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A Measurement Instrument for Fault Diagnosis in Qam-Based Telecommunications

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A Measurement Instrument for Fault Diagnosis in Qam-Based Telecommunications 12th IMEKO TC4 International Symposium Electrical Measurements and Instrumentation September 25−27, 2002, Zagreb, Croatia A MEASUREMENT INSTRUMENT FOR FAULT DIAGNOSIS IN QAM-BASED TELECOMMUNICATIONS Pasquale Arpaia(1), Luca De Vito(1,2), Sergio Rapuano(1), Gioacchino Truglia(1,2) (1) Dipartimento di Ingegneria, Università del Sannio, piazza Roma, Benevento, Italy (2) Telsey Telecommunications, viale Mellusi 68, Benevento, Italy Abstract − A method for diagnosing faults in Some techniques for classifying automatically the main communication systems based on QAM (Quadrature faults on QAM modulation via the constellation diagram Amplitude Modulation) modulation scheme is proposed. were proposed. The approach followed in [4] is based on a The most relevant faults affecting this modulation have been Wavelet Network (WN). This method provides very good observed and modelled. Such faults, individually and results on simulated and actual signals. combined, are classified and estimated by analysing the Another method classifies the faults through an image- statistical moments of the received symbols. Simulation and processing approach [5]. The constellation diagram is experimental results of characterisation and validation digitised, then the obtained image is compared with some highlight the practical effectiveness of the proposed method. fault models, by using a correlation method, and a similarity score is provided. Keywords: Fault diagnosis, telecommunication, testing, However, both the WN- and the image processing-based QAM. methods can recognize and eventually measure only the dominating fault, and can not recognize the simultaneous 1. INTRODUCTION presence of several faults. In this paper, a diagnostics method, based on analytical Quadrature Amplitude Modulation (QAM) is an estimation of the statistical moments of the received symbol attractive method for transmitting two data streams in distribution, is proposed for QAM-modulation. This method channels where the transmitter power can be used to is capable of recognising several faults simultaneously increase the data rate without affecting the signal bandwidth present, and, moreover, estimating the contributes related to [1]. Such a modulation scheme is now used in the European each of them. In particular, in Section 2, main faults Digital Video Broadcasting (DVB) system and the DOCSIS affecting QAM communication are analysed and an cable modem transmission over Hybrid Fibre Coaxial (HFC) analytical model of the actual signal is proposed. In Section channels. 3, the proposed method for classifying the faults is The required quality level needs for a reliable In-Service described. Finally, in Section 4 the first results obtained by Monitoring (ISM) system capable of detecting and removing applying the method on simulated and actual QAM signals fault effects as soon as possible [2]. Moreover, a fault are reported. diagnosis based on the identification of the disturbances could be useful both in identifying the fault in the QAM 2. MAIN FAULTS AFFECTING THE transmission, and in verifying the design of communication QAM MODULATION devices, such as modulators, upconverters, and so on. At to date, instruments for QAM signalling diagnosis are based on The usually effects of the main faults on the QAM the BER (Bit Error Rate) monitoring or on a visual analysis transmission are derived by the constellation diagram [5]. In of the constellation diagram. However, some drawbacks the example of Fig. 1, the classical 16-QAM modulated arise: (i) by a BER monitor, only the fault effect on the signals in an AWGN (Additive White Gaussian Noise) signal can be detected, without providing any additional environment are considered. In presence of AWGN only, the information about the causes; moreover, a large time slot received symbols are distributed around their ideal has to be observed to provide a good estimate of the signal positions. When a fault affects the signal, the spots produced quality loss; (ii) by the visual analysis of the constellation by the symbols have different shapes and positions. In diagram, the fault type has to be diagnosed by a human particular, four typical faults can be considered: operator. - Amplitude Unbalance: it is produced by different actual This kind of analysis is now performed through the gains for the in-phase (I) and quadrature (Q) paths in the EVM (Error Vector Magnitude), that gives a measure of the transmitter and in the receiver; it leads to symmetrically difference between the actual and ideal position of the distributed shifts of the symbol (Fig. 1a). received symbol on the constellation diagram [3]. The phase jitter is a random phase error. Also this disturbance can be modelled as a rotation θ of the constellation diagram, but the angle θ is a random variable with a known distribution. In this work, θ is modelled to have a gaussian distribution with 2 zero mean and variance σ j: y cosθ − sinθ x 1 = j j 1 θ θ , (4) y2 sin j cos j x2 θ σ 2 with j ~ N(0, j ). The interference is produced by a spurious tone and gives rise to a displacement of the symbol on the constellation diagram. It can be modelled by a vector of amplitude equal to the amplitude A of the spurious tone, and phase ϕ depending on the difference between the frequency of this tone and the carrier frequency and the sampling instant. If the Fig. 1. Main faults affecting the QAM modulation: a) amplitude sample number is large enough, the phase of this unbalance, b) phase offset, c) phase jitter, and d) interference. vector can be assumed to have a uniform distribution - Phase Offset: a deterministic error on the carrier phase between 0 and 2π. The resulting model is: estimation gives rise to a rotation of the entire constellation diagram as a whole (Fig. 1b). y x Acosϕ - Phase Jitter: random variations in the carrier phase 1 = 1 + (5) ϕ estimate produces a random rotation of the diagram (Fig. y2 x2 Asin 1c). - Interference: a spurious tone overlapped to the signal in with ϕ ~ U(0 , 2π). the receiver bandwidth causes a typical ring shape of the spot (Fig 1d). The signal, affected simultaneously by all the above disturbances in an AWGN environment, can be modelled as: In the following, each disturbance is modelled separately by observing its effect on the constellation diagram. α θ − θ y1 0 cos sin 1 0 x1 The amplitude unbalance is defined as: = K + y 0 1 sinθ cosθ 0 β x () 2 2 (6) min I n ,Qn Acosϕ n Unb = ⋅100% , (1) + + 1 , max()I ,Q ϕ n n Asin n2 where In and Qn are the amplitudes respectively of the in- phase and quadrature component. where: It can be modelled by introducing two different gains g1 2 - θ ∼ N(θoff,σj ), having a mean value equal to the value of and g2, respectively, on the paths I and Q. 2 the phase offset θoff and a variance σ j equal to the variance of the jitter, takes into account the effects due to y1 g1 0 x1 both the phase disturbances; = , (2) ϕ y 0 g x - A and are the phase and the amplitude, respectively, of 2 2 2 the displacement vector caused by an interfering tone eventually overlapped to the signal; T T where x = (x1 x2) and y = (y1 y2) are the transmitted and - The matrices containing the parameters α and β take the received symbol, respectively. The phase offset is a into account the different gains on the I and Q paths in deterministic phase error, modelled as a rotation by an angle the receiver and the transmitter, respectively; θ off of the ideal point around the centre of the constellation: - K is a gain; and - n1 and n2 are the I and Q components respectively of the y cosθ − sinθ x white noise. 1 = off off 1 θ θ (3) y2 sin off cos off x2 3. THE PROPOSED METHOD Offset and im balan c e identification An algorithm for the estimation of unknown α β,θ Constellation (K, , off) parameters in the model (6), by analysing the statistical mean diagram moments of the received symbols, has been developed. The method of moments is widely known as a simple method for constructing consistent estimators [6]. As an Jitter σ2 identification example, it is used in electromagnetic field modelling [7- j covariance 9] or in image processing [10]. The method works as shown in Fig.2. First, the received symbols are distributed in the decision cells of Interference the constellation diagram. A identification Then, for each cell, by approximating the relation for 4th-order moment small phase angles, the expected value of y is calculated from the (6): σ2 σ2 Ey{}=− Kxααβθ K x ( n1, n2) 11off 2 (7) variance {}=+θβ Ey212 Koff x K x where E{ } is the expected value operator. Fig. 2. Algorithm of the proposed method. By taking the sample mean of the I and Q components of the received symbols fallen within a decision area, for at faults really present in the transmission. The presence of least two areas, the unknown parameter α, β, K and θoff in each kind of fault is detected when its threshold is exceeded. (7) can be estimated. These parameters represent the values of the amplitude unbalance and phase offset. 4. SIMULATION AND EXPERIMENTAL The phase jitter leads to a random rotation of the RESULTS constellation diagram; therefore, in a signal corrupted by TM phase jitter, some dependency between the I and Q The above method was implemented in MATLAB . components can be found. This dependency can be The performance of the method were analyzed in determined by calculating the covariance between the two simulation, in an AWGN environment, with different values components of the received symbol: of the signal-to-noise ratio (SNR) and different values of the disturbance amplitudes. Then, some tests have been carried out on actual signals, affected by the above disturbances.
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