WO2011051627A2

WO2011051627A2 - Method and device for assessing an encoded serial digital transmission on a non-stationary channel

Info

Publication number: WO2011051627A2
Application number: PCT/FR2010/052316
Authority: WO
Inventors: Frédéric LACOSTE; Caroline Amiot-Bazile; Jérôme Lacan; Wilfried Chauvet
Original assignee: Centre National D'etudes Spatiales (C.N.E.S.)
Priority date: 2009-10-30
Filing date: 2010-10-28
Publication date: 2011-05-05
Also published as: FR2952253A1; FR2952253B1; WO2011051627A3

Abstract

The invention relates to a method for assessing the performance of an encoded and modulated serial digital transmission over a noisy channel with non-stationary attenuation, wherein at least one value representing an error rate ER of the received bit stream is produced without decoding. A mutual information value I_k is produced (34) according to a predetermined transmission quality function Q_k, and the average mutual information <I_n > is produced (35) for every encoded word received; then at least one error rate ER value of the received bit stream is produced (38) according to each average mutual information <I_n > value using a predetermined standard function on a channel with added white Gaussian noise. Said invention includes a device, a software product and a recording medium for the implementation of the method.

Description

METHOD AND DEVICE FOR EVALUATING AN ENCODED SERIES DIGITAL TRANSMISSION ON A NON-STATIONARY CHANNEL

The invention relates to a method and a computer device for evaluating a coded and modulated serial digital transmission over a non-stationary attenuation noisy channel between:

an emitter comprising:

a coding device adapted to generate, from a stream of bits to be transmitted, called said transmitted bits stream, at least one stream of coded words, called transmitted streams of coded words, resulting from the coding, according to at least one method; predetermined coding, of said transmitted bit stream,

a modulation device adapted to generate at least one modulated symbol stream, said transmitted stream of modulated symbols, according to a predetermined modulation scheme (in particular PSK phase modulation and / or QAM quadrature amplitude modulation), on at least a carrier signal, each transmitted stream of modulated symbols being representative of at least a part of each transmitted stream of coded words,

a device for transmitting, on a non-stationary attenuation attenuated channel, each transmitted stream of modulated symbols,

- and a receiver comprising:

a reception device adapted to receive, for each transmitted stream of modulated symbols on said channel, a stream of modulated symbols, said received stream of modulated symbols,

a demodulation device adapted to generate at least one stream of coded words, said received stream of coded words, from each received stream of modulated symbols,

- A decoding device adapted to generate a bit stream, said bits received stream, by decoding, according to the coding method implemented by the transmitter, each received stream of codewords.

The coding of such a digital transmission makes it possible to enhance its reliability. In various applications, the transmission channel used, generally of wireless type (radio frequencies and / or microwaves ...) has a non-stationary attenuation, that is to say which varies substantially in time during the transmission. of each code word. This phenomenon is reinforced by the presence of a channel interleaver.

This is the case, for example, with mobile receiver terminals (for example of the GPRS or UMTS type, Satellite DVB-SH) and / or when the coding is of the "turbocode", LDPC or iterative type. Indeed, the channel conditions and its performance can be fluctuating depending on the position of the receiver. In addition, when an interleaver is provided, the function of such an interleaver has the effect of reducing variations in attenuation seen by code word.

Nevertheless, it is possible to obtain or generate by simulation digital data representative of variations over time of attenuation and noise of the channel. These digital data can come from the known characteristics of the interleaver, or from known statistical characteristics from the physical properties of a channel. The channel data is estimated from the received signal on either pilot symbols or modulated symbols. Successive signal-to-noise ratios by codeword are reconstructed from the channel interleaver.

In this general context, a problem that arises is that of the predictive evaluation of the transmission performance, that is to say the determination of an ER error rate (bit error rate BER and / or word error rate PER) in the received stream of bits as a function of attenuation variations of the channel during the reception of each coded word, and this independently of the actual realization of the transmission and its various elements components (transmitter, receiver, other circuits, physical link ...), especially before or during the design of all or part of these constituent elements, and therefore in particular without performing the decoding.

Such a predictive evaluation of performance must make it possible in particular to optimize the design of said constituent elements, and in particular of choose appropriate protocols to ensure good transmission quality: automatic retransmission request (ARQ technique) possibly hybrid (H-ARQ); incremental redundancy (IR); combination of Chase; adaptation of the characteristics of the transmitter and / or the transmission link: choice of the coding method, signal strength, modulation scheme ... In particular, such a predictive evaluation could make it possible to avoid over-sizing of the receivers and of their antennas.

A first known method of predicting performance to take into account the attenuation variations of a channel consists in determining an average value of SNR signal-to-noise ratio on each received codeword. In particular, the same processing is applied for two different coded words having the same average value of the signal-to-noise ratio but different attenuation variations. This method provides in practice overly optimistic performance predictions.

In a second known method, a bit error rate

BER is determined for each elementary bit of each coded word received from a mean value of the average signal-to-noise ratio Ej N _t for this elementary bit, itself calculated from a mean value of the signal-to-noise ratio IN _t of each received modulated symbol divided by the number of bits per symbol, the value of BER being obtained from a known function (in the form of a curve or a table) giving the value of BER as a function of the signal ratio / noise on an additive Gaussian white noise channel. An average of the bit error rate is then calculated for the received code word and is used as a performance criterion. This method is more accurate (that is, provides more realistic results) than the previous one but provides predictions that in practice turn out to be too pessimistic.

EP 1564924 discloses a method in which each received coded signal is divided into a plurality of predetermined fixed length segments, and the average value over the signal to noise ratio per symbol frame (EN _t ) p is obtained by calculation for each segment of a parameter C _m using a convex function f numerical obtained empirically according to the modulation scheme (BPSK or QPSK) applied to the mean value (EN _t ) M <i each segment, then calculation of an average value C of this parameter on the frame, then inverse computation with the function inverse I. Then, the mean value on the average signal-to-noise ratio frame (E] _j / N _t ) p for each elementary bit is obtained from a table, and the error rate per FER frame is obtained as a function of a given reference curve on an additive Gaussian noise channel.

This method is based on a numerical approximation of the function f. It is limited to the modulation schemes for which this digital function is given in this document, namely BPSK and QPSK. It is therefore not applicable to other modulation schemes. Moreover, it does not take into account channel attenuation variations at the symbol level, but with a granularity at segments of determined length. Its accuracy depends in fact on the good adaptation of the fixed size of each segment to the dynamics of the attenuation variations, adaptation that can not be adjusted beforehand according to each application.

Moreover, this predictive evaluation must be able to be performed without modeling and simulation of the physical link itself, such modeling leading to extremely heavy and complex calculations. As such, it should be noted that it is particularly important to be able to perform such a predictive evaluation which simultaneously is highly reliable, correctly takes into account large and realistic fluctuations of the channel (eg similar to those encountered in practice in the case of mobile terminals such as mobile phones type GSM or GPRS, or satellite DVB-SH), and is fast enough to be used on an industrial scale, particularly in the design of the components of the transmission. The rapidity of predictive evaluation is a decisive issue in the context of modern industrial circuit manufacturing in which the durations of the different phases are precisely determined, must be respected, are crucial and constantly tend to shrink.

This predictive evaluation must also be able to be performed without real manufacturing of the constituent elements of the link, in particular the receiver. Indeed, as an alternative to the known simulation methods mentioned above, the only really effective method envisaged so far is to actually manufacture all or part of the receiver elements, especially those that are the most complex and whose computer simulation are the most expensive, especially in computer processing time. Such a method, however, requires a long and expensive manufacturing and different non-simulated elements.

In this context, the aim of the invention is to overcome all these drawbacks by proposing a performance evaluation method able both to take into account the true attenuation variations of the channel, and with a good accuracy of the results, high reliability and computer processing light and fast, and low cost-especially without requiring any real manufacturing of the components of the transmission, including the receiver.

In particular, the purpose of the invention is to propose such a method making it possible to obtain a result in a shorter period of time on the one hand than that necessary to obtain an evaluation from a digital transmission actually produced and implemented. , on the other hand to that necessary for the realization of a modeling and a complete simulation of the physical link of the transmission. More particularly, the invention aims to provide such a method that is compatible with the current constraints of an industrial scale operation, in the design of the constituent elements of the transmission, including the receiver.

The invention also aims at providing such a method which makes it possible to obtain reliable statistics of the performance of said transmission over time.

The invention also aims at providing such a method that optimizes the design of the constituent elements of the transmission, including the receiver, avoiding over-dimensioning.

The invention also aims to propose such a method which can be applicable to any modulation scheme, including other than BPSK or QPSK, including 2 "-PSK n> 3 or QAM.

To this end, the invention relates to a method for evaluating the performance of a coded and modulated serial digital transmission over a non-stationary attenuation noisy channel between:

an emitter comprising:

a modulation device adapted to generate at least one stream of modulated symbols, said transmitted stream of modulated symbols, according to a predetermined modulation scheme, on at least one carrier signal, each transmitted stream of modulated symbols being representative of at least one part of each transmitted stream of codewords,

- and a receiver comprising:

a receiving device adapted to receive modulated symbol streams, called received streams of modulated symbols, corresponding to transmitted streams of modulated symbols on said channel,

at least one decoding device adapted to generate a bitstream, said received bit stream, by decoding each received stream of codewords, according to a decoding method corresponding to a coding method implemented by the transmitter,

method in which at least one value representative of an error rate ER of the received bit stream is generated without performing the decoding, from digital data memorized representative of variations over time of attenuation and noise of the channel,

characterized in that at least one value, called Q _k transmission quality, of formula c _k .EN ₀ , where c _k represents each attenuation value of the channel over time, k being a time index, E _s represents a mean energy per emitted symbol and N ₀ represents a spectral density of Gaussian white noise on the channel, and the variations over time of said Q _k transmission quality are elaborated for each received symbol of the received stream of modulated symbols,

and in that :

in a first step, a mutual information value I _k is elaborated for each value of said transmission quality Q _k , according to a predetermined function of said transmission quality Q _k ,

in a second step, an average of mutual information is elaborated for each coded word of the received stream of coded words, by averaging the different mutual information values I _k elaborated in the first step for the different values taken by said Q _k transmission quality on said coded word,

in a third step, at least one value of the error rate ER of the received bit stream is elaborated for each coded word of the received stream of coded words, from each value of the mutual information mean developed in the second step, and using stored data representative of variations of an equivalent error rate according to at least one function, called standard function, of the signal-to-noise ratio, each standard function being predetermined for the coding devices and decoding on an additive Gaussian white noise channel.

In a first possible and advantageous embodiment of the invention, each mutual information value 1 is elaborated according to the function defined by the following formula (I): oo oo

( ^x _k > y _k ) = - ^o & ₂ (* ^Bc _k -rr) -

-oo v =

M being the cardinal of the alphabet A-

,, ..., S _M _ ₁ } modulated symbols.

Advantageously and according to the invention, this analytical formula can be discretized for its evaluation by digital treatment, for example according to the function defined by the following formula (II):

β threshold threshold

- AuAv Σ / (# Aw, rAv) log ₂ (/ (4Aw, rAv))

q = - threshold r = - threshold

threshold))

threshold

and Au = Av = 2- β

In a second possible and advantageous embodiment of the invention, each mutual information value 1 ^ is elaborated according to the function

mutual information calculated between the j th bit ( ^{0≤ j≤ p 1} ) of the emitted symbol and the received symbol that function being defined by the following formula (III): i ^b i _^ y _k ) ⁼ - \ \ f (, v) log ₂ (f (u, v)) dudv

u = -∞ v = - °°

+ {g _j (u, v) log ₂ (g _j (u, v)) dudv

and

1

m = m

M being the cardinal of Γ alphabet A ^-

} modulated symbols,

mo≤m≤2 ^p -1 being the set of standardized symbols ^m of p bits -iP ^~ ^ whose bit numbered m is 0,

being the set of standardized symbols m depbits ^0≤ i ^≤ P ^{~ l}

whose bit numbered m is 1.

Advantageously and according to the invention, this analytical formula can be discretized for its evaluation by digital processing, for example according to the following function (IV)

threshold

Σf (qAu, rAv) log ₂ (f (qAu, rAv))

r = - threshold

threshold threshold

threshold r threshold

threshold = - c _k

threshold

and Au = Δν = 2- β

In addition, advantageously and according to the invention, the values c _& channel attenuation over time are-especially measured values by the receiver-as and measuring receiving codewords.

In addition, advantageously and according to the invention, a value c _& attenuation of the channel and / or a value of the quality of transmission (¾ is (are) elaborated for each symbol of the received stream of modulated symbols.

Advantageously and according to the invention, in said third step:

an equivalent signal-to-noise ratio value SNR _eq on the received coded word is elaborated from the said mutual information mean by the inverse function 1 ^ ¹ ,

then each ER error rate value is obtained from said equivalent signal-to-noise ratio value SNR _eq and said stored data representative of variations of an equivalent error rate according to a predetermined standard function for the coding devices and decoding on an additive Gaussian white noise channel. Other embodiments are possible.

A method according to the invention is a computer-assisted simulation method, that is to say is capable of being implemented by a device computer science.

An evaluation method according to the invention is implemented by digital data processing, that is to say is a computer process, implemented by a computer device. As with any computer simulation method, the method according to the invention makes it possible to provide directly usable results for the design and manufacture of the constituent elements of the transmission-in particular the receiver. The invention also extends to a computing device for implementing a method according to the invention, that is to say to a computing device comprising digital data processing means, characterized in that it is adapted and programmed for the implementation of a method according to the invention.

The invention also extends to a software product capable of being loaded into the RAM of a computing device, characterized in that it is adapted for the implementation of a method according to the invention. The invention also extends to a recording medium adapted to be read by a reader connected to a computer system, characterized in that it comprises a recorded program adapted to be loaded into the RAM of a computer system. and program it to implement a method according to the invention.

The inventors have found that the invention makes it possible in practice to obtain a fast and accurate performance prediction, and in particular considerably more accurate than in all the known prior methods, while remaining faster than all the previous simulation methods and that prediction of performance on a real channel. This result is surprising, especially since there is no direct relationship between the mutual information on the coded bits and the performance of the decoder.

However, the calculation of this mutual information and its average on each coded word makes it possible in practice to take into account the temporal variations of attenuation with great precision. It appears that two coded words having the same average mutual information have the same performance at the output of the decoder.

In addition, the inventors have determined that the value of the mutual information can even be elaborated from an analytical formula, whose implementation is thus simple and precise by numerical calculation, including for the computation of the inverse function.

The invention also relates to a method, a computing device, a software product and a recording medium characterized in combination by all or some of the characteristics mentioned above or below.

Other objects, features and advantages of the invention will appear on reading the following description which refers to the appended figures representing, by way of non-limiting examples, embodiments of the invention and in which:

FIG. 1 is a block diagram showing a transmission device that can be the subject of an evaluation method according to the invention,

FIG. 2 is a schematic flow chart showing an embodiment of the main steps of a method according to the invention,

FIG. 3 is a schematic diagram of examples of reference curves that can be used, according to different modulation schemes, for a predetermined function for determining a mutual information value on a Gaussian white noise additive-dependent channel; the signal-to-noise ratio of this channel,

FIG. 4 is a schematic diagram showing the use of a reference curve similar to FIG. 3 for performing a first step of a method according to the invention,

FIG. 5 is a schematic diagram showing the use of a reference curve similar to FIG. 3 for performing a first part of a third step of a method according to the invention,

FIG. 6 is a schematic diagram showing the use of a curve representative of a standard function for performing a second part of a third step of a method according to the invention,

FIG. 7 is a block diagram representing the various functions implemented in a method according to the invention, FIG. 8 is a diagram illustrating an example of stored digital data representative of variations over time of attenuation of the channel that can be used in a method according to the invention,

FIG. 9 is a diagram illustrating an example of an error rate per PER code word that can be produced by a method according to the invention,

FIG. 10 is a diagram illustrating another example of data that can be delivered by a method according to the invention,

FIG. 11 illustrates representative curves of the distribution function of shading attenuations of an S-band channel in a suburban environment for different distances traveled.

FIG. 1 generally represents a coded and modulated serial digital transmission device on a non-stationary attenuation attenuated channel. This device comprises a transmitter 11, a receiver 12 and a physical link 13 wireless forming the transmission channel. The physical link 13 may for example be a radio frequency link, such as for example linking mobile terminals such as cellular telephones, personal digital assistants, laptops, wireless cards, land vehicles, ships, aircraft, satellites, space probes or other space systems ... at a base station, itself fixed (terrestrial) or mobile (vehicle, satellite, ...) accessing a data transmission network such as the Internet network or any other private network. In general, the transmission can be bidirectional, that is to say that each mobile terminal is sometimes issuer, sometimes receiver.

The transmitter 11 comprises a first module 14 delivering data in the form of a bit stream (baseband signal) to be transmitted, said transmitted bit stream. This transmitted bit stream is supplied to a coding module which executes a predetermined coding method to form, from the bits, a stream of coded words, the so-called coded word stream. Such a coding method makes it possible in particular to increase the reliability of the transmitted data by increasing the redundancies while ensuring the correction of errors, that is to say the restitution of the initial data despite the disturbances that can undergo the channel 13 of transmission. The coding module 15 delivers coded words, which are then modulated, according to a predetermined modulation scheme, by a modulator circuit 18 which supplies a modulated symbol stream, called the emitted stream of modulated symbols, to an interleaver circuit 17, the latter providing modulated and interleaved symbols to a radiofrequency transmitter circuit 19 capable of transmitting corresponding signals on the physical link 13.

The receiver 12 comprises a radiofrequency reception circuit 20 able to receive the signals transmitted via the physical link 13, and to deliver a stream of modulated and interleaved symbols, said received stream of modulated and interleaved symbols, to a de-interleaver circuit 22 which performs the inverse processing of the interleaver 17 of the transmitter 11, that is to say the progressive reconstitution of a de-interlaced modulated symbol stream, from the digital data stream from the reception circuit 20. The de-interleaver circuit 22 provides the de-interlaced modulated symbols to a demodulator circuit 21 adapted to apply a demodulation, the symbols received, according to the scheme and the modulation map used on transmission. The demodulator circuit 21 allows the progressive reconstitution of a stream of coded words, said stream of received codewords, from the stream of deinterleaved modulated symbols. These received coded words are then supplied to a buffer memory 23 and then progressively processed by a decoding module 25, comprising one or more decoders -in particular two decoders- and making it possible to deliver a stream 27 of received bits included in the signal conveyed by the physical link 13 and corresponding to the stream of bits emitted by the generator circuit 14.

The invention relates to a method for evaluating, by computer simulation, the performance of such a coded serial digital transmission. The invention applies to any coding method, and regardless of the exact nature of the coding method used. It may be in particular an encoding method chosen from the so-called LDPC (hollow matrix parity code) type processes, the turbocode type methods and the other iterative decoding coding methods. In most modern coding methods that provide performance near the Shannon limit, the coding module includes a plurality of encoders -in particular two coders-. The invention, however, applies equally well to a coding module 15 comprising a single coder.

Modulated symbols emitted at the output of the modulator block 18

(which carries out the cartography of the modulation, often designated by the English term "mapping") belong to a constellation of complex symbols of cardinal M which is a power of 2 (M = 2 ^P ). They can only take M complex values. These symbols are then transmitted on the channel 13. The effect of the channel on these symbols x ^ is twofold:

the channel 13 attenuates each symbol and is called c & the attenuation undergone by a symbol X

channel 13 assigns the attenuated symbol x _{½ to a} Gaussian complex white noise additive of power N (2 on the imaginary and real channels, and thus represents a spectral density of a white Gaussian noise on the channel. includes thermal noise and possibly interference.

The symbol received at the input of the demodulator 21 is then called _k corresponding to the symbol Χ transmitted attenuated and noisy. The values of the attenuation modules taken over time are provided by a channel simulation module 24 (FIG. 7), the latter determining the attenuation values from data representative of the speed of movement of the receiver and / or characteristics known predetermined for the channel itself and the physical link. These values are for example determined from true series of attenuation or propagation values as a function of the distance traveled, measured during tests actually performed, then read at a speed adapted to the speed of a mobile terminal considered in the execution of a method according to the invention. As a variant, these values can be determined from a statistical model of the channel (for example the Perez-Fontan tri-state model for a satellite LMS channel) for which successive samples are drawn.

FIG. 8 represents an example of values of the modules of the attenuations that can be provided by the channel simulation module 24. As FIG. 8 is only illustrative, the values are only represented over a small period of time, of 60 seconds. In practice, the period used for evaluation is generally much larger, typically several hours.

If E _S represents an average energy per emitted symbol, E / NQ represents the signal / noise ratio at emission. The quality Q _k of transmission can thus be represented for each received symbol X _k by the formula:

Q _k = c _K ² .EN ₀

If E _B denotes the average energy per transmitted coded bit and E _S the average energy per emitted symbol, these two quantities are linked by the relation:

E _s = E _b x log ₂ (M)

The value of E _S is calculated from the different symbols of the constellation ^ ''^' ^ Ml} p _ar j _{a re} i _al i ₀ n _:

₁ -l

E s = ^ _M y L isj "' ²

m = U

The channel is equalized by defining new standardized symbols

The method according to the invention makes it possible to evaluate by simulation an error rate, for each symbol received, taking into account the attenuation variations of the channel on the received symbols, that is to say on the different parts. corresponding received coded words. The various modules implementing the functions implemented in a method according to the invention are shown schematically in FIG. 7.

The simulation module 24 of the channel provides a simulated stream of symbols that can be received by the receiver 20.

A deinterleaver simulation module 28 makes it possible to simulate the function of the deinterleaver 22 and the demodulator 21, and to group by codewords the different symbols provided by the channel simulation module 24. The stream of de-interleaved and demodulated codewords is stored in a buffer memory 23 (FIG. 1).

For each coded word, an evaluation module 26 (FIG. 7) of a method according to the invention calculates a value of an error rate per BER bit and / or a value of an error rate per word. encoded PER.

FIG. 2 thus represents a flowchart of an example of steps implemented in an evaluation module 26 according to the invention.

In step 33, the different values of the attenuation and / or the signal-to-noise ratio E NQ and / or the transmission quality Q _K are calculated, for each received symbol, and for each received corresponding coded word. stored in the memory 23, the received stream of codewords. From these different values Q _K , a mutual information value 1 ^ is elaborated, in the subsequent step 34, according to a predetermined function.

Two variants of the invention are possible with regard to the choice of the predetermined function for the calculation of said mutual information value 1 ^.

If we consider a received symbol y ^, this symbol corresponds to the emitted symbol attenuated by c & and noisy by additive Gaussian white noise. Due to the selected modulation of cardinal M = 2 ^P , this received symbol y ^ contains the information relating to p bits transmitted b \ b ^k ₂ .. b ^k _p .

A first embodiment of the invention consists in considering the mutual information 7 ((b ^k ₁ , b ^k ₂ ,., B ^k _p ), y ^) equal to the mutual information Tfc between the transmitted symbol and the received symbol y ^. This variant has the advantage of proposing a unique theoretical formula for calculating a reference curve of the mutual information which depends solely on the nature of the modulation considered. This approach does not take into account the actual implementation ("mapping") of the modulation nor that the constituent p bits of the symbol are not all equally protected against the noise of the channel.

In this first variant, each mutual information value 1 ^ is determined according to the function defined by the aforementioned formula (I).

The expression def (u, v) is in analytical form and can therefore be evaluated for all values of u and v. For the integral, it is enough to discretize this integral by any numerical method. For example using a method of rectangles, we obtain each mutual information value 1 ^ according to the function defined by the following formula (II):

threshold threshold

AuAv Σf (qAu, rAv) log ₂ (f (qAu, rAv)) q = - threshold r = - threshold

threshold = + Max _{Q≤m≤M _y} (real (c _k -S _m ), imag (c _k -S _m ))

. . . threshold

and Au = Av = 2

β

As can be seen, for a given modulation, a channel attenuation and a known noise spectral density, the mutual information between the transmitted and received symbols depends only on the transmission quality Q _k . However, each value of the transmission quality Q _k corresponds to the signal-to-noise ratio (SNR) on reception. The mutual information 1 ^ therefore depends only on this SNR signal-to-noise ratio.

A reference curve for each modulation scheme can therefore be obtained by numerical evaluation of the previous expression. For example, the reference curves shown in FIG. 3 are obtained respectively for the following modulation schemes: QPSK, BPSK, 16QAM, 64QAM.

A second variant consists of taking into account the implementation modulation ("mapping") and consider each bit. For each of the constituent _p k bits of the transmitted symbol Xk, the mutual information is calculated

(b ^k ₂ , yk) · · · · (b ^k _p , yk) between each bit and the received symbol yk,

The reference curve used to obtain the mutual information is then the sum of these p curves.

Thus, in this second variant, each mutual information value I _k is determined according to the function I _k (ti _k , yk) of the mutual information computed between the j th bit (^ ^{≤ J≤ p ~} ) of the emitted symbol Xk and the received symbol yk, this function being defined by the above-mentioned formula (III).

This general formula (III) is valid in the case where geometrically these two sets of standardized symbols have the same geometric distribution in the complex plane, that is to say when these two sets are equal to a rotation or translation of the plane by . Otherwise, an analytic formula can also be written but it is more complex. The above hypothesis includes PSK modulations in geometric distribution called "Gray mapping".

The expressions df (u, v) and g (u, v) are in analytical form and can therefore be evaluated for all the values of u and v. For the integral, it is enough to discretize this integral by any numerical method. For example, using a rectan method, we obtain each value of mutual information 1 ^ according to the function - ¹ ) of the symbol

by the following formula (IV): ( ^b y _k = ^u (f (qAu, rAv)) threshold threshold

⁺ Σ Σ 8 days

q = threshold r = threshold

With, if we want to evaluate the different Gaussian df (u, v) and gu, v) up to at least their probability a on a number of points β in the mesh, the following threshold values and ( ^Δ "' ^Δν );

threshold

i At

β

^is between 0 and 1. The reference curve to be used on each symbol is the sum of the curves for each of the p bits.

Whatever the variant used, a reference curve is thus obtained representing a predetermined function providing a mutual information value 1 ^ as a function of a signal-to-noise ratio SNR.

It should be noted that each reference curve referred to throughout the text is in practice materialized by a table of digital values stored in mass memory. The evaluation module 26 uses such a table to determine the appropriate numerical values allowing the use of such a curve.

In the step 34 of calculating the mutual information 1 ^ as shown in FIG. 4, the evaluation module 26 considers the reference curve mentioned above, that is to say the table of values stored digital signals, and each value of the transmission quality Q _k as the value of the signal-to-noise ratio to be plotted as abscissa to determine each value of 1 ^.

In the subsequent step, for each coded word, an average of mutual information is generated by the evaluation module by averaging the different mutual information values 1 i determined in step 33 to the different values taken by said transmission quality Q _k on said code word.

In the subsequent step 36, the evaluation module 26 reuses the same reference curve (i.e., the same table of numerical values) to determine an equivalent signal-to-noise ratio SNR _eq on the codeword from said mutual information mean . In other words, the performance prediction module 28 uses the inverse function I ^ ¹ .

In the subsequent step 37, the evaluation module 26 calculates each value of the ER error rate from said equivalent signal-to-noise ratio value SNR _eq and stored data representative of variations of an equivalent error rate according to a predetermined standard function for the coding and decoding modules used on an additive Gaussian white noise channel.

Indeed, for a predetermined coding module 15 and a decoding module 25, there exists a standard function, obtained in a manner known per se by simulation on the stationary Gaussian channel, expressing the error rate per PER coded word or the rate errors per BER bit as a function of the signal-to-noise ratio. FIG. 6 represents an example of curves representative of such standard functions, the different curves being obtained for the same decoding coding modules and varying from one another as a function of the number of iterations used for the decoding.

For each value of the equivalent signal-to-noise ratio SNR _eq , the evaluation module 26 calculates, from these curves, that is to say tables of corresponding registered digital values, a set of error rates ER c i.e., an error rate value for each number of iterations that can be used at decoding. ERi error rate values are decreasing with the number of iterations. This set of values ERi therefore constitutes an error rate vector (ER), determined for each coded word received.

In the example of FIG. 6, four standard function curves are represented: a first curve CS1 corresponding, for example, to a single iteration, a second curve CS2 corresponding, for example, to four iterations, a third curve CS3 corresponding, for example, to eight iterations, and a fourth curve CS4 corresponding for example to sixteen iterations. Thus, from the value of the equivalent signal-to-noise ratio SNR _eq , an error rate vector having four components is obtained: (ER) = (ERI, ER2, ER3, ER4). It should be noted that the two steps 36, 37 can be combined in one and the same step 38, if the standard functions are combined with the inverse function I ^ ¹ into a single function directly providing, for each number of iterations, curves of variation of the error rate ER as a function of the mean of mutual information .

The evaluation module 26 provides the variations over time, for the channel samples provided by the channel simulation module 24 and on the same time scale, the variations over time of the ER error rate values. (BER and / or PER).

FIG. 9 represents an example of a sample (over a period of only four seconds) of the curve of variations as a function of time of the probability of error rate per PER coded word that can be provided by the evaluation module 26. from the attenuation values (Figure 8 gives an example of a logarithmic and a time-scale representation for an LMS (satellite-ground) satellite channel in an average forested environment with a speed of 50 km / h), in the case of the simulation of a turbo-decoder according to the DVB-SH standard for QPSK modulation in OFDM mode, with a convolutional interleaver that spreads over 100 ms, and a turbo coding rate code 1/2.

All three simulation modules 24 channel 28 deinterleaver simulation and 26 evaluation can be incorporated into a single simulator. This simulator can consist for example of two blocks made according to the Juzzle software platform and libraries.

The input data of the simulator are: a file containing the values representative of the curve represented in FIG. 4 providing the variations of the mutual information as a function of the signal / noise ratio, and a file containing the representative values of the curves represented in FIG. standard functions representing the performance of the turbo code by the variations of the error rate as a function of the signal-to-noise ratio on a Gaussian channel and according to the coding rate considered.

The simulation module 24 of the channel may be formed of a block of generation of the channel, a turbo code modeling library and a propagation library for generating samples according to one or more channel models, for example according to Perez Fontan's models (see Pérez-Fontân, F. , Vazquez-Castro, M., Buonomo, S., Poiares-Baptista, JP, Arbesser-Rastburg, B., "S-Band LMS propagation channel behavior for different environments, degrees of shadowing and elevation angles", IEEE Transactions on Broadcasting , Vol 44, No. 1, March 1998), Rice and Rayleigh, or others.

The deinterleaver simulation module 28 is formed of a library. This library is made to simulate a de-interleaver depending on the type of interleaver considered, which may be any in the context of the present invention. It may be for example a de-interleaver of the block type, in particular of the rows / columns type (filling a matrix in lines and reading in columns), or else of a de-interleaver of convolutional or other type.

For example, for the case of the DVB-SH standard, the interleaver is a 48-branch convolutional type with a 126-bit interleaving unit (UI) and at each of these 48 branches is associated a delay f (i) for 0 <i <47.

This means that the bits at the input of the interleaver are grouped in packets of 126 bits and that these packets are distributed successively on these 48 branches (branch 0, branch 1, ... branch 47 then branch 0 again, branch 1 ..). Each interleaving unit is then delayed by the delay f (i) corresponding to the branch on which it is located. The output interleaving units are then retrieved branch by branch to reform a single stream.

jj inp

So if we denote by "the n-th unit of interlacing

jj OUt

at the input of the interleaver and ^k the k-th interleaving unit at the output of the interleaver, the n-th input interleaving unit is output at the kth position by the interleaver according to the relation next (by numbering from 0 the indices):

with * = π ₄₈ + 48 * (/ (π ₄₈ ) +> Γ ^β )

Euclidean of the whole n by 48.

The interleaver of the DVS-SH standard is defined entirely by 5 parameters which make it possible to calculate the 48 values defli) for 0 <i <47.

The deinterleaver has the same operation as the interleaver with an inverse function f (i).

The simulator according to the invention outputs a file whose curve of FIG. 9 constitutes a partial representation (for a duration of only four seconds, whereas the evaluation period is of course much larger, typically several hours). .

In the example of a mobile receiver terminal, the travel distance to be considered to be representative of the channel statistics depends on the channel considered. For example, in the case of an LMS band S channel in a suburban environment, a distance of the order of 10 km is recommended for a good representation of the performance evaluations.

FIG. 11 illustrates the shading attenuation distribution function of such a S-band channel in a suburban environment (Perez-Fontan models) for several channel distances traveled (100m, 200m, 1km, 5km, 10km, 20 km, 40 km). It can be seen from this figure that when seeking to provide service on 95% of the suburban zone, the worst-case attenuation encountered is representative of the overall statistics only from a distance of the order from 10 km.

As a variant, a simulator according to the invention provides a file representative of the availability of the transmission, that is to say the prediction of the probability over time that a window of Tl seconds has at least T2 seconds without error. (ER less than or equal to a threshold value ERmax), T2 being between zero and T1 (for example, T1 = 20s). FIG. 10 represents an example of such an output as a function of the signal / noise ratio C / N expressed in decibels. Each point of each curve of FIG. 10 corresponds to the execution of the method according to the invention and to the obtaining of variations of ER error rate values over time as provided by the evaluation module. The curve C1 corresponds to T2 = T1; curve C2 corresponds to T2 = T1-1s = 19s; curve C3 corresponds to T2 = T1-2s = 18s; each curve Ci corresponds to T2 = T1- (il) s.

Curve C2, which is often considered in such a context, corresponds to the ESR5 probability of having at least 19 seconds right for each window of 20 seconds, ie a proportion of false seconds per window less than 5%.

The points of these curves corresponding to a given value of C / N given are obtained as follows:

step 1: calculation for each code word of the estimated PER for this code word thanks to the simplified simulator.

step 2: computation for the ith block of one second of the probability Pi that this second is without error

JV

Where PERi _j is the instantaneous Packet Error Rate supplied from the j-th constituent code word,

N is the number of code words per second.

step 3: computation on the ith window of 20 s of the law Yi of distribution of the number of right seconds according to the formula:

Yi is the convolution of the 20 laws of Bernoulli: Ay is a random variable of Bernoulli which is worth 1 if the j-th second of the i-th window (of 20s) is without error with a probability _y and which is equal to 0 with a probability 1- P _y -, the probability P _y - being calculated in step 2. The random variables Ay are independent.

step 4: example of the calculation of the curve C2:

The probability ESR5 is given by the formula:

ESR5 = P (K = 20 + P (Yi = 19)

Such a result, particularly such as that shown in Figure 10, was considered until now as impossible to obtain. In particular, it makes it possible to know the characteristics of the transmission in advance with excellent reliability, without requiring a complete simulation of the physical link itself, and can be used to optimize the design and manufacture of the receiver according to the constraints. transmission quality imposed (probability ordinate in Figure 10), choosing the maximum signal-to-noise ratio to meet these constraints. The invention thus makes it possible in particular to avoid any oversizing.

The invention makes it possible to improve by a factor of the order of 500 the average duration necessary for the evaluation with respect to a complete simulator generating the coded packets. An empirical rule indicates that with such a complete simulator, to know the PER (error rate per packet), it is necessary to generate coded packets until 100 packets are false. Thus, for example, for a PER of 0.01, the number of packets to generate to obtain a single value of PER over time, it will generate 10,000 coded words.

Moreover, the tests show that the evaluation according to the invention is on average faster than the real time. In other words, the performances in PER on a channel of duration D will be obtained in a calculation time slightly lower than the duration D.

The main configuration parameters of the simulator are: the type (row-columns, convolutional ...) and the parameters of the de-interleaver to change the parameters as defined in the DVB-SH standard (interleaving depth, interlace unit (number of symbols) ...); channel settings that allow the user to choose a channel template and modify the parameters associated with this model; the parameters of the physical link that allow the user to modify the parameters of the OFDM mode (guard interval, band, number of carriers per OFDM symbol) as well as the coding rate.

The simulator implementing a method according to the invention can be implemented on any appropriate computer device in the form of a software application which can be in the form of a software product recorded on a recording medium suitable for reading by a user. computer station reader (CD-ROM, DVD, USB key ...).

1 / - Method for evaluating the performance of a coded and modulated serial digital transmission over a non-stationary attenuation noisy channel between:

an emitter (11) comprising:

and a receiver (12) comprising:

method in which at least one value representative of an error rate ER of the received bit stream is generated without performing the decoding, from digital data

Claims

memorized representative of variations over time of attenuation and noise of the channel,

and in that :

in a first step (34), a mutual information value I _k is elaborated for each value of said transmission quality Q _k , according to a predetermined function of said transmission quality Q _k ,

in a second step (35), an average of mutual information is elaborated for each coded word of the received stream of coded words, by averaging the different mutual information values I _k elaborated in the first step for the different values taken by said quality of transmission Q _k on said code word,

in a third step (38), at least one value of the error rate ER of the received bit stream is elaborated for each coded word of the received stream of coded words, from each value of the mutual information average developed in the second step, and using stored data representative of variations of an equivalent error rate according to at least one function, called standard function, of the signal / noise ratio, each standard function being predetermined for the devices. coding and decoding on an additive Gaussian white noise channel.

21 - Process according to claim 1, characterized in that each mutual information value 1 ^ is elaborated according to the function defined by the following formula (I):

M is the cardinal of the alphabet A = {S _0, S ... S _Ml} d _es sym oles modulated.

3 / - Method according to claim 1, characterized in that each mutual information value 1 ^ is developed according to the function defined by the following formula (II):

β threshold threshold

- AuAv Σ / (# Aw, rAv) log ₂ (/ (4Aw, rAv))

q = - threshold r = - threshold

with, to evaluate the different Gaussians of f (u, v) up to at least their probability a on a number of points β in the mesh, the following values of threshold and ^(Δ "' ^Δν) :

threshold = J- and

. . . threshold

and Au = Av = 2

β

M is the cardinal of the alphabet A = {S _0, S ... S _ML} ^ _es sym oles modulated.

4 / - Method according to claim 1, characterized in that each value of mutual information

mutual information calculated between the j th bit (^ ^{≤ J≤ p ~} ^) of the emitted symbol and the received symbol y ^ this function being defined by the following formula (III):

u = -∞ v = - °°

+ {{g _j (u, v) log ₂ (g _j (u, v)) dudv

v = -

1

m = I m M being the cardinal of Γ alphabet A-

modulated symbols

L m ⁾ o≤m≤2 ^p -1 being the set of standardized symbols ^m of p bits -iP ^~ ^ whose bit numbered m is 0, s

b≤m≤2 ^p -1 being the set of normalized symbols ¹⁷¹ of p bits -iP ^~ ^ whose bit numbered m is 1.

5 / - Method according to claim 1, characterized in that

each mutual information value

defined by the following formula (IV):

threshold

I _k (H, y _k ) = Σf (qAu, rAv) log ₂ (f (qAu, rAv))

r = - threshold

threshold threshold

⁺ Σ Σg _j (qu, rAv) log ₂ (g _j (qAu, rAv))

threshold r threshold

with, to evaluate the different Gaussian df (u, v) and gu, v) up to at least their probability a on a number of points β in the mesh, the following values of threshold and ^(Δ "' ^Δν)

threshold = -¾-¾n (a J¾ - ^ / T) + Max _Q≤k≤M _ _l (real (cl ^ S _k im g (c _k ² ^ -S _k )) threshold

and Au = Av = 2- β ç = __! _

m I m

M being the cardinal of the alphabet A = {S ₀ , S ..., S _Ml } of the modulated symbols.

6 / - Method according to one of claims 1 to 5, characterized in that the attenuation values of the channel over time are measured values - in particular by the receiver - as and when the receipt of the coded words .

11 - Method according to one of claims 1 to 6, characterized in that an attenuation value of the channel and / or a value of the transmission quality (¾ is (are) developed (s) for each flow symbol received symbols modulated.

8 / - Method according to one of claims 1 to 7, characterized in that in said third step (38):

an equivalent signal-to-noise ratio value SNR _eq on the received code word is produced (36) from said mutual information mean by the inverse function 1 ^ ¹ ,

then each ER error rate value is obtained (37) from said equivalent signal-to-noise ratio value SNR _eq and said stored data representative of variations of an equivalent error rate according to a predetermined standard function for the coding and decoding devices on an additive Gaussian white noise channel.

91 - Computer device comprising computer means for digital data processing, characterized in that it is adapted and programmed for the implementation of a method according to one of claims 1 to 8.

10 / - Software product capable of being loaded into the RAM of a computing device characterized in that it is suitable for the implementation of a method according to one of claims 1 to 8.

11 / - recording medium adapted to be read by a reader connected to a computer system, characterized in that it comprises a recorded program adapted to be loaded into the RAM of a computer system and program it to implement process according to one of claims 1 to 8.