Power Measurement in DVBT Systems: on the Suitability of Parametrical Spectral Estimation in DSPbased Meters
L. Angrisani1, D. Capriglione2, L. Ferrigno2, G. Miele2
1 DIS, University of Naples Federico II, Napoli, Italy.
Phone: (39) 0817683170, Fax: (39) 0817683816, e-mail:
2 DAEIMI, University of Cassino, Via G. Di Biasio, 43, 03043 Cassino (FR), Italy.
Phone: (39) 0776-2993673, Fax: (39) 0776-2993707, Email: {capriglione, ferrigno, g.miele}@unicas.it
Tab. I. RelevantDVB-T measurement parameters and their applicability according to ETSI TR 101.290 (T=transmitter, R=receiver).
Measurement parameter / T / RRF/IF signal power / X / X
Noise power / X
RF and IF spectrum / X
Linearity characterization (shoulder attenuation) / X
Power efficiency / X
BER vs. C/N ratio by variation of transmitter power / X / X
BER vs. C/N ratio by variation of Gaussian noise power / X / X
Abstract. – Current activity is focused on a wider research program, aimed at the realization of a DSP based instrument for power measurement on DVB-T systems, mainly devoted to performance assessment and large scale monitoring. Satisfying repeatability, reduced measurement time (fast measurement rate) and cost effectiveness are, in particular, pursued. To this aim the paper investigates measurement algorithms, based on PSD parametrical estimations for power measurement in DVB-T systems. The attention is focused on parametric PSD estimators because their low convergence time and chance to realize sequential estimation???. Suitable stages, in simulation and emulation environment, are designed and applied in order to optimally regulate main parameters of the proposed PSD estimation algorithms. The results of a number of experiments on emulated DVB-T signals give also evidence of the algorithm’s efficacy with respect to alternative non parametrical solution (i.e. WOSA). Finally a discussion about the suitability of WOSA and parametric PSD estimation algorithms for a DSP implementation is reported in the paper.
Keywords – Power measurement, Channel power measurement, RF measurements, DVBT, WOSA estimation, Parametrical spectral estimation.
IINTRODUCTION
Digital video broadcasting (DVB) represents a considerable technological opportunity to make innovation in standard television; whether via satellite (DVB-S), via cable (DVB-C), or terrestrial (DVB-T), it is revolutionizing television transmission [1]. With special regard to DVB-T, the complex modulation technique adopted (Coded Orthogonal Frequency Division Multiplexing,COFDM) poses a completely new measurement challenge for radiofrequency (RF) signal integrity and physical layer analysis.
A new set of measurements for monitoring and assessing the performance of DVB-T systems and apparatuses is, in fact, required (see TableI). Power measurements, in particular, play a very important role. Radiofrequency (RF) and intermediate frequency (IF) signal power, RF channel power, RF and IF power spectrum, noise (or unwanted) power, and power efficiency are relevant parameters to be measured as accurately as possible [2]. RF power meters equipped with proper probes and spectrum analyzers can be used to the purpose [2]. The formers are specifically mandated for peak and or average power measurements, while the use of the latter is mandatory whenever the integration of the input signal power spectrum over a certain frequency range (for example, in channel power measurement) is involved [3].
Traditional spectrum analyzers, however, suffer from low accuracy and repeatability problems, the entity of which depends on the specific measurement. This is true in the presence of any signal characterized by high PAR (peak to average power ratio), like OFDM signals. Peak power can be much greater than average one, thus making the signal exhibit rapid changes in time domain (noise like nature) that can disturb the proper operation of these instruments [4],[5]. The cited problems have been mitigated both by modern spectrum analyzers (Express Spectrum Analyzer, ESA, Performance Spectrum Analyzer,PSA, Real Time Spectrum Analyzer, RSA) and high-performance vectorsignal analyzers (VSA).
The authors already showed in [6] that good reliability and repeatability in DVB-T power measurements can be assured through the combined use of a proper digital signal processing algorithm and minimum hardware. A new method was in particular proposed, based on nonparametric power spectral density (PSD) estimation (Fig.1).Only acommon downconversion stage, from RF to IF, and a general purpose data acquisition system (DAS)are required.After digitizing the input RF signal, the method first gains its true power spectrum through the use of a weighted overlapped segment averaging (WOSA) estimator, and then evaluates the quantities of interest by applying very straightforward measurement algorithms to the attained PSD. The method was tested in simulation and emulation environments, as well as applied to a number of actual signals. The obtained results highlighted satisfying performance if compared to thatexhibited by competitive and expansive measurement solutions, like modern spectrum analyzers and high-performance vector signal analyzers.
Current activity is focused on the design and realization of a DSP-based meter for power measurement in DVB-T systems, mainly devotedto performance assessment and large scale monitoring.Satisfying repeatability,reduced measurement time (fast measurement rate) and cost effectiveness are,in particular, pursued.To this aim, a suitabledownconversion circuitry has already been arranged, and a proper digitizing section is going to be selected. Concerning the measurement algorithm,even though that proposed in [6] assures remarkable repeatability, its implementation in cost-effective DSP-based architectures could be very troublesome.
Fig.1. Block diagram of the alreadyproposed method.
More specifically, WOSA estimator requires a great number of fast Fourier transforms (FFTs) to be calculated. To attainan adequate frequency resolution, each FFT has to involve a non trivial number of acquired samples, to be preserved in the local memory of the meter. A relevant storage capability, often incompatible with typical DSP-based architectures and unsuited to the desired research target, is thus claimed. Moreover, any attempt to reduce the record length could severely compromise the achievable repeatability[6].
The paper intends to design and set up an alternative algorithm (in the following referred as new algorithm) for power measurement in DVB-T systems, capable of meeting the reduced memory resources of a cost –effective DSP-based meter and grantingthe same promising performance of the algorithm (old algorithm)peculiar to the method in[6]. The attention is mainly paid to the PSD estimation section of the old algorithm, and in particular to the opportunity of replacing WOSA estimator with a parametric approach.
Several reasons justify the choice.
(i)Parametric spectral estimation can exhibit a reduced convergence time;
(ii)Parametric spectral estimation is entitled to provide more significant results than those achievable from nonparametric approaches when the acquired record covers a relatively short time interval.
(iii)The WOSA method yields PSD estimates from windowed set of data. The unavailable data values outside the window are implicitly zero, normally an unrealistic assumption that can lead to distortions in the spectral estimate. Sometimes it’s possible to have some knowledge about the process from which the data samples are taken. This information may be used to construct a model and regulate its parameters in such away as to best approximate the process that generated the observed time sequence[7].
(iv)Parametric spectral estimation can be implemented in recursive form, thus allowing measurement results to be updated whenever a new sample is available and removing the need of locally storing a large number of acquired samples [7].
The paper is organized as follows. Details on parametric spectral estimation theory, with special regard to itsautoregressive (AR)approach, are given in Section II. Section III aims at optimizing, through a simulation stage,the most relevant parameters of the new algorithm according to the specific features of DVB-T signals; signal conditions very close to real ones are, in particular, induced. In Section IV a thorough performance assessmentof the new algorithm in the presence of a real DAS is carried out and compared to that assured by the old one.
IITHEORETICAL BACKGROUND
Parametric estimation methods suppose that the analyzed signal is the output of a model, represented as a linear system, driven by a noise sequence n. They evaluate the PSD of the signal by estimating the parameters (coefficients) of the linear system that hypothetically "generates" the signal. Among the various methods, autoregressive (AR) approaches are widespread. Computational burden related to AR is, in fact, significantly less than those required to implement Moving Average (MA) or Auto Regressive Moving Average (ARMA) parameter estimation algorithms[7].
A stationaryAR(p) process with zero mean satisfies the equation:
(1)
where ap,1,ap,2,…,ap,p are fixed coefficients and {n} is a white noise process with variance 2p. The PSD for stationary process described by AR(p) is given by:
(2)
whereTs=1/fs is the sampling interval and fN=1/(2Ts) is the Nyquist frequency. A key performance parameter isp, the so calledpolynomial order.
Once p has been fixed, in order to have a sound estimate of S(f), it is necessary to properly estimate the p+1 parameters ap,1,ap,2,…,ap,pand 2p. Several algorithms are availabletothe purpose: LS (Least Square) [8], Burg [9], Modified Covariance[8]. Details on all of them are given in the following.
A.Least square estimation algorithm
Let us consider an AR model with a polynomial order p.Given a sequence x0,…,xn-1,the estimated forward linear predictor can be described as[10]
.(3)
and the forward linear prediction error can be expressed as
n=p,…,N-1(4)
where ap,0=1.
To estimateap,k,the so called prediction error energy, SSp, has to be minimized:
.(5)
Specifically, the derivatives of SSp with respect toap,k are set to zero, obtaining p+1 equations(covariance equations)[10], Morf et al.providein [11] an efficient recursive solution for these equations which requires a number of computations proportional to p2.
B.Burg estimation algorithm
The approach provides for the minimization of the sum of forward and backward linear prediction error energies, namely
(6)
where ep(n) is defined in (4) andbp(n), called backward linear prediction error, is:
n=p,…,N-1,(7)
whereap,0 is equal to 1. Using Levinson-Durbin recursions, it’s possible to demonstrate that SSpdepends only onap,p. Once ap,phas been estimated, theother parameters are obtained through the Levinson-Durbin algorithm[7]. Also in this case, the computational burden is proportional to p2.
C.Modified covariance estimation algorithms
If (4) and (7) are substituted in (6), the minimum for SSp is found by setting the derivatives with respect to the AR(p) parameters ap,1,ap,2,…,ap,p to zero,
(8)
with ap,0=1 by definition, where
. (9)
The algorithm requires a number of computations proportional to p3, which is graterthan thatneeded by Burg’s approach. Marple in [12] suggests a solution requiring a number of computations proportional to p2.
IIIOPTIMIZATION OF PSD ESTIMATION ALGORITHMS
As highlighted in the previous section,the performance of AR estimators depends on the polynomial orderp, while, as reported in [6], the performance of WOSA estimator depends on the window function,(•), and overlap ratio,r. To optimally choose these parameters a suitable simulation stage has been designed. A number of numerical tests havebeen executed in Matlab 7TM environment with the aim of minimizing the same figures of merit defined in [6]and representing:
a) the experimental standard deviation characterizing both total () and channel (C) power measurement results;
b) the difference between the mean value of the results provided by the method and imposed one, considered as reference, for both total () and channel (C) power.
DVB-T reference signals have firstly been generated according to the simulation procedure described in [6].
Their intermediate frequency has been set to 36.13MHz, in order to meet the technical features of the downconversion circuitry the desired DSP-based meter is going to be equipped with Philips TD1316ALF/IHP3TM tuner module for digital terrestrial application is, in particular, enlisted [13]. It is a high performance and cost effective single conversion tuner characterized by an IF center frequency of 36.13MHz and a RF frequency range of 51-858MHz.
The following DVB-T transmission settings have been imposed: 8k transmission mode (k=6817 and Tu=896s), 1/4 (=224s) and 1/32 (=28s) guard intervals. In addition, three values of the oversampling factor (considered as the ratio between the sample rate and IF signal central frequency) have been considered.The hypothesis of acquired records covering from one to 1/128 of a DVB-T symbol has been hold. For each transmission setting and oversampling factor value, 50 different realizations (test signals) have been produced.
As forAR estimation algorithms,taking into account that higher values of p may introduce spuriousdetails in the estimated spectrum, and lower values ofp may drive to a highly smoothed spectral estimate[8], a dual stage optimization procedure has been applied.In the first stage, a rough optimization has been pursued; a suitable operative range forp has been fixed. The second stage has finely tuned the value of p, within the range previously determined, through the minimizationofC, andC.All the algorithms described in Section II have been analyzed, whose Matlab implementations are available in [14].
A.Rough optimization
Suitable figures of merit, addressed to highlight the goodness of the PSD estimates have been enlisted. The attention has been paid to FPE (Final Prediction Error), AIC (Akaike’s Information Criterion) and RMSE (Root Mean Square Error); details can be found in [8],[15].
Tab.II. Some result obtained in the first optimization stage.
AR PSD ESTIMATOR / Guard Interval[µs] / Figures of Merit
Burg / 28 / p / 300
RMSE / 1.20
Mean Time / 375ms
224 / p / 300
RMSE / 1.28
Mean Time / 394ms
LS / 28 / p / 300
RMSE / 1.20
Mean Time / 4204ms
224 / p / 300
RMSE / 1.28
Mean Time / 5637ms
Modified covariance / 28 / p / 300
RMSE / 1.19
Mean Time / 8782
224 / p / 300
RMSE / 1.28
Mean Time / 9865ms
Moreover, taking into account major features of AR estimators and trying to achieve a reduced convergence time, the following values of p have been considered: 60,70,80,90,100,200,300,400,500, and 600. All the algorithms described in Section II have been analyzed.
For sake of brevity, the most relevant results are shown in Tab.II; only RMSE is accounted for because FPE and AIC have exhibited similar behavior. They refer to an oversampling factor equal about to three, two guard intervals equal respectively to 28 and 224s, and an observation period as long as 1/4 DVB-T symbol. The given value of p allows the minimum RMSE, also indicated in the table, to be reached.
Moreover the mean processing time has been evaluated using a common Pentium IV personal computer. Very similar outcomes have been attained in any different operative condition analyzed.
From the analysis of all results some consideration can be drawn.
(i)LS,Burgand Modified covariance estimators reach the lowest value of RMSE for the samepolynomial order.
(ii)RMSE values for LS, Burg and Modified covariancealgorithms are very similar, showing comparable performance in PSD estimation.
(iii)Mean processing time exhibited by Burg estimator is much shorter than those characterizing LS and Modified covariance algorithms.
(iv)The best operative range for p, to be considered in the second optimization stage, has to be set around 300.
From what stated above, LS and modified covariance algorithms have been no longer considered; only Burg estimator has undergone the successive optimization stage.
B.Fine optimization
This stage aims at fixing the optimal value of p within the operative range established in the previous one, and comparing the performance granted by the so-optimized Burg algorithm to that assured by WOSA estimator.
Since the results reported in [6] are related to an intermediate frequency equal to 21.4MHz, a new optimization stage for WOSA estimation algorithm has been carried out. The obtained outcomes completely concur with those already experienced in [6]; for sake of brevity they are not given here.
Tab.III. Results obtained in the simulation stage: Burg estimator is involved.
1/4 DVB-T symbol acquiredOversampling factor
Figure of merit / Guard interval [µs] / ~3 / ~6 / ~12
T[%] / 28 / 0.28
(260) / 0.29
(400) / 0.255
(590)
224 / 0.26
(320) / 0.28
(490) / 0.32
(680)
C[%] / 28 / 0.28
(260) / 0.29
(400) / 0.255
(590)
224 / 0.26
(320) / 0.28
(490) / 0.32
(680)
T[%] / 28 / 0.64
(260) / -0.17
(400) / -0.083
(590)
224 / 0.54
(320) / 0.10
(490) / 0.22
(680)
C[%] / 28 / 0.64
(260) / -0.18
(400) / -0.089
(590)
224 / 0.54
(320) / 0.10
(490) / 0.21
(680)
Measurement time [s] / 28 / 0.241 / 0.823 / 2.745
224 / 0.346 / 1.242 / 5.233
Final results are given in Tab.III. Each pair of round brackets describes the p value that minimizes the related figure of merit. The last row of Tab.IIIquantifies the computational burden in terms of mean processing time.
From the analysis of the resultssome considerations can be drawn.
•Both estimators have assured good and comparable repeatability; experimental standard deviation is always lower than 0.52%.
•WOSA estimator exhibits better performance in terms of and C.
•Measurement time peculiar to the Burg estimator is longer than that taken by WOSA estimator.
IV PERFORMANCE ASSESSMENT
An emulation stage has been designed and executed with the aim of assessing the performance of the proposed Burgestimation algorithm in the presence of a real DAS, and comparing the obtained results to those furnished by the WOSA algorithm. Stemming from the past experience [6] a suitable measurement station, sketched in Fig.2, has been set-up. It has included: (i) a control unit, namely a personal computer (PC); (ii) a RF signal generator equipped with DVB-T personalities, Agilent TechnologiesTM E4438C (250kHz-6GHz output frequency range);(iii) a DAS, LeCroyTM SDA6000A digital scope, (6GHz bandwidth, 20GS/s maximum sample rate),suitably customized, on which the measurement algorithm has run. The considered instruments have been all interconnected through an IEEE-488 interface bus.
Fig.2. Measurement station for performance assessment.
As far as the DAS is concerned, it allows creating custom math functions in its user interface. MATLABcalculations can be selected like any other math function, and the results are displayed on the screen. The function generator has provided 8MHz bandwidth, DVB-T test signals, characterized by a RF central frequency equal to 36.13MHz, a nominal total power of -20dBm, and a 64-QAM modulation scheme. Moreover, the same transmission settings considered in Section III have been imposed.
Different operative conditions of the DAS, in terms of vertical resolution (7 and 8 bit nominal), observation period (1/4, to 1/64of DVB-T symbol), and oversampling factor (~3, ~6 and ~12) have been considered. For each of them,50 sample records have been acquired and analyzedboth through the Burg and WOSA estimation algorithms.