RU2631146C1 - Method for transmitting information by multi-frequency signals by adaptive scaling and limiting method - Google Patents

Abstract

FIELD: radio engineering, communication.

SUBSTANCE: method for transmitting information by multi-frequency signals is characterized by successive steps: converting the sequence of information symbols into a combination of modulating symbols, generating a multi-frequency signal as a sum of orthogonal partial signals of different frequencies, each modulated in phase by an appropriate modulating symbol, scaling the sum signal by multiplying it by a scaling factor, limiting the scaled signal and gaining power. The scaling factor is set such that the coefficients of the Fourier series of the limited signal satisfy the specified quality criteria of the communication system.

EFFECT: increasing the efficiency of the power amplifier, reducing out-of-band radiation.

4 cl, 12 dwg, 2 tbl

Description

FIELD OF THE INVENTION

The invention relates to electrical communication technology and can be used to transmit information by multi-frequency signals, for example, in communication systems based on OFDM technology (Orthogonal Frequency Division Multiplexing - orthogonal frequency division multiplexing).

State of the art

A known method of transmitting information by multi-frequency signals, consisting of converting a sequence of information symbols into a combination of modulating symbols, generating a multi-frequency signal as the sum of partial signals of different frequencies, each of which is modulated by a corresponding modulating symbol and power amplification (Digital radio communication systems: basic methods and characteristics: Textbook allowance / L.N. Volkov, M.S. Nemirovsky, Yu.S. Shinakov. - M .: Eco-Trends, 2005. - 392 s), hereinafter referred to as the analogue method.

In FIG. 1 shows the structure of the algorithm of the method-analogue. The generated multi-frequency signal ν _n (t) is the sum of K partial signals ν _nk (t) modulated by M-ary symbols r _nk . In total, N different combinations of modulating symbols are possible, generating an ensemble of signals of volume N. The volume of the ensemble cannot exceed the value of M ^K. If N is equal to M ^K , then the ensemble is a complete code, i.e. modulating symbols can form all possible combinations. The index n denotes the sequence number (for example, in decimal) of the combination in the full code.

In communication systems based on OFDM technology, elimination of inter-channel interference of symbols in the receiver is achieved by the orthogonality of partial signals ν _nk (t) on a time interval of duration T, for which their frequencies ƒ _k must form an arithmetic progression with a constant difference Δƒ = 1 / Т:

- частота первого парциального сигнала;Where

- the frequency of the first partial signal;

g ₁ is an integer equal to the number of frequency periods ƒ ₁ on the interval T.

The signal ν _n (t) has a variable envelope even with constant envelopes of partial signals, which occurs with phase (FM) or relative phase (OFM) modulation:

where V _k is the amplitude of the k-th partial signal;

V _n (t) is the envelope of the signal ν _n (t):

Ψ _n (t) is the phase of the signal ν _n (t).

The envelope and phase in (1.2) are determined by the following relations:

The power amplifier of multi-frequency signals must be such that when amplifying a harmonic signal with an amplitude of V _max it does not introduce significant non-linear distortions. Then the signals at its input ν _n (t) and output u _n (t), their envelopes V _n (t) and U _n (t) coincide up to a constant factor, i.e. they are proportional. Therefore, the output signals are orthogonal and have the same peak factors as the input:

- пиковое значение огибающей V_n(t);Where

- peak value of the envelope V _n (t);

- наибольшее пиковое значение огибающей;

- the highest peak value of the envelope;

- пиковое значение огибающей U_n(t);

- peak value of the envelope U _n (t);

V _{n sqr} U _{n sqr} - root mean square values of the envelopes V _n (t), U _n (t);

P _{n max} = 0,5U _{n max} - peak signal power u _n (t);

- мощность сигнала u_n(t).

- signal power u _n (t).

The largest peak value V _{max of the} input signal corresponds to the largest peak value U _{max of the} signal at the output of the amplifier and its power P _pek must correspond to the peak power of this signal:

When using FM, RPM for any values of K and M, the largest peak envelope value, as follows from (1.2), is equal to the signal value at time t = 0 when all modulating symbols are equal to zero:

- наибольшая амплитуда парциального сигнала;Where

- the largest amplitude of the partial signal;

ν _k = V _k / V is the normalized amplitude of the k-th partial signal.

When using FM, OFM, the maximum peak factor is limited from above:

The non-rigorous equality on the right-hand side of (1.7, 1.8) becomes strict with the same amplitudes of partial signals, i.e. when they are equally powerful.

In FIG. Figure 2 shows a histogram of the peak factors of the full code of equally probable, equally powerful signals with binary phase modulation (K = 8).

The power of the signal at the amplifier output is equal to the sum of the powers P _{nk of the} partial signals due to their orthogonality:

where U _nk is the amplitude of the k-th partial signal of the n-th signal implementation.

From (1.9) and (1.5) it follows that when using FM, OFM, the power of any signal implementation at the amplifier output is unchanged and P _max times less than the peak power of the amplifier:

The non-strict equality in the right-hand side of (1.10) turns into strict for equipotential partial signals. Then the power of each of them is K ² times less than the peak power of the amplifier:

As can be seen from (1.10, 1.11), the disadvantage of the analogue method is the low use of the peak power of the amplifier.

The power gain efficiency is characterized by the efficiency of the amplifier as the ratio of the signal power at the amplifier output to the power consumed by the amplifier from the power source.

The efficiency of a push-pull power amplifier in class B mode when the harmonic signal is amplified is (Amplification devices. Textbook for high schools / I.G. Mamonkin. - Ed. 2, revised and additional - M .: Communication. 1977. - 360 from.):

where U _E is the voltage of the power source of the amplifier;

U _a = U _E -ΔU is the amplitude of the harmonic signal at the output of the amplifier:

ΔU is the voltage drop across the active elements of the amplifier.

The proportionality between the input and output signals of the amplifier will be observed if the voltage of the power source satisfies the condition:

Then the current consumed from the power source will be proportional to 2U _n (t) / π and the power consumption is a function of time:

The signal amplification efficiency is characterized by local efficiency as the ratio of the signal power at the amplifier output to the average value of power consumption:

where V _nT , U _nT are the average values of the envelopes V _n (t), U _n (t).

The rms values of all envelopes are the same when using FM, RPM, and the local efficiency in this case is equal to:

By virtue of the Cauchy-Bunyakovsky inequality (Schwarz inequality), the average value of the envelope is less than the mean-square value, and inequality follows from (1.16):

Inequality (1.17) is valid for all local efficiencies. therefore, the quantity η _i , is a strict lower limit of the minimum efficiency for amplification of multi-frequency signals with FM, OFM.

From (1.15) it can be seen that the local efficiency reaches a maximum if V _{n max} = V _max . When using FM, OFM, this is the case for ν _n (t) signals with a maximum peak factor. One of these implementations is the implementation of ν ₀ (t) with the envelope V ₀ (t) and efficiency when amplifying this implementation with equally powerful partial signals:

- среднее значение функции V₀(t)/V.Where

is the average value of the function V ₀ (t) / V.

When amplifying multi-frequency signals with FM, OFM, the local efficiency is within the limits:

The gain of the ensemble of signals is characterized by the average efficiency as the mathematical expectation of all local efficiencies:

where m ₁ 〈⋅〉 is the operation of mathematical expectation.

In FIG. Figure 3 shows a histogram of local efficiency when amplifying the full code of equally probable, equally powerful signals with binary phase modulation for the analogue method (K = 8 δ _U = 0). The maximum efficiency is η _max = 42.9%, the average is η _med = 31.4%, the minimum is η _min = 28.7%, which is 0.9% higher than the lower limit η _i = 27.8%. The analogue method is characterized by low values of efficiency, which is also its disadvantage.

Closest to the claimed invention is a method of transmitting information by multi-frequency signals, consisting of converting a sequence of information symbols into a combination of modulating symbols, generating a multi-frequency signal in the form of a sum of orthogonal partial signals of different frequencies, each of which is phase-modulated by a corresponding modulating symbol, scaling the total signal by multiplying it by the scaling factor, limiting the scaled signal and gain oschnosti (digital information transmission equipment MS-5, Ed AM zaezdnyh, YB Okuneva -... M .: Communication, 1970. 152 pp.)., hereinafter referred to as the prototype method. In FIG. 4 shows the structure of the algorithm of the prototype method. In the prototype method, the generated signal ν _n (t) is scaled by multiplying it by a scaling factor y ₀ . The result of scaling is an increase in y ₀ times the peak, average and rms values of the original signals and their envelopes. The scaled signal y ₀ ν _n (t) as a result of the restriction converts into a signal s _n (t) with the envelope S _n (t):

where V _s - clipping threshold.

In FIG. Figure 5 shows the graphs of the signals at the input, output of the limiter, the envelope of the limited signal.

There is no restriction for those signals for which the peak value of the envelope increased by a factor of ₀ does not exceed the limit threshold:

In the prototype method, each partial signal is phase-modulated, therefore, the rms values of all generated signals are the same (ν _{n sqr} = ν _sqr ) and the condition for the absence of restriction, equivalent to relation (2.3), expressed through the peak factor signal:

where X _s = V _s / V _sqr is the relative threshold of restriction.

By setting the limit threshold and the scaling factor, the set of all amplified signals is divided into two subsets. The first subset (subset A) consists of signals that are not subject to restriction, i.e. signals with a peak factor not exceeding the critical value of P _s . The second subset (subset B) consists of signals subject to restriction, i.e. signals with a peak factor above a critical value. Obviously, at П _s > П _max all signals are not limited, and at П _s > П _min - they are limited. In FIG. 6 shows the dependence P _s = φ _P (y ₀ , X _s ) for the full code of equally probable, equally powerful signals with binary phase modulation in the prototype method (K = 8).

In the prototype method, the power amplifier is selected so that when amplifying the harmonic signal with an amplitude equal to the threshold threshold V _s , it does not introduce significant nonlinear distortions. Then the signals at its input s _n (t) and output u ' _n (t). their envelopes S _n (i), U ' _n (t) are proportional and the peak power of the amplifier P' _pek can be reduced relative to the peak power of the amplifier P _pek in the analogue method:

where U _s is the amplitude of the output signal corresponding to the amplitude of V _s .

Therefore, the voltage of the power source of the amplifier in the prototype method should be:

раз больше, чем в способе-аналоге:where ΔU 'is the voltage drop across the active elements of the amplifier. Then, when amplifying the signals of the subset A, their power is equal to the sum of the powers of the partial signals, each of which

times more than in the analogue method:

The increase in power reduces the probability of an error in the reception of these signals in the prototype method relative to the analogue method.

The power consumed by the amplifier and local efficiency when amplifying the signals of subset A:

By the appropriate choice of the active elements of the amplifier in the prototype method, it is possible to ensure the commensurability of δ ' _U with δ _U in the analogue method. Then, from a comparison of (2.9) with (1.16), it follows that the local efficiency when amplifying the signals of the subset A is higher than the local efficiency when amplifying the same signals in the analogue method:

The current flowing through the active elements of a class B power amplifier has the form of half cosine pulses with an amplitude I _a proportional to the amplitude V _{a of the} voltage of the input harmonic signal with a frequency ƒ _a .

When the input harmonic signal is limited at the level of V _{s, the} current has the form of half cosine pulses truncated at the level of I _s , as shown in FIG. 7. The constant component of the current I ₀ when amplifying the limited input harmonic signal, normalized relative to the peak current I _s :

where T _a = 1 / ƒ _a is the period of the harmonic signal;

z = V _a / V _s = I _a / I _s is the level of restriction;

ϕ = across (1 / z) is the restriction angle characterizing the duration of the restriction.

The absence of limitation corresponds to ϕ = 0, c ₀ = 1 / π, the current in the load has the form of a harmonic signal, and the efficiency of the amplifier is determined by the relation (1.12). A strict limitation (clipping) corresponds to ϕ = π / 2, _{0 0} = 1/2, the current in the load has the shape of a meander, the Fourier series of which contains odd harmonics of frequency ƒ _a with decreasing amplitudes (Radio engineering circuits and signals. Textbook for high schools / I. S. Gonorovsky. - Ed. 3rd, revised and enlarged. - M .: Communication, 1977, - 608 p.):

The power in the load is equal to the sum of the powers of all harmonics:

The power and efficiency consumed by the amplifier when amplifying a clichéd harmonic signal;

As you can see, with an increase in the level of limitation of the input signal, the efficiency of the amplifier increases and in the limit is limited only by the voltage drop across the active elements.

The restriction is a nonlinear operation and the harmonic components of the Fourier series of the signals of the subset B at the input and output of the limiter are different. The components at the input have frequencies ƒ _k = g _k Δƒ of partial signals and amplitudes y ₀ V _k . The components at the output have frequencies ƒ _m = mΔƒ and amplitudes in accordance with Parseval's equality;

where S _n0 is the constant component of the signal s _n (t);

S _nm is the amplitude of the mth harmonic of the Fourier expansion of the signal s _n (t) in the interval T.

The signal restriction level of subset B is a function of time .:

The restriction level, as follows from (2.2, 2.17), the higher, the greater the peak factor of the signal. The power consumed by the amplifier and local efficiency when amplifying the signals of the subset B:

Where

The gain efficiency in the prototype method is characterized by the average efficiency as the mathematical expectation of local efficiency when amplifying the signals of subsets A and B:

In FIG. Figure 8 shows the dependence η ' _med = ϕ _η (y ₀ , X _s ) for the full code of equally probable, equally powerful signals with binary phase modulation in the prototype method (K = 8). As you can see, the average efficiency in the prototype method is higher than the average efficiency of the analogue method.

When amplifying the signals of the subset B, the output signal power is distributed between the useful partial signals at frequencies частот _k = g _k Δƒ and signals at frequencies частот _m = mΔ m (m ≠ g _k ).

The power of each partial signal is determined by the corresponding coefficient of the Fourier series of the limited signal s _n (t):

- относительная амплитуда k-го парциального сигнала n-й реализации выходного сигнала.Where

- the relative amplitude of the k-th partial signal of the n-th implementation of the output signal.

раз больше, чем в способе-аналоге, то при усилении сигналов подмножества В мощность каждого парциального сигнала определяется величиной c_nk, которая, в свою очередь, зависит от величии y₀,X_s и реализации сигнала. Вероятность ошибки приема парциальных сигналов подмножества B в способе-прототипе будет не хуже, чем в способе-аналоге, если для любого, сигнала этого подмножества значения y₀,X_s таковы, что выполняется нестрогое равенство:If, when amplifying the signals of the subset A, the power of each partial signal in

times more than in the analogue method, then when amplifying the signals of the subset B, the power of each partial signal is determined by the quantity c _nk , which, in turn, depends on the magnitude y ₀ , X _s and the implementation of the signal. The probability of receiving partial signals of subset B in the prototype method will not be worse than in the analogue method, if for any signal of this subset the values y ₀ , X _s are such that the equality is not strict:

Failure to fulfill condition (2.22) means that the power of some partial signals in the implementation of the multi-frequency signal at the amplifier output in the prototype method is less than their power in the analogue method and the probability of receiving errors of such signals increases.

In FIG. Figure 9 shows the dependence c _min = ϕ _c (y ₀ , X _s ) for the complete code of equally probable, equally powerful signals with binary phase modulation (K = 8). As can be seen, condition (2.22) is satisfied for certain values of the relative limiting threshold and scaling factor. Excessive decrease in the relative limiting threshold (decreasing the power P ' _pek relative to the power P _pek ) leads to the failure of condition (2.22) at any value of the scaling factor and the probability of error in the prototype method will be worse than in the analogue method.

The components of the output signal at frequencies ƒ _m = mΔƒ (m ≠ g _k ). called out-of-band radiation, interfere with neighboring communication systems. Their power decreases (not necessarily monotonously) as they move away from the frequency band of partial signals. Therefore, the out-of-band emission level is mainly characterized by the power of signals in a limited frequency range. For example, in the region L of K frequencies, the maximum of which is 2Δƒ less than the frequency of the first partial signal ƒ ₁ and in the region R of K frequencies, the smallest of which is 2Δƒ higher than the frequency of the Kth partial signal ƒ _K. The power of each signal P _nm in these regions is proportional to the square of the amplitude of the corresponding harmonic of the Fourier expansion of the limited signal s _n (t) on the interval T and the relative level of out-of-band emissions is determined by the coefficients of the Fourier series of the restricted signal s _n (t) in these regions, frequencies:

The maximum relative level of out-of-band radiation during amplification of a limited signal s _n (f) is the largest of the values of w _{mn, L} , w _{mn, R} :

The power amplification of the signals of the subset B is characterized by the range of the relative level of out-of-band radiation from w _min to w _max :

In FIG. Figure 10 shows the dependence w _max = ϕ _w (y ₀ , X _s ) for the complete code of equally probable, equally powerful signals with binary phase modulation.

For small scaling factors, the maximum out-of-band level. radiation occurs when the signals with the maximum peak factor are limited, for example, the signal ν ₀ (t).

With increasing scaling factor, the maximum out-of-band emission level, as can be seen from the graphs in FIG. 11 occurs when restricting signals with lower peak factors.

In FIG. Figure 12 shows the dependence w _min = ϕ _{w min} (y ₀ , X _s ) for the full code of equally probable, equally powerful signals with binary phase modulation in the prototype method (K = 8). The sharply expressed nonmonotonic character of w _min with a change in the scaling factor is due to the dependence (2.4) of the critical peak factor on this coefficient - with its growth, more and more signals are subject to restriction.

For some systems, communication, for example, hydroacoustic, the problem of “tightness on the air” is not relevant and a high level of out-of-band radiation is insignificant. Therefore, for such systems, it is advisable to obtain a high amplifier efficiency at the cost of high out-of-band radiation, i.e. setting the patient scaling factor. But its increase is limited by condition (2.22), as a result of which the efficiency of the amplifier is also limited, otherwise the probability of an error in reception increases.

For other communication systems, the level of out-of-band radiation is significant and its decrease in the prototype method, due to the dependence of the critical peak factor on the scaling factor, is associated with a decrease in the efficiency of the amplifier.

As you can see, the prototype method is characterized by limited performance in terms of amplifier efficiency and out-of-band radiation, which is its drawback.

Disclosure of invention

The problem to which the invention is directed, is to increase the efficiency of the amplifier and out-of-band radiation.

The technical results in the implementation of the invention is to increase the efficiency of the power amplifier, improving the out-of-band emission.

These technical results are achieved by the fact that in the method of transmitting information by multi-frequency signals, consisting of converting a sequence of information symbols into a combination of modulating symbols, generating a multi-frequency signal in the form of a sum of orthogonal partial signals of different frequencies, each of which is phase-modulated by a corresponding modulating symbol, scaling the total signal by multiplying it by the scaling factor, limiting the scaled signal and gain Nia power scaling factor is set so that the coefficients of the Fourier limited signal satisfies predetermined quality criteria communication system.

Brief Description of the Drawings

The accompanying drawings, histograms and graphs, which are part of the present description, illustrate the essence of the known and the claimed methods of transmitting information by multi-frequency signals.

FIG. 1 - The structure of the algorithm of the method is similar, where:

1 - transformation of a sequence of information symbols b into a combination of modulating symbols r _nk ;

2 - formation of a multi-frequency signal;

3 - power gain;

ν _n (t) is the generated signal;

u _n (t) is the signal at the output of the power amplifier.

FIG. 2- Histogram of peak factors of the full code of equally probable, equally powerful signals with binary phase modulation (K = 8), where:

P _j - peak factor, P _med - average peak factor of the ensemble of signals;

q _j - number of signals with peak factor P _j.

FIG. 3 - A histogram of local efficiency when amplifying the full code of equally probable, equally powerful signals with binary phase modulation for the analogue method (K = 8, δ _U = 0). Where;

η _i - local efficiency; η _med is the average efficiency;

q _i - the number of signals, the amplification of which the efficiency of the amplifier is η _i .

FIG. 4 - The structure of the algorithm of the prototype method, where:

1 - transformation of a sequence of information symbols b into a combination of modulating symbols r _nk ;

2 - formation of a multi-frequency signal;

4 - scaling the generated signal;

5 - limitation of the scaled signal;

3 - power gain;

y ₀ is the scaling factor;

y ₀ ν _n (t) is the scaled signal at the input of the limiter;

s _n (t) is the signal at the output of the limiter;

u ' _n (t) is the signal at the output of the power amplifier,

FIG. 5 - Signals at the input, output of the limiter, the envelope of the limited signal, where:

y ₀ ν (t) is the scaled signal at the input of the limiter;

s (t) is the signal at the output of the limiter;

S (t) - envelope, limited signal.

FIG. 6 - Dependence P _s = ϕ _P (y ₀ , X _s ) for the full code of equally probable, equally powerful signals with binary phase modulation in the prototype method (K = 8), where;

P _s is the critical peak factor, P _min is the minimum peak factor;

y ₀ is the scaling factor;

X _s is the relative threshold of restriction,

FIG. 7 - Current shape in the active element of the power amplifier, where:

1 - input harmonic signal is not limited;

2 - input harmonic signal is limited;

ƒ _a is the frequency of the input harmonic signal;

I _a - current amplitude - input harmonic signal, not limited;

I _s - peak current - input harmonic signal is limited.

FIG. 8 - Dependence η ' _med = ϕ _η (y ₀ , X _s ) for the full code of equally probable, equally powerful signals with binary phase modulation in the prototype method (K = 8). Where:

η'med - average efficiency;

y ₀ is the scaling factor;

X _s is the relative threshold of restriction,

FIG. 9 - Dependence c _min = ϕ _s (y ₀ , X _s ) for the full code of equally probable, equally powerful signals with binary phase modulation (K = 8), where:

c _min is the minimum relative amplitude of the partial signal;

y ₀ is the scaling factor;

X _s is the relative threshold of restriction.

FIG. 10 - Dependence w _max = ϕ _w (y ₀ , X _s ) for the full code of equally probable, equally powerful signals with binary phase modulation (K = 8), where:

w _max is the maximum relative level of out-of-band radiation;

y ₀ is the scaling factor;

X _s is the relative threshold of restriction,

FIG. 11 - Dependence Δw _m = w _max -w _{0 max of the} full code of equally probable, equally powerful signals with binary phase modulation (K = 8), where:

w _max is the maximum relative level of out-of-band radiation;

w _{0 max} - the maximum relative level of out-of-band radiation of the signal with a maximum peak factor ν ₀ (t);

y ₀ is the scaling factor;

X _s - relative - limit threshold.

FIG. 12 - Dependence w _min = ϕ _{w min} (y ₀ , X _s ) for the full code of equally probable, equally powerful signals with binary phase modulation in the prototype method (K = 8), where;

w _min is the minimum relative level of out-of-band radiation;

y ₀ is the scaling factor;

X _s is the relative threshold of restriction.

The implementation of the invention

The formation of a multi-frequency signal ν _n (t) in communication systems based on OFDM technology is usually carried out by the method of inverse discrete Fourier transform of modulating symbols by means of digital computer technology. These tools also perform all the actions necessary for the implementation of the proposed method.

In the inventive method, the scaling factor is set such that the coefficients of the Fourier series of the limited signal satisfy the specified criteria for the quality of the communication system. The scaling factor, in the general case, is determined by repeating the same procedure: the generated signal ν _n (t) is multiplied by a number greater than unity, the resulting signal is limited, the Fourier series coefficients of this signal are calculated and their values are checked for compliance with the specified quality criteria. If the match is not achieved, then set a different number and repeat the procedure. The number at which compliance is achieved is the required scaling factor and the corresponding scaled, limited signal is supplied to the power amplifier. Scale factors determine; directly in the process of operation of the communication system, or in advance, choosing the required process of operation of the communication system, or directly in the process of operation of the communication system, for some signals, for others - in advance, choosing the required during the operation of the communication system. The examples show the implementation of the proposed method for different quality criteria of a communication system. The numerical values of the characteristics are given for an ensemble of signals whose peak factors are shown in FIG. 2.

Quality criterion: maximum amplifier efficiency

Enhancing the efficiency of the amplifier c. the prototype method is carried out by setting the maximum possible value of the scaling factor y ₀ at which the value c _min corresponds to condition (2.22). For example, as can be seen from the graphs in FIG. 9, with a relative threshold X _s = 2.75 and a scaling factor y ₀ = 2.5, the value of c _min corresponds to the required condition, therefore, the probability of an error in receiving limited signals in the prototype method will be no worse than in the analogue method.

With a conditional unit level of amplitudes of all partial signals (V = 1), the peak power of the amplifier in the analogue method should be 32 rel. units According to the relation (2.5), the peak power of the amplifier in the prototype method can be reduced to 15.125 rel. units - more than twice.

In the inventive method, the same amplifier is used as in the prototype method and impose the condition that the probability of receiving errors of limited signals in the inventive method is no worse than in the prototype method. Then the scaling factor of each generated signal ν _n (t) is determined as a solution to the equation of the objective function:

where c ' _{n min} is the minimum relative coefficient of the Fourier series in the frequency domain of partial signals, is determined similarly to relation (2.22);

w ' _n is the relative level of out-of-band radiation in the claimed method, which is determined similarly to the relation (2.24).

Rule (3.1) allows you to get the highest efficiency when amplifying each signal, without compromising the probability of an error in its reception, at the cost of a large number of calculations: it is necessary to determine and analyze the coefficients of the Fourier series both in the region of out-of-band radiation and in the frequency region of partial signals.

A computationally less expensive scaling factor of the generated signal ν _n (t) is defined as a solution to a simpler objective function;

where w _{0 max} is the relative level of out-of-band radiation in the prototype method when the signal is ν ₀ (t).

Rule (3.2), without worsening the probability of reception error of limited signals, reduces computational costs at the cost of reducing efficiency relative to that achievable by rule (3.1).

Table 1. Characteristics of the transmission methods by the efficiency of the amplifier (δ ₁ = 0).

As can be seen from table 1, the inventive method allows to obtain a higher efficiency of the amplifier, without compromising the probability of error when receiving limited signals. A characteristic feature of rule (3.2) is the same level of out-of-band radiation for all signals.

Quality criterion: increasing the efficiency of the amplifier at a given level of out-of-band radiation

In the prototype method, this is done by setting such a value of the scaling coefficient y ₀ at which the value c _min corresponds to condition (2.22), and the relative level of out-of-band radiation of the signal ν ₀ (t) does not exceed a given value.

In the inventive method, the same amplifier is used as in the prototype method and impose the condition that the probability of receiving errors of limited signals in the inventive method is not worse than in the prototype method. Then the scaling factor of each generated signal ν _n (t) is determined as a solution to the system of equations of the objective functions:

The first objective function of rule (3.3) does not require determining the coefficients of the Fourier series of the signal at the output of the limiter, since signals with peak envelope values not exceeding the limit threshold form a non-limitable subset A ':

where S _{n max} - peak value of the envelope of the signal at the output of the limiter.

Out-of-band radiation during amplification of the signals of the subset A 'in the present method is absent.

The condition that the signal belongs to the subset A ', expressed through its peak factor:

In the claimed method, the critical peak factor P ' _s does not depend on the scaling factor and is always greater than the critical peak factor in the prototype method:

Therefore, all the signals of the subset A are part of the subset A 'and the higher the requirements for out-of-band radiation, the stronger are the relations y _n > y ₀ ≈1, therefore the power of these signals and local efficiencies when amplified in the claimed method is higher than in the method prototype;

Signals with peak values of envelopes, not less than the threshold threshold, form a subset of B 'and for these signals the scaling factor is determined as the solution of the second objective function of rule (4.1), which allows obtaining out-of-band emission level not higher than the specified one without deteriorating the probability of error during their reception. In the inventive method, the maximum scaling factor for signals of the subset B ′ is equal to the scaling factor y ₀ in the prototype method, and the minimum scaling factor is equal to one (if there are signals with a peak factor in the ensemble equal to the critical value P ′ _s ). Therefore, the local efficiency when amplifying the signals with the maximum peak factor is the same in the claimed method and the prototype method, and for other signals of the subset B 'the local efficiency in the claimed method is lower than in the prototype method, the Signals of the subset B' are only part of the subset B Therefore, low values of local efficiency make up a small fraction of the average value of efficiency.

The signals, the peak factors of which are between the values of P _s and P ' _s , in the prototype method are subject to limitation and create out-of-band radiation, in the claimed method, these signals are not subject to limitation and do not create out-of-band radiation. In the inventive method, the scaling factors of these signals are greater than unity, but less than the scaling factor in the prototype method y ₀ . Consequently, the local efficiencies, when amplified, are between the values of the local efficiencies for the subsets B 'and A and are close to local ones. The efficiency when amplifying these signals in the prototype method. As a result, the average value of the efficiency in the claimed method, the higher the average value of the efficiency in the prototype method, the higher the requirements for out-of-band radiation are presented to the communication system.

A computationally less expensive scaling factor of the generated signal ν _n (t) is defined as a solution to a simpler system of objective functions that do not require determining the coefficients of the Fourier series of the signal at the output of the limiter:

Rule (4.7) leads to the identity of out-of-band radiation and local efficiency when amplifying the signals of the subset B 'in the prototype method in the inventive method, as a result of which the average efficiency will be slightly higher than for rule (4.1). but at the cost of out-of-band emission for signals with a peak factor equal to P ' _s .

Table 2 shows the characteristics of the out-of-band transmission methods and amplifier efficiency (δ _U = 0).

As can be seen from table 2, the inventive method, without compromising the probability of error when receiving limited signals, allows you to get the higher efficiency of the amplifier, the higher the requirements for out-of-band radiation. For the relative limiting threshold, X _s = 3.5, the critical peak factors in both methods are higher than the second highest level of the peak factor of the ensemble of signals P _max2 = 4,500 (see Fig. 2), therefore, only signals with the maximum peak factor P _max are subject to restriction = 8,000 and out-of-band radiation is the same for both methods, and the rules (4.1) and (4.7) in the claimed method give the same results.

The above rules for determining scaling factors are not the only ones possible. For example, rule (4.7) can be modified to exclude out-of-band radiation in signals with a peak factor equal to the critical value of P ' _s :

The scaling factor of such signals is equal to unity, therefore, the local efficiency of the amplifier will reach a minimum, which will lead to some decrease in the average efficiency.

The inventive method provides ample opportunity to improve the characteristics of the communication system, not achievable in the prototype method.

Claims (4)

 1. A method of transmitting information by multi-frequency signals, consisting of converting signals of a sequence of information symbols to signals of a combination of modulating symbols, generating a multi-frequency signal as a sum of orthogonal partial signals of different frequencies, each of which is phase-modulated by a signal with a corresponding modulating symbol, scaling the total signal by multiplication by the scaling factor, the limitations of the scaled signal with Fourier expansion and gain power, characterized in that the scaling factor is set in such a way that the coefficients of the Fourier series of the limited signal satisfy the specified criteria for the quality of the communication system. 2. The method according to p. 1, characterized in that for the generated multi-frequency signal with a peak envelope value not higher than the limit threshold, the scaling factor is set equal to the ratio of the limit threshold to the peak envelope value. 3. The method according to p. 1, characterized in that for the generated multi-frequency signals with peak envelope values not lower than the limit threshold, the scaling factor is set equal to the scaling factor for the multi-frequency signal with the highest peak envelope value. 4. The method according to p. 1, characterized in that during the operation of the communication system, the scaling factor is selected from a pre-calculated set of values for multi-frequency signals with the corresponding peak values of the envelopes.

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