GNU RADIO : MODULATIONS DE BASE : QUELQUES DIAGRAMMES... Objectifs : Etre capable d'utiliser GNU RADIO pour les modulations courantes
1. Introduction.......................................................................................................3 2. QAM..................................................................................................................4 2.1. Introduction................................................................................................4 2.2. Les différentes étapes et réglages...............................................................5 2.3. Diagramme complet...................................................................................8 3. PSK....................................................................................................................9 3.1. Les différentes étapes et réglages...............................................................9 3.2. Le diagramme complet.............................................................................13 4. Delta modulation.............................................................................................14 4.1. Les différentes étapes et réglages............................................................14 4.2. Le diagramme complet.............................................................................17 5. GMSK.............................................................................................................18 5.1. Introduction..............................................................................................18 5.2. Les différentes étapes et réglages............................................................19 5.3. Le diagramme complet.............................................................................21 6. GFSK...............................................................................................................22 6.1. Les différentes étapes et réglages............................................................22 6.2. Le diagramme complet.............................................................................24 7. OFDM.............................................................................................................25 7.1. Introduction..............................................................................................25 7.2. Les différentes étapes et réglages............................................................26 7.3. Diagramme complet et courbe obtenue....................................................28 8. Un récepteur FM.............................................................................................29 8.1. Les différentes étapes et réglages............................................................29 8.2. Le diagramme complet.............................................................................31 9. Traitement du signal........................................................................................32 9.1. La décimation...........................................................................................32 9.2. L'interpolation..........................................................................................35 9.3. La quantification......................................................................................39 10. Filtre réjecteur...............................................................................................43 10.1. Introduction............................................................................................43 10.2. Les différentes étapes et réglages..........................................................43 10.3. Le diagramme complet...........................................................................45 10.4. Les courbes résultantes..........................................................................45 1/48
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11. DELAY.........................................................................................................46 11.1. Le diagramme complet...........................................................................46
1. INTRODUCTION GNU Radio est un logiciel libre permettant de faire de la radio logiciel. Le ''companion'' permet de créer des diagrammes afin de réaliser vos montages en assemblant des blocs visuels. Ces blocs sont en fait des scripts Python ou des objets développés en C++ (rapidité). Voici quelques exemples pour des modulations numériques de base. Ces diagrammes sont tirés du site http://fr.scribd.com et publiés par Rakesh S K .
Au fur et à mesure des exemples les blocs sont expliqués. Important les instruments doivent être pris soit dans QT GUI ou dans WX GUI en fonction du paramètrage du bloc ''option''.
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2. QAM 2.1. Introduction What do you mean by QAM modulation? Quadrature amplitude modulation (QAM) is both an analog and a digital modulation scheme. It conveys two analog message signals, or two digital bit streams, by changing (modulating) the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or amplitude modulation (AM) analog modulation scheme. The two carrier waves, usually sinusoids, are out of phase with each other by 90° and are thus called quadrature carriers or quadrature components hence the name of the scheme. The modulated waves are summed, and the final waveform is a combination of both phase-shift keying (PSK) and amplitude-shift keying (ASK), or (in the analog case) of phase modulation (PM) and amplitude modulation. In the digital QAM case, a finite number of at least two phases and at least two amplitudes are used. PSK modulators are often designed using the QAM principle, but are not considered as QAM since the amplitude of the modulated carrier signal is constant. QAM is used extensively as a modulation scheme for digital telecommunication systems. Arbitrarily high spectral efficiencies can be achieved with QAM by setting a suitable constellation size, limited only by the noise level and linearity of the communications channel. In a QAM signal, there are two carriers, each having the same frequency but differing in phase by 90 degrees (one quarter of a cycle, from which the term quadrature arises). One signal is called the I signal, and the other is called the Q signal. Mathematically, one of the signals can be represented by a sine wave, and the other by a cosine wave. The two modulated carriers are combined at the source for transmission. At the destination, the carriers are separated, the data is extracted from each, and then the data is combined into the original modulating information
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2.2. Les différentes étapes et réglages
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2.3. Diagramme complet
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3. PSK 3.1. Les différentes étapes et réglages
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3.2. Le diagramme complet
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4. DELTA MODULATION 4.1. Les différentes étapes et réglages
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4.2. Le diagramme complet
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5. GMSK 5.1. Introduction What is GMSK modulation? Gaussian Minimum Shift Keying, or to give it its full title Gaussian filtered Minimum Shift Keying, GMSK, is a form of modulation used in a variety of digital radio communications systems. It has advantages of being able to carry digital modulation while still using the spectrum efficiently. One of the problems with other forms of phase shift keying is that the sidebands extend outwards from the main carrier and these can cause interference to other radio communications systems using nearby channels. In view of the efficient use of the spectrum in this way, GMSK modulation has been used in a number of radio communications applications. Possibly the most widely used is the GSM cellular technology which is used worldwide and has well over 3 billion subscribers. Generating GMSK modulation There are two main ways in which GMSK modulation can be generated. The most obvious way is to filter the modulating signal using a Gaussian filter and then apply this to a frequency modulator where the modulation index is set to 0.5. This method is very simple and straightforward but it has the drawback that the modulation index must exactly equal 0.5. In practice this analogue method is not suitable because component tolerances drift and cannot be set exactly.
A second method is more widely used. Here what is known as a quadrature modulator is used. The term quadrature means that the phase of a signal is in quadrature or 90 degrees to another one. The quadrature modulator uses one signal that is said to be in-phase and another that is in quadrature to this. In view of the in-phase and quadrature elements this type of modulator is often said to be an I-Q modulator. Using this type of modulator the modulation index 17/48
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can be maintained at exactly 0.5 without the need for any settings or adjustments. This makes it much
5.2. Les différentes étapes et réglages
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5.3. Le diagramme complet
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6. GFSK 6.1. Les différentes étapes et réglages
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6.2. Le diagramme complet
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7. OFDM 7.1. Introduction What is OFDM? Cyclic prefix insertion is commonly used in orthogonal frequency division multiplexing (OFDM) systems as a way to mitigate the effects of intersymbolinterference (ISI). It copies the end section of an inverse fast Fourier transform (IFFT) packet to the beginning of an OFDM symbol. Usually the length of the cyclic prefix is longer than the length of the dispersive channel to completely remove ISI. OFDM modulation therefore mostly revolves around cyclic prefix: OFDM modulation includes IFFT operation and cyclic prefix insertion; OFDM demodulation includes cyclic prefix removal and FFT operation. Modern communications systems feature highly dynamic scalability, which often requires changing system parameters on-the-fly based on channel conditions and user quality of service (QoS) requirements. This design example demonstrates cyclic prefix insertion and removal for a reconfigurable OFDM system using the Altera FFT MegaCore function. It supports run-time reconfiguration of FFT size and cyclic prefix size. You can apply such designs to many different systems, such as OFDM-based wireless communications systems, including WLAN, WiMAX, and 3GPP2 long term evolution (LTE) systems, as well as digital video broadcast (DVB) systems. Orthogonal frequency-division multiplexing (OFDM) is a method of encoding digital data on multiple carrier frequencies. OFDM has developed into a popular scheme for wideband digital communication, whether wireless or over copper wires, used in applications such as digital television and audio broadcasting, DSL Internet access, wireless networks, power line networks, and 4G mobile communications. OFDM is a frequency-division multiplexing (FDM) scheme used as a digital multi-carrier modulation method. A large number of closely spaced orthogonal sub-carrier signals are used to carry data on several parallel data streams or channels. Each sub-carrier is modulated with a conventional modulation scheme (such as quadrature amplitude modulation or phase-shift keying) at a low symbol rate, maintaining total data rates similar to conventional single-carrier modulation schemes in the same bandwidth The primary advantage of OFDM over single-carrier schemes is its ability to cope with severe channel conditions (for example, attenuation of high frequencies in a long copper wire, narrowband interference and frequencyselective fading due to multipath) without complex equalization filters. Channel equalization is simplified because OFDM may be viewed as using many slowly 24/48
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modulated narrowband signals rather than one rapidly modulated wideband signal. The low symbol rate makes the use of a guard interval between s ymbols affordable, making it possible to eliminate intersymbol interference (ISI) and utilize echoes and time-spreading (on analogue TV these are visible as ghosting and blurring, respectively) to achieve a diversity gain, i.e. a signal-tonoise ratio improvement. This mechanism also facilitates the design of single frequency networks (SFNs), where several adjacent transmitters send the same signal simultaneously at the same frequency, as the signals from multiple distant transmitters may be combined constructively, rather than interfering as would typically occur in a traditional single-carrier system.
7.2. Les différentes étapes et réglages
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7.3. Diagramme complet et courbe obtenue
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8. UN RÉCEPTEUR FM 8.1. Les différentes étapes et réglages
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8.2. Le diagramme complet
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9. TRAITEMENT DU SIGNAL 9.1. La décimation Introduction La décimation consiste à diminuer le nombre d'échantillon par seconde dans un signal. Les différentes étapes et réglages
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Le diagramme complet
Les courbes résultantes
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9.2. L'interpolation Introduction L'interpolation permet d'augmenter le nomre d'échantillon par seconde dans un signal. What do you mean by interpolation? In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate (i.e. estimate) the value of that function for an intermediate value of the independent variable. This may be achieved by curve fitting or regression analysis. A different problem which is closely related to interpolation is the approximation of a complicated function by a simple function. Suppose the formula for some given function is known, but too complex to evaluate efficiently. A few known data points from the original function can be used to create an interpolation based on a simpler function. Of course, when a simple function is used to estimate data points from the original, interpolation errors are usually present; however, depending on the problem domain and the interpolation method used, the gain in simplicity may be of greater value than the resultant loss in accuracy. There is also another very different kind of interpolation in mathematics, namely the "interpolation of operators". The classical results about interpolation of operators are the Riesz – Thorin theorem and the Marcinkiewicz theorem. There are also many other subsequent results. In the domain of digital signal processing, the term interpolation refers to the process of converting a sampled digital signal (such as a sampled audio signal) to a higher sampling rate (Upsampling) using various digital filtering techniques (e.g., convolution with a frequency-limited impulse signal). In this application there is a specific requirement that the harmonic content of the original signal be preserved without creating aliased harmonic content of the original signal above the original Nyquist limit of the signal (i.e., above fs/2 of the original signal sample
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rate). An early and fairly elementary discussion on this subject can be found in Rabiner and Crochiere's book Multirate Digital Signal Processing Les différentes étapes et réglages
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Le diagramme complet
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9.3. La quantification Introduction What do you mean by Decimation? In digital signal processing, decimation is the process of reducing the sampling rate of a signal. Complementary to interpolation, which increases sampling rate, it is a specific case of sample rate conversion in a multi-rate digital signal processing system. Decimation utilizes filtering to mitigate aliasing distortion, which can occur when simply down sampling a signal. [3] A system component that performs decimation is called a decimator. Decimation reduces the data rate or the size of the data. The decimation factor is usually an integer or a rational fraction greater than one. This factor multiplies the sampling time or, equivalently, divides the sampling rate. For example, if 16-bit compact disc audio (sampled at 44,100 Hz) is decimated to 22,050 Hz, the audio is said to be decimated by a factor of 2. The bit rate is also reduced in half, from 1,411,200 bit/s to 705,600 bit/s, assuming that each sample retains its bit depth of 16 bits. Decimation by an integer factor, M, can be explained as a 2-step process, with an equivalent implementation that is more efficient: 1.Reduce high-frequency signal components with a digital low-pass filter. 2.Down sample the filtered signal by M; that is, keep only every sample. Down sampling alone causes high-frequency signal components to be misinterpreted by subsequent users of the data, which is a form of distortion called aliasing. The first step, if necessary, is to suppress aliasing to an acceptable level. In this application, the filter is called an anti-aliasing filter, and its design is discussed below. Also see under sampling for information about down sampling band-pass functions and signals.
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Les différentes étapes et réglages
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Le diagramme complet
La courbe résultantes
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10. FILTRE RÉJECTEUR 10.1. Introduction In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the opposite of a band-pass filter. A notch filter is a bandstop filter with a narrow stopband (high Q factor). Narrow notch filters (optical) are used in Raman spectroscopy, live sound reproduction (public address systems, or PA systems) and in instrument amplifiers (especially amplifiers or preamplifiers for acoustic instruments such as acoustic guitar, mandolin, bass instrument amplifier, etc.) to reduce or prevent audio feedback, while having little noticeable effect on the rest of the frequency spectrum (electronic or software filters). Other names include 'band limit filter', 'T-notch filter', 'band-elimination filter', and 'band-reject filter'. Typically, the width of the stopband is 1 to 2 decades (that is, the highest frequency attenuated is 10 to 100 times the lowest frequency attenuated). However, in the audio band, a notch filter has high and low frequencies that may be only semitones apart. A bandpass filter allows signals within a selected range of frequencies to be heard or decoded, while preventing signals at unwanted frequencies from getting through. A bandpass filter also optimizes the signal-to-noise ratio and sensitivity of a receiver 10.2. Les différentes étapes et réglages
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10.3. Le diagramme complet
10.4. Les courbes résultantes
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11. DELAY 11.1. Le diagramme complet
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