M), wherein k is modulation layering number of times, p _iBe the probability of every layer of appearance, G _PiFor every layer average Gray punishes the factor, represent the error bit number (can be punished factor weighted average by the Gray of every layer of each symbol tries to achieve) that every group code mistake causes, n is a symbolic number, P _SijMistake symbol probability (i is the number of plies, and j is a symbolic number) for every part.Need to prove since in every layer the error sign ratio of each symbol very little, so only can simultaneously wrong symbol in every layer of the acquiescence in the formula (4).

$P_{\mathrm{sij}}\left(M\right)=N_{\mathrm{adj}}\&CenterDot;\frac{1}{2}\mathrm{erfc}\left\{\frac{d}{\sqrt{N_0}}\right\}---\left(3\right)$

$P_b\left(M\right)=\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}(p_i\&times;G_{\mathrm{pi}}\&times;\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{\mathrm{sij}})---\left(4\right)$

Formula (3) and formula (4) are used for its practicality is verified in the calculating of deriving of the performance of BER of the qam mode of newly designing.

Embodiment 1

Present embodiment is to dwindling the modulation intervals between 16QAM and the 32QAM, be intended to design a modulation system in addition its performance between 16QAM and 32QAM.

Step 1: the bit rate of setting modulation system to be designed:

Its bit rate k/n bit/symbol should be between the bit rate of the bit rate of 16QAM and 32QAM, and 16QAM and 32QAM are traditional qam mode.The interval of the bit rate of setting is:

${\log }_2^{16}=4<\frac{k}{n}<{\log }_2^{32}=5$

N, k are positive integer in the formula, consider that n should be as much as possible little so that design process is simple, make n equal its minimum probable value 2, and then k is only to equal 9.The bit rate of setting is 4.5 bit/symbol.

Step 2: selected order of modulation:

According to the bit rate of setting in the step 1, select order of modulation in this step.According to two rules in the specific embodiments:

(1) order of modulation must be enough big to satisfy the requirement of bit rate.According to bit rate 4.5 bit/symbol of setting, promptly transmit the data of 9 bits, in order to make M with continuous 2 symbols ²Plant and select to shine upon 9 Bit datas, its theoretical lowest modulation exponent number M need satisfy following condition:

$2^{\frac{k}{n}}=2^{4.5}=22.63\&le;M$

Be that order of modulation should be more than or equal to 23, this condition is for realizing that bit rate is the necessary condition of the M-QAM modulation of 4.5 bit/symbol.

(2) selection of order of modulation should be easy to subsequent design as far as possible.Consider the selection of enriching packet mode, simplify and confirm mapping relations and avoid ceiling capacity signal energy in the signal excessive and bring the excessive problem of peak-to-average force ratio, order of modulation often to be chosen in possible maximum modulation exponent number under the situation that the constellation point ceiling capacity confirms.As shown in Figure 5, the point that the constellation point energy is identical couples together with line, and is visible, between 16 and 32, has only 24 to meet this standard in order of modulation, and 24 conditions that satisfy more than or equal to 23.

According to two criterions, this step selects 24 as order of modulation.

Step 3: selected constellation point packet mode:

This step is according to two steps in front selected bit rate, order of modulation, and exhaustive computations goes out possible packet mode, selects wherein relatively to be easy to a packet mode of realizing then.

For design processes simplified, setting the modulation number of plies is 2.According to the parameter request of mentioning in the preceding text, the design's parameter should satisfy:

$\underset{w=1}{\overset{2}{\mathrm{\&Sigma;}}}\underset{s=1}{\overset{2}{\mathrm{\&Pi;}}}{M}_{\mathrm{sw}}=M_{11}{\mathrm{<figure-callout\; id="21"\; label="M"\; filenames="HDA00001639118900021.png,HDA00001639118900032.png"\; state="\{\{state\}\}">M</figure-callout>}}_{21}+M_{12}{\mathrm{<figure-callout\; id="22"\; label="M"\; filenames="HDA00001639118900032.png,HDA00001639118900041.png"\; state="\{\{state\}\}">M</figure-callout>}}_{22}=2^9=512$

$\underset{w=1}{\overset{2}{\mathrm{\&Sigma;}}}{M}_{1w}={\mathrm{<figure-callout\; id="11"\; label="M"\; filenames="HDA00001639118900032.png,HDA00001639118900041.png"\; state="\{\{state\}\}">M</figure-callout>}}_{11}+{\mathrm{<figure-callout\; id="12"\; label="M"\; filenames="HDA00001639118900021.png,HDA00001639118900032.png"\; state="\{\{state\}\}">M</figure-callout>}}_{12}=M=24$

According to Fig. 3 exhaust algorithm sketch map, its exhaustive method such as Fig. 6 according to going out all possible packet modes as Fig. 6 method is exhaustive, exclude M ₁₁Greater than M ₁₂Situation (for fear of for no other reason than that the different repetitions that cause of number of plies numbering), total following 13 kinds of packet modes, see table 1:

Table 1 packet mode and packet parameters

In order to simplify follow-up design process, exclude the situation that has odd number in the parameter, also surplus packet mode 1,4,6,8,12 these five kinds of possible situation.In order to optimize performance, select all bigger packet mode of packet parameters as far as possible, there is 2,4 packet mode 1,4,6 in the packet parameters so exclude; Observe these the two groups of parameters in the packet mode 8,12, find in the packet mode 12 to have in 4 parameters 3 to be 2 integer power, consider the difficulty of subsequent design, so select for use packet mode 12 to design.

Step 4: the constellation point of arranging position:

This step is according to order of modulation selected in the step 2, and the constellation point of arranging position obtains the QAM modulation constellation.

As shown in Figure 5, the little constellation point of preferential selection energy in the qam constellation point selection, convenient so the constellation point of arranging of this paper design is as shown in Figure 7 for follow-up explanation, constellation point is numbered like Fig. 7.

Step 5: set the sign bit mapping relations:

This step is set up the packet design scheme according to constellation point position and packet mode earlier, sets up the mapping relations of constellation point combination and bit sequence then according to the modulation parameter of packet design scheme and setting before.

According to the packet parameters in the packet mode 12, the design modulation number of plies is 2, and it is 16 that one two-layer of first parameter is 8, one, all is 2 integer power, through computes,

16×24＝384＞128＝8×16

Can know that parameter is that 16,24 the possible number of combinations of layer is more, thus in first allocation of symbols the preferential constellation point that energy is little distribute to parameter be 16,24 layer.Second follow-up symbol adopts the preferential mentality of designing of bit error rate, preferentially uses the little constellation point of constellation point energy.In view of as above reason, in conjunction with the numbering of Fig. 7, packet design scheme such as following table 2.

Table 2 packet design scheme

First symbol	Second symbol
		In the constellation point of numbering 1-16, select	In the constellation point of numbering 1-24, select
In the constellation point of numbering 17-24, select	In the constellation point of numbering 1-16, select

The packet design scheme can begin to set the sign bit mapping relations after confirming, observes packet parameters, confirms reason with the packet design scheme, and the priority allocation parameter is 16,24 layer.

Design should make symbol and specific bit section correspondence as far as possible; 2 corresponding 9 Bit datas of parameter in the present design; 16 is 24 powers; 24 between 24 powers (16) and 5 powers (32), so set cardinal principle by corresponding preceding 4 bits of first symbol, second corresponding back 5 symbol of symbol.Shown in Figure 8 is the optimum gray mappings of 16QAM.

For parameter is 16,24 layer, and with reference to Fig. 8,16 constellation point that first symbol is corresponding are shone upon 4 Bit datas according to optimum gray mappings; The constellation point of numbering 1-16 is according to 5-8 bit in the gray mappings criterion mapped bits sequence in 24 constellation point of second symbol correspondence; Bit sequence Hamming distance for fear of adjacent constellation point mapping is big; So setting the 9th bit of the constellation point mapping of numbering 1-16 is 0; The 5-8 bit of peripheral numbering 17-24 constellation point is identical with the bit sequence of the numbering 1-16 constellation point that is adjacent mapping, and the 9th bit is set at 1.Shown in Fig. 9 and following table 3, misjudge the mistake that a constellation point (acquiescence only can be misjudged and be adjacent constellation point) only can be brought 1 bit like this.

Table 324QAM sign bit mapping relations (1)

With parameter is after 16,24 layer mapping relations are confirmed, confirms that parameter is the mapping relations of another layer of 8,16.For first parameter, 8 is 3 powers of 2, makes preceding 3 bits of its corresponding bit sequence, and with the constellation point that be numbered 1-16 close with its constellation point position before 3 bits are identical gets final product; Observe remaining for setting up the bit arrangement combination of mapping relations, like following table 4:

Table 4 is not set up the mapping relations bit sequence

b 4	b 5	b 6b 7b 8	b 9
				0/1	0/1	000/011/100/111	1

In first group of parameter designing, the 4th bit and the 2nd symbol are irrelevant, needn't consider the 4th bit from the performance of BER angle.Design will make between the bit sequence that adjacent constellation point representes Hamming distance little; And will with parameter be 16,24 layer second sign map relation relatively; Make the corresponding bit sequence Hamming distance of two-layer same constellation point little (guaranteeing that cost is little on first symbol misjudgement back bit error rate), design is shown in Figure 10 and following table 5:

Table 524QAM sign bit mapping relations (2)

So far, the symbol of this modulation system and the mapping relations of bit sequence confirm that new modulation system design is accomplished.

Sign bit mapping relations according to setting obtain simulation result shown in figure 11 through emulation, and the simulation curve of visible 24QAM can effectively dwindle the performance interval between two modulation systems between 32QAM and 16QAM, meet design requirement.

Embodiment 2

Modulation makes its performance between 24QAM (embodiment 1) and 32QAM performance to present embodiment to design one QAM, dwindles the performance interval between two modulation systems.

Step 1: the bit rate of setting modulation system to be designed:

The bit rate of selected modulation system to be designed in this step.Its bit rate k/n bit/symbol should be between the bit rate of the bit rate of 24QAM and 32QAM, and the bit rate of 24QAM is 4.5 bit/symbol, and the bit rate of 32QAM is 5 bit/symbol.The interval of the bit rate of setting is:

$4.5<\frac{k}{n}<{\log }_2^{32}=5$

N, k are positive integer in the formula, consider that n should be as much as possible little so that design process is simple, make n equal its minimum probable value 3, and then k is only to equal 14.The bit rate of setting is

bit/symbol.

Step 2: selected order of modulation:

According to the bit rate of setting in the step 1, select order of modulation in this step.According to two rules in the specific embodiments:

(1) order of modulation must be enough big to satisfy the requirement of bit rate.According to bit rate

bit/symbol of setting; Promptly transmit the data of 14 bits with continuous 3 symbols; In order to make the M3 kind select to shine upon 14 Bit datas, its theoretical lowest modulation exponent number M need satisfy following condition:

$2^{\frac{k}{n}}=2^{\frac{14}{3}}=25.40\&le;M$

Be that order of modulation should be more than or equal to 26, this condition is for realizing that bit rate is the necessary condition of the M-QAM modulation of

bit/symbol.

(2) selection of order of modulation should be easy to subsequent design as far as possible.Consider the selection of enriching packet mode, simplify and confirm mapping relations and avoid ceiling capacity signal energy in the signal excessive and bring the excessive problem of peak-to-average force ratio, order of modulation often to be chosen in possible maximum modulation exponent number under the situation that the constellation point ceiling capacity confirms.In embodiment 1, can know between order of modulation 16 and 32 to have only 24 to meet this standard, but 24 do not meet order of modulation more than or equal to 26 these conditions.Consider to make subsequent design be easy to realize, should select an even number here, then have only 26,28,30 these three numbers conformance with standard; Consider being restricted to of order of modulation more than or equal to 25.40; 26 some is too little, and 30 is too approaching with 32 again, so order of modulation selects 28 here.

According to above two conditions, this step selects 28 as order of modulation.

Step 3: selected constellation point packet mode:

This step is according to two steps in front selected bit rate, order of modulation, and exhaustive computations goes out possible group technology, selects wherein relatively to be easy to a group technology that realizes then.

For design processes simplified, setting the modulation number of plies is 2.According to the parameter request of mentioning in the preceding text, the design's parameter should satisfy:

$\underset{w=1}{\overset{2}{\mathrm{\&Sigma;}}}\underset{s=1}{\overset{3}{\mathrm{\&Pi;}}}{M}_{\mathrm{sw}}=M_{11}{M}_{21}{\mathrm{<figure-callout\; id="32"\; label="M"\; filenames="HDA00001639118900062.png,HDA00001639118900071.png"\; state="\{\{state\}\}">M</figure-callout>}}_{32}+M_{12}{M}_{22}{\mathrm{<figure-callout\; id="32"\; label="M"\; filenames="HDA00001639118900062.png,HDA00001639118900071.png"\; state="\{\{state\}\}">M</figure-callout>}}_{32}=2^{14}=16384$

$\underset{w=1}{\overset{2}{\mathrm{\&Sigma;}}}{M}_{1w}={\mathrm{<figure-callout\; id="11"\; label="M"\; filenames="HDA00001639118900032.png,HDA00001639118900041.png"\; state="\{\{state\}\}">M</figure-callout>}}_{11}+{\mathrm{<figure-callout\; id="12"\; label="M"\; filenames="HDA00001639118900021.png,HDA00001639118900032.png"\; state="\{\{state\}\}">M</figure-callout>}}_{12}=M=28$

According to Fig. 3 exhaust algorithm sketch map, its exhaustive method such as Figure 12 because the bit rate precision is 3, have strengthened exhaustive amount of calculation greatly, can know through the method for exhaustion to have 142 kinds of constellation point group technologies that can realize modulating, and do not list one by one at this, get rid of M ₁₁Greater than M ₂₁, the very few and constellation point number of constellation point number is the situation of odd number in the constellation point group, 10 kinds of packet modes shown in the total table 6.

Table 6 packet mode and packet parameters

Observe the packet parameters in this 10 component prescription formula; Can find in the packet parameters in the 5th group and the 6th component prescription formula, to exist 2 16 (4 powers of 2); The number of times of 2 integral number power two of less thaies all in the packet parameters in other the packet mode; So confirm to design packet parameters indistinction on performance of two component prescription formulas with the packet parameters of the 5th component prescription formula or the packet parameters of the 6th component prescription formula.This instance adopts the 6th component prescription formula corresponding packet parameter to design.

Step 4: the constellation point of arranging position:

This step is according to order of modulation selected in the step 2, and the constellation point of arranging position obtains the QAM modulation constellation.

This instance order of modulation is 28, and the preferential little constellation point of energy of selecting like Figure 13, is cross 32QAM planisphere in the qam constellation point selection, and the energy of numbering 1-24 constellation point is less than the constellation point of numbering 25-32, so the 1-24 constellation point should add planisphere; The constellation point energy of numbering 25-32 is identical; Consider the symmetry of planisphere about I, Q diaxon; Can in the 1-24 constellation point, add and be numbered 25,26,29,30 or 27,28,31,32 constellation point and gather into the 28QAM planisphere, select the constellation point of numbering 25,26,29,30 among this paper.So the constellation point of arranging of this paper design is shown in figure 14, convenient for follow-up explanation, constellation point is numbered like Figure 14.

Step 5: set the sign bit mapping relations:

This step is set up the packet design scheme according to constellation point position and packet mode earlier, sets up the mapping relations of constellation point combination and bit sequence then according to the modulation parameter of packet design scheme and setting before.

According to the 6th component prescription formula corresponding packet parameter, the design number of plies is 2, and one two-layer of first parameter is 16 (4 powers of 2), and one is 12, and through computes,

16×28×28＝12544＞3840＝12×20×16

Can know, can know that packet parameters is that 16,28,28 the possible number of combinations of layer is more, thus in first allocation of symbols the preferential constellation point that energy is little distribute to packet parameters be 16,28,28 layer.Second follow-up symbol adopts the preferential mentality of designing of bit error rate, preferentially uses the little constellation point of constellation point energy.In view of as above reason, in conjunction with the numbering of Figure 14, packet design scheme such as following table 7:

Table 7 packet design scheme

The 1st symbol	The 2nd symbol	The 3rd symbol
			In the constellation point of numbering 1-16, select	In the constellation point of numbering 1-28, select	In the constellation point of numbering 1-28, select
In the constellation point of numbering 17-28, select	In the constellation point of numbering 1-20, select	In the constellation point of numbering 1-16, select

The packet design scheme can begin to set the sign bit mapping relations after confirming, observes packet parameters, confirms reason with the packet design scheme, and the priority allocation packet parameters is 16,28,28 layer.

Design should make symbol and specific bit section correspondence as far as possible; 3 corresponding 14 Bit datas of parameter in the present design; 16 is 24 powers, and 28 between 24 powers (16) and 5 powers (32), so set substantially by the corresponding 1-4 bit of first symbol; Second corresponding 5-9 symbol of symbol, the 3rd corresponding 10-14 symbol of symbol.

In packet parameters 16,28,28 these layers, with reference to Fig. 8,16 constellation point that first symbol is corresponding are shone upon 4 Bit datas according to optimum gray mappings; The constellation point of numbering 1-16 is according to 5-8 bit in the gray mappings criterion mapped bits sequence in 28 constellation point of second symbol correspondence; Bit sequence Hamming distance for fear of adjacent constellation point mapping is big; So setting the 9th bit of the constellation point mapping of numbering 1-16 is 0; The 5-8 bit of peripheral numbering 17-28 constellation point is identical with the bit sequence of the numbering 1-16 constellation point that is adjacent mapping; The 9th bit is set at 1; The constellation point of numbering 1-16 is according to 10-13 bit in the gray mappings criterion mapped bits sequence in 28 constellation point of the 3rd symbol correspondence, and the bit sequence Hamming distance that shines upon for fear of adjacent constellation point is big, so the 14th bit that the constellation point of setting numbering 1-16 is shone upon is 0; The 10-13 bit of peripheral numbering 17-28 constellation point is identical with the bit sequence of the numbering 1-16 constellation point that is adjacent mapping, and the 14th bit is set at 1.Shown in Figure 15 and following table 8, declare the mistake that a constellation point (acquiescence only can be misjudged and be adjacent constellation point) only can be brought 1 bit in this fault.

Table 828QAM sign bit mapping relations (1)

With packet parameters is after 16,28,28 layer mapping relations are confirmed, confirms that packet parameters is the mapping relations of another layer of 12,20,16.Observe the remaining bit arrangement combination of not setting up mapping relations, like following table 9:

Table 9 is not also set up the bit sequence of mapping relations

With (numbering 21-28), 16 (the numbering 1-16) that split out 8 in 12,20,16 parameters in the second layer parameter, 16 one group; 8 constellation point that wherein first symbol is corresponding are the constellation point of numbering 21-28; It is identical to set the corresponding bit sequence of its corresponding 1-3 bit and the numbering 1-16 constellation point adjacent with it; 16 constellation point of second symbol correspondence are according to gray mappings as shown in Figure 84,5,6,10 bits; 16 constellation point of the 3rd symbol correspondence are according to gray mappings 11-14 bit as shown in Figure 8, and 7,8,9 bits are set at 001.Concrete mapping relations such as Figure 16 and following table 10.

Table 1028QAM sign bit mapping relations (2)

Observe second layer parameter; (numbering 21-28), 4 (the numbering 17-20) that split out 8 therein, 16 one group; 8 constellation point that wherein first symbol is corresponding are the constellation point of numbering 21-28, and it is identical to set the corresponding bit sequence of its corresponding 1-3 bit and the numbering 1-16 constellation point adjacent with it, and 4 constellation point of second symbol correspondence are the constellation point of numbering 17-20; Its corresponding the 5th, 6 bits; The 3rd corresponding 16 constellation point of symbol, according to corresponding the 10th, 11,7,4 bits of gray mappings, the 8th, 9,12,13,14 bits are set at 11001.Concrete mapping relations are shown in Figure 17 and following table 11.

Table 1128QAM sign bit mapping relations (3)

For second layer parameter, also remaining one group of parameter is 4 (numbering 17-20), 20,16 part, and 4 constellation point that wherein first symbol is corresponding are the constellation point of numbering 17-20; It is identical to set the corresponding bit sequence of its 2,3 corresponding bits and the numbering 1-16 constellation point adjacent with it; Second 20 corresponding constellation point of symbol is the constellation point of numbering 1-20, its corresponding 5-9 bit, and wherein the constellation point of 1-16 is according to gray mappings mapping 5-8 bit shown in Figure 8; The 9th bit is set at 0; It is identical that the constellation point 5-8 bit of numbering 17-20 is set at the bit sequence that shines upon with the constellation point of its immediate numbering 1-16, and the 9th bit is made as corresponding 16 constellation point of 1, the three symbol; According to corresponding the 11st, 1,4,10 bits of gray mappings, the 12nd, 13,14 bits are set at 001.Concrete mapping relations are shown in Figure 18 and following table 12.

Table 1228QAM sign bit mapping relations (4)

So far, the symbol of this modulation system and the mapping relations of bit sequence confirm that new modulation system design is accomplished.

Sign bit mapping relations according to setting obtain simulation result shown in figure 19 through emulation, and the simulation curve of visible 28QAM can effectively dwindle the performance interval between two modulation systems between 32QAM and 24QAM, meet design requirement.

Claims (7)

1. the QAM modulation design method on one kind non-2 integer power rank is characterized in that comprising the steps:

Step 1: the bit rate of setting modulation system to be designed:

The bit rate of setting adopts the form k/n bit/symbol of mark, and denominator is the precision n of bit rate; If the order of modulation of two kinds of adjacent modulation systems is W and 2 * W, then sets the bit rate interval and be:

${\log }_{2}W<\frac{k}{n}<{\log }_2(2\&times;W);$

Step 2: according to the selected order of modulation of selected bit rate; The selected of described order of modulation M should be with reference to following two conditions:

(1) $\sqrt[n]{2^k}=2^{\frac{k}{n}}\&le;M,$

(2) under the situation that the constellation point ceiling capacity is confirmed, select maximum order of modulation;

(1) individual condition is a necessary condition; (2) individual condition is inessential condition;

Step 3: selected constellation point packet mode:

According to the value of selected order of modulation M, exhaustively go out possible packet mode, select one group of minimum parameter of implementation complexity as the constellation point packet mode therein;

According to above-mentioned packet mode, if the packet mode that meets the demands is arranged, then change step 4, if do not have, then return step 2, selected again order of modulation;

Step 4: the constellation point of arranging position:

Set the position of constellation point according to order of modulation M and arrange, promptly set the planisphere of new QAM modulation, the packet mode that should combine to select and the restriction of modulation system signal peak-to-average ratio carried out of arranging;

Step 5: set symbol bit sequence mapping relations; If the above-mentioned modulation system performance that obtains meets the requirements then finishes this design,, then return step 2 and confirm that again order of modulation designs if undesirable.

2. the QAM modulation design method on a kind of non-2 integer power rank according to claim 1 is characterized in that: described constellation point packet mode, and concrete grammar is following:

If the modulation layering number of plies is m, modulation system is chosen continuous n constellation point mapping k bit, packet parameters M from M constellation point _SwShould satisfy following two rules:

$\underset{w=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{s=1}{\overset{n}{\mathrm{\&Pi;}}}{M}_{\mathrm{sw}}=2^k---\left(1\right)$

$\underset{w=1}{\overset{m}{\mathrm{\&Sigma;}}}{M}_{1w}=M---\left(2\right)$

Wherein, s=1,2 ..., n, w=1,2 ..., m is divided into the m group with M constellation point, and for the corresponding constellation point group of first symbol, wherein every group of constellation point number is M _1w, the constellation point that each group comprises does not repeat, when the corresponding constellation point of first symbol S1 that sends is in the w group, and s the symbol S that sends subsequently _sBe specific M _SwIn the individual constellation point one, s=2 ..., n, the constellation point in the constellation point group that wherein non-first symbol of each layer is corresponding allows identical, like this, selects possibly making up of a continuous n constellation point total

Kind, be the possible permutation and combination several 2 of the bit sequence of k as long as make itself and length ^kEquate, set up mapping relations one by one, just can be through sending n constellation point transmission k Bit data continuously;

For confirming the suitable constellation point number M of respectively organizing _Sw, confirm modulation layering number of stories m earlier, use the method for exhaustion to seek possible group technology, select packet mode according to following rule then:

(1) select the constellation point number be 2 integer power maximum or the pairing packet mode of packet parameters as much as possible;

(2) packet parameters in the selected packet mode should satisfy as far as possible: packet parameters is the enough big or maximum parameter of even number entirely.

3. the QAM modulation design method on a kind of non-2 integer power rank according to claim 1 is characterized in that: confirming according to as follows of described sign bit mapping relations is regular:

(1) make in the mapping relations the some bit section in the bit sequence only relevant with a certain special symbol;

(2) make the Hamming distance between the bit sequence that adjacent constellation point is shone upon in the sign bit mapping relations minimum.

4. the QAM modulation design method on a kind of non-2 integer power rank according to claim 1 is characterized in that: the confirming according to following steps of described sign bit mapping relations:

(1) according to the packet mode of selecting corresponding relation is set up in bit sequence segmentation and symbol; The maximum d layer of constellation point combination selection is paid the utmost attention in the foundation of this corresponding relation; Wherein d is the value of the s that to make

maximum; W=1; 2 ..., m;

(2) all constellation point of d layer are arranged combination according to segmentation corresponding relation and bit sequence foundation mapping;

(3) will except that the constellation point of other layers the d layer arrange the combination with bit sequence set up mapping relations.

5. the QAM modulation design method on a kind of non-2 integer power rank according to claim 1 is characterized in that: gray mappings or approximate gray mappings are adopted in described foundation mapping.

6. the QAM modulation design method on a kind of non-2 integer power rank according to claim 1 is characterized in that: bit rate precision n does not surpass 4.

7. Bit Error Rate Computation method, it is characterized in that: through type (3) calculates the mistake symbol probability P of j symbol in the i layer _Sij(M), will go into formula (4), calculate theoretical bit error rate P by each layer mistake symbol probability band that formula (3) calculate _b(M):

$P_{\mathrm{sij}}\left(M\right)=N_{\mathrm{adj}}\&CenterDot;\frac{1}{2}\mathrm{erfc}\left\{\frac{d}{\sqrt{N_0}}\right\}---\left(3\right)$

$P_b\left(M\right)=\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}(p_i\&times;G_{\mathrm{pi}}\&times;\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{P}_{\mathrm{sij}})---\left(4\right)$

Wherein, N _AdjThe number of representing the adjacent constellation point of each constellation point,

For half of constellation point distance after the adjacent power normalization multiply by

Square root; Wherein k is modulation layering number of times, p _iBe the probability of every layer of appearance, G _PiFor every layer average Gray punishes the factor, represent the error bit number that every group code mistake causes, n is a symbolic number, P _SijBe the mistake symbol probability of every part, i is the number of plies, and j is a symbolic number; Simultaneously wrong symbol of a meeting in giving tacit consent to every layer in the formula (4);

Formula (3) and formula (4) are used for its practicality is verified in the calculating of deriving of the performance of BER of qam mode.

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