Method and device for demodulation using relaxed solution for quadrature amplitude modulation

FIELD: physics.

SUBSTANCE: method of relaxed solution for demodulating a received signal α+iβ with quadrature amplitude modulation (QAM) involves deriving several values of a conditional probability vector, where each is a relaxed solution value which corresponds to the position of a stiff solution bit, using a function which includes an operation for conditional definition from the quadrature phase component and inphase component of the received signal. The method of solving for the conditional probability vector for demodulation of the first half of the complete number of bits is identical to the solution method for demodulating the remaining half of bits, and is determined by replacing the value of the quadrature phase component and the value of the inphase component with each other.

EFFECT: more accurate processing a received signal.

29 cl, 15 dwg

 

The technical field

The present invention relates to demodulation with soft decision signal quadrature amplitude modulation (QAM), and in particular to a method of demodulating with a mild solution providing increased processing speed soft solutions using predefined functions and template for demodulation of the received signal.

Prior art

Scheme QAM can transmit the load of two or more bits for the symbol specified oscillations, which can be mathematically expressed by two real numbers and imaginary numbers, which do not interfere with each other. I.e. a complex number α+βi changing the value of α does not affect the value of β. Due to this reason the quadrature component of the signal may correspond to α, and the in-phase component of the signal may correspond to β. In General, the quadrature component of the signal is referred to as the quadrature channel, and the in-phase component of the signal is referred to as in-phase channel.

Constellation chart KAM provides the binding of the amplitudes of the two waveforms with each other for some combinations, the positioning of these combinations on the plane of complex numbers with the same conditional probability and prediction of such positioning. Figure 2 presents the diagram, depicting an example of such constellations chart, the size of which is 16 combinations. Also, each point shown in figure 2, referred to as point constellation. Also, combinations of binary numbers recorded under each point of the constellation, are symbols that can be set for each point, i.e. the group of bits.

In principle, the QAM demodulator is used to convert the signals into in-phase (I) channel and quadrature (Q) channel, i.e. the received signal, a specific α+βi, in the initial group of bits according to the projected position mentioned above, i.e. constellations chart combinations. In this case, however, the received signals are in most cases not positioned in locations previously assigned, due to the influence of noise interference, and therefore, the demodulator must restore the signals converted due to noise in the original signal. However, since there is often some redundancy to ensure reliable communication, the demodulator performs the function of compensating interference, so that it is possible to implement a more efficient and reliable communication system for the transfer of this function to the next stage of the channel decoder. However, since there is a loss of information in the process of quantization bits is performed by the detector binary bits, as when jesd the m decision by the signal demodulation having a continuous value, takes the value of discrete signals 2 levels to perform such a process, the degree of similarity in relation to the distance between the received signal and the expected point constellations change with the Hamming distance on the Euclidean distance without the use of a detector of binary bits, so there may be obtained an additional benefit.

As shown in figure 1, to modulate and transmit a signal encoded channel encoder, and to demodulate the signal in channel demodulator using an encoding process with a hard decision, the demodulator must have a schema for generating values of hard decisions corresponding to each output bit of the channel encoder, the received signal comprising in-phase component signal and a quadrature (phase) component of the signal. This scheme mainly includes two procedures, i.e. the procedure is simple metric, proposed by Nokia and the dual minimum metric proposed by Motorola, both of which procedure calculates a logarithmic likelihood ratio (LOP) in respect of each output bit and use it as the input values of the soft decision channel demodulator.

The procedure is simple metric is an event-driven algorithm, which is the first converts complex equation calculations LOP in a simple form of the approximate equations, which is characterized by the deterioration of the characteristics due to distortion LOP caused by the use of approximate equations, although it simplifies the calculation of the LOP. On the other hand, the procedure of the dual minimum metric is an event-driven algorithm, which uses LOP calculated using the more accurate the approximate equation as an input signal of the channel demodulator, and the dignity of which is to reduce the degradation that occurred when using the procedure of simple metrics, however, the expected problem is more computationally expensive compared with the procedure simple metric and the increasing complexity of hardware implementation.

Disclosure of invention

Therefore, the aim of the present invention is to solve the problems caused by the prior art, and creating a schema soft solutions for demodulation of the received signal with a quadrature amplitude modulation (QAM), consisting of in-phase component signal and a quadrature component signal, where the value of the vector of conditional probabilities that represent each value of the soft decision corresponding to the bit position tough decisions, can be obtained using functions, including the calculation of conditional determine the value of a quadrature the component and the values of the inphase component of the received signal, and so it is expected that the processing speed can be increased and the real costs of production of hardware can be reduced. To perform this procedure, described below, which is known to form combinational constellational chart KAM and her characteristic diagram of the demodulation. Raman constellation chart KAM can be mainly divided into 3 forms according to the configuration of the group of bits that is installed at the point constellation. The first of these is a form of grouped, as shown in Fig.2-4, the second is a form of grouped, as shown in figure 5-7, and the third is a form that is not included in the present application.

Characteristic of the form shown in figure 2, can be summarized as follows. When the magnitude of QAM is equal to 22nthe number of bits in each point is equal to 2n, where values of the vector of conditional probabilities corresponding to the first half of the numbers, i.e. from the first to n-th bits, demodulated through one of the received signals α and β, and the values of the vector of conditional probabilities corresponding to the second half of the numbers, i.e. with (n+1)th to 2n-th bit, demodulated through the other of the received signals. Also, the equation applies to both demodulation, has an identical procedure when de is odulele the first half and second half. I.e. when the value of the received signal corresponding to the second half, substitute into the way demodulation of the first half, may be the result of the second half. (Below this form is referred to as the "first form".)

The characteristic shape shown in figure 5, can be summarized as follows. When the magnitude of QAM is equal to 22nthe number of bits set in each of the pixels becomes equal to 2n, and the way demodulation vector of conditional probabilities, the corresponding bit of odd order is identical to the method of calculating the vector of conditional probabilities corresponding to the next bit of even order. However, the value of the received signal, is used to compute the vector of conditional probabilities, the corresponding bit odd order, uses one of the signals α and β according to the diagram the constellation of this combination, and the value of the received signal for a bit of even order is used for the other of them. In other words, in the case of computing the first and second vector of conditional probabilities they use the same way demodulation, but the received signals are different. (Below this form is referred to as the "second form".)

Brief description of drawings

The above-mentioned purpose, other distinctive features and advantages of the present izaberete the Oia explained in the description of its preferred option execution with reference to the drawings, which presents the following:

figure 1 - block diagram for explaining a General digital communication system;

figure 2 is a view depicting point constellation combinations to explain the way demodulation with soft decision in accordance with the first variant implementation of the present invention;

3 and 4 are views for explaining a bit constellation chart constellation combinations, shown in figure 2;

5 is a view depicting the chart constellation combinations to explain the way demodulation with soft decision according to the second variant of implementation of the present invention;

6 and 7, views for explaining a bit constellation chart constellation combinations, shown in figure 5;

Fig - views depicting the decision-making procedure for the vector of conditional probabilities according to the present invention as a functional unit;

Fig.9 - output chart for each vector of conditional probabilities of the first form 1024-QAM;

figure 10 - output chart for each vector of conditional probabilities of the second form 1024-QAM;

11 is a view depicting the function applied to the first vector of the probability of the third variant of implementation of the present invention;

Fig - views depicting the function applied to the second vector of the probability of the third variant of implementation of the present invention;

Fig - views depicting the function applied to the first vector of the probability of the fourth variant of execution of the present invention;

Fig - views depicting the function applied to the second vector of probabilities of the fourth variant of execution of the present invention; and

Fig - views depicting a hardware configuration for soft decisions of the first form 64-QAM according to the present invention.

The best option of carrying out the invention

Below is described the preferred embodiment of the present invention, examples of which are illustrated on the accompanying drawings.

The present invention significantly increases the speed of processing by use of the equation of the vector of conditional probabilities instead of the logarithmic likelihood ratio, which is the way demodulation with soft decision signal of rectangular QAM, which is typically used in the industry.

The newly developed method demodulation rectangular QAM is divided into 2 forms, the first and third embodiments of the used for the first form and the second and fourth embodiments of the used for the second form. Also, output the final value of the vector of conditional probabilities covers the area between the actual number of "a" and the other on istically number "-a".

First, explaining some basic terms and conditions before the beginning of the description, the magnitude of QAM can be characterized by the mathematical expression 1, and therefore the number of bits in each point of the constellation diagram can be characterized by the mathematical expression 2.

Mathematical expression (1):

22n-KAM. n=2, 3, 4 ...

Mathematical expression (2):

the number of bits in each point=2n

Therefore, the number of values of the vector of conditional probabilities, which are the final output values, also becomes 2n.

The following explains the first way demodulation of the rectangular QAM according to the present invention.

First, due to the way the soft decisions in the case of reception of a signal of rectangular QAM corresponding to the first form. In the case of the first form, although it was mentioned that one of the values of the quadrature component (real part of the number or α) or in-phase component signal (imaginary part number or β) is used to compute the vector of conditional probabilities corresponding to the combination of bits of the first half when explaining the features of the first form, for the sake of convenience in the following description, to accept that the demodulation of the first half and the second half uses the values of β and the values of α, respectively, and the output area according to the demodulation is installed is foreseen as a value between 1 and-1. Also k is used as the parameter indicating the order of each bit.

The method of calculating the vector of conditional probabilities, corresponding to the case where the first bit, i.e. k = 1 in the first form, can be expressed in the form of a mathematical expression (3), and figure 5 is a visual representation.

Mathematical expression (3):

In the case of the first vector conditional probability (k=1) the output value is determined asHowever, the value of n is determined by the size of the CAM, using the mathematical expression (1).

The method of calculating the vector of conditional probabilities corresponding to the second bit (k=2) in the first form, can be expressed by the mathematical expression (4), and 6 is its visual representation.

Mathematical expression (4):

In the case of the second vector conditional probability (k=2) the output value of course is defined as

In this case, n represents the value of KAM in the mathematical expression (1), and C is a constant.

The method of calculating the vector of conditional probabilities corresponding to the third through n-th bit (k=3, 4, ... n-1, n) in the first form, can be expressed in the form of a mathematical expression (5). In this case, as can be seen in figure 9, as the vector of conditional probabilities corresponding to the third or sleduushemu bat, indicates some form of iteration (v-shaped), it is noted that the expression is used again with the use of such property.

Mathematical expression (5):

First, dividing the output chart on the main v-shaped, the vector of conditional probabilities corresponding to each bit is divided into (2k-3+1) scope.

2) the expression under the basic form is defined as

3) When the field facilities in the form given β and replacing the values of |β|-m, i.e. it subtracts the mean value m of each area (for example, because the repeat region is equal to one when k=4, the area becomes 2n-2≤|β|<3·2n-2and the average value becomes equal to m=2n-1), in basic terms as a new β can be determined output value.

4) Finally, in the left and right outer areas of the divided regions, i.e. the (2k-2-1)2n-k+2<|β|, the output value can be determined by substituting the average value of m=2nand values (|β|-m) for the new β in the main expression.

In this case, d is a constant that varies in accordance with the value of k.

The method of calculating the vector of conditional probabilities, the corresponding bits of the second half of the first form, i.e. the number of bits from n+1 to 2n can be obtained p is the solution to replace the β to α in the method of producing the vector of conditional probabilities in the first half according to the characteristic of the first form. In other words, the condition that all β in mathematical expression (3) are replaced by α, becomes an expression to calculate the first vector of conditional probabilities of the second half, i.e. the vector of conditional probabilities corresponding to the (n+1)-th bit. The vector of conditional probabilities corresponding to the (n+2)-th bit of the second vector of conditional probabilities of the second half, can be determined by replacing β by α in mathematical expression (4), i.e. the condition for calculating a second vector of conditional probabilities of the first half, and the vector of conditional probabilities corresponding to the bit number n+3 2n, which is the next case can be determined by converting mathematical expressions in the above description.

The following explains a method for performing a soft decision on the received signal of rectangular QAM corresponding to the second shape. Performs demodulation to determine the vector of conditional probabilities, the corresponding bits of odd order, using the value of α, and to determine the vector of conditional probabilities corresponding to the bits of the even-order, using the value of β, and therefore, the output scope is defined between 1 and -1, as in the first form, for convenience.

In the second form, the method of calculating the vector of conditional probabilities, corresponding to the first bit (k=1), m which can be expressed as a mathematical expression (6), and 6 is its visual representation.

Mathematical expression (6):

(a) In the case of the first bit (k=1) the output value is determined as

However, the value of n is determined by the mathematical expression (1) in accordance with the magnitude of CAM.

In the second form the vector of conditional probabilities corresponding to the second bit (k=2)can be obtained by replacing α by β in the mathematical expression (6) to calculate the first vector of conditional probabilities in accordance with the characteristic of the second form.

In the second form, the method of calculating the vector of conditional probabilities corresponding to the third bit (k=3), can be expressed as a mathematical expression (7).

Mathematical expression (7):

If α·β≥0,

(a) In the case of the third bits (k=3) the output value is determined as

If α·β<0, the expression for the calculation is defined as the expression in which all α replaced by β in the expression for calculation in the case of α·β≥0.

In this case, n represents the value of KAM in the mathematical expression (1), and C is a constant.

Essentially, can take place another feature KAM second form that the vector of conditional probabilities obtained in the cases α·β≥0 and α·β<0 separately. This feature is used when the vector conditions the probability, the corresponding third or subsequent bit of the second form, and includes the characteristics of mutually reverse lookup, like replacing β by α.

The expression for obtaining the vector of conditional probabilities corresponding to the fourth bit (k=4) the second form can be obtained by replacing α by β and β to α in the mathematical expression (7)is used to obtain a third vector of conditional probabilities in accordance with the second form.

The expression used to obtain the vector of conditional probabilities corresponding to the fifth bit (k=5) of the second form can be obtained by applying the mathematical expression (8). In this case, as can be seen in figure 10, as the vector of conditional probabilities corresponding to the fifth or subsequent bit indicates some form of iteration (v-shaped), it should be noted that expression is used again with the use of such properties. However, when computing the vector of conditional probabilities corresponding to the fifth or subsequent bit values determine the even-order use the expression that was used to calculate the value before the definition of odd order in accordance with a property of the second form, which is used only when the value is less than 64 QAM. And when the value is greater than 256, the rest can be divided into the two parts, and the calculation can be performed in the first half and then in the second half as in the first form.

Mathematical expression (8):

If α·β≥0,

(a) First, when dividing the output graph on the main V-shaped, the vector of conditional probabilities corresponding to each bit may be divided into (2k-5+1) regions.

(b) the expression under the basic form is defined as

(C) When the area of facilities in a given α and replacing the values of |α|-m, which is subtracted the average value m of each area (for example, because the repeat region is equal to one when k=6, the region is defined,

as 2n-2≤|α|<3·2n-2and the average value is m=2n-1), mainly because of the expression on the new α, can be determined output value.

(d) Finally, in the left and right outer areas of the divided regions, i.e. the (2k-2-1)2n-k+2<|α|, the output value can be determined by replacing the mean value of m=2nand values (|α|-m) new β in the main expression.

In the case of α·β<0, the output value can be obtained by replacing α by β in expression (a), (b), (c) and (d).

The calculation of the vector of conditional probabilities corresponding to the sixth bit of the second form may be provided by replacing α by β and β to α is the mathematical expression (8), used to obtain the fifth vector of conditional probabilities using the properties of the second form when the magnitude of QAM 64-QAM. However, when the magnitude of QAM is greater than 256-QAM, the first half is obtained by dividing the total of the remaining vectors in 2, and the second half is obtained by replacing the values (α or β) in terms of the first half. The modified value in terms of the first half represents only accept the value, and the value (k) is the bit number is not changed, but is replaced by the number of the first half.

Therefore, when the magnitude of QAM 256, computing a vector of conditional probabilities, the corresponding bits from the fifth to the (n+2)-th bit of the second half, determined by the mathematical expression (8).

The calculation of the vector of conditional probabilities corresponding to the bits of the (n+3)th to the last 2n-th bit of the second form is determined by replacing the parameter α to β in mathematical terms, as mentioned above.

Demodulation with soft decision rectangular QAM can be performed using the received signal, i.e. α+βi, using the above procedure. However, although the above-described method, for ease of understanding, arbitrarily defined procedure for selecting the received signal and substituting it in the expression for determining the Oia, the method is applicable in real applications more generally, so that the symbol α or β, which is a mathematical expression that can be freely replaced by another in accordance with the shape of the constellation combination of CAM, and the scope of output values may be asymmetrical, as values between a and b and between a and-a. We can say that this fact extends the versatility of the present invention and increases its importance. Also, although the above-described mathematical expressions seem very complicated, they are summarized for General applications, so it is clear that they are really easy to apply variants of execution.

The first version of the runtime

The first variant implementation of the present invention is a case corresponding to the first form, and apply the property of the first form. The first version of the runtime includes the example 1024-QAM, where the value is equal to 1024 QAM. The choice of the order of the received signal, as expected, α applies in the first half and β in the second half.

Essentially, KAM in two variants of execution of the present invention can be defined as the following expression. Mathematical expression (1) defines the amount of CAM, and the mathematical expression (2) shows the number of bits in each point of the constellation diagram of the combinations according to Velicina.

Mathematical expression (1):

22n-QAM, n=2, 3, 4 ...

Mathematical expression (2):

the number of bits in each point=2n

Essentially, the amount of CAM in the first embodiment, the present invention is defined as the following expression, and, consequently, the value of the vector of conditional probabilities of the final output value becomes 2n.

Case when 22·5-QAM 1024-QAM according to the mathematical expression (1), and the number of bits in each point of the constellation, is 2·5=10 bits according to the mathematical expression (2), is explained using the mathematical expressions (1) and (2). First, before applying expressions to calculate, it is noted that if the expression evaluates to 5 bits of the first half of the 10 bits is known by the properties of the first form, it is directly known expression for calculating the remaining 5 bits of the second half.

The first expression vector conditional probability represents the case k=1, and its output is of course defined as

The output value of the second (k=2) vector of conditional probability isIn this case, is a constant.

The expression to calculate the third (k=3) vector of conditional probability is defined as follows, where the main expression is according to their basic form is defined as

The calculation is divided into 2 regions, and the output value is determined asif |β|<24and the output value is determined asfor other cases.

The expression for calculating the fourth (k=4) vector of conditional probabilities is given in the following form, where the expression under the basic form is defined asand is divided into 3 areas.

In this case, the output value is determined asif |β|<23the output value is defined asif 23≤|β|<3·23and the output value is determined asfor other cases.

Then the expression evaluates to five (k=5) vector of conditional probabilities is given in the following form, where the expression is defined asand is divided into 5 regions. In this case, the output value is determined asif |β|<22.

The output value is determined asif 22≤|β|<3·22the output value is defined asif 3·22≤|β|<5·22the output value is defined asif 5·22≤|β|<7·22and the output value of ODA is determined as for other cases.

Then realized expression for calculating, from 6 th to 10-th vector of conditional probabilities by replacing α+β α+β between the first and fifth vector of conditional probabilities according to the property of the first form.

The second option run

The second variant of implementation of the present invention is a case corresponding to the second shape, and apply the property of the second form. The second embodiment of includes example 1024-QAM, where the value is equal to 1024 QAM. The choice of the order of the received signal, as expected, applies a first α.

As in the first embodiment, the mathematical expression (1) defines the amount of CAM, and the mathematical expression (2) specifies the number of bits in each graph point constellation combinations according to the amount of CAM.

Mathematical expression (1):

22n-QAM, n=2, 3, 4 ...

Mathematical expression (2):

the number of bits in each point=2n

Essentially, the value of the CAM in the second embodiment, the present invention is determined in the above expression, and, consequently, the value of the vector of conditional probabilities of the final output value becomes 2n.

The case when n is 5, i.e. the 22·5-QAM 1024-QAM according to the mathematical expression (1), and the number of bits in each point of the constellation, is 2·5=10 bits according to mathematics is self expression (2), explains when n is 5, with the use of such mathematical expressions (1) and (2).

Calculating a first vector conditional probability represents the case k=1, where the output value of course is defined as

The expression for calculating the second (k=2) vector of conditional probabilities is a case where replaced by the first expression to calculate where the output value is determined as

For the expression to calculate the third (k=3) vector of conditional probabilities, where αβ≥0, is the following, where the output value of course is defined asthiswithis constant.

If αβ<0, the expression for the calculation is obtained by replacing α by β in the expression used for the method of determining the output value of the third vector of conditional probabilities, explained just above (αβ≥0).

To calculate the fourth (k=4) vector of conditional probabilities,

(1) when αβ≥0, is given next, where the output value of course is defined as

(2) When αβ<0, this expression for the calculation is obtained by replacing α by β in the expression used for the method of determining the output value of the fourth vector of conditional probabilities, explained above (αβ≥).

For the expression to calculate the fifth (i.e. k=5) vector of conditional probabilities,

when αβ≥0, is given next, where the expression under the basic form is defined as

In this case, the expression is divided into 2 areas where, if |α|<24the output value is defined asand the output value is determined asfor other cases.

(2) When αβ<0, this expression for the calculation is obtained by replacing α by β in the expression used for the method of determining the output value of the fifth vector of conditional probabilities, explained above (αβ≥0).

For the sixth vector (i.e. k=6) conditional probability

when αβ≥0, the main expression according to the basic form is defined asand, in this case, the expression is divided into 3 areas where, if |α|<23the output value is defined asthe output value is determined asand the output value is determined asfor other cases.

When αβ<0, this expression for the calculation is obtained by replacing α by β in the expression used for the method of determining the output value of the sixth vector of conditional probabilities, explained above (αβ is 0).

For the expression to compute the seventh (k=7) vector of conditional probabilities,

when αβ≥0, the main expression according to the basic form is defined asand, in this case, the expression is divided into 5 regions :

where, if |α|<22the output value is defined as

if 22<|α|<3·22the output value is defined as

if 3·22<|α|<5·22the output value is defined as

if 5·22<|α|<7·22the output value is defined asand

the output value is determined asfor other cases.

When αβ<0,

this expression for the calculation is obtained by replacing α by β in the expression used for the method of determining the output value of the seventh vector of conditional probabilities, explained above (αβ≥0).

The method of obtaining from the eighth to tenth vector conditional probability is obtained by replacing α by β and β to α in the expression for obtaining the fifth to seventh vector of conditional probabilities.

The following explains the second method demodulation rectangular QAM.

First, due to the way the soft decision rectangular QAM corresponding to the first form. If what erway form, although any of a valid part number and the imaginary part of the number from the received signal is used to compute the vector of conditional probabilities corresponding to the bit pattern of the first half, the first half is demodulated using the values of β, and the second half is demodulated using the values of α, and its output scope is defined between 1 and -1 for the sake of convenience in the following description.

The method of calculating the vector of conditional probabilities, corresponding to the first bit in the first form, can be expressed in the form of mathematical expressions (13), and 3 and 11 are its visual representation.

Mathematical expression (13):

If |β|≥2n-1, the output value is defined as sign(β).

(2) if |β|≤1, the output value is determined as 0,9375·sign(β).

(3) if 1<|β|≤2n-1, the output value is defined as

sign(β) denotes the sign of the sign of β values.

In the first form of the method of calculating the vector of conditional probabilities corresponding to the second bit can be expressed as a mathematical expression (14), and 4 and 12 are its visual representation.

Mathematical expression (14):

(1) If 2n-2n(2-m)≤|β|≤2n-2n(2-m)+1, the output value is defined as (-1)m+1;

(2) if 2n-1-1≤|β|≤2n-1+1, o is the initial value is defined as 0,9375(2 n-1-|β|);

(3) if 2n-1-2(n-1)(2-m)+m≤|β|≤2n-2(n-1)(2-m)+m-2, the output value is defined as

In this case, m=1 or m=2.

In the first form of the method of calculating the vector of conditional probabilities, the corresponding bits from the third to the (n-1)-th bit can be expressed as a mathematical expression (15).

Mathematical expression (15):

(1) if m·2n-k+2-1≤|β|≤m·2n-k+2+1, the output value is defined as (-1)m+1;

(2) if the (2l-1)·2n-k+1-1<|β|≤(2l-1)·2n-k+1+1, the output value is defined as (-1)l+10,9375{|β|-(2l-1)·2n-k+1};

(3) if (P-1)·2n-k+1+1<|β|≤P·2n-k+1-1, the output value depends on the value R, where, if P is an odd number, the output value is defined as

However, if the P value is an even number, the output value is defined as

In this case, m=0, 1 ... 2k-2and l=1, 2, ... 2k-2also P=1, 2, ... 2k-1.

In this case, k represents a number of bits that is an integer greater than 3.

In the first form of the method of calculating the vector of conditional probabilities, corresponding to the n-th bit, which is the last bit in the first half, can be expressed in the form of a mathematical expression (16). This spiral is hydrated case of the mathematical expression (16), in which k=n and apply only conditional expressions (1) and (").

Mathematical expression (16):

(1) If m·22-1≤|β|≤m·22+1, the output value is defined as (-1)m+1.

(2) if the (2l-1)·21-1<|β|<(2l-1)·21+1,

the output value is determined as 0,9375{|β|-(2l-1)·21}.

In this case, m=0, 1, ... 2n-2and l=1, 2 ... 2n-2.

The method of calculating the vector of conditional probabilities, the corresponding bits of the second half of the first form, i.e. the number of bits from n+1 to 2n, can be performed by replacing β by α in the method of producing the vector of conditional probabilities of the first half, according to the property of the first form. I.e. the condition where all β in the mathematical expression (13) are replaced by α, is the first vector of conditional probabilities of the second half, i.e. the expression for calculating the vector of conditional probabilities corresponding to the (n+1)-th bit. Also, the vector of conditional probabilities corresponding to the (n+2)-th bit, i.e. the second vector of conditional probabilities of the second half, can be determined by replacing β by α in the mathematical expression (14), which is a condition where the calculated second vector of conditional probabilities of the first half, and the vector of conditional probabilities corresponding to the bit number n+3 2n, that is, the following cases can be defined by the mathematical transformation is iraani (15) and (16), as explained above.

The following explains how soft decisions for the received signal of rectangular QAM corresponding to the second shape. Also, for ease of understanding, the value of α is used to determine the vector of conditional probabilities, the corresponding bit of odd order, and the value of β is used to determine the bits of the even-order.

In the second form, the method of calculating the vector of conditional probabilities, corresponding to the first bit can be expressed as a mathematical expression (17), and Fig is its visual representation.

Mathematical expression (17):

(a) if |α|≥2n-1, the output value is defined as-sign(α);

(b) if |α|≤1, the output value is determined as 0,9375·sign(α);

(C) if 1<|α|≤2n-1, the output value is defined aswhen this sign(α) denotes the sign of the value α.

In the second form, the method of calculating the vector of conditional probabilities corresponding to the second bit can be obtained by replacing all α to β in the mathematical expression (17)is used to calculate the first vector of conditional probabilities according to the second form.

In the second form, the method of calculating the vector of conditional probabilities corresponding to the third bit can be expressed as a mathematical expression (18).

Math you shall agenie (18):

When α·β≥0,

(a) if 2n-2n(2-m)≤|α|≤2n-2n(2-m)+1, the output value is defined as (-1)m;

(b) if 2n-1-1≤|α|≤2n-1+1, the output value is determined as 0,9375(|β|-2n-1);

(C) if 2n-1-2(n-1)(2-m)+m≤|α|≤2n-2(n-1)(2-m)+m-2, the output value is defined as

If α·β<0, the expression for the calculation is defined as an expression, where all α replaced by β in the expression for calculation in the case of α·β≥0.

Essentially, the way to obtain a vector of conditional probabilities in each case, α·β≥0 and α·<0, is a different property. This property always applies when it receives a vector of conditional probabilities corresponding to the third or subsequent bit of the second form, and the property of mutual replacement, such as replacing β by α, is also included in this property.

The expression for obtaining the vector of conditional probabilities corresponding to the fourth bit of the second form is obtained by replacing α by β and β to α in the mathematical expression (18)is used to obtain a third vector of conditional probabilities using the properties of the second form when the magnitude of QAM 64-QAM. However, the case when the magnitude of QAM is greater than 256-QAM, is expressed as a mathematical expression (19).

Mathematical expression (19):

(a) if m·2n-k+ -1≤|α|≤m·2n-k+3+1, the output value is defined as (-1)m+1;

(b) if the (2l-1)·2n-k+2-1<|α|<(2l-1)·2n-k+2+1,

the output value is defined as (-1)l+1{0,9375|α|-0,9375(2l-1)·2n-k+2};

(C) if (P-1)·2n-k+2+1<|α|≤P·2n-k+2-1,

the output value is determined in accordance with the value of R, where, if P is an odd number, the output value is defined as

if P is an even number, the output value is defined as

In this case, k represents a number of bits, and m=0, 1 ... 2k-3, l=1, 2, ... 2k-3p=1, 2, ... 2k-2.

The expression for obtaining the vector of conditional probabilities corresponding to the fifth bit of the second form, can be expressed as a mathematical expression (20) in the case when the value QAM 64-QAM, and can be applied mathematical expression (19) in the case when the magnitude of QAM is greater than 256-QAM.

Mathematical expression (20):

When α·β≥0,

(a) if m·22-1<|β|≤m·22+1, the output value is defined as (-1)m+1;

(b) if the (2l-1)·22-1<|β|≤(2l-1)·22+1,

the output value is determined as 0,9375(-1)l+1{|β|-(2l-1)*22}.

In this case, m=0, 1, 2 and l=1, 2.

If α·β<0, the output value is obtained by replacing β by α in the expression is (a) and (b) in accordance with a property of the second form.

The calculation of the vector of conditional probabilities corresponding to the sixth bit of the second form, is achieved by replacing α by β and β to α in the mathematical expression (20), which is an expression used to obtain the fifth vector conditional probability in accordance with a property of the second form when the magnitude of QAM 64-QAM. However, the case when the magnitude of QAM is greater than 256-QAM, expressed as a mathematical expression (19).

The calculation of the vector of conditional probabilities, the corresponding bits from the seventh through n-th bits of the second form, is defined as a mathematical expression (19).

The calculation of the vector of conditional probabilities corresponding to the (n+1)-th bit of the second form, is expressed in the form of mathematical expressions (21), which represents a case study of the mathematical expression (19).

Mathematical expression (21):

(a) if m·22-1≤|α|≤m·22+1, the output value is defined as (-1)m+1;

(b) if the (2l-1)·21-1<|α|≤(2l-1)·21+1,

the output value is defined as (-1)l+1{0,9375|α|-0,9375(2l-1)·21}.

In this case, m=0, 1, ... 2n-2and l=1, 2 ... 2n-2.

The calculation of the vector of conditional probabilities corresponding to the (n+2)-th bit of the second form, is achieved by replacing α by β and β to α in the mathematical expression (18).

The calculation of the vector from lowney probability the relevant bits from the (n+3)-th through (2n-1)-th bit of the second form, is implemented by replacing α by β in the mathematical expression (19). However, the bit number of values of k, which is in this case equal to 4 and n that are sequentially substituted in the expression n+3 2n-1.

Demodulation with soft decision rectangular QAM can be performed using the received signal, i.e. the values of α+βi, throughout this process. However, although in the above-described method arbitrarily decided to order when selecting a received signal and substituting it in the expression to determine for ease of understanding, the way in its real application is more generalized, so that the symbol α or β, expressed in terms that can be easily replaced according to the shape of the constellation combination of CAM, and the scope of the output values may be asymmetric, such as a value between "a" and "b"and the value "a" or" -". This expands the versatility of the present invention and increases its importance. Also, although the above-described mathematical expressions seem very complicated, they are summarized for generalized applications, so they are simplified when considering the actually used variants of execution.

The third embodiment of the

The third alternative implementation of the present invention is the case with the corresponding first form, and apply the property of the first form. The third embodiment of includes example 1024-QAM, where the value is equal to 1024 QAM. The choice of the order of the received signal involves the use of α in the first half and β in the second half (see 11 and 12).

Essentially KAM in two variants of execution of the present invention can be defined as the following expression. Mathematical expression (1) defines the amount of CAM, and the mathematical expression (2) represents the number of bits in each graph point constellation combinations according to the amount of CAM.

Mathematical expression (1):

22n-QAM, n=2, 3, 4 ...

Mathematical expression (2):

the number of bits in each point=2n

Essentially, the value of KAM in the third embodiment, the present invention is defined as the following expression, and, consequently, the number of values of the vector of conditional probabilities of the final output value becomes 2n.

Case when 22·5-QAM 1024-QAM according to the mathematical expression 1, and the number of bits in each point of cancellarii, is 2·5=10 bits according to the mathematical expression (2), explains when n is 5, using mathematical expressions (1) and (2). Before applying expressions to calculate it should be noted that the expression for the calculation of the 5 bits of the first half of the 10 bits is known in paasivirta first form, the expression for calculating the remaining 5 bits of the second half also precisely known.

For the expression to calculate the first vector of conditional probabilities,

if |β|>25-1, the output value is defined as sign(β).

(2) if |β|≤1, the output value is determined as 0,9375·sign(β);

(3) if 1<|β|≤25-1, the output value is defined as

For the second (i.e. k=2, m=1, 2) vector of conditional probabilities,

if 0≤|β|≤1, the output value is determined as 1.

If 25-1≤|β|≤25, the output value is determined as -1;

if 24-1≤|β|≤24+1, the output value is determined as 0,9375(24-|β|);

if 1≤|β|≤24-1, the output value is defined asand

if 24+1≤|β|≤25-1, the output value is defined as

For the expression to calculate the third (k=3, m=0, 1, 2, l=1, 2, p=1, 2, 3, 4) vector of conditional probabilities,

(1) if m·24-1≤|β|≤m·24+1, the output value is defined as (-1)m+1.

By substituting m=0, 1, 2,

if -1<|β|≤1, the output value is defined as 1;

if 24-1<|β|≤24+1, the output value is defined as 1;

if 25-1<|β|≤25+1, the output value is determined as -1;

(2) if the (2l-1)·23-1<|β|≤(2l-1)·23+1, the output C is Uchenie is determined by substituting l=1, 2 (-1)l+10,9375{|β|-(2l-1)·23}. If 23-1<|β|≤23+1, the output value is determined as 0,9375(|β|-23), and, if 3·23-1<|β|≤3·23+1, the output value is determined as -0,9375(|β|-3·23).

(3) When (P-1)·23+1<|β|≤P·23-1 and using the substitution P=1, 2, 3 and 4 according to whether P is an odd number or an even number,

1<|β|≤23-1, the output value is defined as

if 23+1<|β|≤24-1, the output value is defined as

if 24+1<|β|≤3·23-1, the output value is defined as

if 3*23+1<|β|≤25-1, the output value is defined as

For the expression to calculate the fourth (k=4, m=0, 1, 2, 3 and 4, l=1, 2, 3 and 4, p=1, 2, 3, 4, 5, 6, 7 and 8) the vector of conditional probabilities,

if -1<|β|≤1, the output value is determined as -1,

if 23-1<|β|≤23+1, the output value is determined as 1,

if 24-1<|β|≤24+1, the output value is determined as -1,

if 3*23-1<|β|≤3·23+1, the output value is determined as 1,

if 25-1<|β|≤25+1, the output value is determined as -1,

if 22-1<|β|≤22+1, the output value is determined as 0,9375{|β|-22},

if 3·22-1<|β|is 3·2 2+1, the output value is determined as -0,9375{|β|-3·22},

if 5·22-1<|β|≤5·22+1, the output value is determined as 0,9375{|β|-5·22},

if 7·22-1<|β|≤7·22+1, the output value is determined as -0,9375{|β|-7·22}if 1<|β|≤22-1, the output value is defined as

if 22+1<|β|≤23-1, the output value is defined as

if 23+1<|β|≤3·22-1, the output value is defined as

if 6·22+1<|β|≤7·22-1, the output value is defined as

if 7·22+1<|β|≤25-1, the output value is defined as

For the expression to calculate the fifth (i.e. k=5, m=0, 1, 2, ... 7, 8, l=1, 2, 3, ... 7, 8) vector of conditional probabilities,

if -1<|β|≤1, the output value is determined as -1,

if 22-1<|β|≤22+1, the output value is determined as 1,

if 3·22-1<|β|≤3·22+1, the output value is defined as-1.

...

...

if 7·22-1<|β|≤7·22+1, the output value is determined as 1,

if 25-1<|β|≤25+1, the output value is determined as -1,

if 1<|β|≤3, the output value is determined as 0,9375(|β|-2),

if 5<|β|≤7, the output value of opredelaetsa is how -0,9375(|β|-6),

if 9<|β|≤11, the output value is determined as 0,9375(|β|-10),

...

...

if 25<|β|≤27, the output value is determined as 0,9375(|β|-26),

if 29<|β|≤31, the output value is determined as -0,9375(|β|-30).

Expressions for calculating from the sixth to the tenth, the vector of conditional probabilities can be obtained by replacing β by α in between the first and fifth vector conditional probability in accordance with a property of the first form.

The fourth embodiment of the

The fourth alternative implementation of the present invention is a case corresponding to the second shape, and apply the property of the second form. The fourth embodiment of includes example 1024-QAM, where the value is equal to 1024 QAM. The choice of the order of the received signal involves the use of first α.

Mathematical expression (1) defines the amount of CAM, and the mathematical expression (2) shows the number of bits in each point of the constellation diagram of the combinations according to the size of the CAM, as in the third embodiment.

Mathematical expression (1):

22n-QAM, n=2, 3, 4 ...

Mathematical expression (2):

the number of bits in each point=2n

Essentially, the value of KAM in the fourth embodiment, the present invention is determined in the above expression, and, consequently, the number of values of the vector of conditional probabilities con is knogo output value becomes 2n.

Case when 22·5-QAM 1024-QAM according to the mathematical expression (1), and the number of bits in each point of the constellation, is 2·5=10 bits according to the mathematical expression (2), explains when n is 5, using mathematical expressions (1) and (2) (see Fig and 14).

To calculate the first vector of conditional probabilities:

if |α|>25-1, the output value is defined as-sign(α),

if |α|≤1, the output value is determined as -0,9375sign(α),

if 1<|α|≤25-1, the output value is defined as

The expression for calculating a second vector of conditional probabilities is a form of replacement of the first expression to calculate as follows.

(a) If |β|>25-1, the output value is defined as-sign(β).

(b) If |β|≤1, the output value is determined as -0,9375sign(β).

(C) If 1<|β|≤25-1, the output value is defined as

For the expression to calculate the third vector of conditional probabilities,

when αβ≥0,

(a) if 25-25(2-m)≤|α|<25-25(2-m)+1, the output value is defined as (-1)m.

In this case, since m is equal to 1 and 2 after the substitution,

if 0≤|α|≤1, the output value is defined as-1.

If 25-1≤|α|<25the output value is defined as 1

(b) if 24-1≤|α|<24+1, the output value is determined as 0,9375(|α|-24),

(c) if 24-24(2-m)+m≤|α|≤25-24(2-m)+m-2, the output value is defined as

In this case, the substitution m=1, 2,

if 1≤|α|<24-1, the output value is defined as

if 24+1≤|α|<25-1, the output value is defined as

When αβ<0,

in this case, the expression for the calculation is obtained by replacing α by β in expression (a), (b), (C) method for determining the output value of the third vector of conditional probabilities described above.

To calculate the fourth (k=4, m=0, 1, 2, l=1, 2, p=1, 2, 3, 4) vector of conditional probabilities,

when αβ≥0,

(a) if m·24-1≤|α|<m·24+1, the output value is defined as (-1)m+1.

In this case, the substitution m=0, 1, 2, if -1<|α|≤1, the output value is determined as -1,

if 24-1≤|α|<24+1, the output value is determined as 1,

if 25-1≤|α|<25+1, the output value is determined as -1;

(b) if the (2l-1)·23-1≤|α|<(2l-1)·23+1, the output value is determined by substituting l=1, 2 (-1)l+1{0,9375|α|-0,9375(2l-1)·23},

in this case, if 23-1≤|α|<23+1, the output value is determined ka is 0,9375(|α|-2 3),

if 3·23-1≤|α|≤3·23+1, the output value is determined as -0,9375(|α|-3·23);

(C) if (P-1)·23+1≤|α|≤P·23-1 and P is an odd number, the output value is defined as

However, if P is an even number, the output value is defined as

In this case, the substitution p=1, 2, 3, 4,

if 1<|α|≤23-1, the output value is defined as

if 23+1<|α|≤24-1, the output value is defined as

if 24+1<|α|≤3·23-1, the output value is defined as

if 3·23+1<|α|≤25-1, the output value is defined as

When αβ<0,

in this case, the expression for the calculation is obtained by replacing α by β in expression (a), (b), (C) method for determining the output value of the fourth vector of conditional probabilities described above.

Then for the fifth (i.e. k=5, m=0, 1, 2, 3, 4, l=1, 2, 3, 4) vector of conditional probabilities,

(1) when αβ≥0,

(a) if m·23-1<|α|≤m·23+1, the output value is defined as (-1)m+1.

In this case, the substitution m=0, 1, 2, 3, 4,

if -1<|α|≤1, the output value is determined as -1,

if 2 3-1<|α|≤23+1, the output value is determined as 1,

if 24-1<|α|≤24+1, the output value is determined as -1,

if 3·23-1<|α|≤3·23+1, the output value is determined as 1,

if 25-1<|α|≤25+1, the output value is determined as -1;

(b) if the (2l-1)·22-1<|α|≤(2l-1)·22+1, the output value is determined by substituting l=1, 2, 3, 4

(-1)l+10,9375{|α|-0,9375(2l-1)·22},

in this case, if 22-1<|α|≤22+1, the output value is determined as 0,9375(|α|-22),

if 3·23-1<|α|≤3·23+1, the output value is determined as -0,9375(|α|-3·22),

if 5·22-1<|α|≤5·22+1, the output value is determined as 0,9375(|α|-5·22),

if 7·22-1<|α|≤7·22+1, the output value is determined as -0,9375(|α|-7·22);

(c) when (P-1)·22+1<|α|≤P·22-1 and using the substitution p=1, 2, 3, ... 7, 8 according to whether P is an odd number or an even number,

if 1<|α|≤22-1, the output value is defined as

if 22+1<|α|≤23-1, the output value is defined as

if 23+1<|α|≤3·22-1, the output value is defined as

if 3·22+1<|α|≤24-1, the output value is defined as

if 24+1<|α|≤5·22-1, the output value is defined as

if 5·22+1<|α|≤6·22-1, the output value is defined as

if 6·22+1<|α|≤7·22-1, the output value is defined as

if 7·22+1<|α|≤25-1, the output value is defined as

When αβ<0,

in this case, the expression for the calculation is obtained by replacing α by β in expression (a), (b), (C) detection method of the fifth vector of conditional probabilities (αβ<0), described just above.

Then for the sixth (i.e. k=6, m=0, 1, 2, ...7, 8, l=1, 2, 3, ... 7, 8) vector of conditional probabilities,

(1) when αβ≥0,

(a) if m·22-1<|α|≤m·22+1, the output value is defined as (-1)m+1.

In this case, the output value is obtained by applying m=0, 1, 2, ... 7, 8.

I.e. if -1<|α|≤1, the output value is determined as -1,

if 22-1<|α|≤22+1, the output value is determined as 1,

if 3·22-1<|α|≤3·22+1, the output value is defined as-1.

...

...

if 722-1<|α|≤7·22+1, the output value is determined as 1,

if 25-1<|α|≤25+1, the output value is determined as -1;

(b) if the (2l-1)·2-1<|α|≤(2l-1)·2+1,

output Zn is an increase is determined by the substitution l=1, 2, 3, ... 7, 8

(-1)l+1{0,9375|α|-0,9375(2l-1)·2}.

in this case, if 1<|α|≤3, the output value is determined as 0,9375(|α|-2).

if 5<|α|≤7, the output value is determined as -0,9375(|α|-6).

if 9<|α|≤11, the output value is determined as 0,9375(|α|-10).

...

...

if 25<|α|≤27, the output value is determined as 0,9375(|α|-26).

if 29<|α|≤31, the output value is determined as -0,9375(|α|-30).

(2) When αβ<0,

in this case, the expression for the calculation is obtained by replacing α by β in expression (a), (b) method for determining the output value of the fifth vector of conditional probabilities (αβ≥0), described above.

Then the expression for the calculation of the seventh to tenth vector of conditional probabilities are obtained by replacing α by β and β to α in the expressions for calculating from the third to the sixth vector of conditional probabilities.

Figure 11 presents a view depicting the functional block for the decision-making process on the vector of conditional probabilities according to the present invention.

On Fig presents a view depicting an example of the hardware configuration for the vector of conditional probabilities of the first form 64-QAM according to the present invention. Specialist in the art will be able to configure the hardware through the implementation of modification without departure from the scope of the present image is etenia.

Although the present invention is described on the example of preferred embodiments, it is not limited to the above description, but covers changes, modifications and variations according to the nature and scope of the attached claims.

Industrial applicability

According to the present invention, it is expected a significant increase in processing speed and economy of production costs when implemented in hardware by applying a linear equation of the vector of conditional probabilities instead of the logarithmic likelihood ratio, which is the way demodulation with soft decision signal of rectangular QAM, which is commonly used in this technical field.

1. How soft solutions for demodulation of a received signal α+iβ rectangular quadrature amplitude modulation (QAM), consisting of in-phase component signal and a quadrature phase component signal, the method comprises the steps are:
take the signal α+iβ in the radio communications device;
get the set of values of the vector of conditional probabilities, each representing the value of the soft decision corresponding to the bit position tough decisions, using functions, including the operation of a conditional definition of the quadrature phase component and sinpas the th component of the received signal,
moreover, the solution vector of conditional probabilities for demodulation of the first half of the total number of bits is identical to the solution for demodulation of the remaining half of the bits, and is defined by replacing each other the values of the quadrature phase component and the values of the in-phase component, and
in a way demodulation vector of conditional probabilities, the corresponding bit of odd order is identical to the method of calculating the vector of conditional probabilities corresponding to the next bit of even order, the value of the received signal, is used to compute the vector of conditional probabilities, the corresponding bit odd order, uses one of α and β in accordance with this constellation combinations, and the value of the received signal for bit even-order uses one of the remaining α and β.

2. How soft solutions for demodulation of a received signal a+iβ rectangular quadrature amplitude modulation (QAM), consisting of in-phase component signal and a quadrature phase component signal, the method comprises the steps are:
take the signal α+iβ in the radio communications device;
get the set of values of the vector of conditional probabilities, each representing the value of the soft decision corresponding to the bit position of the hard decisions using the funk is AI, includes the operation of a conditional definition of the quadrature phase component and a phase component of the received signal,
moreover, the solution of the first vector of conditional probabilities for demodulation of the first half of the total number of bits is identical to the solution of the second vector of conditional probabilities for demodulation of the second half of bits, and is defined by replacing each other the values of the quadrature phase component and the values of the in-phase component,
moreover, the signal demodulation has 2n bits,
moreover, the values of the vector of conditional probabilities, the corresponding bits from the first to the n-th bit of the first half, demodulated through one of the components α and β of the received signal, and the values of the vector of conditional probabilities corresponding to the bits of the (n+1)th to 2n-th bit of the second half, demodulated through the remaining one of the components α and β of the received signal, when this equation is applied to both demodulate is identical to the first half and second half, and
and the first vector of conditional probability is defined by selecting one of the components of the received signal α and β in accordance with the constellation combinations and application of the following mathematical expression, where (1) the output value of course is defined as where Ω is a selected received value, which is one of α and β, andandis an arbitrary real number set in accordance with the required output area.

3. How soft solutions for demodulation of a received signal α+iβ rectangular quadrature amplitude modulation (QAM), consisting of in-phase component signal and a quadrature phase component signal, the method comprises the steps are:
take the signal α+iβ in the radio communications device;
get the set of values of the vector of conditional probabilities, each representing the value of the soft decision corresponding to the bit position tough decisions, using functions, including
itself the operation of a conditional definition of the quadrature phase component and a phase component of the received signal,
moreover, the solution vector of conditional probabilities for demodulation of the first half of the total number of bits is identical to the solution for demodulation of the remaining half of the bits, and is defined by replacing each other the values of the quadrature phase component and the values of the in-phase component,
moreover, the signal demodulation has 2n bits,
moreover, the values of the vector of conditional probabilities, the corresponding bits from the first to the n-th bit of the first half, demodul is that through one of the components α and β of the received signal, and values of the vector of conditional probabilities corresponding to the bits of the (n+1)th to 2n-th bit of the second half, demodulated through the remaining one of the components α and β of the signal when this equation is applied to both demodulate is identical to the first half and second half, and
the second vector of the conditional probability is determined by the received value selected when determining the first vector of conditional probabilities, and by applying the following mathematical expression, where:
(1) the output value of course is defined aswhere Ω is a selected and accepted the value n represents the size of the CAM, i.e. the parameter used to determine the 22n,andis an arbitrary real number set in accordance with the required output region, and is an arbitrary constant.

4. How soft solutions for demodulation of a received signal α+iβ rectangular quadrature amplitude modulation (QAM), consisting of in-phase component signal and a quadrature phase component signal, the method comprises the steps are:
take the signal α+iβ in the radio communications device;
get the set of values of the vector of conditional probabilities, each representing the Wallpaper is soft solutions corresponding to the bit position tough decisions, using functions, including the operation of a conditional definition of the quadrature phase component and a phase component of the received signal,
moreover, the solution vector of conditional probabilities for demodulation of the first half of the total number of bits is identical to the solution for demodulation of the remaining half of the bits, and is defined by replacing each other the values of the quadrature phase component and the values of the in-phase component,
moreover, the signal demodulation has 2n bits,
moreover, the values of the vector of conditional probabilities, the corresponding bits from the first to the n-th bit of the first half, demodulated through one of the components α and β of the received signal, and the values of the vector of conditional probabilities corresponding to the bits of the (n+1)th to 2n-th bit of the second half, demodulated through the remaining one of the components α and β of the signal when this equation is applied to both demodulate is identical to the first half and second half, and
with the vectors of conditional probabilities from the third to the nth is determined by the adopted value set when determining the first vector of conditional probabilities, and apply the following mathematical expression (A),
in which the mathematical expression (A:
first divide the output diagram form the main V-shaped, with the vector of conditional probabilities corresponding to each bit is divided into (2k-3+1),
define the basic terms according,
determine the output value by finding involved area using the given Ω and substituting the value (|Ω|-m), so that the average value is subtracted from each area in the main expression as a new Ω, and
represent the average value in the form m=2nand substitute the value (|Ω|-m) in the main expression as a new Ω in the region, which is located on the outer left and right sides from among the divided areas, ie (2k-2-1)2n-k+2<|Ω|, where Ω is a selected and accepted the value n represents the size of the CAM, i.e. the parameter used to determine the 22n, k is a number (k=3, 4, ...n) vector of conditional probability, d is a constant that varies in accordance with the value of k, andandis a constant that determines the output area.

5. The method according to claim 4, in which successively receive the vector of conditional probabilities with (n+1)th to 2n-th using one of the accepted values of α and β, which is not selected when determining the first vector conditional ve is hatnote, and the mathematical expressions described above, except that the number k of the vector of conditional probabilities that are included in the mathematical expression (A), sequentially replaced with 3 n n+1 through 2n.

6. The method according to claim 1, wherein receiving the first vector of conditional probabilities by selecting any one of the components α and β of a received signal in accordance with the form of the constellation combinations and then in accordance with the following mathematical expression:
the output value of course is defined aswhere Ω is a selected and accepted value, which is one of α and β, n represents the size of the CAM, i.e. the parameter used to determine the 22nandandis an arbitrary real number, installed in accordance with the required output area.

7. The method according to claim 6, which define a second vector of conditional probabilities by replacing the selected received value to the received value that is not the way to obtain the first vector of conditional probabilities.

8. The method according to claim 1, which define a third vector of conditional probabilities by selecting one of the received values of α and β in accordance with the form of the constellation combinations using the following mathematical expression (In) if αβ≥, and replacing the received value selected in the mathematical expression (In), to the received value that is not selected in the expression in the case αβ<0, where in the mathematical expression (In) the output value is determined aswhere Ω is a selected and accepted the value n represents the size of the CAM, i.e. the parameter used to determine the 22nand is an arbitrary real number, installed in accordance with the required output region, and is an arbitrary constant.

9. The method according to claim 8, which calculates the fourth vector of conditional probabilities by replacing each used accepted values for each received value, not used in the way to obtain a third vector of conditional probabilities in cases αβ≥0 and αβ<0.

10. The method according to claim 1, which define the fifth vector of conditional probabilities by selecting one of the received values of α and β in accordance with the form of the constellation combinations using the following mathematical expression (C) if αβ≥0, and define by replacing the received value selected in the mathematical expression (S)to the received value that is not selected in the expression in the case αβ<0, where in the mathematical expression (S):
(1) first, divide the output di is the grams on the main form V-shaped, and the vector of conditional probabilities corresponding to each bit is divided into 2 regions,
(2) the expression under the basic form is defined as,
(3) the output value is determined by finding the involved area using the given Ω and substituting the values (|Ω|-m), so that the average value is subtracted from each area, in basic terms as a new Ω,
(4) represent the average value in the form m=2nand substitute the value of |Ω|-m in the main expression as a new Ω in the field, which is located on the outer left and right sides from among the divided areas, ie 7·2n-3<|Ω|, where Ω is a selected received value, n represents the size of the CAM, i.e. the parameter used to determine the 22n, d is a constant, andandis a constant that determines the output area.

11. The method according to claim 10, in which when the value QAM 64-QAM, get the sixth vector of conditional probabilities by replacing each used accepted values for each received value, not used in the way to obtain the fifth vector of conditional probabilities in cases αβ≥0 and αβ<0.

12. The method according to claim 1, wherein, when the magnitude of QAM is greater than 256-QAM, define the vectors conditional verojatno and from the fifth to the (n+2)-th by selecting one of the received values of α and β in accordance with the form of the constellation combinations using the following mathematical expression (D) if αβ≥0, and replacing the received value selected in the mathematical expression (D), to the received value that is not selected in the case αβ<0, where in the mathematical expression (D):
(1) first, divide the output diagram form the main V-shaped, and the vector of conditional probabilities corresponding to each bit is divided into (2k-5+1),
(2) the expression under the basic form is defined as,
(3) the output value is determined by finding the involved area using the given Ω and lookup values |Ω|-m, so that the average value m (for example, in the case k=6, as the repeat region is equal to 1, this area is a 2n-2≤|Ω|<3·2n-2and the average value is m=2n-1) is subtracted from each area in the main expression as a new Ω,
(4) represent the average value in the form m=2nand substitute the value of |Ω|-m in the main expression as a new Ω in the region, which is located on the outer left and right sides from among the divided areas, ie (2k-2-1)2n-k+2<|Ω|, where k is a number (5, 6, ... n) vector of conditional probabilities, Ω is a selected and accepted the value n represents the size of the CAM, i.e. the parameter used to determine the 22nbut a constant is s, defines the output area, and d is a constant that varies in accordance with the value of k.

13. The method according to item 12, wherein, when the magnitude of QAM is greater than 256-QAM, are selected vectors conditional probability C (n+3)th to (2n)-th through the mathematical expression (D) using the accepted value, which is selected when receiving vectors of conditional probabilities from the fifth to the (n+2)-th if αβ≥0, and
receive by replacing the received value selected in the mathematical expression (D), to the received value that is not selected in the expression in the case αβ<0.

14. The method according to claim 1, wherein receiving the first vector of conditional probabilities by selecting any one of the accepted values of α and β in accordance with the form of the constellation combinations, and then in accordance with the following mathematical expression (E), where in the mathematical expression (E):
(1) if |Ω|≥2n-1, the output value is determined as a*sign(Ω),
(2) if |Ω|≤1, the output value is determined as a*0,9375*sign(Ω),
(3) if 1<|Ω|≤2n-1, the output value is defined as,
where Ω represents any one of the accepted values of α and β, sign(Ω) indicates the sign is selected and the received values, and is an arbitrary real number, installed in accordance with the required output is the area α represents the accepted value of the in-phase channel I (a real number), and β represents the accepted value of the quadrature channel Q (imaginary number).

15. The method according to claim 1, wherein to determine the second vector of conditional probabilities by the received value selected when determining the first vector of conditional probabilities, and the following mathematical expression (F), where in the mathematical expression (F):
(1) if 2n-2n(2-m)≤|Ω|≤2n-2n(2-m)+1, the output value is defined as a*(-1)m+1,
(2) if 2n-1-1≤|Ω|≤2n-1+1, the output value is determined as a*0,9375(2n-1-|Ω|),
(3) if 2n-1-2(n-1)(2-m)+m≤|Ω|≤2n-2(n-1)(2-m)+m-2, the output value is defined as,
where Ω is a selected and accepted the value n represents the size of the CAM, i.e. the parameter used to determine the 22nand is an arbitrary real number, installed in accordance with the required output region, and m=1, 2.

16. The method according to clause 15, which define the vectors of conditional probabilities from the third to the (n-1)-th through the received value selected when receiving the first vector of conditional probability, and mathematical expression (G), where in the mathematical expression (G):
(1) if m*2n-k+2-1<|Ω|≤m*2n-k+2+1 the output value is determined as a*(-1) m+1,
(2) if the (2l-1)*2n-k+1-1<|Ω|≤(2l-1)*2n-k+1+1,the output value is defined as a*(-1)l+10,9375{|Ω|-(2l-1)*2n-k+1},
(3) if (P-1)*2n-k+1+1<|Ω|≤P*2n-k+1-1 when P is an odd number, the output value is determined as

when P is an even number, the output value is determined as

where m in the mathematical expression (G) is equal to 0, 1...2k-2and 1 is 1, 2, ... 3k-2, k is a number (k=3, ...n-1) vector of conditional probabilities.

17. The method according to clause 16, which define the n-th vector of conditional probabilities by the received value selected when receiving the first vector of conditional probabilities, and the following mathematical expression (N), where in the mathematical expression (N):
(1) if m*22-1≤|Ω|≤m*2n2+1, the output value is defined as a*(-1)m+1,
(2) if the (2l-1)*21-1<|Ω|≤(2l-1)*21+1, the output value is defined as a*(-1)l+10,9375{(|Ω|-(2l-1)*21),
where m in the mathematical expression (N) is equal to 0, 1...2n+2and 1=1, 2, ...3n-2.

18. The method according to 17, in which successively receive the vectors of conditional probabilities with (n+1)th to 2n-th using the accepted value, which is not selected when receiving the first vector of conditional probability, and mathematical expressions (F)-(H) according to the government, except for the fact that the number k of the vector of conditional probabilities that are included in the mathematical expression (G), successively used as 3 to n-1 instead of n+3 2n-1.

19. The method according to claim 1, wherein defining the first vector of conditional probabilities by selecting any one of the accepted values of α and β in accordance with the form of the constellation combinations and further, in accordance with the mathematical expression (I), where in the mathematical expression (I):
(1) if |Ω|≥2n-1, the output value is determined as a*sign(Ω),
(2) if |Ω|≤1, the output value is determined as a*0,9375*sign(Ω),
(3) if 1<|Ω|≤2n-1, the output value is determined as

where sign(Ω) specifies the character selected and accepted value.

20. The method according to claim 1, in which calculates a second vector of conditional probabilities by replacing the received value selected in the way to obtain the first vector of conditional probabilities to the received value that is not selected in the method.

21. The method according to claim 1, which define a third vector of conditional probabilities by selecting any one of the values of α and β in accordance with the constellation combinations, using the following mathematical expression (J) in the case of α*β≥0, and replace the selected and received values in the mathematical expression (J) to the received value is the which is not selected in the mathematical expression (J) in the case of α*β<0, where in the mathematical expression (J):
(1) if 2n-2n(2-m)≤|Ω|≤2n-2n(2-m)+1, the output value is defined as a*(-1)m,
(2) if 2n-1-1≤|Ω|≤2n-1+1, the output value is determined as a*0,9375(|Ω|-2n-1),
(3) if 2n-1-2(n-1)(2-m)+m≤|Ω|≤2n-2(n-1)(2-m)+m-2, the output value is determined as
,
where Ω is a selected and accepted value, and is an arbitrary real number, installed in accordance with the required output region, α is a received value of the in-phase channel I (a real number), β represents the accepted value of the quadrature channel Q (imaginary number), and m=1, 2.

22. The method according to claim 1, wherein, when the magnitude of QAM 64-QAM, calculate the fourth vector of conditional probabilities by replacing each used accepted values for each received value, not used in the way to obtain a third vector of conditional probabilities in the cases α*β≥0 and α*β<0.

23. The method according to claim 1, wherein, when the magnitude of QAM 64-QAM determine the fifth vector of conditional probabilities by selecting one of the received values of α and β in accordance with the form of the constellation combinations, and use after the respective mathematical expressions (K) if α*β≥0, and replace the adopted value chosen in the mathematical expression (To), to the received value that is not selected in the expression if α*β≥0, where in the mathematical expression (To):
(1) if m*2n-1-1≤|Ω|≤m*2n-1+1, the output value is defined as a*(-1)m+1,
(2) if the (2l-1)*2n-1-1<|Ω|≤(2l-1)*2n-1+1,
the output value is determined as a*(-1)l+1{0,9375|β|-0,9375(2l-1)*2n-1},
where Ω is a selected and accepted value, and is an arbitrary real number, installed in accordance with the required output region, α is a received value of the in-phase channel I (a real number), β represents the accepted value of the quadrature channel Q (imaginary number), m=0, 1, 2, and 1=1, 2.

24. The method according to claim 1, wherein, when the magnitude of QAM 64-QAM, calculate the sixth vector of conditional probabilities by replacing each used accepted values for each received value, not used in the way to obtain the fifth vector of conditional probabilities in the cases α*β≥0 and α*β<0.

25. The method according to claim 1, wherein, when the magnitude of QAM is greater than 256-QAM, define the vectors of conditional probabilities from the fourth to the nth by selecting one of the received values of α and β in accordance with the form of the constellation combinations, use the following math is irginia (L) if α*β≥0, and replace the adopted value chosen in the mathematical expression (L), to the received value that is not selected in the expression if α*β<0, where in the mathematical expression (L):
(a) if m*2n-k+3-1<|Ω|≤m*2n-k+3+1, the output value is defined as a*(-1)m+1,
(b) if the (2l-1)*2n-k+2-1<|Ω|≤(2l-1)*2n-k+2+1, the output value is defined as a*(-1)l+1{0,9375(|Ω|-0,9375(2l-1)*2n-k+2),
(c) if (P-1)*2n-k+2+1<|Ω|≤P*2n-k+2-1 when P is an odd number, the output value is determined as

when P is an even number, the output value is determined as

where k represents a number (4, 5, ...n) vector of conditional probabilities, Ω is a selected and accepted value, and is an arbitrary real number, installed in accordance with the required output region, α is a received value of the in-phase channel I (a real number), β represents the accepted value of the quadrature channel Q (imaginary number), m=0, 1, ...2k-3, 1 is 1, 2, ...3k-3and p=1, 2, ...2.

26. The method according to claim 1, wherein, when the magnitude of QAM is greater than 256-QAM, define (n+1)-th vector of conditional probabilities using the following mathematical expression (M) if α*β≥0, and replacing the received value is s, select in the mathematical expression (M), to the received value that is not selected in the expression if α*β<0, where in the mathematical expression (M):
(a) if m*22-1≤|Ω|≤m*22+1, the output value is defined as a*(-1)m+1,
(b) if the (2l-1)*21-1<|Ω|≤(2l-1)*21+1, the output value is defined as a*(-1)l+1{0,9375{|Ω|-0,9375(2l-1)*21},
where Ω is a selected and accepted value, and is an arbitrary real number, installed in accordance with the required output region, α is a received value of the in-phase channel I (a real number), β represents the accepted value of the quadrature channel Q (imaginary number), m=0, 1, ...2k-2and 1 is 1, 2, ...3k-2.

27. The method according A.25, in which, when the magnitude of QAM is greater than 256-QAM, get (n+2)-th vector of the conditional probability method identical to the method for producing a fourth vector of conditional probabilities in the case when the magnitude of QAM is less than 256-QAM.

28. The method according A.25, in which, when the magnitude of QAM is greater than 256-QAM, compute the vectors of conditional probabilities with (n+3)th to (2n-1)-th by replacing each used accepted values for each received value, which is not used when determining the vectors of conditional probabilities from the fourth to n-th in the cases α*β≥0 and α*β<0 when the value of KA is greater than 256-QAM.

29. The method according A.25, in which, when the magnitude of QAM is greater than 256-QAM, compute the 2n-th vector of conditional probabilities by replacing each used accepted values for each received value, which is not used when determining the vectors of conditional probabilities from the fourth to the (n+1)-th in the cases α*β≥0 and α*β<0 when the magnitude of QAM is greater than 256-QAM.



 

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