JPH042025B2 - - 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 reception method 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
It is an object of the present invention to provide an optimal reception method that allows good reception characteristics to be obtained through processing that is easy to implement in terms of physical and circuit aspects, 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 expressed as m as shown in equation (2.2) under the condition that the impulse index A is small (when impulsiveness is significant) Approximating P〓(z) with the terms up to =2, and further considering the distribution consisting of the maximum value of the three terms for this P〓(z), P^(z) shown in equations (2 and 3) It is characterized by approximating and applying this simplified P^(z) 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 is characterized by being able to easily realize an arithmetic circuit.

<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 noise bandwidth wider than the bandwidth of the front end of the receiver, and class C has both. In the optimal reception system 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 _G =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! By focusing on the fact that it has the form of a sum of Gaussian distributions weighted by
This formula (2・1) is expressed as P〓(z) in terms up to m=2.
Approximate it as

Here, δ ² ₀ =′/1+′ δ ² ₁ =1/A+′/1+′ δ ² ₂ =2/A+′/1+′.

Furthermore, considering the distribution consisting of the maximum values of the three terms in equation (2.2), P^ shown in equation (2.3)
(z).

That is, It is. Here, a and b (>0) satisfy P^ ₀ (a)=P^ ₁ (a) P^ ₁ (b)=P^ ₂ (b), and the relationship of the following equation (2.5) is satisfied. It is in.

<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 mentioned above, it is difficult to actually physically realize a receiver because it includes terms where m is infinite.

Therefore, formula (2.3) or formula (2.4)
Let's organize the likelihood ratio test formula of equation (1.1) by applying the approximation pdfP^(z) obtained earlier shown in . 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 we set P^(z)=√2e ^A P(z),
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) According to (2.4), 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 [Max ^m=0,1,2 {Km(xn-S ₂ n) ² +Lm} − Max ^m=0,1,2 {Km(xn-S ₁ n) ² +Ln} ]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・
The optimal receiver based on 8) can be easily constructed physically and circuit-wise.

<3.6> Description of Embodiments FIG. 1 shows the basic configuration of an optimal receiver to which the present invention is applied. The configuration of this figure is the expansion of the theoretical formula (3.8) described in detail earlier into an arithmetic circuit, and includes 9 adder circuits, 2 squaring circuits, 6 multiplier circuits, and 2 multiplication circuits. Maximum value detection circuit
It consists of one statistical circuit, which inputs xn・S ₁ n・S ₂ n and performs linear calculation and square calculation. If the resulting output y is smaller than 0, the hypothesis H ₁ (S ₁ is sent ), and if y is greater than or equal to 0, then hypothesis H ₂ (S ₂ was sent) is selected.

Received signal wave xn and synchronization signal wave each sampled at a rate N times the data transmission rate
S ₁ n and S ₂ n are applied to adder circuit 1 and adder circuit 2, respectively. In addition circuit 1, (xn−
S ₂ n) is calculated, and in the adder circuit 2, (xn−
S ₁ n) is calculated. The outputs of adder circuits 1 and 2 are squared in squaring circuits 3 and 4, respectively, and (xn−
S ₂ n) ² and (xn−S ₁ n) ² are output from the square circuits 3 and 4, respectively.

The multiplier circuits 50 and 80 are set with a coefficient K ₀ =-1/2δ ² ₀ , and the adder circuits 60 and 90 are set with a coefficient L ₀ =log.
(1/δ ₀ ) is set. Also, the multiplication circuit 5
1 and 81 are set to a coefficient K ₁ =-1/2δ ² ₁ , and adder circuits 61 and 91 are set to a coefficient L ₁ =log(A/δ ₁ ). Further, a coefficient K ₂ =−1/2δ 2 2 is set in the multiplication circuits 52 and 82, and a coefficient K 2 =−1/2δ ² ₂ is set in the multiplication circuits 52 and 82, and
2 has a coefficient L ₂ =log(A ² /2δ ₂ ) set.

A signal {K ₀ (xn−S ₂ n) ² +L ₀ } is calculated from the output of the squaring circuit 3 by the multiplication circuit 50 and the addition circuit 60 . Furthermore, the signal {K ₁ (xn−S ₂ n) ² +L ₁ } is calculated by the multiplication circuit 51 and the addition circuit 61.
Further, the signal {K ₂ (xn−S ₂ n) ² +L ₂ } is calculated by the multiplication circuit 52 and the addition circuit 62. These three signals are input to the maximum value detection circuit 7, and the maximum value among them is extracted.

Similarly, by the multiplication circuit 80 and addition circuit 90,
Signal from the output of the square circuit 4 {K ₀ (xn−S ₁ n) ² +L ₀ }
is calculated. Also, a multiplication circuit 81 and an addition circuit 91
Accordingly, the signal {K ₁ (xn−S ₁ n) ² +L ₁ } is calculated. Further, the signal {K ₂ (xn−S ₁ n) ² +L ₂ } is calculated by the multiplication circuit 82 and the addition circuit 92. These three signals are input to the maximum value detection circuit 10, and the maximum value among them is extracted.

The difference between the outputs of the maximum value detection circuits 7 and 10 is calculated in the adder circuit 11, and the difference signal is sent to the summation circuit 1.
2 and is accumulated. A determination output is taken out from this summation circuit 12 for each 1-bit data length, and it is determined whether the output is smaller than 0 or greater than 0, and it is verified whether the signal S ₁ or the signal S ₂ has been sent.

Here, the coefficients K ₀ , K ₁ , K ₂ , L ₀ , L ₁ , and L ₂ are uniquely determined if the parameters ′ and A of the impulsive noise pdf are known in advance, and It is easier to set it appropriately than by adjusting the circuit.

FIGS. 2 and 3 show a more specific configuration of the optimal receiver shown in FIG. 1.

As shown in FIG. 2, the adder circuits 1, 2, and 11 are
This can be easily achieved using an OP amplifier (operational amplifier). Further, the multiplication circuit 50 and the addition circuit 60 are also connected to the third
As shown in the figure, it can be easily configured using an OP amplifier. In FIG. 3, the multiplication circuit 5
The coefficient K ₀ of 0 can be easily set by adjusting the gain of the OP amplifier with the variable resistor VR ₁ . Further, the coefficient L ₀ of the adder circuit 60 can be easily set by adjusting one input voltage of the OP amplifier with the variable resistor VR ₂ . Note that the circuits 51 and 61, the circuits 52 and 62, and the circuit 80
and 90, circuits 81 and 91, and circuits 82 and 92 are also the third
It is configured as shown in the figure.

Further, as shown in FIG. 2, maximum value detection circuits 7 and 10 can be easily constructed using three diodes each. In addition, the summing circuit 12 can be replaced with an integrating circuit, and as shown in FIG.
This can be easily achieved using an integrating circuit. This integrating circuit 12
A maximum likelihood test can be performed by binarizing the output by a level discrimination circuit 13 using the OV line as a reference.

<3.7> Effects of the invention The optimal reception method 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.

In the approximation formula for Middleton's class A noise model, the impulse index A is small (for example, A<
0.25), it is possible to apply the approximation formula up to the term m = 2, and the calculation is linear and
Since it can be limited to multiplication operations, a maximum likelihood test circuit can be realized using a simple analog circuit (a combination of OP amplifiers).

Since Equation (3.8) is adopted as the maximum likelihood test formula, it operates as an optimal receiver regardless of the size of the SN ratio, and is more practical than the LOBD method (which can be said to be an optimal receiver only in areas where the SN ratio is small). It is superior.

The circuit for the maximum likelihood test is an analog calculation circuit, which has few restrictions on calculation speed and can handle fairly high carrier frequency levels. As a result, there are advantages such as the ability to omit a frequency conversion stage before being input to the optimum receiver.

Noise feedback can be provided in the form of OP amp gain adjustment and OP amp summing input voltage adjustment. This is a simple adjustment/setting.

The maximum likelihood test circuit according to the present invention can operate not only with two-phase PSK (phase shift keying) but also with binary FSK (frequency shift keying) if a synchronized signal wave can be obtained, and can be applied to a wide range of modulation and demodulation methods. can.

<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 type 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 basic configuration of the maximum likelihood test circuit, which is the main part of an optimal receiver to which the present invention is applied; FIG. 2 is a block diagram showing the configuration of FIG. 1 in more detail; FIG. 3 is a block diagram showing a specific example of some of the circuits in FIG. 2. 1, 2, 60, 61, 62, 90, 91, 9
2, 11... Addition circuit, 3, 4... Square circuit, 5
0, 51, 52, 80, 81, 82... multiplication circuit, 7, 10... maximum value detection circuit, 12... totalization circuit.

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 reception method in which x(t) and binary synchronization signals S ₁ (t) and S ₂ (t) are sampled N times and a maximum likelihood test is performed 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, 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 equation, under the condition that the impulse index A is small, equation (2.2) is As shown, m=
Approximating P〓(z) with terms up to 2, As shown in equations (2 and 3), this approximate formula P〓(z) is further transformed into a distribution P^ consisting of the maximum value of the three terms.
Approximate by (z), 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 ) Lm=log(Am/ ^m !・δm). ] An optimal reception method for impulsive noise characterized by extracting a signal by performing this maximum likelihood test.