JP2967193B2 - Information transmission method using orthogonal wavelets - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a digital modulation method using orthogonal wavelets, and more particularly to a digital modulation method in a case where information to be transmitted has a hierarchical importance.

[0002]

2. Description of the Related Art Conventionally, when UEP is realized by encoding, there is a method using a generalized concatenated code as shown in FIG. Code length at C 'encoder figure nN, number information symbol becomes _{K 1 k 1 + K 2 k} 2 + .. + K L k L. By the minimum Hamming distance of outer code C _i to different by i, UEP
Can be realized. However, this method generally increases the redundancy and lowers the transmission efficiency.

In the case of a method based on signal point arrangement, FIG.
When the transmission is performed using the signal point constellation as shown in FIG. ₂ , since the Euclidean distances of d ₁ and d ₂ are different, when d ₁ > d ₂ in an additional noise environment, the error rate of a ₁ bit is a _It is lower than the _2- bit error rate. UEP
Can be realized, but in this case, the information hierarchy can be set only in two stages. Also 16QAM etc.
If an attempt is made to arrange the signal points with more symbols, the structure of the signal surface becomes complicated.

Further, in the case of a method using coded modulation, there is a method using a coded modulation method as a technique for integrating the above two techniques. In this method, generally, a difference in Euclidean distance is given to a signal point arrangement, a trellis code or the like is used for encoding, and the encoding rate is changed according to the importance of bits.
By using this, a degree of freedom in setting is obtained, and UEP is realized without significantly reducing transmission efficiency.

[0005]

However, this method has a problem that the encoding and decoding procedures are complicated and the amount of calculation is increased.

[0006]

SUMMARY OF THE INVENTION The present invention has been proposed in view of the above-mentioned conventional drawbacks. In a digital modulation system, when a UEP is performed on transmission information, an average bit error rate can be obtained by using a quadrature wavelet. An object of the present invention is to provide a digital modulation method using orthogonal wavelets that enables information having different BER characteristics to be transmitted by modulation.

According to the present invention, since a discrete wavelet using orthogonal wavelets is a one-to-one reversible transform, one signal point is assigned to a subband-decomposed component to create a composite wave f ₀ , An object of the present invention is to provide a digital modulation method using an orthogonal wavelet for transmitting the synthesized wave f ₀ as a baseband modulation signal.

Another object of the present invention is to provide a digital modulation method using orthogonal wavelets that can be used as a modulation method when information to be transmitted has a hierarchical importance.

Furthermore, the present invention provides a digital communication system using a quadrature wavelet which can be used as an adaptive modulation method for demodulating only a layer having a good BER characteristic due to a reception deterioration condition in a land-based or satellite mobile communication system. A modulation method is provided.

[0010]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows the principle of this method. Horizontal axis x
Is the time axis. By utilizing the fact that the discrete wavelet transform using the orthogonal wavelet is reversible conversion of 1-to-1, assigned to one signal point in the sub-band decomposed components, making the composite wave f _0, the modulation of the baseband this Transmit as a signal.

FIG. 1 shows an example in which 16QAM is used for the signal surface, and information of 16 symbols is collectively transmitted by wavelets. In this case, first, the information bits to be transmitted are 4 bits.
By dividing by bits, 16 16QAM signal points are created. Then, those symbols are referred to as subband waves g _-1 to
Assigned as coefficients of g _-4 and f _-4 , wavelet synthesized wave
f ₀ is created and transmitted. On the receiving side, the received wave is wavelet-decomposed and similarly decoded from signal points decomposed into sub-band components. The signal point arrangement is selected according to the relationship between the transmission efficiency and the Euclidean distance between signal points.

Although FIG. 4 shows only the real part, the calculation is performed in the complex domain. The mother wavelet may be anything as long as it is orthogonal. The transmission data needs to be framed by the power of the number of data 2 and if the number is N _w = 2n (n is a positive integer), the subband can be decomposed from the level of −1 to −n.

When the subband decomposition is represented by a continuous signal equation, the following equation is obtained.

[0014]

(Equation 1)

[0015]

(Equation 2)

Here, f ₀ (x) is a composite wave, g _i (x) is a subband wave, and takes an integer value from i = −n to −1, i = −1 is a high frequency component, and −n is a low frequency component. It becomes a frequency component. In addition, f _j (x) (−
(n + 1 ≦ j ≦ −1, j is an integer) is a composite wave of level j−1 or less. When f and g are represented using a scaling function φ (x) and a mother wavelet Ψ (x), the following is obtained.

[0017]

(Equation 3)

[0018]

(Equation 4)

Where k is an integer, and c ^(j) _k , d ^(j)
_k is a coefficient of subband level j, and a transmission symbol is assigned to these. This method is a multicarrier modulation method using a wavelet as a carrier.

The scaling function and the mother wavelet satisfy the following to-scale relationship.

[0021]

(Equation 5)

[0022]

(Equation 6)

Where {p _k } and {q _k } (k is an integer) are
This is a sequence called a scale sequence. If the wavelets are orthogonal, they are called the decomposition sequence {γ _k }, {η
_k } has the following relationship:

[0024]

(Equation 7)

The principle of transmission wave synthesis will be described below. X is used for the time axis at the time of wavelet synthesis and decomposition, and is considered separately from the time axis t when an actual transmission sequence is handled. This is because the equations of decomposition and synthesis using wavelets are expressed by Equations 3 and 4 using x, and it is easier to think as it is than to convert x to t here. Actually, the wavelet synthesized wave and the decomposition wave can be obtained discretely, so only by applying the obtained discrete values to the transmission sequence
A conversion from x to t can be performed. Equation 1, Equation 3,
From Expression 4, when the synthesized wave is represented as a continuous signal, it is as follows.

[0026]

(Equation 8)

Then, a complex signal point is assigned to {d ^(j) _k } and c ^(-n) ₀ . At this time, in the orthogonal wavelet transform as shown in Expression 8, the time resolution changes depending on the subband level, and the lower the lower the frequency, the lower the frequency. Therefore, the number of signal points to be allocated changes according to the level. Specifically, at subband j = −1 level, the number of signal points is halved when the level decreases by N _{w /} 2, and when the level decreases by one, the level (−n + 1) is 2
C ⁽ −n ⁾ ₀ and d ⁽⁻ⁿ⁾ ₀ at the level −n, two each.

The composite wave f ₀ (x) can also be expressed by Equation 3, and if a sequence of coefficients c ⁽⁰⁾ _k of the composite wave is transmitted, {d ^(j) _k }, c ^{(− n)} ₀ information can be obtained.

[0029]

(Equation 9)

The reconstruction algorithm obtained from Equations (2) to (6) discretely gives the synthesis process of Equation (8).

[0031]

(Equation 10)

Here, I is an integer.

FIG. 4 shows a state of synthesis when N _w = 16. However, only the real part is displayed. A transmission sequence {c ⁽⁰⁾ _k } is created from the data symbols {d ^(j) _k } and c ^(-4) _0, but from Equation 10, the synthesis is performed in order from the lower subband level. In the figure, c ^{( -4)} _k and d ^(-4) _k to c ^(-3) _k
C ^(-3) _k , d ^(-3) _k to c ^(-2) _k and c ⁽⁰⁾
_{Find k} .

Then, c ⁽⁰⁾ _k is used as a baseband transmission sequence. The total number of signal points allocated as can be seen from the figure, since equal to N _w total levels -1 to 4, it is possible to transmit data signal point sequence N _w in the transmission sequence of N _w symbols.

The energy of the composite signal f ₀ is given by the following equation from Equation 9.

[0036]

[Equation 11]

However, in this calculation, the following formula indicating the orthogonality of the scaling function was used.

[0038]

(Equation 12) Here, j, k, and l are integers.

[0039]

(Equation 13)

[0040]

[Equation 14]

<U | v> is the inner product of the function and is defined by the following equation.

[0042]

(Equation 15)

Similarly,

[0044]

(Equation 16)

Then, the orthogonality becomes

[0046]

[Equation 17]

[0047]

(Equation 18)

The following equation can be derived from Equation 8 using (j, k, l, and m are integers) and the to-scale relationship.

[0049]

[Equation 19]

Then, from Expressions 11 and 19, the following Expressions are obtained.

[0051]

(Equation 20)

Thus, the relationship between the power of the transmission sequence and the power of the data signal point sequence is represented.

A description will be given of received wave decomposition. In the following, a discrete signal sampled at the receiving baseband is considered.

Assuming that the received signal is c ' ⁽⁰⁾ _k , a transmitted data signal point sequence can be obtained by subjecting this sequence to discrete wavelet decomposition. The following decomposition algorithm is used for the decomposition.

[0055]

(Equation 21)

[0056]

(Equation 22)

Using formulas 21 and 22, d ' ^(j-1) _k of a level lower than level 0 is sequentially obtained, and finally c' ^(-n)
_{Find 0} . Then, demodulation is performed by comparing these subband components with the original signal point arrangement.

As described above, although the discrete wavelet transform is used for the synthesis of the transmission wave from the subband and the decomposition of the subband from the reception wave, the mother wavelet is not actually used. The calculation is relatively easy because only the algebraic calculation of the decomposition sequence is required.

Next, the hierarchical structure according to the present invention will be described. The signal point constellation of the signals assigned to c ⁽⁻ⁿ⁾ ₀ and d ^(j) _k is determined by the relationship between the energy assigned to one bit and the transmission efficiency (bit / symbol), as in normal modulation. Further, by changing the modulation method for each level, the distance between signal points can be set flexibly.

From Equation 20, when the same signal point constellation is applied to all subbands, in the transmission sequence c ^{( 0)} _k ,
The lower the sub-band level, the more energy per symbol is relatively allocated. In other words, even if the signal point constellation size is the same, if the level of the sub-band is decreased by one, the energy per symbol in the transmission sequence is doubled. As a result, gains different by 3 dB are obtained for each subband, and hierarchical transmission can be realized. Note that the depth of the hierarchy is a power multiplier of N _w .

A case is considered where a transmission signal is not assigned to a certain subband level and is set to 0. At this time, the transmission efficiency decreases because information that can be transmitted with the same number of transmission symbols decreases, but the relative energy of other subband levels in the transmission symbol increases according to Equation 20, so that
The BER characteristics are generally improved. By allocating or not allocating data only to a certain subband level in this way, the transmission efficiency can be flexibly set, and the hierarchical BER characteristic that has a trade-off relationship therewith can be flexibly set. it can.

[0061]

DESCRIPTION OF THE PREFERRED EMBODIMENTS Embodiments of the present invention will be described below in detail. The first embodiment will be described below. In the following, it is assumed that 16QAM of the same size is applied to all subbands and transmission data symbol generation probabilities are equal. As shown in FIG. 1, the signal point arrangement is Gray coded 16QAM. If the minimum Euclidean distance of the code is a, the average energy s ² of the signal generated from the signal surface becomes the following equation.

[0062]

(Equation 23)

General Uncoded 1 with Equivalent Transmission Efficiency
In the case of 6QAM (hereinafter referred to as uncoded 16QAM) transmission, this is the average energy of the transmission signal. When data to be transmitted is assigned to all subbands,
The average energy of the transmission sequence by wavelet synthesis is given by the following equation.

[0064]

(Equation 24)

From Equations 23 and 24, when the average energy of the signal is 1, the square of the relative Euclidean distance Δ2 at the subband level, and the uncoded 16QA
The gain for M is as shown in Table 1 when N _w = 16.

[0066]

[Table 1]

As described above, even if signal points having the same size are arranged in all subbands, the energy allocation per symbol in the transmission sequence is different, so that the effective 2Δ is doubled for each subband. different.

As the orthogonal wavelets to be used, a Haar function, which has a small support and is easy to calculate at the time of synthesis and decomposition, and a function of DaubechiesN = 2 were used. At this time, in the case of the Haar function, the to-scale sequence is expressed by the following equation.

[0069]

(Equation 25)

When DaubechiesN = 2, it is expressed by the following equation.

[0071]

(Equation 26)

According to Equation 7, the decomposition sequence is represented by the following equation in the case of the Haar function.

[0073]

[Equation 27]

When DaubechiesN = 2, it is represented by the following equation.

[0075]

[Equation 28]

Other p, q, fl, and j are all 0, and equations 10, 21, and 22 end where appropriate.

Considering an equivalent low-pass system as shown in FIG. 4, BER characteristics in an AWGN environment were calculated. Using Haar function in the mother wavelet, wavelet synthesis, the frame length N _w of at decomposition and 16 were transmitting the frame as a unit. It was also assumed that the receiver synchronization was perfect.

FIG. 5 shows the BER characteristics for each subband level and for the whole. The horizontal axis of the figure is the uncoded 16
Was the E _b / N ₀ at the time of QAM transmission. Note that the subband level -4 was evaluated collectively because the energies of c ^(-4) ₀ and d ^(-4) ₀ are equal. As shown in FIG.
ER is different, and at level-4, as shown in Table 1, uncoded 1
A gain of about 5 dB is obtained as compared with the 6QAM theoretical value. However, the number of transmission symbols at subband level -4 is / of the total, and 全体 of the total is transmission at subband level −1.
The characteristic deteriorates by about 4 dB from the theoretical value.

As described above, since the energy of the transmission signal is concentrated on the low sub-band level, the overall characteristics are degraded. However, according to this method, a hierarchical BER characteristic is obtained.
It is suitable for transmission when hierarchical importance is given to information sources.

Second Embodiment If the transmission efficiency can be made lower than that of uncoded 16QAM, the present system can be set flexibly. As an example, consider a case where data is allocated only to subband levels -1 and -2, and all other levels are set to 0. At this time, the transmission efficiency is the same as that of coded 16QAM of rate 3/4.
Then, from Equation 20, the relative energy per symbol at the -1 and -2 levels increases, and the characteristics are improved. When the gain is calculated in the same manner as in Table 1, as shown in Table 2, the level -1 is zero. Same characteristics as coded 16QAM, level-2
However, 3 dB better characteristics can be obtained therefrom.

[0081]

[Table 2]

FIG. 6 shows the calculation results of the BER characteristics. In the figure, the characteristic of level-1 and the theoretical value of uncoded 16QAM overlap, and the characteristic almost as shown in Table 2 is obtained.
Of course, there are codes with the same transmission efficiency, that is, better BER characteristics with the same frequency utilization efficiency, but in this method, the modulation itself can obtain a stepwise BER characteristic without the need for complicated coding and decoding operations. There are features.

As shown in this example, by allocating or not allocating data only to a certain subband level, the transmission efficiency can be flexibly set.
Since a 3 dB difference in BER characteristic occurs for each level,
This scheme can be considered as a kind of UEP code. By changing the modulation method for each subband level, it is also possible to adjust the difference in BER characteristics for each level.

In the third embodiment, it is assumed that synchronization is achieved by inserting a pilot symbol into a transmission symbol sequence, and at the same time, a computer simulation system that performs uniform fading compensation using the pilot symbol is considered. FIG. 7 shows a system under a fading environment, and FIG. 8 shows a frame configuration of a transmission sequence.

This transmission frame is a framing different from the wavelet decomposition and synthesis frames.
Means that the wavelet frame is interleaved in the data symbol of.

Nw is 16, and the symbol transmission rate is 16 Ksymbol / se
c and synchronization is assumed to be perfect. The fading is gradual Rayleigh fading at the maximum Doppler frequency f _D = 80 Hz (f _D T _s = 1/200, T _s is the symbol period),
Symbol interleaving with a width of 16 and a depth of 15 and a compensation method using FFT were applied. The pilot symbol used for fading compensation uses point A in FIG. 3, the pilot symbol interval is 16, and the number of pilot symbols used for compensation is 3
There were two.

FIG. 9 shows the calculation results. Like the AWGN environment, the difference in the BER of approximately one by 3dB in each subband per level occurs, the level-4 appeared how the progressively characteristics are improved with respect to E _b = N ₀ compared to other levels I have. This means that one level-4 symbol is the transmission time series
Since c ⁽⁰⁾ _k is distributed over 16 symbols, it is considered that interleaving works effectively and the effect of fading is further suppressed. Further, in the fading compensation method, since a deterioration of about 2.2 dB occurs including the insertion of the pilot symbol, the overall BER characteristic is deteriorated by about 7 to 8 dB as compared with the theoretical value of uncoded 16QAM.

Thus, as in FIG. 6, transmission data is allocated only to subband levels -1 and -2, and BER under fading is calculated. FIG. 10 shows the result. In this case, level -1 is approximately 3 from the uncoded 16QAM theoretical value.
Deterioration of dB, level-2 indicates a BER characteristic of about the theoretical value. Since one symbol at level-2 is only dispersed in four symbols in the transmission time series, it can be seen that the effect of interleaving is not obtained as compared with level-4 in FIG.

As described above, a hierarchical BER characteristic can be obtained even in a fading environment, and it can be seen that the present invention is applicable to mobile communication and the like.

The present invention has been described based on the embodiments shown in the drawings. However, the present invention is not limited to the above-described embodiments, but may be implemented in any manner unless the structure described in the claims is changed. can do.

[0062]

As described above, according to the present invention, it is possible to: 1. Create a transmission sequence in which two or more hierarchical BER characteristics can be obtained without performing encoding. 2. UEP can be realized without requiring a special signal point arrangement. 3. The transmission efficiency and the BER characteristic in a trade-off relationship therewith can be flexibly set. 4. There is no energy loss in the modulation method itself. Therefore, it is easy to extend the transmission method, for example, by further performing encoding using the present modulation method. And so on.

[Brief description of the drawings]

FIG. 1 is a conceptual diagram showing a transmission principle using a discrete wavelet of the present invention.

FIG. 2 is a conceptual diagram illustrating transmission wave combining according to the present invention.

FIG. 3 is a schematic diagram showing an arrangement of signal points of Gray-coded 16QAM of the present invention.

FIG. 4 is a block diagram showing a system configuration according to the first embodiment of the present invention.

FIG. 5 is a characteristic diagram showing a BER characteristic under an AWGN environment of the present invention.

FIG. 6 is a characteristic diagram showing BER characteristics when transmitting only subband levels -1 and -2 of the present invention.

FIG. 7 is a block diagram illustrating a system configuration according to a third embodiment of the present invention.

FIG. 8 is a schematic diagram illustrating a transmission frame configuration according to a second embodiment of the present invention.

FIG. 9: BE under mild fading environment of the present invention
It is a characteristic view showing R characteristic.

FIG. 10 is a characteristic diagram showing BER characteristics when transmitting only subband levels −1 and −2 of the present invention.

FIG. 11 is a block diagram showing a configuration of a conventional concatenated code encoder.

FIG. 12 is a conceptual diagram showing a conventional arrangement state of non-uniform signal points.

Claims (1)

(57) [Claims] 1. An information transmission method using orthogonal wavelets.
In the method , when performing unequal error protection (hereinafter referred to as UEP) on transmission information, support is provided using orthogonal wavelets.
Without using all of the components that are decomposed into subbands,
Assign signal points only to subbands selected from the band group.
Ri hit by Rukoto, average bit error rate (hereinafter BER
A state was different et according to the importance of the referred) characteristic information and
Create a synthesized wave f ₀ from all subbands groups, the composite wave
Information transmission method using orthogonal wavelets, characterized in that the f ₀ as modulated and transmitted.