~

314 IEEE TRANSACTIONS ON BROADCASTING, VOL. 35, NO. 3, SEPTEMBER 1989

METHOD FOR THE COMPUTATION OF INTERFERENCE AND DISTORTION LEVELS IN SATELLITE FM-TV SYSTEMS

A.M. B&k, A.P. Gallois Coventry Polytechnic, Coventry, U.K.

D.C. Carpenter University of Bath, Bath, U.K.

*

Abstract

A new method for the prediction of interference and distortion levels in satellite FM-TV systems is proposed. The procedure, which is based on a statisti- cal model for the random process of live video signals, makes it possible to predict the levels of both inter- system interference and intra-system signal distortion.

Statistical properties of video baseband spectra are investigated by evaluating the results of long-term measurements of live satellite TV channels. In particular, the joint probability distribution for the random variables describing luminance and chromi- nance components of the video signal is derived from the measurements. The spectrum of the frequency modulated signal is then analysed and the cumulative distribution of signal distortion due to bandlimiting is computed. Similarly, the distributions of adjacent and co-channel interference levels are also calculated, with examples illustrating influences of subcarrier loading and energy dispersion.

Since the proposed procedure derives the trans- mitted spectrum from the baseband signal, it is par- ticularly useful for the investigation of relative effects of system parameters, such as energy dispersion or subcarrier loading, on interference and distortion levels.

Introduction

The demand for satellite systems is con- tinuously growing with the increase in international and national telecommunication requirements. One of the more popular applications, especially in North America, is the use of medium power satellites, to provide additional television services over wide coverage areas. This application is also steadily growing in Europe (ECS, Astra). In an attempt to operate such systems economically, data subcarriers are often added to the channel, thus increasing in- formation transfer capacity [ l ] . As more systems become operational, the spectrum available for future systems decreases. To make efficient use of the available spectrum, careful planning is required so that the channel spacing is minimised, but interference levels are not compromised. The requirement for more accurate, reliable interference models to assist in planning procedures has been recognised for some time i 2 ,31 .

To facilitate the planning process of new satellite services, it is evident that a suitable model is required for the spectral densities of the signals involved. This can then be used in an overall modelling procedure [ 4 , 5 ] , so that accurate interference levels can be calculated.

It is necessary to consider both CCI (co-chan- ne1 interference) and ACI (adjacent channel inter-

ference) with the interference criterion being C/I (carrier-to-interference ratio) or S/ I (signal-to- interference ratio). The latter depends on receiver characteristics, thus, in a planning procedure, C/I is usually chosen. This would be equally applicable in bi-lateral and in multi-lateral co-ordination.

The determination of interference levels relies heavily on accurate computations of the transmitted spectra concerned. While spectra of digital satellite communication systems are usually readily calculated, a closed form derivation of FM-TV spectra is, due to the complexity of the analysis involved, only possible if the video signal can be approximated by a simple model.

Alternatively, interference levels can be pre- dicted by modelling the transmitted spectrum itself. This approach has been pursued elsewhere and statisti- cal models for FM-TV spectra have been proposed [ 6 , 7 , 8 ] . fact that it cannot predict the influence of system parameters on interference levels. Therefore, new sets of measurements and approximations would be re- quired if the effect of certain parameters, such as energy dispersion or subcarrier loading, is to be investigated. Baseband modelling, on the other hand, offers greater flexibility and makes it possible to study the relationship between any system parameter and the resulting interference levels.

The disadvantage of this method lies in the

Once the spectrum of the frequency modulated TV signal has been derived, it can likewise be applied to the analysis of intra-system distortion levels. The signal-to-distortion ratio has been defined as the ratio of total signal power to out-of-band power [ 9 ] , i.e.

total signal power SDR = 10 log dB

total signal power - in-band power

(1)

Based on this definition, the cumulative dis- tribution of signal distortion due to bandlimiting in satellite FM-TV systems will be calculated below. Depending on other system non-linearities, bandlimiting can be a significant source of distortion in some satellite TV transmission systems.

Video Baseband Model

Statistical properties of monochrome video signal have been derived in literature 1101 and an approximation of the resulting spectrum of FM-TV signals has been deduced [11,12]. The model was developed further and the analysis was extended to include the chrominance subcarrier [ 1 3 ] . Recently, several approaches for modelling FM-TV spectra have been compared [ 1 4 ] .

* A.M. B6ck is now with the Independent Broadcasting Authority, Winchester, U . K .

0018-9316/89/0900-0314$01.00 0 1989 IEEE

Generally, luminance and chrominance components are treated as two independent Gaussian random proces- ses with double-sided power spectra described by

> f

SAT E L LIT E T V SPECTRUM MICRO RECEIVER DEMOD. ANALYSE R COMPUTER

1 PIBl s (f) = - ~

n B 2 + f2 1 1

MAIN- FRAME

1 1 I 1 ( 3 ) PcBc s (f) = - 1

VIDEO FILTER

277 B '+ (f-f ) ' B '+ (f+f ) '

DISC DRIVE

1 where P

B1

pc

BC

fS

is the total power of the luminance component is the bandwidth of the luminance component

is the total power of the chrominance component is the bandwidth of the chrominance component is the frequency of the chrominance subcarrier

Extensive measurements of live television channels were carried out in order to validate the given models. Four different channels, which are presently being broadcast via European EUTELSAT 1-F1 transponders, have been considered. The programme material of these channels is quite diverse and represents a wide cross-section of channel traffic. Particular care was taken to exclude test charts, such as colour bar test signals, which would distort the results, since their power spectrum deviates consider- ably from the equations given above [15].

The arrangement for the measurements is shown in Figure 1. In order to cover the entire video base- band with a single sweep, a frequency resolution of 500 kHz/division was selected. With a bandwidth of 100 kHz and a sweep speed of 50 ms/division each measurement was taken over 25 successive fields. This represents a good compromise between measurement band- width (resolution in frequency domain) and measurement speed (resolution in time domain). Over a period of about 200 hours a total of 40,000 measurements were carried out. The results are summarised in Figure 2, where the probability densities of spectral levels are plotted against frequency.

Previous investigations showed that in extreme cases of colour saturation, such as in colour bar

315

signals, equation (2) fails to describe the spectrum of the chrominance subcarrier accurately [15]. Detailed analysis of the above mentioned measurements, however, reveals that, taken as a long-term average, the shape of the spectrum of live TV signals generally does converge towards the shape described by equations (1) and (2). Picture content, such as the amount of high frequency luminance detail and colour saturation merely affects the values of the parameters P1, P B required for convergence.

and

In particular, the luminance power depends strongly on picture detail, whereas both chrominance power and bandwidth change with colour saturation. The luminance bandwidth can be assumed to be constant, since it affects only the lowest part of the spectrum, which is not under investigation here.

In order to derive a model for the video spectrum which would provide the basis for an analysis of interference and distortion levels, both luminance and chrominance power were treated as random variables. The probability density of both variables was derived from the measurements. Both densities were found to be asymmetric with a slight skew to higher power levels. Thus a Pearson-Type I11 distribution was chosen to approximate the measured distribution because it allows independent adjustment of mean, variance and skewness [16]. The concept of a finite minimum for both power levels, given by the Pearson distribution, is intuitively justified by inspection of the composite video signal.

For the determination of interference and distortion levels, extremes of power levels and the probability of these extremes occurring are of utmost importance. In particular, high power levels will spread the spectrum, causing an increase of ACI and non-linear distortion, whereas low power levels will tend to increase CCI.

The parameters of the Pearson distribution were optimised using a method of least-square fitting, with particular empasis on the tails of the distribu- tion.

Figure 1 Configuration for measurements on video signals.

Figure 2 Spectral probability density of live television signals.

b

d

4

Thus, the probability density function of both The constants b, d and q, as well as the variables can be approximated by statistical properties of the distributions, are

summarised in Table 1.

The measurements of video spectra also reveal (4) that the chrominance bandwidth generally decreases

with increasing chrominance power. In fact, the elsewhere correlation between these two parameters was found to

be sufficiently high (95 % ) to be able to express one parameter as a function of the other, rather than introducing a third random variable.

Y qx-'exp(-Y Px>bx p(PXJ = dx r(qx) i, where Y = (Px-bx)/dx

x = 1 , c

-19.8

1.03

13.9

Table 1 Summary of statistical properties of luminance and chrominance power.

prior to pre-emphasis. The power levels are measured in 100 kHz bandwidth at video baseband

I Luminance power /dBm

mean

median

mode

variance

skewness

excess

-5.51

-5.84

-6.54

14.8

0.536

0.432

Chrominance power /dBm

-35.9

1.00

14.9

-21.0

-21.3

-22.0

14.9

0.518

0.403

By plotting the measured results of chrominance power and chrominance bandwidth in xy-coordinates, several approximations for the relationship between these two parameters have been investigated. The simplest case, a least-square fit of a linear relation- ship, was found to result in large errors at the tails of the P -distribution. Similarly, second and third-

order polynomials were not considered to yield the desired degree of accuracy. Thus, the relationship between chrominance bandwidth and chrominance power is approximated by the following fourth-order polynomial

C

B = -12.2 x‘-75.8 x’-137.9 x’-98.9 x + 23.7 kHz

where x = P /10 dBm ( 5 )

The coefficients of equation ( 5 ) have been optimised using a least-square approximation to the measured results.

The correlation between luminance and chromi- nance power was also investigated. As one would intuitively expect, the measurements showed that the correlation coefficient converges to zero for large numbers of measurements. Therefore, the joint probability density is calculated as the product of the two densities [ 171

Expressions (5) and (6) in conjunction with (2), ( 3 ) and (4) represent the complete video baseband model. The probability of the luminance or chrominance power not exceeding a certain level is given by the corresponding joint cumulative distribution. Con- sequently, for any given pair of power levels, the percentage of time (taken as a long-term average) for which these levels are not exceeded can be deduced.

FM-Spectrum and Signal Distortion

A significant part of the distortion in FM-TV systems is due to bandlimiting of the transmitted signal. Bandlimiting distortion in FM-TV systems, as defined in equation (l), has first been calculated in [la]. The spectrum of the FM signal is derived as the Fourier transform of its autocorrelation. It has been shown elsewhere [19] that the autocorrelation of audio and data subcarriers with a video signal, modelled by Gaussian random processes, is given by

where w

In general

is the carrier frequency and (7)

the indices 1, c, a and sl ... sN refer to the luminance, chrominance, audio and N data parts of the spectrum respectively.

20 I

where S is the double-sided baseband spectrum.

Substitution of extressions ( 2 ) and (3) into (8) and integration yield [la]

kl(T) = ml2[exp(-2nBllr I )+2nBll~ 1-11 (9)

317

kc(?) = m ’[2nl-rlB -cos(Zn-rf -e)exp(-Zn/rlB )+case]

where m ’= P /B ’ (10) 1 1 1

m ’= PC/(BC2+fs2)

e = tan-1(2Bcfs/(fs‘-Bc’))

Similarly, expressions for analogue FM and digital FSK and PSK subcarriers have been derived elsewhere [19].

In expression (7) no energy dispersion signal is considered because such a signal would normally have little effect on bandlimiting distortion. The Fourier transform of (7) is carried out numerically, using fast Fourier transform techniques. Since the autocorrela- tion converges to 1 at f + 0, the derived power spectrum is normalised and the signal-to-distortion ratio is calculated as

B/2

SDR = -10 log (1 - fSFM(f)df) dB (11)

-B/2

where B is the IF-bandwidth of the receiver and SFM is the Fourier transform of R with the vv carrier shifted to zero.

In equation (11) bandlimiting distortion is calculated as a function of the FM power spectrum, which ultimately depends on luminance and chrominance power. Thus, a functional relationship is given between bandlimiting distortion and the random variables describing the baseband signal. Therefore, the cumulative distribution of SDR can be derived from the joint density [17] of the baseband variables

Expression (12) is evaluated numerically in the following manner: both P and P are varied in

small steps over the whole range of significant probability; for all combinations of P1 and P resulting SDR is calculated, as is the probability of this combination occurring; the cumulative distribution is then given as the summation of the probabilities over all SDRs. The results are shown in Figure 3. The abscissa in Figure 3 is normalised to the median value (60.8 dB at B = 27 MHz) with no data subcarriers present. The graphs correspond to different system configurations with up to four data subcarriers. The total transmission rate of each subcarrier system is equal to 150 ksymbols/s. A channel spacing of 4 times the symbol rate and a subcarrier level of -18 dBm are assumed.

1

the

It can be seen that, on average, a single additional subcarrier reduces the SDR by about 3.4 dB. The corresponding values for 2, 3 and 4 subcarriers are 6.0 dB, 8.0 dB and 9.7 dB respectively. Further- more, the percentage of time, taken as a long-term average, for which a certain value of SDR is exceeded can also be read from the cumulative distribution. In order to demonstrate the effect of subcarriers on peak distortion levels more clearly, the results are replotted in Figure 4 with the lower part of the cumulative distribution expanded on a logarithmic scale.

318

!x 0

NORMALISED SDR d B

Figure 3 Cumulative distribution of relative S D R .

0 90 9 9 99.9%

[4

U PSK SUBCARRIER(S)

Figure 4

PERCENTAGE OF T I M E

Long-term average of relative S D R .

As an example, it can be seen that the SDR, which, for systems without additional subcarriers, is exceeded for 98 % of the time, is 11.5 dB lower than the median value. With one additional subcarrier, the same S D R is exceeded for only 97 % of the time and with 2, 3 and 4 subcarriers the figure drops to 95 %, 91 % and 82 % respectively. Generally, it can be seen that subcarriers reduce 'average' S D R s but have little effect on peak distortion levels.

It should be noted that whilst the transmission rates of these subcarrier systems are equal, their total channel capacities are not. This is due to the fact that multiple subcarrier systems operate under improved noise conditions if the subcarrier power remains the same. Hence their channel capacities, according to the Hartley-Shannon law, are increased.

Inter-system Interference

For the computation of adjacent and, more importantly, co-channel interference, an energy dis- persion signal should be included in the analysis. Such a signal is usually added to the basic modulation signal in order to reduce components with high-power density, which would otherwise occur in the trans- mitted spectrum. Various waveforms and frequencies have been suggested for this signal [21]. The analysis below, however, is based on a triangular waveform, synchronised to the frame rate, which appears to be the energy dispersion signal most commonly in use for TV signals. This is not a restriction of the general procedure and any periodic signal could be used.

In order to analyse the effect of the energy dispersion signal on the power spectrum of the trans- mitted signal, the autocorrelation of the energy dispersion signal is derived and multiplied with the autocorrelation of the modulation signal [22,23]. Subsequent Fourier transformation yields the modified power spectrum. This method was chosen because the autocorrelation of the modulation signal has already been calculated, so that only the autocorrelation of the energy dispersion signal needs to be derived.

In general, the autocorrelation function of a real valued, periodic waveform is calculated as follows

where l/fo is the period of g(t)

The instantaneous frequency of a triangular energy dispersion signal, with the carrier shifted to zero, is

' AF(l+4fot) -1 / 2 f o< t< 0 f (t) = i (14)

0 AF(1-4fot) O<t<1/2f

where AF is the peak frequency deviation

hence the energy dispersion signal is

Substitution of (15) into (13) and integration yield [ 241

where C(z) and S ( z ) are Fresnel cosine and sine integrals respectively

B = 1

1+0.5JfO/AF 0. 5+JhF/f0' -- A =

X = 2nAFT(1-2fOT)

y1 = 2 n ~ F ( 0 . 2 5 - f ~ ~ ~ ~ ) / f ~

y2 = 2nAF~(l-f~~) -

Z = 2 T q z 1 = v'AF/fo(l-2foT) 2

The spectrum of the transmitted FM signal is then given as the Fourier transform of the product of expressions (7) and (16). Since expression (16) has also been normalised, the total power of the trans- mitted signal remains unchanged.

Having derived the spectrum of the transmitted signal, the fraction of power which falls into the frequency band of the adjacent channel is given by

f +B/Z

ACI = 10 log 1 gt(f)df dB

'f -B/2

where f is the channel spacing

S is the spectrum of the transmitted signal including energy dispersion

Figure 5 shows the cumulative distributions of ACI, which are calculated in a similar manner as the distributions of bandlimiting distortion. The cal- culations are based on the WARC '77 frequency plan, which recommends a channel spacing of 19.18 MHz and a bandwidth of 27 MHz [25]. Expansion of the upper part of the cumulative distributions (Figure 6) reveals that, like bandlimiting distortion, subcarriers in- crease ACI for average power levels but have little effect on peak interference levels.

h

H U a

~

a -0

H U

W > H !-

_I W E

a

a

319

/" PSK SUBCARRIER(S)

90 9 9 99.9% PERCENTAGE OF TIME

Figure 6 Long-term average of relative ACI.

CO-channel interference is mainly caused by high-power densities in transmitted spectra. In the analysis given, spectral peaks occur at the carrier frequency and at the frequencies of the subcarriers on either side of the carrier. The power spectral density at carrier frequency, which represents the greatest peak, increases with decreasing luminance power. Therefore, the spectral density near carrier frequency provides an indication of how co-channel interference is affected by the composite modulation signal in- cluding energy dispersion. In analogy with the analy- sis above, co-channel interference is defined as

CCI = 10 log/ St(f)df dB

-f cc

where f is a constant, typically f = 50 kHz cc cc

In Figure 7, the cumulative distributions of co-channel interference, as calculated by equation (18), are plotted. Figure 8 shows the upper part of the distributions in expanded form. It can be seen that additional subcarriers help to reduce CCI, although their effect, compared with an energy dispersion signal, may be considered negligible. In order to demonstrate the effect of the energy dispersion signal, a plot without energy dispersion is shown for comparison.

It should be noted that more severe cases of CCI can occur when the video signal contains strong periodic components. These cases are often treated seperately and illustrate a limitation of the model [261*

NORMALISED A C I d B

Figure 5 Cumulative distribution of relative ACI.

4 PSK

m -0

H U U

W > H I- U J w E

ENERGY DISPERSION

~~

Figure 7

10 -

0 -

6 -

NORMALISED CCI d B

Cumulative distribution of relative CCI.

99.9 %

PERCENTAGE OF TIME

Long-term average of relative CCI.

Conclusions

It has been demonstrated that, by use of sta- tistical techniques at the baseband level, a suitable model for both the baseband TV spectrum and FM-TV spectrum can be obtained. These models include practi- cal system considerations of additional subcarriers, as well as energy dispersion signals, thus providing more realistic solutions.

The particular advantage of this approach is that it provides the means for investigating the effects of any system parameter on resulting interference levels. Therefore, the proposed model will be of benefit both for the design of additional subcarrier systems on existing satellite channels and for the planning process of new satellite services.

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321

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