Basic Algorithm for the Noncoherent Digital. Processing of the Narrowband Radio Signals

Transcription

1 Applied Mathematical Sciences, Vol. 9, 2015, no. 95, HIKARI Ltd, Basic Algorithm for the Noncoherent Digital Processing of the Narrowband Radio Signals A. N. Glushkov, V. P. Litvinenko and B. V. Matveev Department of Radio Engineering Voronezh State Technical University, Voronezh, Russia O. V. Chernoyarov Department of Radio Engineering Devices National Research University MPEI, Moscow, Russia Copyright 2015 A. N. Glushkov, V. P. Litvinenko, B. V. Matveev and O. V. Chernoyarov. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract We suggest a basic fast algorithm for the noncoherent digital processing of the radio signals consisting of the minimum number of simple arithmetic operations over a signal period. On its basis there can be realized the algorithms and the correspondent digital devices for detection and noncoherent demodulation of signals with amplitude, frequency modulation and differential phase keying. Digital signal processors and modern programmable logic devices can be effectively used for their practical implementation. Keywords: amplitude modulation, frequency modulation, differential phase keying, detection, demodulation, digital processing, noncoherent processing 1 Introduction Radio signal processing presupposes the solution of the problem of the received signal extraction, detection, demodulation, decoding and parameter estimation, as well as synchronization. These problems can be combined and supplemented. Theoretical studies, for example [1-4], suggest optimal or near optimal algorithms and devices for analog and digital processing of received signals against hindrances. As a rule, they are complicated enough and difficult-to-make

2 4728 A. N. Glushkov et al. for digital implementation in real time. There are effective techniques of dealing with that kind of problems by means of fast algorithms containing the detailed description of the computing procedures with complex calculation ways of an output signal in reference to the specified input signal [1]. Therefore, the fast algorithm sacrifices computational convenience for the efficiency of computations. 2 Basic algorithm In this work we present the basic (universal) fast algorithm for noncoherent digital processing of narrowband radio signals. On its basis there can be implemented the algorithms and the corresponding devices for detection and demodulation of signals with various modulation formats. We write down the input narrowband signal as st St 2f 0t t S t (amplitude) and t cos, (1) where (initial phase) are slowly varying functions of time defined by modulation format and transmission, f 0 is carrier frequency. In order to provide the quadrature radio signal (1) processing, it is necessary to form samples through quarter-period T0 1 f0, so sample rate is equal Thereby, the four samples i, 0 is shown in Fig. 1. s, 1 f Q 4 f 0. (2) s i,, s i, 2 and s i, 3 are formed over i-th period, as it Fig. 1. Signal quantization. It allows us to obtain the following sample values within i-th signal period: si,0 S cos, si,1 S cos 2 S sin, (3) si,2 S cos S cos, si,3 S cos 3 2 S sin,

3 Basic algorithm for the noncoherent digital processing 4729 where S and ψ are amplitude and initial phase for i-th period which are approximately constant within one period. Thus, it is possible to form two quadrature samples of a kind xi,0 si,0 si,2 2S cos, (4) xi,1 si,1 si,3 2S sin. According to Eq. (4), the following equality holds x 2 2 i, 0 i, 1 2 x S, (5) and the result does not depend on initial phase and quantization points positions within the period. The sampling obtained for N periods s i, 0, s i, 1, s i, 2, s i, 3, i 1, N is divided into two numerical sequences containing even and odd samples. For each period differences of even and odd samples are calculated and then are summarized for N periods: N N yi, 0 xi j,0 si j,0 si j,2, (6) j1 N j1 N yi, 1 xi j,1 si j,1 si j,3. (7) j1 j1 Sequences of even and odd samples are shifted for a signal quarter-period in time, making two quadrature channels y i, 0 and y i, 1 of a narrowband signal processing. The block diagram of basic fast digital processing algorithm of a narrowband signal is presented in Fig. 2. The input narrowband signal s t (1) is received to the analog-to-digital converter (ADC) input, which is gated by clock pulse generator (CPG) with frequency f Q (2) and forms the four samples s i, 0, s i, 1, s i, 2 and s for i-th signal period. They are fed into the multibit shifter containing four i,3 samples (MS4), and then the computational procedure (6), (7) is run according to computing fast algorithm described below. In subtracters SUB0 and SUB1 the differences of even x i, 0 and odd x i, 1 samples (4) are calculated. Then, they are summarized with content of multibit registers MR01 and MR11, each of which contains one value x i1, 0 or x i1, 1 accordingly received in the course of previous processing period. Further, the sums of two samples differences x i, 0 x i 1, 0 and x i, 1 x i 1, 1 are computed, after that new values x i, 0 and x i, 1 are put into registers in MR01 and MR11 exchanging their previous content. Afterwards the sums of four adjacent samples differences x x x x x x x are calculated x and i, 0 i1,0 i2,0 i3,0 i, 0 x i 1, i, 1 x i 1, i, 1 i1,1 i2,1 i3,1 where x 0 and x 1 have been generated in summators SUM01 and

4 4730 A. N. Glushkov et al. SUM11, and x i, 2,0 x i 3, 0 and x i, 2,1 x i 3, 1 have been written down into last cells of multibit shifters МR02 and МR12 occupying two memory cells for each. Further, contents of registers is shifted, out-of-date values are lost, and the values x i, 0 x i 1,0 and x i, 1 x i 1, 1 obtained in SUM01 and SUM02 are recorded in the first deallocated cells. Then device operation repeats differing only by number of memory cells in multibit shifters being equal to 4, 8 and so forth up to n 2 1 N 2, and the sums on 8, 16 and more of the last received differences are formed. In the end of the accumulation, the responses of quadrature channels y i, 0 and y i, 1 are calculated in summators SUM0n and SUM1n. Fig. 2. Basic algorithm. Based on the various responses transformations of quadrature channels y i, 0 and y i, 1, there can be constructed various algorithms and devices of noncoherent processing of the received signal. 3 Amplitude demodulator Using the samples transformation of quadrature channels of a kind z i 2 2 i, 0 y i, 1 y. (8) the fast digital algorithm (and device) of the narrowband signal detection and amplitude demodulation is realized (patent [5] and [7, 8]). Computational costs of the values (8) formation can be reduced according to [4]. The block diagram of the narrowband signal detector is shown in Fig. 3а where the basic algorithm (BA) is illustrated in Fig. 2, and the demodulator frequency response H f

5 Basic algorithm for the noncoherent digital processing 4731 H f z S Nf f cosf 2 sin 0 f0 (9) is presented in Fig. 3b. Here z is a response on a frequency f, and S is the input signal amplitude. Detuning between maximum of frequency characteristic and its first zero is f N. (10) f 0 a) b) Fig. 3. Narrowband signal detector (a) and its frequency response (b). The decision on presence or absence of a signal is made by the comparison of the values z i (8) or their means with a threshold. There is a possibility of the estimation of signal and noise levels and of the construction of the adaptive detection algorithm [8]. Fig. 4. Amplitude demodulator response. When the amplitude-modulated signal is demodulated in the presence of the white noise, the response z changes in proportion to the modulating signal. It is shown in Fig. 4 by the solid curve for the carrier frequency f 0 10 MHz, modulation frequency 1 khz, modulation depth 100%, and root-mean-square deviation of white noise rms. Here and upward i is number of the current carrying oscillation period, S H is carrying oscillation amplitude, and N By dashed curve in Fig. 4 the modulating signal at the device input is shown. It is seen that the demodulator possesses good filtering properties and the output signal delay is caused by the accumulation of samples in registers.

6 4732 A. N. Glushkov et al. 4 Angle-modulated signal processing In [4] there are considered the possibilities of determining of instantaneous phase and frequency of the complex signal by means of Hilbert transform. Then for the estimate of the current phase of the received narrowband signal we obtain arctg yi1 yi0, if yi0 0, C t i (11) arctg yi1 yi0, if yi0 0, and for the current frequency estimate f t f t t 2 (Hz). (12) i 0 C i C i The algorithm of the received signal phase and frequency detection is shown in Fig. 5а, where BA is the basic fast algorithm of digital signal processing (Fig. 2), F is function generator (11), and D is differentiator (12). For example, we consider the tone phase modulation signal of a kind s t S 2f t b sin2ft 1 sin 0, (13) where f 0 is carrier frequency, F is phase modulation frequency, b is amplitude of phase change. In Fig. 5b the detection effect i (11) of analog phase modulation signal (13) is shown, if f 0 10 MHz, modulation frequency F 1 khz and amplitude of phase change b 3 radians. Bias of initial phase value is caused by absence of phase alignment (coherence) between received and clock signals. If b, then there is phase estimate ambiguity, which can be easily overcome all the same. As the tests conducted by us have shown, the presented phase demodulation algorithm possesses a high-noise immunity. a) b) Fig. 5. Phase demodulator (a) and result of phase demodulation (b). But, our studies show that the received signal frequency f (i) estimate (12) at the differentiator D output (Fig. 5а) possesses a low immunity.

7 Basic algorithm for the noncoherent digital processing Frequency-modulated signal demodulator Demodulation of the frequency-modulated signal should be employed by means of the algorithm and the corresponding device (patent [9]), its block diagram is presented in Fig. 6а. It is implemented by the two amplitude demodulators having various clock frequencies f QU 0 and f QU1 at input ADCs: fqu 0 4( f0 f ), (14) fqu1 4( f0 f ). Here f is defined from Eq. (10). Responses z 0 and z 1 of these amplitude demodulators pass to the substractor (SUB) forming the frequency demodulator output signal z z1 z0. (15) Demodulator frequency characteristic is drawn in Fig. 6b by solid line (by dashed line the straight line is plotted here). a) b) Fig. 6. Frequency-modulated signal demodulator (a) and its frequency characteristic (b). 4.2 Phase-shift keyed signal demodulator Based on the basic algorithm, the noncoherent phase-shift keyed signal digital demodulator can be implemented according to the patent [10], the analysis of its noise immunity was conducted in [11]. The block diagram of the demodulator is shown in Fig. 7. Values y 0 and y 1 of BA responses are added in summators i i SUM0n and are subtracted in subtracters SUB0n with values y0( i N ) and y1 ( i N ) for the previous information element recorded in multibit shifters MR0n and MR1n. Results u 00, u 01 and u 10, u 11 after their quadratic transformation (QT) z z u00 u01, 1 u 2 10 u 2 11 (16)

8 4734 A. N. Glushkov et al. are compared in the resolver (RS) and the information symbol s I is chosen on greatest of them. Fig. 7. Phase-shift keyed signal demodulator. The analysis and statistical simulation modeling show that the considered noncoherent demodulation algorithms of the binary frequency-modulated and differential phase-shift keyed signals provide a potential immunity in Gaussian noises [1]. 5 Conclusion The suggested basic fast digital algorithm of noncoherent signal processing allows to construct the various devices for radio signal detection and demodulation with minimal requirements to the calculator speed on a uniform hardwaresoftware basis. It can be implemented on the base of both modern digital signal processors and programmable logic devices or in the form of specialized highlyintegrated chips. Acknowledgements. The reported study was supported by Russian Foundation for Basic Research (research projects No , ). References [1] L. M. Fink, Discrete-message communication theory, Sovetskoe Radio, Moscow, (in Russian)

9 Basic algorithm for the noncoherent digital processing 4735 [2] J. Proakis, M. Salehi, Digital Communications, McGraw-Hill, New York, [3] B. Sklar, Digital Communications: Fundamentals and Applications, Prentice Hall, New Jersey, [4] R. G. Lyons, Understanding Digital Signal Processing, Prentice Hall, New Jersey, [5] A. V. Glushkov, V. P. Litvinenko, Ju.D. Proskuryakov, Digital narrowband signals detector, Certificate of Authorship , Russia, IPC H04B 1/10 (patent application /09, appl , publ. by Federal Service for Intellectual Property Patents and Trademarks of the Russian Federation , Bull. 21). [6] A. N. Glushkov, V. P. Litvinenko, P. A. Popov, Fast digital detection algorithm of a narrowband signal (in Russian). Herald of the Voronezh State Technical University. Series Radio Electronics and Communication Systems, 4.2 (2002), 6-8. [7] S. V. Bukharin, A. N. Glushkov, N. A. Kostrov, V. P. Litvinenko, Fast digital algorithms for detecting narrowband signals. Telecommunications and Radio Engineering, 3 (2005), [8] S. V. Bukharin, V. P. Litvinenko, A. N. Glushkov, Detection of narrowband signals with noise level assessment. Telecommunications and Radio Engineering, 1 (2008), [9] A. V. Glushkov, V. P. Litvinenko, Digital demodulator for frequencymodulated signals, Certificate of Authorship , Russia, IPC H04B 1/10, H03D 3/00 (patent application /08, appl , publ. by Federal Service for Intellectual Property Patents and Trademarks of the Russian Federation , Bull. 19). [10] V. P. Litvinenko, A. N. Glushkov, Differential phase-shift keyed signal digital demodulator, Certificate of Authorship , Russia, IPC H04B 1/10, H03D 3/02 (patent application /08, appl , publ. by Federal Service for Intellectual Property Patents and Trademarks of the Russian Federation , Bull. 3). [11] A. N. Glushkov, V. P. Litvinenko, P. A. Popov, Interference immunity for quadrature demodulation of phase-shift keyed signals (in Russian). Herald of the Voronezh State Technical University. Series Radio Electronics and Communication Systems, 4.3 (2003), Received: May 3, 2015; Published: July 3, 2015