Rec. ITUR SF.766
RECOMMENDATION UITR SF.766^{*}
METHODS FOR DETERMINING THE EFFECTS OF INTERFERENCE ON THE PERFORMANCE
AND THE AVAILABILITY OF TERRESTRIAL RADIORELAY SYSTEMS
AND SYSTEMS IN THE FIXEDSATELLITE SERVICE
(1992)
Rec. 766
The ITU Radiocommunication Assembly,
considering
a) that it is necessary to evaluate the effects of interference on the performance and the availability of terrestrial radiorelay systems and systems in the fixedsatellite service;
b) that, in general, the determination of interference criteria requires suitable calculation methods;
c) that calculation methods for determining interference to FDMFM systems are fairly well established;
d) that calculation methods for interference to singlechannelpercarrier (SCPC) FM telephony are to be established;
e) that calculation methods for interference to FM television are to be established;
f) that calculation methods for interference to amplitude modulated (AM) telephony are to be established;
g) that calculation methods for interference to digital transmissions are to be established;
h) that, in future, calculation methods for interference to systems employing new modulation techniques may need to be established;
j) that it is desirable to provide spectra of signals for determination of interference from the general formulation,
recommends
1. that the methods described in Annex 1 be used for calculation of interference to FDMFM systems;
2. that in the absence of more accurate information the methods described in Annex 2 be used provisionally for wanted signals other than FDM FM.
ANNEX 1^{**}
Calculation methods for the interference of FDMFM systems
Given below is the method of calculation to determine the effects of interference to the FDMFM systems in terrestrial radiorelay systems and systems in the fixedsatellite service.
1. Calculation methods 1.1 General formulation
The relationship (this linear relationship is only valid for the lower levels of interference into FDMFM telephony signals) between baseband interference power in a telephone channel and the carriertointerference ratio involves the interference reduction factor B (in dB), defined as follows:
(1)
where:
S : test signal power in a telephone channel = 1 mW
N_{i} : unweighted interference power in a telephone channel (bandwidth: 3.1 kHz)
C : power of the wanted signal carrier (W)
I : power of the interfering signal carrier (W).
The weighted interference power N_{p} (pW) is obtained as unweighted power in 1.75 kHz, which gives:
10 log N_{p} 87.5 – B – 10 log (C/I) (2)
The interference reduction factor B is expressed as:
(3)
with:
D
(4)
P_{1}() = P() A^{2}() (5)
P_{10}_{ }=_{ }P_{0} A^{2}(0) (6)
( – _{0}) = 1mmmmmmwhenmmmmmm = _{0}_{ (6a)}
_{ }( – _{0}) = 0mmmmmmwhenmmmmmm _{0}
where:
: r.m.s. test tone deviation (without preemphasis) of the wanted signal (kHz)
: centrefrequency of channel concerned, within the wanted signal baseband (kHz)
_{m} : upper frequency of the wanted signal baseband (kHz)
p(/_{m}) : preemphasis factor for centrefrequency of channel concerned, within the wanted carrier baseband
b : bandwidth of telephone channel (3.1 kHz)
_{0} : separation between carriers of the wanted and interfering signals (kHz)
S() : continuous part of the normalized power spectral density of the wanted signal with preemphasis (Hz^{ 1})
^{ S}_{0} : normalized vestigial carrier power of the wanted signal
P() : continuous part of the normalized power spectral density of the interfering signal (Hz^{}^{1})
^{ P}_{0} : normalized vestigial carrier power of the interfering signal
A() : amplitudefrequency response of the wanted signal receiving filter, the origin of the frequencies being the centre frequency of the interfering signal carrier.
The power spectral densities are normalized to unity and are assumed to be onesided (only positive frequencies).
The expression of N_{p} in terms of the ratio C/I is derived from expressions (2) and (3). In order to determine N_{p}, it is necessary to determine:
– the wanted signal spectrum (analogue telephony),
– the interfering signal spectrum.
The expressions of these spectra are given in § 2 below and in § 3 of Annex 2.
1.2 Interference from a lowmodulationindex FDM/FM signal to a highmodulationindex FDMFM signal
This case represents a terrestrial radiorelay system interfering into a system of the fixed satellite service. The baseband channel which receives the most interference is not easily identified. However, the worst interference condition results when the wantedtounwanted carrier frequency separation is equal to, or less than, the top baseband frequency of the wanted signal.
The factor B can be determined from the following formula:
B = 10 log (7)
If the modulation index of the wanted signal is greater than 3, the signal spectrum shape is near Gaussian, and formula (7) takes the following form:
B = 10 log (7a)
The definitions of the parameters in formulae (7) and (7a) have been given in § 1.1 with the exception of the following:
_{s} : r.m.s. multichannel deviation of the wanted signal (kHz)
f 10 (LF)_{ }^{½ (8)}
LF : load factor, which is less than unity when not in the busy hour;
^{ }y ^{ }^{ }(–15 + 10 log N_{c})/20mmmmmmfor 60 < N_{c} 240
y (–1 + 4 log N_{c})/2050mmmmmmfor 60 N_{c} 240 (9)
y (2.6 + 2 log N_{c})/20,mmmmmm–for 12 N_{c} 060
N_{c} : number of voice channels in the baseband.
1.3 Interference from a highmodulationindex FDMFM signal to a highmodulation index FDMFM signal
The same comments as in § 1.2 apply concerning the baseband channel with the most interference and the worst frequency separation. Moreover, the factor B is identical to that given in formula (7) of § 1.2 with substitution of F_{s} for _{s}.
F_{s} is defined as follows:
(10)
where _{and } _{are the r.m.s. multichannel frequency deviations of the wanted and interfering signals (kHz).}
1.4 Interference between FDMFM signals with intermediate modulation indices
_{ Figure 1 contains a number of curves of normalized spectra as a function of the modulation index for given normalized frequency values. These curves may readily be used to plot the spectrum graph for any modulation index from 0.1 to 3. When m > 3, the signal spectrum shape is near Gaussian. If the modulation indices of the wanted and interfering signals are greater than 3, formula (7) should be applied to calculate interference, taking into account § 1.3.}
_{ In certain special cases, where the interfering signal may be characterized by its r.m.s. modulation index, and the upper baseband frequency is equal to the wanted signal (i.e. = = }) there is the possibility of calculating the interference function, D(, _{0}), very simply from the normalized curves of Fig. 1.
FIGURE 1 [D01] = 11 cm
The equivalent modulation index is determined by:
^{ (11)}
and for this value of m on the curves in Fig. 1 we find the values _{m}S(_{1}) and _{m}S(_{2}),
where:
and (12)
and further:
(13)
The same method may be used for the approximate determination of D (f, f_{0}) according to the value of the “equivalent” modulation index:
(14)
when:
(15)
The symbols used are defined as follows:
_{0} : carrier frequency separation
, : mid frequency of the top baseband channel of the desired and interfering signals respectively
m_{1}, m_{2} : r.m.s. modulation indices of desired and interfering signal respectively.
1.5 Interference from a highmodulationindex FDMFM signal to a lowmodulationindex FDM FM signal
This case is typically that of a system in the fixedsatellite service causing interference in a terrestrial radiorelay system. Lowindex angle modulation can be regarded as quasilinear with respect to some types of interfering signal; the calculation of interference in these cases is performed by a simple procedure analogous to that employed for linear DSBAM.
The following approximate formula can be used:
1.6 Interference from anglemodulated digital signals into FDMFM signals
Digital systems using PSK or FSK modulation are classes of anglemodulated systems. Consequently, the interference from these systems into analogue, anglemodulated systems is computed by the convolution integral. However, the spectral densities of digital, anglemodulated signals cannot be easily generalized; a specific spectrum is, however, provided in § 3.2 of Annex 2. More generalized computation would involve the calculation of the digital spectral density (see § 3.2 of Annex 2), the calculation of the analogue spectral density, the convolution of the two densities, and the computation of the factor B.
When a highmodulationindex FDMFM carrier receives interference from angle modulated digital signals that occupy a bandwidth small compared with that of the wanted signal, factor B is given roughly by formula (7).
If a wanted FDMFM signal suffers interference from an unwanted PCMPSK or DPSKPM signal that occupies a bandwidth which is large compared with that of the wanted signal, factor B is given by the following simplified formula:
B = 10 log (17)
The normalized spectral power density of the interfering signal P() used in this formula is determined by the formulae (36a  36d) given in § 3.2 of Annex 2.
1.7 Interference from AM signals into FDMFM signals
The quasilinear properties of lowmodulationindex anglemodulated signals with respect to interfering signals whose spectral densities do not exhibit excessive variations within the receiver passband, permit the use for such cases of the following approximate formula:
Two 4 kHz bands are used in the formula since there may be asymmetry of the interfering spectrum with respect to the wanted carrier. When a highmodulationindex anglemodulated system receives interference from amplitudemodulated digital signals that occupy a bandwidth small compared with that of the wanted signal, factor B is given roughly by the formula of § 1.2.
1.8 Interference from a narrowband system into an FDMFM system
The theoretical expression of § 1.1 can be applied to the case of an interfering signal of arbitrary modulation, but with a bandwidth small compared with that of the interferedwith signal. Interference from SCPC to FDM FM signals is an example of such a situation.
In particular, for evenly spaced SCPC carriers, the aggregate interference power in the baseband from all SCPC interference entries from one interfering network is close to thermal noise with equal power starting from five to six carriers.
1.9 Interference from FMTV signals into FDMFM signals
When the FMTV signal modulated only by the dispersal waveform is the interfering signal, the FDMFM wanted signal with a low number of telephone channels has a spectrum with a width commensurate with that of the interfering signal spectrum, and the carrier frequencies coincide, then formula (4) takes the form:
(18)
where:
f : frequency deviation of dispersal waveform (peaktopeak)
P : spectral power density of interfering signal (see Fig. 4, i = 1)
P = 1/.
In the conditions described above, and with reference to formula (3), we may consider that:
(19)
so that:
(20)
1.10 Residual tone interference of FDMFM system with low modulation index
Special attention should be given to the severe effects of tone interference due to the residual carrier in FDM FM systems with a low modulation index. The interference noise power P_{} at the point of zero relative level is given by:
(21a)
where:
k = (I /C) ^{½}
^{2}mmmmfor unmodulated carrier interference (21b)
mmmmfor same typemodulated FDMFM interference (21c)
(21d)
(21e)
: upper to lower frequency ratio in the wanted signal baseband
= / (21f)
p() = C_{0} + C_{2}()^{2} + C_{}()^{4} (21g)
( – _{d}) = 1mmfor = _{d }(21h)
( – _{d})_{I} = 0mmfor _{d}
The influence of tone interference tends to become substantial in cases where the frequency separation f between carriers of the wanted and interfering signals falls into the baseband or particular regions, such as the pilot, the frequency slot of detected noise, a possible superbaseband service channel and DAV subscriber. In this case, the design requirements with respect to interference should be determined in the light of the tone interference.
2. Signal spectra 2.1 Analogue telephony (FDMFM) signal
The signal’s normalized power spectral density centred on the carrier frequency is expressed as:
(22)^{*}
where:
() : Dirac delta function
S()n _{* }S() : convolution of the function S() n times itself
S() : normalized spectral density of the signal phase:
(23)
where is the lower to upper frequency ratio in the wanted signal baseband.
The ITUR preemphasis characteristics are well approximated by the expression:
p (/_{m}) = 0.4 00+ 1.35 + 0.75 , when (24)
Here:
a = R_{s}(0) – R_{s}( (0.4 + 1.6 + 0.25 ^{} + 0.25 ^{3}) (0.4 + 1.6 ) (25)
where:
^{ }^{R}_{s}() : the autocorrelation function of S().
The normalized power of the vestigial signal carrier is expressed as e^{–}^{a}.
When m > 1:
(26)
where:
_{s} : r.m.s. multichannel signal frequency deviation
: normalized Hermite polynomial.
Figures 2a to 2e contain spectral graphs plotted according to formulae (22) and (26) for modulation indices m adopted in typical radiorelay and communicationsatellite systems.
The curves are approximate in the region /_{m} near 0 and 1. The exact values depend upon the particular value of . The exact curves for several values of are given in Figs. 2f to 2j for /_{m} near zero. (The inset curves in Figs. 2d and 2e are also accurate enough for /_{m} near zero if is equal to or greater than 0.02.)
For modulation indices greater than 1.1, the following empirical formula has been found to fit adequately the curves of P() and is a good approximation of equation (26):
_{m} P() = e (26a)
where:
x = /_{m}.
This empirical formula is an adaptation of the Gaussian formula for large modulation indices.
FIGURE 2a [D02] = 12 cm
FIGURE 2b [D03] = 11 cm
FIGURE 2c [D04] = 11 cm
FIGURE 2d [D05] = 10 cm
FIGURE 2e [D06] = 10 cm
FIGURE 2f [D07] = 15 cm 586% diminuée à 300% pour entrer sur la page
Montage: A monter format A4
FIGURE 2g [D08] = 18 cm
FIGURE 2h [D09] = 18 cm
FIGURE 2i [D10] = 18 cm
FIGURE 2j [D11] = 18 cm
ANNEX 2^{*}
Calculation methods for interference to systems other than FDMFM systems
Rec. 766
Given below is the method of calculation for wanted signals other than FDMFM
1. General
Formulae and/or graphs in which the degradation due to interference can be readily seen are presented for most cases. Spectra of signals are also provided to allow determination of interference from the general formulation, and to assist in calculations of power densities used in Recommendation ITUR SF.675.
Further studies are necessary on analogue singlesideband (SSB) telephony, companded SSB, companded FDM FM, hybrid dataandvoice (DAV) and dataandvideo (DAVID), multiplexed analogue component television MAC TV, high definition TV (HDTV), time division multiplex access (TDMA), spread spectrum code division multiple access (CDMA) signals, etc.
The performance degradation of analogue telephony transmission can be expressed in terms of noise (pW) and unavailability. In the case of digital transmission, it can be expressed in terms of bit error ratio (BER), severely errored seconds, degraded minutes and unavailability. In the case of FM television, the expressions given in this Annex make it possible to estimate the permissible value of carriertointerference ratio.
Precautionary notes are included with respect to interference effects which are not predictable by determination based on spectra and with respect to nonlinear channel effects.
2. Interference formulations 2.1 Singlechannelpercarrier FM telephony wanted signal
Further studies are required on this item.
2.2 Frequencymodulated television wanted signal
A protection ratio R which can be introduced, represents the carriertointerference ratio corresponding to a given impairment. As a result of tests carried out in France, with the interfering signal being an unmodulated carrier, the values of R given in Fig. 3 are expressed as a function of the frequency separation _{0} between the wanted and interfering signal carriers. The curve in Fig. 3, composed of two straight line segments and two halflines, is an empirical curve plotted from test data (F = frequency deviation in the low frequencies of the wanted signal (MHz)).
The subjective interference level chosen was that corresponding to the perceptibility threshold without thermal noise, for an observer placed in a dimly lit room at a distance from the screen equal to six times the height of the picture.
The permissible value (C/I)_{a} of this ratio is obtained from the expression:
R( – _{0}) A( ) [P( ) + P_{0} ] d (27)
where P(), P_{0} and A() have the same meaning as in § 1.1 of Annex 1.
Calculation of (C/I)_{a} can be performed once the interfering spectrum is specified (see § 3).
Figure 3 [D01] = (13 cm 508%)
2.3 Amplitude modulated telephony wanted signal 2.3.1 General information
Further studies are required on this item.
2.3.2 Interference between amplitudemodulated signals
The K_{4} factor is defined as the amount (dB) by which the signaltointerference power ratio exceeds the ratio of the signal spectral density in the appropriate 4 kHz band at the receiver input to the interference density at the same bandwidth.
In consequence of the property of linear modulation of translating interfering signals directly to baseband, the value of the factor K_{4} is simply 0 dB for SSBSC, and 3 dB for DSBSC.
The values of factor K_{4} are again 0 dB for SSBSC, and 3 dB for DSBSC.
The baseband spectrum of the interference will be identical with that of the RF interfering spectrum in the SSBSC case, and with the sum of the RF interfering spectra falling on the upper and lower sidebands in the DSBSC case. As a result, anglemodulated interference with strong carriers will generate toneinterference at baseband. The channel arrangement of AM systems will generally need to take account of this mode of interference.
Figure 4 [D02]= (13 cm 508%)
2.4 Digital wanted signal
The expressions for the performance of noncoded coherent digital modulation systems in a Gaussian channel are wellknown. However, in practice a perfect Gaussian channel environment rarely occurs. The received signal is a random process consisting of two components, the first contributed by thermal white Gaussian noise and the second by all other sources such as cochannel interference (CCI), adjacent channel interference (ACI) and intersymbol interference (ISI). The effects on the error probability performance due to this interference can be obtained in principle. Possible methods include direct calculation/simulation, numerical method with computer simulation GramCharlier series, Gaussian quadrature rule, complex integration, and bound methods.
2.4.1 Gaussian interference environment
The probability of error performance of binary phase shift keying (BPSK = 2 PSK), Mary PSK (MPSK) (M > 2), Mary quadrature amplitude modulation (MQAM) and Mary quadrature partial response (MQPR) and differential BPSK (DBPSK) modulation schemes is given by the following expressions:
mmmmmm(BPSK) (28)
(29)
(MPSK, M 2) (30)
(MQAM) (31a)
(MQPR) (32a)
(MQAM and MQPR) (31b) (32b)
where:
(33)
P_{B} :_{ }probability of error performance of BPSK system
P_{M} : symbol error rate for the MPSK (M > 2), MQAM and MQPR systems
P_{L} : probability of error of the baseband signal in each of the two quadrature components of QAM or QPR system
P_{DBPSK} : probability of error performance of differential BPSK system
_{av} : average signaltonoise ratio per kbit symbol
k = log M where M is the number of states
L : number of baseband levels, i.e. M = L^{2}
_{b} : energy per bittonoise ratio
C/N : carriertothermal noise ratio
_{b} : bit rate (bit/s)
B : doublesided noise bandwidth (Hz). We assume B is equal to the doublesided Nyquist bandwidth.
Expressions (28), (30) and (31) give the probability of error performance curves illustrated in Fig. 5.
In the case of MQAM systems, which employ very tight filtering (such as Nyquist raised cosine) the interference may be treated as Gaussianlike noise. A victim MQAM receiver may be interfered with from one or several sources. The amplitude distribution of a tightly filtered interferer exhibits a high peaktoaverage ratio which could be approximated by an equivalent Gaussianlike noise source. In the case of several interferers the sources of interference are considered to be independent random variables. The centrallimit theorem says that, under certain general conditions, the resultant equivalent interference probability density function approaches a normal Gaussian curve as the number of sources increases. In both the single and multiple interference cases, the equivalent interference may be treated as Gaussianlike noise. This practical approach yields useful performance curves in which the degradation due to interference can be readily seen.
The Gaussianlike interference is combined with the assumed white Gaussian noise channel to produce a total carriertonoise ratio (C/N)_{T} given by:
(34a)
(34b)
where N/C is the thermal noisetocarrier ratio, I/C is the equivalent interferencetocarrier ratio, and I_{i}/C (i = 1, . . ., n) is the interferencetocarrier ratio of the ith random source. Expressions such as equations (28) to (31) are used to calculate performance of coherent digital modulation systems in the presence of interference by replacing C/N by (C/N)_{T} and having C/I as a variable parameter. Inclusion of C/I as a variable parameter produces a series of curves shown in Figs. 6 and 7. The degradations (dB) of (C/N)_{T} – C/N for P_{e} = 10^{–6} versus C/I for the MQAM systems are summarized in Fig. 8. If a carriertointerference ratio is at least 10 dB higher than a carriertothermal noise ratio required for
the P_{e} = 10^{–6}, the degradation due to interference will be less than 1 dB. Although not shown in Fig. 8, it can be calculated that if the C/I is at least 6 dB higher than a C/N for P_{e} = 10^{–3}, the degradation due to interference will be less than 1 dB.
Figure 5 [D03] = 15.5 cm 606%
However, Gaussianlike interference is not necessarily the worst case. Administrations are urged to study new methods for determining the mutual effects of interference between MQAM and other digital and analogue schemes.
2.4.2 Gauss quadrature rule method
This section presents performance curves for bit error ratios of 10^{–3}^{ }and 10^{–6}^{ }and C/I and C/N as variables. These curves are obtained by using the Gauss quadrature rule method. These curves refer to coadjacent and channel interference in 4PSK, 16QAM and 64QAM carriers due to several types of interfering carriers. Transmit and receive filters of wanted and interfering systems are assumed to have square root raised cosine transfer functions with rolloff factors of 0.4 and 0.5 typical for satellite systems. The transmit filter also includes an aperture equalizer to achieve the intersymbol interference free condition. A curve obtained assuming Gaussian interference (see § 2.4.1) is also indicated in each figure, for comparison purposes.
Figure 6 [D04] = 16.5 cm 645%
In Figs. 9 to 13, C/I is defined as the ratio between carrier power at the receive filter input and interference power at the receive filter output. Carriertointerference power ratio at the receive filter input can be determined by subtracting the corresponding interference reduction factor which is given in the figures. Also, in these figures, C/N represents the ratio between the carrier power at the receive filter input and the noise power at the receive filter output. The carriertonoise ratio at the receive filter output is around 0.5 dB lower because of the attenuation of the spectrum of the desired carrier by the receive filter.
Figures 9 to 11 refer to cochannel and adjacent channel interference in systems with 4PSK, 16QAM and 64 QAM modulations, considering several values of frequency separation between two equally modulated carriers. Figure 12 addresses cochannel interference between two 4PSK carriers with different relative bandwidths. Figure 13 shows the interference effect of different modulations on the performance of a 4 PSK system.
Figure 7 [D05] = 17.5 cm 684%
The following general conclusions can be drawn by inspection of the figures:
– when the interfering signal power is equal to, or larger than, the thermal noise power, the effect of anglemodulation interference is considerably less than that of an equal amount of white Gaussian noise power;
– when the interfering signal power is small compared to the thermal noise power, the effect on error rate can be estimated safely by assuming that the interfering signal is equivalent to Gaussian noise of equal power;
– at a given carriertointerference ratio, the vulnerability to interference increases substantially as the number of transmitted symbols, M, increases;
– for the same interfering power after filtering, interference effects tend to become larger as the frequency separation between carriers increases. These effects also tend to increase with the interfering carrier bandwidth and with the number of interfering carriers. They are approximately the same for an interfering 4PSK or 8PSK carrier but they increase with the number of symbols for a QAM interfering signal. All the above situations can be interpreted in
terms of an increase in the interference peak factor: for large values of frequency separation (adjacent channel interference), for large values of interfering carrier bandwidth and for a large number of interfering carriers, the interference effect approaches that of an equal amount of white Gaussian noise.
Figure 8 [D06] = 15.5cm 606%
2.4.3 Numerical method with computer simulation
A computation method (numerical method with computer simulation) can be used to evaluate the performance of general PSK and QAM multistate modulation schemes staggered, and nonstaggered, in an environment of additive noise, interference and distortion, including modified constellation QAM schemes. Figure 14 shows the computation results of single interference for a 16QAM system. The curves represent the results obtained from the computation method mentioned above. For purposes of comparison, the symbol + on the curves in Fig. 14 has been used to indicate the results obtained by using pure numerical computation of a series expansion technique. They are in good agreement with each other.
This method can also be used for analysis of the combined effects of interference and implementation distortion.
Figure 9 [D07] = 14.5 cm 567%
Figure 11 [D09] = 15 cm 586%
2.4.4 Bounds methods
In many practical situations where an exact statistical distribution of the various interferences is not available, a useful technique is to compute an upper bound on the probability of error. This method requires knowledge only of the carriertonoise ratio at the demodulator input, C/N, the peaktor.m.s. ratio of the interference and the ratio of the powers of the wanted signal and interference, C/I. It should be noted that the results apply to a theoretical system and take no account of practical system restraints; they may be substantially modified by the presence of jitter and other degradations encountered in practical systems.
Other studies provide results for various cases of practical interest, including the effect of frequency separation between the wanted and unwanted carriers.
Curves of combinations of C/N and C/I ratios that give rise to upperbound biterror probabilities of 10^{–3} and 10^{–7} are presented in Figs. 15 and 16 respectively. These curves apply to cases of single or multiple interferences. The parametric curves are presented as a function of the interference peak factor, PF:
(35)
where:
R : peak value of the interference envelope
_{r} : root mean square value of the interference envelope.
Figures 12 et 13 [D10] et [D11] = 16 cm 625%
An unfiltered anglemodulated signal has a value of:
PF = 0
Results identical with those for a single anglemodulated signal (FM, PM, CPSK, or DPSK) interfering with binary CPSK can be obtained directly from the PF = 0 curves of Figs. 15 and 16. The corresponding results for interference to ternary and quaternary CPSK can be obtained indirectly from the same curves through the use of the foregoing formulae.
The following general conclusions can be drawn by inspection of the figures:
– when the interfering signal power is equal to, or larger than, the thermal noise power, the effect of anglemodulation interference is considerably less than that of an equal amount of white Gaussian noise power;
– when the interfering signal power is small compared to the thermal noise power, the effect on error ratio can be estimated safely by assuming that the interfering signal is equivalent to Gaussian noise of equal power;
– at a given carriertointerference ratio, the vulnerability to interference increases substantially as the number of transmitted symbols, M, increases.
Figure 14 [D12] = 13 cm 508%
2.4.5 Interference to DSPK signals from anglemodulated signals
Curves of symbol error ratio against C/N ratio, with C/I ratio as a parameter, for differentiallycoherent signals with 2, 4, 8 and 16 transmitted phases, are shown in Fig. 17. The error probability for differential detection is seen to be dependent on an additional parameter, , which is the relative phase slip of the interference from one sample to the next. However, the dependency diminishes as the number of transmitted phases increases. As a result, is assumed as a uniformly distributed random variable for systems with higher than four transmitted phases. Hence, average error probabilities have been derived for M = 8, 16; and probability bounds have been derived for the binary and quaternary cases.
The curves for DPSK imply the same conclusions as to the CPSK curves regarding the relative interference effects of white noise and anglemodulated signals, and the dependence of these effects on M. In addition, it can be seen that, in general, differential detection suffers more degradation than coherent detection, except that binary DPSK performs about as well as binary CPSK. Interference degradation is used as a basis for comparison because any disparities in the noiseonly performance are reconciled.
A method, simulating an FM signal passing through an ideal band filter, has been used to calculate the error probability for FM interference on a binary PSK system. Figure 18 shows the error probability P_{e} as a function of the ratio of the r.m.s frequency deviation of FM interference _{g} to the PSK signal receiver filter band _{c}. Calculations were carried out at five different interference levels relative to intrinsic noise: 3 dB (curve A), 0 dB (curve B), –3 dB (curve C), –6 dB (curve D), –10 dB (curve E). The signaltonoise ratio was taken as 12.4 dB, since the error probability (also in the presence of interference) does not exceed 10^{–6}, which corresponds to a signaltonoise ratio of 10.5 dB, while the total interference margin from all terrestrial and satellite systems amounts to at least 35%. The upper modulating frequency of the FM interference _{B} was taken to be _{c}. Figure 18 thus also shows the error
probability P_{e} as a function of the effective FM interference modulation index, as well as the error probability values in the presence of additional thermal noise, instead of FM interference, at the same demodulator input levels as for FM interference (horizontal lines A, B, C, D and E).
Figure 15 [D13] = 21.5 cm 840%
Figure 16 [D14] = 22 cm 860%
In practice, satellite and radiorelay systems operate with effective modulation indices of not more than 3. In analyzing the effect of existing FM systems on PSK systems, a Gaussian approximation provides the upper estimate. The increase in error probability proves substantially lower for FM interference than for thermal noise of the same power level, so that the permissible level of FM interference may be increased over the 6% provisionally established in Recommendation ITUR S.523, for this particular case up to 1.4 dB.
Figure 18 [D16] = 11.5 cm 449%
3. Signal spectra 3.1 Single channel per carrier FM telephony
Further studies are required.
3.2 Digital modulation signal of PSK, QAM and CPM type
The normalized power spectral density of the signal centred on the carrier frequency is expressed as follows:
for Mary PSK and QAM (36a)
for MSK (36b)
(36c)
for IJFOQPSK (36d)
3.3 Frequencymodulated television signal (FMTV)
After examining the spectrum, the following expression is taken as the upper bound of the normalized signal spectral power density centred on the carrier frequency:
P( ) = Sup (37)
where i may assume three different values (Sup (x, y) designates the greater of the two functions x and y). The interference obtained for each one of these values is examined in turn, and the highest level of interference is adopted.
Measurements have shown that the P() of an FMTV signal with dispersion is more accurately defined by the following formula:
P( ) = Sup (37a)
When determining the allowable level of interference for 20% of the time from an FMTV signal with dispersion, this value can be assumed to be 10 dB lower than that calculated by formula (37a).
The first part of the expression between square brackets represents the “continuous background” of the spectrum, which is Gaussian; F having the meaning given in § 2.2 and f being the frequency (MHz). The second part, g_{i}( f ), represents the “central” part of the spectrum essentially linked with the lines corresponding to “black” and “white”. If f is the frequency deviation of the energy dispersal, g_{i}( f ) has the values given in Fig. 4 for i = 1, 2 and 3. These values correspond respectively to the case of a uniform picture (black or white), strongly contrasted (typically, “halfline bar” test pattern), slightly contrasted (typically, “staircase” test pattern). The effect of the synchronization line and the colour subcarrier was disregarded in these models, since the lines concerned are less important in terms of power than the lines taken into account in these models.
However, the model corresponding to i = 1 can only be used as it stands for AC coupled modulators in which case the spectrum remains centred on the nominal frequency for a black (or white) picture. However, if a DC coupled modulator is used, the nominal frequency corresponds in all cases to medium grey; the function g_{i}( f ) must then be centred on a frequency separated by F/3 from the nominal frequency.
3.4 Amplitude modulated telephony signal
If f_{min}_{ and}_{ }f_{max}_{ are the lower and upper frequencies of the baseband signal, the normalized spectral power density is equal to:}
(38)1)
_{inside the bandwidth of the signal; equal to zero outside.}
4. Nonspectral interference effects – linear channel
_{ Besides the spectral interference effects, consideration must be given to effects which are not predictable from power spectral densities. Various interference degradations require examination of time related characteristics. Examples of such degradations are:}
– impulse noise in FDMFM communications systems can result from adjacent channel FM interference. In this case an FDMFM carrier located in an adjacent frequency band will occasionally deviate into the desired carrier's passband. If the interference to desired carrier power ratio and the time versus deviation statistics are improper, impulsive or click noise will result;
– interference to television can result from a burst transmission carrier such as TDMA. In this case the envelope of the interfering carrier may have frequency components to which the video signal is sensitive. Frequencies near the television line or frame rate may be expected to provide subjectively disturbing degradations;
– interference effects may result from a large carrier, modulated only by the energy dispersal waveform, sweeping past a small narrow passband carrier such as singlechannelpercarrier (SCPC). This situation produces transient effects related to the interference duty factor and sweep rate.
This list of examples is not complete but is meant to illustrate several time dependent interference mechanisms.
Another nonspectral effect in relation to interference performance is dependent on the demodulation technique. Depending on the nature of the interference, one demodulation technique may be preferable. As an example, adjacent channel induced impulsive noise in a wideband FM system may be reduced by the use of a properly designed phase locked loop or frequency modulated feedback demodulator. In the case of digital reception, different carrier and clock timing recovery techniques will have differing sensitivities to specific types of interferences.
5. Nonlinear channel effects 5.1 General
Most satellite transmission channels in use today have nonlinear transmission properties resulting from the transponder and earth station equipment employed. A nonlinear relation exists in the transponder between the input and output amplitude (AMAM) in addition to which the phase transfer function is related to input amplitude (AM PM conversion). These characteristics have implications for the interference susceptibility of a given communications system. With both the desired signal and interference present at the input of the nonlinear device, a multiplicative (non additive) degradation is generated. Depending on the modulation technique employed, this degradation will manifest itself on baseband performance.
5.2 Analogue FDMFM telephony wanted signal
In dealing with interference to FM analogue signals, two areas should be considered. The presence of the desired carrier and an interfering carrier(s) at the nonlinear device input will result in the generation of intermodulation spectral components. These components may then appear as additional interfering carriers. The second area of consideration is when the input combination of desired and interfering signals results in amplitude modulation; this modulation is converted to phase modulation by the AMPM conversion process. The phase modulation is imparted on the desired carrier and when finally demodulated at the receiver, results in baseband degradation.
Incomplete suppression of the amplitude modulation of the wanted signal by the limiter of the receiver can generate baseband interference, or adjacent channel interference on the slope of the wanted channel's filter can be amplitude modulated; this AM converted to PM thus appears at baseband. The nonlinearity of power amplifiers and demodulators are the usual sources of this type of interference.
The nonlinear interference can have a severe subjective effect because it can appear as direct crosstalk. Moreover, it can degrade the threshold of the receiver, and this effect is particularly applicable to satellite signals where the level of the wanted signal is usually near the threshold level, and adjacent channel interference may generate a burst of threshold noise.
The nonlinear interference mechanisms require investigation when the more conventional linear mechanisms appear to produce negligible interference. The calculation of this interference requires information on the specific receivers, filters, and AMPM conversion constants.
In the investigation and analysis of FDMAFM systems for the transmission of multi channel telephony, calculations of interference noise in individual channels should take account of the following sources of interference:
– nonlinearity of a realizable limiter;
– nonlinearity of a realizable frequency detector;
– threshold effect of an FM receiver (taking account of the modulation index of the interference);
– AMPM conversion in the RF channel.
5.3 Digital PSK wanted signal
The treatment of interference to digital PSK carriers is more complex than the analogue case. Bandpass filtering of the PSK carrier to minimize bandwidth requirements results in significant envelope amplitude modulation at frequencies related to the symbol rate. This, when converted to phase modulation by the AMPM conversion mechanism, reduces the interference immunity of the system. Separate consideration must be given to the performance of the carrier and clock reference recovery functions of the system. Specification of the modulator and demodulator characteristics with respect to filtering, carrier and clock reference recovery techniques and sampling methods, may be expected to have significant impact on the interference immunity of the system. At the present time there are no analytic expressions available for the computation of the interference effect to PSK carriers transmitted over a nonlinear channel. Laboratory measurements on various specific systems have been presented and can be used for guidance.
6. Measurements of interference into digital systems
One study shows that a considerable reduction in interference is possible from angle modulation systems into pulsecode modulation systems using phaseshift keying as compared to the mutual interference between two anglemodulation systems.
Other tests showed agreement between theory and measured data.
Experiments conducted on the effect of PSK interference and noise on PSK signal demodulators make it possible to determine the validity of a Gaussian approximation in estimating the effect of PSK interference. Figure 19 shows the error ratio of a coherent 4PSK demodulator as a function of the energy/bittonoise density ratio for two fixed C/I ratios, 10 and 13 dB, and different ratios between interference R_{i} and signal R_{s} channel transmission rates (R_{i}_{ }/R_{s} = 0; 0.5; 1; 2; 5). The carriertointerference ratio was established at the demodulator receiving filter output with a band 1.1 times that of the Nyquist band. Figure 20 shows the error ratio as a function of the R_{i}_{ }/R_{s} ratio for a fixed C/N ratio = 13 dB and three values of C/I (C/I = C/N, C/I = C/N + 2 dB, C/I = C/N – 2 dB). Figure 21 shows the relationship for the use in the wanted signal channel of a convolution code codec at = 1/2 for the code speed with Viterbi decoding.
Examination of the results obtained shows that the representation of cochannel PSK interference as Gaussian noise is correct for R_{i} > (4 – 5) R_{s}, and this applies both to the ordinary channel and to systems using coding, although in the latter case the character of the variation in error ratio is not monotonic. In the region of values of levels of interference commensurate with the thermal noise level, wideband PSK interference produces an increase in error ratio roughly of an order of magnitude in comparison with unmodulated interference of the same level, which is equivalent to a difference in their levels of up to 3 to 4 dB at a constant error ratio. It should also be noted that 2PSK interference produces a more perceptible effect on error ratio than 4PSK interference.
Figure 19 [D17] = 17 cm 665%
Figure 20 [D18] = 17.5 cm 684
Figure 21 [D19] = 16 cm 625%
