JPH042026B2 - - Google Patents

Description

[Detailed Description of the Invention] <3.1> Field of the Invention The present invention provides a probability density function (p .
The present invention relates to an optimal receiver for a synchronous system that improves transmission characteristics on the receiving side alone by analyzing and understanding fd) in advance and performing a maximum likelihood test using it as a parameter.

<3.2> Background of the Invention When considering the influence of noise on digital signal transmission systems or improvements thereto, Gaussian noise has conventionally been considered in most cases.

On the other hand, many of the artificial noises that are noticeable these days, especially in urban areas, have impulse-like characteristics, and it is unreasonable to treat them as Gaussian noise. However, impulsive noise has extremely complex statistical properties, and although there are some studies on the influence of impulsive noise on transmission characteristics (References 1, 2, and 3), it is difficult to improve its characteristics. There has not been much study on this.

Bello (Reference 4) and the present inventors (Reference 5) have analyzed the case where a nonlinear device is inserted in the middle of a transmission system as a measure to improve characteristics against impulsive noise. However, little consideration has been given to optimal receivers that operate optimally against impulsive noise.

<3.3> Purpose of the invention The purpose of the present invention is to use Middleton (Reference 6), which is known as a statistical model for impulsive noise.
Introducing the class A type impulsive noise model of
In a synchronous optimal receiver that performs a maximum likelihood test,
Linear calculations and 2 for input and synchronization signal waves
The object of the present invention is to provide an optimal receiver that can obtain good reception characteristics through processing that can be easily implemented using a microprocessor, such as multiplication operations.

<3.4> Key points of the invention In order to achieve the above object, this invention is expressed by formula (2.1), which will be described in detail below.
The probability density function P(z) of Middleton's class A type impulsive noise model is calculated by the coefficient
A ^m /m! Under the condition that is sufficiently small,
As shown in equation (2.2), in terms up to m=M≧3
Approximating P〓(z), and further considering the distribution consisting of the maximum value of its (M+1) terms for this P〓(z),
It is characterized in that it is approximated by P^(z) shown in equations (2 and 3), and this simplified P^(z) is applied to the likelihood ratio test formula. In this case, the processing for sample values is limited to linear or square operations, and the parameters obtained from the statistical properties of noise become constant terms in the calculation process for sample values. 8), and the calculation process can be easily realized using a microprocessor.

<3.5> Theoretical background of the structure of the invention <3.5.1> Optimal receiver using likelihood ratio test In general, the probability density function of the target noise (p.
df) is given by P(z), the optimal synchronous receiver uses the binary synchronizing signals S ₁ (t), S ₂ (t) and the received signal x during the time width T of 1 data bit.
It is well known that this can be achieved by sampling (t) N times and performing a maximum likelihood test using the operation expressed by equation (1.1).

Here, Λ(〓) is the likelihood ratio; when Λ is less than 1, hypothesis H ₁ (S ₁ was sent) is selected, and when Λ is greater than or equal to 1, hypothesis H ₂ (S ₂ was sent) is selected. Equation (1.1) shows that the following is selected. Also, xn is the nth sample value of the received signal wave, S ₁ n・S ₂ n is the nth sample value of the synchronization signal, and Xn=S ₁ n+Zn(signal is S ₁ )=S ₂ n+Zn( The relationship between the signals is S ₂ )...(1・2). Here, Zn is a random variable representing noise.

<3.5.2> Simplification of Middleton's class A noise model Impulsive noise is classified into class A, class B, and class C according to its bandwidth in Middleton's statistical model. Class A has a noise bandwidth narrower than the front end bandwidth of the receiver, Class B has a wider noise bandwidth, and Class C has both. In the optimal receiver according to the present invention, noise belonging to class A is introduced as an impulsive noise model.

The probability density function (p, d, f) of class A type impulsive noise is expressed by the following equation (2.1).

Here Z is the noise amplitude normalized by the effective value (√ ² _G + _2A ). However, δ ² _G is Gaussian noise power, and Ω _2A is impulse noise power. Also A
is called the impulse index and is the product of the average number of impulse noises incident on the receiver per unit time and the average duration of the impulses. Furthermore, if ′=δ ² _G /Ω _2A , then δ ² _n =m/A+′/1+′.

Equation (2.1) is complicated to actually apply to the configuration of an optimal receiver, including a term where m is infinite, and is physically difficult to realize.

Therefore, the formula (2.1) is A ^m /m! Noting that it has the form of a sum of Gaussian distributions ^weighted by By adding the condition that is sufficiently small (approximately 10 ^-5 or less), this equation (2.1) can be modified in terms up to m=M≧3.
Approximate it as P〓(z).

Furthermore, considering the distribution consisting of the maximum value of M+1 terms in equation (2.2), it is shown in equation (2.3).
Let it be P^(z).

<3.5.3> Application of the simplified formula to the likelihood ratio test formula When performing the likelihood ratio test to realize an optimal receiver, the probability density function (p・d・f) of impulsive noise is Ideally, P(z) of (2.1) should be applied. However, as already mentioned, it is difficult to actually physically realize a receiver because it includes terms where m is infinite.

Therefore, by applying the previously obtained approximate pdfP^(z) shown in Equation (2.3), we will rearrange the likelihood ratio test formula in Equation (1.1). The likelihood ratio test formula when P^(z) is applied is shown in the following formula (3.1).

Taking the logarithm of both sides of this, we get the following formula (3.2)
becomes.

y=logΛ(〓) Here, if P^(z)=√2πe ^A P^, the above equation (3.2) can be rewritten as the following equation (3.4).

Further modification of this results in the following.

y=logP( _x1 - _S21 )xP( _x2 - _S22 )x...xP
(x _N −S _2N )/P(x ₁ −S ₁₁ )xP(x ₂ −S ₁₂ )x…xP(x _N
−S _1N ) H ₁ 〓 H ₂ 0 = logP(x ₁ −S ₂₁ )/P(x ₁ −S ₁₁ )+l
ogP(x ₂ −S ₂₂ )/P(x ₂ −S ₁₂ )+…+logP^(x _N −S _2N
)/P(x _N −S _1N )H ₁ 〓 H ₂ 0 = _N 〓 ⁿ⁼¹ logP(xn−S ₂ n)/P(xn−S ₁ n)H ₁ 〓 H ₂ 0 = _N 〓 ^{n= 1} {logP^(xn−S ₂ n)−P^(xn−S ₁ n)}H ₁ 〓 H ₂ 0 ……(3・4) P^(z)=√2e ^A P^(z) Therefore, the formula (2・
3), P^(z) becomes as follows.

Considering that the logarithmic function is a monotonically increasing function, by taking the logarithm of the equation (3.5), it can be rewritten as the following equation (3.7).

Here, it can be seen that the coefficients Km and Lm are constant terms that are uniquely determined once the parameters of the statistical noise model are determined. Therefore, by inserting the above equation (3.7) into the equation (3.4) obtained by transforming the likelihood ratio test equation, the following relational expression is obtained.

y= _N 〓 ⁿ⁼¹ [ _N 〓 ⁿ⁼¹ _N 〓 ⁿ⁼¹ {Km(xn-S ₂ m) ² +Lm} − _N 〓 ⁿ⁼¹ _N 〓 ⁿ⁼¹ {Km(xn-S ₁ n ) ² +Lm}〓H ₁ 〓 H ₂ 0...(3・8) In this likelihood ratio test formula (3・8),
As explained above, Km and Lm are constant terms that are uniquely determined when the parameters δm and A of the statistical noise model are determined. In addition, the sample value xn of the received signal wave, the sample value S ₁ n・S ₂ n of the synchronization signal
It is easy to see that it can be processed using only linear operations and squaring operations. Therefore, this formula (3・
An optimal receiver based on 8) can be easily constructed using a microprocessor.

<3.6> Description of Embodiments FIG. 1 shows the configuration of an optimal receiver according to the present invention. Reception input x(t) is A/D conversion circuit 1
The sample value xn is sampled and digitized by the microprocessor (hereinafter referred to as CPU) 3 and input to the IN terminal.

The synchronous clock CK is a clock that indicates the transmission speed.
The period is equal to the 1-bit time width T of the transmitted data. This synchronous clock CK is the interrupt pin of CPU3.
Applied to INT ₂ and frequency multiplier circuit 2
The signal is inputted into the system and converted to a frequency N times higher. The output of the multiplier circuit 2 is applied to the interrupt terminal INT ₁ of the CPU 3 and is also applied as a timing signal to the A/D conversion circuit 1. In other words, receive input x
(t) is synchronized with the output of the multiplier circuit 2 at a speed N times the synchronous clock CK (N times the data transmission speed).
sampled). This sampling timing signal is also applied to the interrupt terminal INT ₁ of the CPU 3.

The CPU 3 executes the maximum likelihood test process described below in accordance with the instructions stored in the program memory 5 and with reference to the data in the data memory 4.
A signal indicating the test result is output to terminal RD.

The data memory 4 includes a noise parameter setting area 41 and a waveform data setting area 42 for synchronizing signals S ₁ and S ₂ . In the noise parameter area setting 41, specific values of the above-mentioned impulse index A and impulse noise power ratio' are set in advance. In addition, _the waveform data _setting area 42 contains data S ₁ n, S ₂ n (n= 1, 2,...
N) is set in advance in the form of a table.

FIG. 2 is a flowchart showing the processing contents of the maximum likelihood test executed by the CPU 3. The operation of the CPU 3 will be explained below in order according to this figure.

As an initial process at the start of operation, the upper limit number M of m and the coefficients Km and Lm (m = 0, 1, 2, ..., M) in the above-mentioned likelihood ratio test formula (3.8) are determined based on the noise parameters. demand. That is, first, interrupts are prohibited, and the above-mentioned impulse index A is read from the noise parameter setting area 41 of the data memory 4 (step 201). Next, based on that value A,
A ^m /m! Find the smallest integer m that makes 10 ^-5 or less, and store that integer as M (step 202). Next, based on the impulse index A and the impulse noise power ratio' read from the area 41 of the memory 4, calculate the coefficients Km and Lm mentioned above for m=0, 1, 2, ..., M, respectively, and store them. (Step 203). After the above processing,
Enable INT ₁ and INT ₂ interrupts and wait for the interrupt (step 204).

When an interrupt signal is applied to terminal INT ₁ , first
The sampling number counter n in the CPU 3 is incremented (step 206). Next, the output of the A/D conversion circuit 1 at that time, that is, the sample value xn of the received input x(t) is read and stored in a predetermined register (step 207). Next, data S _{1 n} and S _{2 n are read from the waveform data table of the synchronizing signals S 1 and S 2 in} the waveform data setting area 42, using the _coefficient value n of the sampling number counter as an argument (step 208). .

Next, based on xn, S ₁ n, and S ₂ n read as described above, C=(xn-S ₂ n) ² D=(xn-S ₁ n) ² is calculated (step 209). Next, the calculated C,
Em=Km.C+Lm Fm=Km.D+Lm are calculated for m=0, 1, 2, . . . , M, respectively, based on D and the coefficients Km and Lm obtained in the previous step 203 (step 210). Next, the difference between the calculated maximum value of Em and the maximum value of Fm, that is, yn = Max (E ₀ , E ₁ , E ₂ , ...E _M ) - Max (F ₀ , F ₁ , F ₂ , ...F _M ) and store this yn in a predetermined register (step 211).

The above is the processing in response to one interrupt INT ₁ , and this processing is executed every time the interrupt signal INT ₁ occurs, and as a result, data y ₁ , y ₂ , y _{3 ,} . . . are sequentially stored. When the count value of the sampling number counter n reaches the N value, an interrupt signal _INT2 is applied to the CPU 3, as is clear from the operation of the multiplier circuit 2 described above.

When the interrupt signal INT ₂ is applied, the interrupt is first
Inhibit INT ₁ (step 212). Next, except for the first interrupt INT ₂ after the start of operation, y ₁ , which has been accumulated by executing step 211 N times, is
The _total value ^of y ₂ , y _{3 ,} . And when y≧0, hypothesis H ₂
(S ₂ was sent) is adopted, and when y<0, the hypothesis
H ₁ (S ₁ was sent) is adopted, and the judgment result is output to the output terminal RD (steps 216, 217,
218). After that, the sampling number counter n
At the same time, the interrupt INT ₁ is cleared and the interrupt is set to wait (step 219). Repeat the above process.

<3.7> Effects of the invention The optimal receiver according to the invention statistically grasps the properties of impulsive noise according to Middleton's class A noise model, and uses the parameters in the form of operating parameters of a maximum likelihood test circuit. This method operates by providing feedback on the receiving side, and can improve transmission characteristics only on the receiving side.

The approximate formula for Middleton's class A type noise model is its coefficient Am/m! is sufficiently small (e.g.
10 ^-5 or less) and up to M-order terms of 3 or more, the range of impulse index A to which the approximation formula can be applied expands (for example, the approximation formula can be applied even when A is 0.25 or more.) Maximum likelihood test By adopting equations (3 and 8) as equations, calculations on the CPU are limited to linear and square calculations, and the calculation routine for each sampling of received data is simple, so it can be used on small-scale and low-speed CPUs.
But it is practical.

The feedback of the statistical parameters of the noise is
Only the impulse index A and the impulse noise power ratio' are required, making it easy to respond to changes in the noise state.

The maximum likelihood test formula of this invention has no restrictions on the size of the SN ratio, so it operates as an optimal receiver regardless of the size of the SN ratio, so it is more advantageous than the LOBD method (optimal only in areas where the SN ratio is small). It is.

The present invention operates not only in two-phase PSK (phase shift keying) but also in binary FSK (frequency shift keying) if a synchronized clock can be obtained, and can be applied to a wide range of modulation and demodulation systems.

<References> (1) REZtemer: “Character Error
Probabilities for M-ary Signaling in
“Impulsive Noise Emvironments” IEEE
Trans.Commun.Vol.COM−15, No.1, P.32,
February 1967. (2) PABello and R. Espsito: “A New
Method for Calculating Probabilities of
Errors Due to Impulsive Noise” IEEE
Trans.Commun.Vol.COM−17, No.3, P.368,
June 1969. (3) Hiroshi Kusao, Ikuo Oka, Norihiko Morinaga, and Toshihiko Namekawa: “Error rate characteristics of PSK signals under impulsive electromagnetic interference” Information Theory and Its Applications Research Series 1981
December (4) A.Bello and R.Esposito: “Error
Probabilities Due to Impulsive Noise in
Linear and Hard−Limited DPSK
Systems” IEEE Trans.Commun.Vol.COM
-19, No. 1, P. 14, February 1971. (5) Hiroshi Kusao, Ikuo Oka, Norihiko Morinaga, Toshihiko Namekawa: “PSK signal transmission characteristics in a hard limiter repeater under impulsive electromagnetic interference” IEICE Tech. Information
EMCJ81−77 January 1982 (6) D.Middleton: “Statistical−Physical
Models of Electromagnetic Interference”
IEEE Trans.Electoromag.Compat, Vol.1
EMC-19, No. 3, P. 106, August 1977.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing the main part configuration of an optimal receiver according to the present invention, and FIG.
7 is a flowchart showing the contents of maximum likelihood test processing executed by the CPU. 1...A/D conversion circuit, 2...Frequency multiplier circuit, 3...CPU (microprocessor), 4...
Data memory, 5...program memory.

Claims (1)

[Claims] 1. In order to improve the influence of impulsive noise on a digital signal transmission system, the probability density function of the target noise is known in advance, and the received signal is In an optimal receiver that samples x(t) and binary synchronization signals S ₁ (t) and S ₂ (t) N times and performs a maximum likelihood test using the operation expressed in equation (1.1), [Here, Λ(〓) is the likelihood ratio, and when Λ is smaller than 1, the hypothesis H ₁ (S ₁ was sent) is
Equation (1.1) shows that in the above cases, hypothesis H ₂ (S ₂ was sent) is selected. Also, xn is the nth sample value of the received signal wave, S ₁ n · S ₂ n is the nth sample value of the synchronization signal, xn = S ₁ n + Zn (signal is S ₁ ) S ₂ n + Zn (signal is S ₂ ). Zn is a random variable representing noise. ] Introducing Middleton's class A type impulse noise model expressed by equation (2.1) as a statistical model of noise, [Here, Z is the noise amplitude normalized by the effective value (√ ² _G + _2A ). However, δ ² _G is Gaussian noise power,
Ω _2A is the impulse noise power. A is the impulse index, which is the product of the average number of impulse noises incident on the receiver per unit time and the average duration of the impulses. Furthermore, if ′=δ ² _G /Ω _2A , then δ ² _n =m/A+′/1+′. ] When applying the probability density function (pdf) of the noise represented by P(z) as a random variable to the above maximum likelihood test formula, the coefficient A ^m /m! Under the condition that is sufficiently small, as shown in equation (2.2),
Approximate as P〓(z) with terms up to m=M≧3, This approximation formula P〓(z) is further approximated by a distribution P^(z) consisting of the maximum value of its (M+1) terms, as shown in equations (2 and 3), For this simplified approximation formula P^(z), apply the maximum likelihood test formula converted from formula (1.1) to formula (3.8), and obtain y= _N 〓 ⁿ⁼¹ [ Max ^m=0,1,2 {Km(xn-S ₂ n) ² +Lm} − Max ^m=0,1,2 {Km(xn-S ₁ n) ² +Lm}〕H ₁ 〓 H ₂ 0 … (3・8) [However, Km=−(1/2δ ² _n L _n =log(A ^m /m!・δm).] This equation (3・8) is calculated by a microprocessor. Optimal receiver for impulsive noise characterized by: