A novel effective approach to weak continuous and digital signals processing in communication channels with high noise levels is proposed and investigated. The essence of proposed approach is illustrated by examples of various electronic devices. The conditions which allow obtaining the maximal gain in signal to noise ratio are found. This gain exceeds 50 dB for sensitive amplifier and approximately equals to 30 dB for detector of digital cosine video impulse. It is shown that the proposed approach ensures obtaining a lot more gain in signal to noise ratio compared to existing technical solutions. The considered advantages of the described devices allow employing the proposed approach to effective information processing in communication systems with low operating power.Статья посвящена решению проблемы обнаружения слабых аналоговых сигналов на фоне сильного шума с обеспечением гораздо большего выигрыша в отношении сигнал/шум в сравнении с уже существующими техническими решениями. В статье рассматривается устройство обработки сигналов, описывается сущность способа, условия достижения поставленной задачи получения максимального выигрыша в отношении сигнал/шум, превышающего 50 дБ, и преимущества рассмотренного устройства, которое является эффективным для систем обработки информации с малым уровнем мощности

Makarenko, Oleksandr S.

Melnichuk, Oleksiy V.

Electronic Archive of Kyiv Polytechnic Institute

5 ISSN 2219-9454, Telecommunication Sciences, 2013, Volume 4, Number 1 © 2013, National Technical University of Ukraine “Kyiv Polytechnic Institute” UDC 621.396.6  A NOVEL APPROACH TO WEAK SIGNAL PROCESSING  Oleksandr S. Makarenko, Oleksiy V. Melnichuk  National Technical University of Ukraine “KPI”, Kyiv, Ukraine  A novel effective approach to weak continuous and digital signals processing in communication channels with high noise lev-els is proposed and investigated. The essence of proposed approach is illustrated by examples of various electronic devices. The conditions which allow obtaining the maximal gain in signal to noise ratio are found. This gain exceeds 50 dB for sensi-tive amplifier and approximately equals to 30 dB for detector of digital cosine video impulse. It is shown that the proposed approach ensures obtaining a lot more gain in signal to noise ratio compared to existing technical solutions. The considered advantages of the described devices allow employing the proposed approach to effective information processing in communi-cation systems with low operating power.   Introduction  The modern technological advances are largely de-termined by extensive use of various communication systems. Usually, the electromagnetic compatibility requirements dictate the transmitter power limitation. In the case of lower transmitted power, the necessary sig-nal level is achieved by increasing the receiver sensitiv-ity. Typically, the receivers with high sensitivity are composed of significant number of amplification stages. Therefore, the power of desired signals is commensura-ble with the level of intrinsic noises. This creates con-siderable difficulties in processing of these signals [1]. There is the problem of detecting the weak signals from the additive mixtures of signals and noises also for digi-tal communication systems [2, 3]. For detection of co-sine video impulses in digital communication systems, the optimal filters or low-pass filters with optimal bandwidth (quasi-optimal filters) are applied [3]. For weak signals processing in strong noises, a large number of methods were developed. The methods of optimal filtering using the various criteria of optimality are widely applied [4]. The criteria of maximal signal to noise ratio, minimum of average error square and max-imum of a posteriori probability are most commonly used. Optimal filters are well understood and described in the literature [5]. It should be noted that the power gain in signal to noise ratio, when using the optimal filtering for signal detection, is equal to the signal base sM T f= ⋅ ∆ , where sT  denotes the signal duration and f∆  is the frequency band in which it is transmitted. When using the quasi-optimal filtering in analog devis-es, this gain is less on 0.9 dB [5]. The purpose of this paper is the development of novel technique of weak signal processing in strong noise condition and its application to the creation of sensitive amplifier and detector of cosine impulses to be applied in digital communication systems. To solve the named problem, the paper discusses and substantiates the essence of proposed technique of desired signal de-tection on strong noise background, describes the op-eration of sensitive amplifier and detector of cosine video impulses, reveals advantages and areas of the de-scribed devices application.  A technique of weak signal processing  in strong noise condition  To overcome the limitations of existing methods based on optimal filtering, we propose a novel tech-nique of weak signal processing in strong noise condi-tion allowing us to reach much higher values of signal to noise ratio. The essence of the technique proposed consists in the following. The desired signal ( )f t  with the noise is amplified. This amplified mixture exercises the amplitude modulation of the carrier frequency oscil-lation. The received oscillation is limited by means of the fast-response nonlinear circuit. At that, the positive half-period of amplitude-modulated signal and positive peaks of noise are extracted on resistive load. The obtained total oscillation, containing the se-quence of cosine impulses and noise, is passed through a filter. The filter cutoff frequency is chosen from the condition of undistorted transmission of cosine impuls-es. After such filtering, the mixture of signal and noise undergoes a doubled differentiation. As a result, the investigated signal is converted into the sequence of cosine impulses of opposite sign. Each of these cosine impulses is in equal measure weakened and contains two delta functions, which are eliminated. At the same time, the noise becomes the high-frequency one be-cause under noise doubled differentiation its power spectral density is changed proportional to 4ω , since TELECOMMUNICATION SCIENCES  VOLUME 4  NUMBER 1  JANUARY ─ JUNE 2013 6the power spectral density of the noise on the output of linear four-pole circuit is equal to its input power spec-tral density multiplied by square of this circuit trans-mission coefficient modulus [4]. The obtained mixture is supplied to Butterworth low-pass filter of fourth or-der. This filter allocates the signal ( )f t  and significant-ly attenuates the noise.  Analysis of sensitive amplifier  The described technique of weak signal processing in strong noise condition has been applied to the devel-opment of sensitive amplifier. The block diagram of considered sensitive amplifier is presented in Fig. 1.    Fig. 1. Block diagram of sensitive amplifier: (1) source of the signal with the noise; (2) amplifier; (3) modulator; (4) filter; (5) differentiator; (6) isolation amplifier; (7) differentiator; (8) isolation amplifier; (9) electronic key; (10) low-pass fil-ter; (11) amplifier-inverter.  Let us consider the operation principle of sensitive amplifier. The signal of source 1 with internal re-sistance sR  is amplified to the desired level by amplifi-er 2. Both the amplified signal and the oscillation of carrier frequency 0f  are supplied to the amplitude modulator 3. From the modulator output, the signal is supplied to the inertialess nonlinear circuit in the form of diode D with resistive load R. This circuit forms a sequence of cosine impulses which amplitude is varied according to the law of control signal ( )f t . Thus, the input of the Butterworth filter of second order 4 re-ceives the sequence of cosine samples satisfying the Kotelnikov theorem. Fig. 2 illustrates the named se-quence of cosine samples. The cutoff frequency of the filter 4 is selected from the condition of undistorted transmission of cosine im-pulse with duration 0 / 2sT T= , where 0 01/T f= . The form of cosine impulse shown in Fig. 3 is described by the expression ( ) cos( / )sS t A t T= pi , / 2 / 2s sT t T− ≤ ≤ , where A  is impulse amplitude and sT  denotes its dura-tion. The spectrum of such impulse can be written in the form [3] 2( ) 2 / cos( ) / [1 4( ) ]s s sS f AT fT fT= pi ⋅ pi − .    Fig. 2. The sequence of cosine samples.  The chart of this impulse spectrum is shown in Fig. 4. With accuracy sufficient for practical purposes, one can assume that the impulse spectrum is concentrated in the frequency band 0 – averf , where 3 / (2 )aver sf T= . Since 0 / 2sT T=  then 03averf f= .  Fig. 3. Cosine impulse.  As a filter 4, it is advisable to use the Butterworth filter of second order passing the signals in frequency band 0 – averf . The Butterworth filter of second order provides the decline slope of amplitude-frequency char-acteristic of 12 dB per octave that allows reducing the noise level outside the pass band to the necessary ex-tent. Both the noise of input signal source and noise of amplifier are independent and centered therefore they are summarized in power on the output of the filter 4 [6]. Further, the mixture of signal and noise undergoes a doubled differentiation. Since the circuit from input of the filter 4 to output of considered sensitive amplifier is linearly parametric, the superposition principle can be applied. According to this principle, passing the signal and the noise through processing device can be calcu-lated separately. O. MAKARENKO, O. MELNICHUK:  A NOVEL APPROACH TO WEAK SIGNAL PROCESSING  7   Fig. 4. Cosine impulse spectrum.  From output of the filter 4 through the first differen-tiator 5, signal or noise enter input of the first isolation amplifier 6 and further they enter input of restriction low-pass filter with cutoff frequency 03 f . From the output of this RC filter, signal or noise are successively passed through the second differentiator 7, the second isolation amplifier 8 on input of the second restriction RC filter with cutoff frequency 03averf f= . The capaci-ty C of this filter can be short-circuited by means of electronic key 9. As it is shown below, this allows elim-inating delta functions generated during the doubled differentiation of the signal. From the output of second restriction RC circuit through low-pass Butterworth fil-ter 10 of fourth order, the signal enter the input of am-plifier-inverter 11 finishing the processing device. The RC circuits are included into processing device in order to restrict the noise increase on outputs of iso-lation amplifiers because of their differentiation. A se-quence of control impulses is supplied on the electronic key 9 making possible to eliminate delta functions of signal. These impulses are generated by control circuit from carrier frequency oscillations creating by separate generator of frequency 0f .  Theoretical justification of processing technique  Let us consider the noise suppression in processing device. It is known [7] that spectral density of noise power after doubled differentiation is expressed by 40 ( )out r dG G K= τ ω , where 0G  denotes the uniform en-ergetic spectrum of the noise on output of the filter; rK  designates the resulting transmission coefficient of the differentiator and isolation filter; dτ  is the time con-stant of the differentiator chosen from the condition 0.1d averτ ω = .  The noise dispersion at output of the low-pass filter 10 can be expressed as follows [7]:  2 4 2001/ (2 ) ( ) ( )owerout out r dP G K K dω= σ = pi τ ω ω ω ≈∫  401/ (10 ) ( )m r d mG K≈ pi Ω τ Ω ,                  (1)  where 0G  denotes the energetic spectrum on input; 4( )r dK τ ω  designates the square of transmission coeffi-cient modulus of two differentiators with isolation am-plifiers; mΩ  is the cutoff frequency of low-pass But-terworth filter of fourth order which is equal to maximal frequency in the input signal spectrum; 2 ( )K ω  defines the square of transmission coefficient modulus of low-pass Butterworth filter of fourth order wherein it is equal to 2 ( ) 1K ω ≈  in the frequency band from 0 to mΩ  and it is equal to zero beyond boundaries of this band. Without doubled differentiation, the noise power on output of the low-pass filter can be present as  2 20 001/ (2 ) ( ) 1 / (2 )owermG K d Gωσ = pi ω ω ≈ pi Ω∫ .    (2)  Then, the power odd coefficient for the noise can be obtained in the form  2 2 4/ 5 / ( )n out r d mK K= σ σ = τ Ω .               (3)  Let us introduce the condition that the noise power on input of the low-pass filter 10 at doubled differentia-tion would be the same as on output of filter 4. Since 0.1d averτ ω =  and 45 / ( ) 1r d averK τ ω = , we find that 1/410(5)rK = . Then, the expression (3) is reduced to the form:  4( / )n aver mK = ω Ω .                         (4)  Let us consider passing the signal through pro-cessing device. After first differentiation, the signal has the form shown in Fig. 5 and can be described by rela-tion  ( ) ( / )sin( / )r d s sS t A K T t T′ = − pi τ pi .             (5)  The second differentiation transforms the signal in accordance with following expression:  2( ) ( / ) cos( / ) ( / )r d s s r d sS t A K T t T A K T′′ = − pi τ pi + pi τ ×   [ ( / 2) ( / 2)]s st T t T× δ + + − .                   (6) TELECOMMUNICATION SCIENCES  VOLUME 4  NUMBER 1  JANUARY ─ JUNE 2013 8  Fig. 5. Signal after first differentiation.   The signal form is illustrated by Fig. 6. According to this figure and using relations (5)─(6), we can find the degree of signal attenuation in device taking into ac-count the delta function elimination by means of elec-tronic key 9 shorting the capacity of second restricting filter for a short time. As a result, we get the following value of signal attenuation coefficient  2 1/2( / ) 5 / 9att r d sK K T= pi τ = .                (7)    Fig. 6. Signal form after second differentiation.  Thus, the power signal attenuation is 12 dB under its doubled differentiation. One can show that the signal samples attenuation constitutes 10 dB in output filter 10. Thus, the summarized attenuation of the signal in processing device is 22 dB. The noise attenuation is defined by expression (4) and depends from relation /aver mω Ω . It is obvious that nK  can be significant with an appropriate choice 0 / 3averω = ω . For instance, when / (2 ) 10m mF = Ω pi =  kHz, 0 300f =  kHz, 900averf =  kHz, the noise attenua-tion coefficient 78nK =  dB. Taking into account the signal attenuation, the gain with respect to the signal to noise ratio is 78 22 56gK = − =  dB. The attenuated signal is amplified and inverted by means of low noise amplifier-inverter 11 installed at output of the low-pass filter 10. It should be noted that cosine impulse is only one of known signals which retains own shape up to sign un-der doubled differentiation. It contains two delta func-tions of opposite sign which can be eliminated. In con-trast to signal, the noise under doubled differentiation has energetic spectrum changing proportionally to 4ω  becoming high frequency that provides background for its significant attenuation by means of output low-pass filter 10 as shown in Fig. 7.    Fig. 7. Illustration of noise attenuation by means of low-pass filter: 2 ( )K f  denotes the square of transmission coefficient modulus of Butterworth filter of fourth order; 0G  designates the spectral density of noise power before differentiation; ( )G f  defines the spectral density of noise power after dou-bled differentiation; hatched region under curves denotes the noise power at output of low-pass filter 10 indicating a signif-icant reduction of noise power at output of processing device.   Fig. 8 presents the impulse sequence for controlling the operation of electronic key 9 eliminated the delta functions.  Detector of cosine video impulses  Let us consider the detector of weak cosine video impulses widely used in digital communication systems [3]. The block diagram of considered detector is pre-sented in Fig. 9. In contrast to sensitive amplifier which block diagram is shown in Fig. 1, the detected video impulse enters the input of filter 2 from output of re-ceiver demodulator 1. Moreover, the pass band of low-O. MAKARENKO, O. MELNICHUK:  A NOVEL APPROACH TO WEAK SIGNAL PROCESSING  9 pass filter 7 is chosen from conditions of obtaining the maximal signal to noise ratio and making the minimal inter-symbol distortions [6].     Fig. 8. Sequence of control impulses.    Fig. 9. Block diagram of cosine impulses detector: (1) syn-chronous demodulator; (2) filter; (3) differentiator; (4) isola-tion amplifier; (5) differentiator; (6) isolation amplifier; (7) low-pass filter; (8) amplifier-inverter.  To eliminate the delta functions generated by dou-bled differentiation, the inertia-less nonlinear circuit consisting of diode D with resistive load R is installed between output of second isolating filter and input of low-pass filter 7 instead of electronic key requiring the synchronous control. Because the positive noise releas-es are truncated by diode and do not passed further, the additional gain in signal to noise ratio equaled to 3 dB is guaranteed. The results of MATLAB computation show that the optimal pass band of output low-pass filter 7 is 20 kHz for cosine video impulses at following values of param-eters: 10sT =  sµ , 150averf =  kHz. The resulting gain in signal to noise ratio is 15 dB that is substantially bet-ter than in existing detection systems with optimal fil-tering or quasi-optimal filtering at the signal basis 1.5M = . The gain in signal to noise ratio at optimal filtering with 1.5M =  constitutes 10log 1.76M =  dB. It is also possible to use the fourfold differentiation of signal and noise mixture. Of course, this leads to a complication of processing device, however, it allows obtaining the gain in signal to noise ratio exceeding 30 dB. Application of such detectors in modern digital communication systems will significantly reduce the powers of transmitters of cell phones and base stations of mobile communication systems.  Conclusion  A novel effective approach to weak continuous and digital signals processing in communication channels with high noise levels is proposed and investigated. The essence of proposed approach is illustrated by examples of sensitive amplifier and detector of digital cosine vid-eo impulses. It is shown that the proposed approach ensures obtaining a lot more gain in signal to noise ratio compared to existing technical solutions. In the elec-tronic equipment based on proposed technique, there is a significant noise attenuation not only of amplifiers prior to processing units but also noise of input signal source. It is a prerequisite for the creation of electronic equipment with new functional possibilities. The pro-posed technique can be successfully applied in digital communication systems which employ the quadrature processing circuit with synchronous detectors. The con-sidered advantages of the described devices allow em-ploying the proposed approach to effective information processing in communication systems with low operat-ing power including cell phones and base stations of mobile communication systems. It is possible to implement the proposed technique for creating the modern electronic equipment of satellite communication systems, radiolocation, radio naviga-tion, and various diagnostic systems.  References  1. Noghin V. N. Analog electronic devises. ─ Moscow: Radio and Svyaz, 1992. ─ 304 p. [in Russian]. 2. Sklar B. Digital communications: Fundamentals and applications. ─ Hardcover: Prentice Hall, 2001. ─ 1080 p. 3. Galkin V. A. Digital mobile radio communications. ─ Moscow: Hotline ─ Telecom, 2007. ─ 432 p. [in Russian]. 4. Gonorovsky I. S. Radio circuits and signals. ─ Mos-cow: Soviet Radio, 1977. ─ 608 p. [in Russian]. 5. Lezin Yu. S. Introduction to theory and technique of radio systems. ─ Moscow: Radio and Svyaz, 1986. ─ 280 p. [in Russian].  6. Lathi B. P. Information transmission systems. ─ Mos-cow: Svyaz, 1971. ─ 324 p. [in Russian]. 7. Tikhonov V. I. Statistical radio techniques. ─ Moscow: Radio and Svyaz, 1982. ─ 624 p. [in Russian]. 8. Makarenko O. S. Detection device of cosine digital and radar signals // Patent of Ukraine No. 75231 from November 26, 2012 [in Ukrainian].  Received in final form January 19, 2013  

Усиление слабых аналоговых сигналов в сильных шумах

A novel effective approach to weak continuous and digital signals processing in communication channels with high noise levels is proposed and investigated. The essence of proposed approach is illustrated by examples of various electronic devices. The conditions which allow obtaining the maximal gain in signal to noise ratio are found. This gain exceeds 50 dB for sensitive amplifier and approximately equals to 30 dB for detector of digital cosine video impulse. It is shown that the proposed approach ensures obtaining a lot more gain in signal to noise ratio compared to existing technical solutions. The considered advantages of the described devices allow employing the proposed approach to effective information processing in communication systems with low operating power.Статья посвящена решению проблемы обнаружения слабых аналоговых сигналов на фоне сильного шума с обеспечением гораздо большего выигрыша в отношении сигнал/шум в сравнении с уже существующими техническими решениями. В статье рассматривается устройство обработки сигналов, описывается сущность способа, условия достижения поставленной задачи получения максимального выигрыша в отношении сигнал/шум, превышающего 50 дБ,  и преимущества рассмотренного устройства, которое является эффективным для систем обработки информации с малым уровнем мощности

Усиление слабых аналоговых сигналов в сильных шумах

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