WO2002052792A1

WO2002052792A1 - Method for evaluating channel performance based on moment

Info

Publication number: WO2002052792A1
Application number: PCT/KR2000/001517
Authority: WO
Inventors: In-Kwan Hwang
Original assignee: In-Kwan Hwang
Priority date: 2000-12-22
Filing date: 2000-12-22
Publication date: 2002-07-04

Abstract

A method for evaluating channel performance of a system affected by a noise, e.g., a communication system includes the steps of : a) calculating a discrete probability density function of a signal received at a receiver through a channel based on moments of the received signal or moments of a phase of the received signal; and b) calculating an error rate of the channel based on the discrete probability density function.

Description

METHOD FOR EVALUATING CHANNEL PERFORMANCE BASED ON MOMENT

Technical Field

The present invention relates to a method for evaluating channel performance of a communication system; and, more particularly, to a method of evaluating channel performance based on moments of an output signal for overcoming complexity and computer run time of conventional methods.

Description of the Prior Art

A Monte-Carlo method, which is generally used in evaluating channel performance of digital communication systems, carries out many calculations in a high-speed transmission system such as a digital TV broadcasting system or an asynchronous transfer mode (hereinafter, referred to as an ATM) . For example, when evaluating an error rate of 10^-9, 10¹⁰ or more than calculations should be performed.

Therefore, a detailed analysis of a substantial communication system is impossible due to a limitation of computer processing time, so the channel performance is approximately evaluated by simply modeling the communication system.

To overcome the above-referenced problem, many theoretical research results are proposed and published, e.g., an importance sampling method and an improved importance sampling, but fundamental problems are not solved yet.

An evaluation method based on a central moment

(hereinafter, referred to as a "central moment method") is proposed as another method to solve the problem. One of the central moment methods titled "Method for evaluating channel performance of a digital communication system" was filed with the Korean Industrial Property Office (KIPO) by the same applicant and registered (Patent No. 264687). However, the central moments of a received signal can be measured only after calculating a mean value of the received signal, so lots of processing time is required.

Fig. 1 is a diagram for illustrating a conventional method for evaluating channel performance of a digital communication system. The Monte-Carlo method is used as an example for explaining a method for evaluating channel performance of a satellite communication system.

Referring to Fig. 1, the satellite communication system includes a transmitter 1, a repeater 2 and a receiver 3. A signal generator 4 is a function block library that generates a simulated signal of a signal inputted to a modulator (not shown) .

An error counter 5 is a function block library and compares a signal received from a demodulator (not shown) of the receiver 3, with a transmitted signal and determines if a received signal has an error or not due to noise generated in a first noise generator 6 and a second noise generator 7, and adds a number of the errors and then divides the number of the errors with a total test number N_MC , to thereby calculate an average error rate.

The Monte-Carlo method is a method for evaluating channel performance of every digital communication system and usually used in a commercial simulator. In the Monte- Carlo method, the simulator can be easily programmed, however, due to limitation of the ^• computer run time, an advantage of various functions of the commercial simulator cannot be used sufficiently.

To overcome the disadvantage of the Monte-Carlo method, many types of importance sampling methods are in studying.

However, in case of a nonlinear channel having a memory, realizing of the importance sampling methods is considerably difficult due to a complicated mathematical optimization process and for a digital communication system, which has a memory characteristics, an improved efficiency of the computer operation time is not so big.

Summary of the Invention

It is, therefore, an object of the present invention to provide a method of evaluating channel performance, which shortens computer run time even though a digital communication system has a nonlinearity and memory elements, and can be easily realized in a commercial simulator to thereby perform a detailed analysis and design of the digital communication system in a short run time.

The present invention provides a method of evaluating a system performance to achieve the above-referenced object. In a channel which is not includes encoder/decoder of a channel, a phase of the received signal of transmitted symbol H_k is turned to φ_k and moments of the received signal are measured up to N_; and N_Q orders. In case of a M-ary phase shift keying (PSK) system, moments of phase of a rotated signal are measured to obtain a discrete cumulative probability distribution function and by • using an interpolation and an extrapolation methods in the discrete cumulative probability distribution function obtained, an accurate continuous cumulative probability distribution function is obtained and then, they are applied to error determining threshold value to simply evaluate an average error rate of a channel.

In accordance with an aspect of the present invention, there is provided a method for evaluating channel performance of a system affected by a noise, e.g., a communication system, comprising the steps of: a) calculating a discrete probability density function of a signal received at a receiver through a channel based on moments of the received signal or moments of phase of the received signal; and b) calculating an error rate of the channel based on the discrete probability density function.

A method of evaluating a channel performance of a satellite communication channel according to the present invention generates a simulated signal of a signal that is inputted to a modulator in the transmitter and inputs an added output signal of a first noise generator to a repeater and then inputs the added the output signal to a receiver after adding it to an output signal of a second noise generator. The receiver demodulates the received signal according to a demodulating algorithm and determines if an error is generated or not.

At this time, to evaluate the error rate in a short time, in an error counter of the receiver, a received signal which is in condition of H_k transmit symbol is turned to φ_k and moments up to N_; and N₀ orders are evaluated and then based on the evaluated moments, a discrete probability density function and a discrete cumulative probability function are calculated.

A new discrete cumulative probability distribution function ^i vi^' ) ^an<^ ^o Vo)

( X {y_k)= 0.5{F;{y_Ik )+ F;{y_!k__x F_Q (y_Qk )= 0.5(F_Q{y_Qk)+ F_Q{y_Qk > are calculated by taking a predetermined number v of the cumulative probability values in the discrete cumulative probability distribution function (in this case, N, = N_Q = 2v - \ ) .

Subsequently, take v -κ units of F,

(or

~ 100/N_{/ /r} ) and F_ρ (y_Qk )≥ lO/N_MT (or ~ 100/N_MT ) between the new discrete cumulative probability distribution functions

X

) . Then obtains a cumulative probability distribution function, which connects ΛΓ + 1 ^th and v ^th cumulative probability value by using an interpolation. To the K ^th and xr+l^th cumulative probability value and an outer small error region thereof, adapts an extrapolation by using

ln(-ln2E_e) ≤ of linear characteristics which is extrme

value chanraracteric of all exponential random variable or adapts a general extrapolation to (log(E [y_k ^'

)) or

(log(E

so that completes a discrete cumulative probability distribution function estimation to the whole region. So error determining threshold value is substituted for the cumulative probability distribution function to produce an average error rate in each channel .

In case of M-ary system, evaluating up to N_Θ ^th order moments of phase of a rotated received signal and calculating a discrete probability density function by using the evaluated moment and then calculating a discrete cumulative probability distribution function.

A new discrete cumulative probability distribution function F_@ θ_k ) ( F_Θ [θ_/. J= 0.5ψ_Θ {θ_k ^' )+ F_Θ [θ_k ^'__l J) is calculated by taking a predetermined number v (in this case, N_Θ = 2v —1) of the discrete cumulative probability distribution function values. A cumulative probability distribution function is obtained by using an interpolation after establishing a reliable section of the new discrete cumulative probability distribution function and adapts an extrapolation to an

outer small error region by using In(-In 2E_e) of

linear characteristics which is extreme value characteristic of all exponential random variables or adapts a general extrapolation to (log(F_Q (θ_k ^' )](θ_k ^' )) or (log(E_Θ (θ_k ^' )}logfø)) so that completes a discrete cumulative probability distribution functions estimation of the whole region. So an error determining threshold value is substituted for the cumulative probability distribution function to produce an average error rate in each channel .

Therefore, the present invention can make an accurate performance evaluation for a channel with a few numbers of samples and has versatility and can simply realize a program by using a commercial simulation.

Brief Description of the Drawings

Other objects and aspects of the invention will become apparent from the following description of the embodiments with reference to the accompanying drawings, in which:

Fig. 1 is a diagram for illustrating a method for evaluating channel performance of a conventional digital communication system;

Fig. 2 is a block diagram for showing a general digital communication system; and

Fig. 3 is a flow chart for showing a method for evaluating channel performance in accordance with the present invention.

Detailed Description of the Preferred Embodiments

Hereinafter, a method for evaluating channel performance according to the present invention will be described in detail referring to the accompanying drawings.

The present invention adapts a coordinate transformation unit of a received signal and in case of a M- ary system, treating to a phase of a transformed received signal to realize the present invention more accurately and simply, and materialize a method of evaluating a cumulative probability distribution function in accordance with a general extrapolation, which is not considering probability characteristics of a received signal, so as to reduce operation time epochally. Also, the moments used in the evaluation method according to the present invention simplifies the process than that of central moments.

Fig. 2 is a block diagram for showing a general digital communication system. Referring to Fig. 2, a digital communication system 20 includes a transmitter 21, a repeater 22 and a receiver 23.

A signal generator 28 generates a simulated signal of a signal inputted to a modulator (not shown) . The transmitter 21 includes simulated functions of the entire functions of a transmitter except a channel encoder and an interleaver.

A first noise generator 26 and a second noise generator 27 generate simulated noises of noises, which are inputted to a channel of the digital communication system. The repeater 22 is a function block library that simulates a repeater of the satellite communication system, a mobile satellite communication system and a ground communication system.

The receiver 23 includes a simulated function of the entire transmitter such as an active filter, except a deinterleaver and a channel demodulator.

An error counter 24 compares a signal, which is received from a demodulator (not shown) of the receiver 23, with a transmitted signal and calculates an error rate of the received signal. The error is generated by a noise of a first noise generator 26 and a second noise generator 27.

Fig. 3 is a flow chart for showing a method for evaluating channel performance in accordance with the present invention. In Fig. 3, a method of counting an error rate of a received signal which is adapted to the error counter 24 coupled to the receiver 23 in Fig. 2 is described.

At step 31, a coordinate transformation unit rotates a received signal H_k which is a symbol based signal by^' φ_k

(φ_k = - 2πk/M , k = 0,- - -,M - \) , and at step 32, a moment evaluation unit calculates moments up to N, and N₀ orders of a rotated received signal y_u (In-phase received signal) and y_0l

(Quadrature-phase received signal) or calculates moments up to N_Θ orders of a phase component of the rotated received signal θ_t . At step 33, a discrete probability density function generating unit calculates a discrete probability density function by using moments and at step 34, a discrete cumulative probability distribution function generating unit calculates a discrete cumulative probability distribution function and by taking a predetermined number v of a cumulative probability in the discrete cumulative probability distribution function (in this case, N, - N₀ = 2v - l ), calculating a new discrete cumulative probability distribution function F,

) and Fo vo)

Subsequently, takes v ~ κ F, [y_Ik ) and F₀ y_okj which satisfied

F_; {y_Ik ) > 10/N_MT (or ~ 100/N_Λ/7. ) and F_Q (y_Qk)> 10/ N_MT (or ~ 100/N_wr ) condition among the new discrete cumulative probability distribution functions F,

) and F₀ y₀ ^' _k ) . At step 35, a cumulative probability distribution function including κ + l ^th through v ^th cumulative probability values is obtained by using an interpolation. To the ι ^th and the κr +l^th cumulative probability values and an outer low error region thereof, an

extrapolation is adapted by using ln(-ln2E_β) of

linear characteristics which is extreme value characteristic of all exponential random variables or a general extrapolation is adapted to (log(E (y_k ^'

)) or (log(E (y_k ^' )) log(y_k ^' )) , to thereby complete discrete cumulative probability distribution function estimation of the whole region. In case of a M-ary system, a cumulative probability distribution function is obtained by using an interpolation after establishing a reliable section to the new discrete cumulative probability distribution . function and an extrapolation is adapted to a low error region by_. using

ln(-ln2E ≤ of linear characteristics which is extreme

value characteristic of all exponential random variables or a general extrapolation is adapted to (log(E_Θ ψ_k JJ, [θ_k ^' jj or

(log(E_Θ ψ_k )j,log[θ_k JJ to thereby complete discrete cumulative probability distribution function estimation of the whole region. At this time, the extrapolation which uses

ln(-ln2E_e) ≤ of linear characteristics is used when it

requires an accurate calculation than the error region is corresponded to the tail region of the probability density function, otherwise, the general extrapolation is adapted to (log(E_Θ (θ_k ^' I {θ_k' ))or (log(E_β (θ_t ^' ))logfø )) .

At step 36, in case of a binary communication method, a channel performance evaluation unit calculates an error rate by substituting a signal detection threshold value ( Ω, ) for F_[ y)) and in case of a quadrature phase shift keying (QPSK) communication method, calculates an average internal channel error rate F_I (Ω₁ ) + F₀ (Ω₀) by substituting a signal detection threshold value ( Ω_; ) for F,

) and a signal detection threshold value ( Ω._Q ) for F₀(y₀) , and in case of a M-ary communication method, calculates an error rate by using the cumulative probability distribution function of the phase component of the rotated received signal.

The present invention can provide a method of evaluating channel performance which reduces computer operation time, even if a general system including a digital communication system has a nonlinearity and memory elements, and can be easily realized in a commercial simulator to thereby perform a detailed design of the digital communication system in a short time. Although the preferred embodiments of the invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible, without departing from the scope and spirit of the invention as disclosed in the accompanying claims.

Claims

1. A method for evaluating channel performance of a system affected by a noise, e.g., a communication system, comprising the steps of: a) calculating a discrete probability density function of a signal received at a receiver through a channel based on moments of the received signal or moments of a phase of the received signal; and b) calculating an error rate of the channel based on the discrete probability density function.

2. The method as recited in claim 1, wherein the step b) includes the steps of: bl) calculating up to ,N ' and N₀" moments of a rotated

^" received signal or up to N_Θ ^th moments of a phase component of the rotated received signal and calculating a discrete cumulative probability distribution function based on the calculated moments; b2) calculating a continuous cumulative probability distribution function from the discrete cumulative probability distribution function by using an interpolation/extrapolation regarding probability characteristics of the received signal; and b3) calculating a channel error rate from the continuous cumulative probability distribution function.

3. The method as recited in claim 2, if a binary, a quadrature phase shift keying (QPSK) or a M-ary modulation method is used in the communication system, calculates the channel error rate from the continuous cumulative probability distribution function.

4. The method as recited in claim 1, before the step a) , further comprising the step of rotating the received signal to φ_k according to H- transmission symbol condition so that the moment of the received signal is' evaluated accurately and rapidly.

5. The method as recited in claim 1, before the step a) , further comprising the step of calculating a phase of the rotated received signal.

6. The method as recited in claim 2, wherein the step c) includes the steps of: cl) calculating new discrete cumulative probability distribution function values , y] J and F₀

)

{ F, [y_Λ by taking a

. predetermined number v of the cumulative probability values in the discrete cumulative probability distribution function (in this case, N, = N₀ = 2v-l ) ; c2) taking v — κ units of F, y_Ik ) > 10/N_A/r (or ~ IQ0/N_MT ) and

F_o y_Ok)≥ 10/N_Mr (or ~ 100/N_MT ) between the new discrete cumulative probability distribution functions E_y

and

F₀ y_0k J _r then connecting κ + \ ^th and V^th cumulative probability

^' value by using an interpolation; and c3) adapting an ^{" '}extrapolation by using

ln(-ln2E„) of linear characteristics which is extreme

value characteristic of all exponential random variables or adapting a general extrapolation to (log(E

)) or

jj to the K ^th and ΛΓ + 1 ^th cumulative probability values.

7. The method as recited in claim 2, wherein the step c) comprising the steps of: c4 ) calculating a new discrete cumulative probability ^• distribution function F_Q (θ_k ^' ) ( F_Q (θ_k ^' ) = 0.5(E_Θ(^)+ E_Θ(^)) by taking a predetermined number v of the discrete cumulative probability distribution function to a phase of a rotated received signal, in case of a M-ary modulation method; c5) obtaining a cumulative probability distribution function by using an interpolation after establishing a reliable section to the new discrete cumulative probability distribution function; and c6) adapting an extrapolation by using

ln(-ln2E ≤ of linear characteristics which is extreme

value characteristic of all exponential random variables to an outer small error region or adapting a general extrapolation to (log(E_Θ (θ_k ^' )) (θ_k ^' )) or (log(F_Θ (θ_k ^' )}log(θ_k ^' )} .

8. A computer readable recording media storing instructions for executing a method for evaluating channel performance of a system affected by a noise, e.g., a communication system, the method comprising the steps of: a) calculating a discrete probability density function of a signal received at a receiver through a channel based on moments of the received signal received or moments of a phase of the received signal; and b) calculating an error rate of the channel based on. the discrete probability density function.

9. The computer readable recording media as recited in claim 1, wherein the step b) includes the steps of: bl) calculating up to N," and N₀" moments of a rotated received signal or up to N_Θ ^th moments of a phase component of the rotated received signal and calculating a discrete cumulative probability distribution function based on the 02/052792

calculated moments; b2) calculating a continuous cumulative probability distribution function from the discrete cumulative probability distribution function by using an interpolation/extrapolation regarding probability characteristics of the received signal; and b3) calculating a channel error rate from the continuous cumulative probability distribution function.

10. The computer readable recording media as recited in claim 2, if a binary, a quadrature phase shift keying

(QPSK) or a M-ary modulation method is used in the communication system, calculates the channel error rate from the continuous cumulative probability distribution function.

11. The computer readable recording media as recited in claim 1, before the step a), further comprising the step of rotating the received signal to φ_k according to H_k transmission symbol condition so that the moment of the received signal is evaluated accurately and rapidly.

12. The computer readable recording media as recited in claim 1, before the step a), further comprising the step^" of calculating a phase of the rotated received signal.

13. The computer readable recording media as recited in claim 2, wherein the step c) includes the steps of: cl) calculating new discrete cumulative probability distribution function values F, ^, ) and F₀ [y₀)

by taking a predetermined number v of the cumulative probability values- in the discrete cumulative probability distribution function (in this case, N₇ = N_υ = 2v-l ) ; c2) taking v - κ units of F, y]_k J ≥ 10/N_MT (or ~ 100/N_MT ) and

F₀ y_ok J≥ 10/ N_Mr (or ~ 1Q0/N_MT ) between the new discrete cumulative probability distribution functions F, [y_!k J and

F₀ y_0k ) , then connecting /c +l^th and v ^th cumulative probability value by using an interpolation; and c3) ^■ adapting an extrapolation by using

ln(-.n2E s of linear characteristics which is extreme

value characteristic of all exponential random variables or adapting a general extrapolation to (log(E (y_k JJ,

JJ or (log(E y_k Jμog y_k JJ to the K ^th and κ + 1 ^th cumulative probability values .

14. The computer readable recording media as recited in claim 2, wherein the step c) comprising the steps of: c4) calculating a new discrete cumulative probability distribution function F_Θ [θ_kJ ( F_Θ [θ_k ^' J= 0.5[F_e [θ_k ^' )+ F_@ ψ_k__] JJ by taking a predetermined number v of the discrete cumulative probability distribution function to a phase of a rotated received signal, in case of a M-ary modulation method; c5) obtaining a cumulative probability distribution function by using an interpolation after establishing a reliable section to the new discrete cumulative probability distribution function; and cβ) adapting an extrapolation by using

ln(-ln2E_c) of linear characteristics which is extreme

value characteristic of all exponential random variables to an outer small error region or adapting a general extrapolation to (log(F_Θ (θ_k ^' )) or (log(E_Θ (θ_k ^' )}logfø )) .