1、 STD-ITU-R RECMN SN-1235-ENGL 11777 48552112 05287711 7T7 Rec. ITU-R SM.1235 3 RECOMMENDATION ITU-R SM. 1235 PERFORMANCE FUNCTIONS FOR DIGITAL MODULATION SYSTEMS IN AN INTERFERENCE ENVIRONMENT (Questions ITU-R 44/1 and ITU-R 45/1) (1997) The ITU Radiocommunication Assembly, considering that the valu
2、e of the performance function at the receiver input for various combinations of modulation types of that performance functions depend on the criteria for estimation of the signai reception quality and the modulation that performance functions can be defined either experimentally, graphically or calc
3、ulated by means of formulae, a) interference and desired signals essentially can define spectrum utilization efficiency; b) types of the interference and desired signals; c) recommends 1 calculated graphs presented in Annex 1 should be used; 2 from one or more emitters, calculated graphs or the anal
4、ytical method presented in Annex 2 should be used. that for the performance estimation of various digital modulation systems, receiving interference from one emitter, that for the performance estimation of multiple digital phase shift keying (MPSK) systems, receiving interference ANNEX 1 Performance
5、 function for various digital modulation systems with only one interfering system 1 Digital receiver model A simplified model of a communications receiver is shown in Fig. 1. The input to the channel interface is the superposition of the desired and undesired signals appearing at the receiver antenn
6、a output. The channel interface is composed of a number of circuit elements and is characterized by a receiver selectivity and by desired and undesired signal characteristics. Several Reports provide means to determine the nature of desired and undesired signals at the input to the demodulator given
7、 channel interface characteristics. The most important channel interface Characteristics to consider are the bandwidth relationship between the undesired signal and the channel interface, off-tuning between the receiver and the undesired signal, and non- linear effects. FIGURE 1 General communicatio
8、n system receiver model Transmission channel processing Demodulator STD*ITU-R RECMN SM-1235-ENGL 1777 q855212 0528772 835 = 2 Rec. ITU-R SM.1235 Undesired signals are characterized as follows: - Undistorted The ideal waveform transmitted by the interfering transmitter. The signal may be specified in
9、 the frequency domain in terms of power spectral density. - Noiselike: The signal varies in amplitude according to a normal (Gaussian) distribution. The signal may have a flat spectrum and is referred to as additive white Gaussian noise (AWGN). - Continuous wave (CW): A constant frequency sinusoid w
10、hose phase with respect to the receiver is assumed to be a uniformly distributed random variable. - Impulsive: A sequence of periodic or randomly spaced pulses, each of which is of short duration compared to the time between pulses. Undesired signals may be either continuous or intermittent. An inte
11、rmittent undesired signal may be defined as a signal whose statistics such as amplitude distribution function, mean and variance are time-varying when observed at a victim receiver. Interference due to a Co-located frequency hopper is an example of an intermittent undesired signal in the sense that
12、the victim receiver will typically exhibit time-varying performance degradation. The recommended analysis procedure for the case of intermittent undesired signals involves partitioning the observation interval into contiguous time segments, or epochs, during each of which the undesired signal statis
13、tics are (approximately) constant. A separate degradation analysis is performed for each epoch, and the results are time-averaged. It is important that the time-averaging not be performed on signals until they have been demodulated. For electromagnetic compatibility (EMC) analyses using the performa
14、nce curves in this Recommendation, the undesired signal at the receiver input can usually be assumed to be either undistorted (Le., the output of an interfering transmitter with known waveform characteristics) or noiselike. The channel interface characteristics are then used to determine the undesir
15、ed signal at the demodulator input. The curves show the demodulator output bit error rate as a function of the ratio of the desired symbol energy-to-noise power spectral density (E/No) or the ratio of the desired symbol energy-to-interference energy (Elle) at the demodulator input. The noise is assu
16、med to be Gaussian, and the interference is assumed to be continuous-wave. The analyst must determine whether the undesired signal at the input to the demodulator more closely resembles noise or CW interference or some combination of the two. This determination may include a prediction regarding the
17、 nature of the interfering signal spectrum at the demodulator input based on the passband of the channel interface and the interfering signal RF characteristics. The remainder of the Recommendation addresses the individual sections of the receiver model shown in Fig. 1 following the channel interfac
18、e. The output of any particular section may be found by concatenating the effects of that section and any preceding sections. 2 Performance of digital demodulators Typical M-ary digital demodulator performance is given in terms of P, versus EIN0 and E/I. These terms are defined as follows: M: P, : n
19、umber of possible distinct symbols. For binary signalling, M= 2 symbol-error probability. The bit error probability Pb, which is also often used, cannot exceed P,. When M= 2, Pb = p, E/No : ratio of average signal energy (J)-to-noise power spectral density (W/Hz) as specified at the demodulator inpu
20、t (dB) E/Ie : ratio of average signai energy per symbol (or per bit)-to-interference energy per symbol (or per bit), as specified at the demodulator input (dB). STD=ITU-R RECMN SM-1235-ENGL 1997 4855232 0528773 771 = I 3 Rec. ITU-R SM.1235 CPSK, M-ary CPSK, M= 2 Power ratios, in particular the signa
21、l-to-noise ratio (SIN), may be used instead of energy ratios by noting that: EIN0 = (SIN (B T) (1) P, versus EdNo N 2 P, versus ElNo, EIIe I, 3 where: B : receiver bandwidth (Hz) T: symbol duration (s) SIN : measured at the demodulator input. Table 1 summarizes the types of modulation presented, whi
22、ch curve to use for each, and the undesired signal (CW or noise) for which probabilities of bit or symbol errors may be obtained. The curves identified in Table 1 are provided in Figs. 2 through 24. These curves relate receiver performance in terms of symbol or bit error rate in the presence of nois
23、e and/or interference. The noise is assumed to be Gaussian, and the interference is assumed to be CW. The curves have been developed assuming optimum receiver design, Le., bandwidths associated with the demodulator were designed for the associated system bit durations and data rates. CPSK, M= 4 CPSK
24、, M= 8 TABLE 1 Summary of digital modulation types considered P, versus EIN, EMe I, 4 P, versus EINo, EIIe I, 5 Modulation type QPSK O-QPSK (offset-QPSK) Plot of P, versus EINo, EM, 4 4 P, versus ElNo, EII, I, 4 Interfering I Figure I number signai (1) DPSK, M= 2 DPSK, M= 4 P, versus EINo, EMe N, I,
25、 7 P, versus EINn, EIIe N, I, 8 DPSK, M= 8,16 CFSK, M-w I CPSK, M= 16 I P. versus EINn. ElIo 11,161 P, versus EIN, EUe It! 9 Ph versus E,INo N I 10 CFSK, M= 2 MSK NCFSK, M- ar P, versus EIN, Elr, je 11 P, versus EINo, EDe 1, 4 P, versus EJNn N 12 NCFSK, M= 2 NCFSK, M= 2 P, versus EIN, El& 1, 13 (int
26、erference in one channel) P, versus EINo, EUe 4 14 (equal interfering tones in each channel) NCFSK, M= 4 NCFSK, M= 8 CASK, M-ary, bipolar P, versus EIN, EII, 4 15 P, versus EINo, EUe Ie 16 P, versus EJNn N 17 CASK, M= 16, bipolar CASK, M-ary, unipolar CASK, M= 2, unipolar I P, versus EN, EII I (also
27、 called OOK or on off keying) P, versus EIN, EMe It! 18 P, versus E,IN, N 19 . - NCASK, M-w P, versus EdNo N 21 QAMM-WY P., versus EdNo N 22 (quadrature amplitude modulation) QAM, M= 4 QAM, M= 16 QAM, M= 64 P, versus EINo, EMe I, 4 P, versus EINo, ElI, 1, 23 P, versus EINo, EMe 4 24 STD-ITU-R RECMN
28、SM*1235-ENGL 1997 VA55212 0528774 bOB 4 Rec. ITU-R SM.1235 When using the curves, be alert to the parameters used. Bit energy-to-noise ratio (&/No) rather than symbol energy-to-noise (EINo) was used in most of the figures comparing M-ary schemes for different values of M in order to simplie the grap
29、hs. The value E represents the average symbol energy. The relationship between symbol energy and the equivalent bit energy is: Some of the figures presented have the probability of a bit error, Pb, rather than the probability of a symbol error, Pr The relationship between the two, for orthogonal sig
30、nalling (coherent frequency shift keying (CFSK), non-coherent frequency shift keying (NCFSK), minimum shift keying (MSK), is: where k = log2 M (number is equivalent bits). For M-ary coherent phase shift keying (CPSK) and differential phase shift keying (DPSK) (Gray encoding is assumed) and for coher
31、ent amplitude shift keying (CASK) and non-coherent amplitude shift keying (NCASK) the relationship is: Pb = P,Ik FIGURE 2 P, versus EbINo for M-ary CPSK 1 1 o- 1 0-2 4: 1 0-3 10-4 1 0-5 (4) STDoITU-R RECHN SM=L235-ENGL L777 4855232 0528775 5L(L( 9 Rec. ITU-R SM.1235 FIGURE 3 P, versus EINo and EMe f
32、or binary CPSK 1 o- 1 o-* 10-3 1 10-5 104 1 0-7 1 0-8 1 0-9 5 6 10 14 18 22 26 30 E/N, (dB) FIGURE 4 P, versus EINo and EMe for 4-ary CPSK, QPSK, O-QPSK, MSK and 4-ary QAM 10-1 1 0-2 1 0-3 10-4 10-5 1 0-6 1 0-7 10-8 10-9 8 12 16 20 24 28 32 “0 (dB) 6 STD-ITU-R RECMN SM-1235-ENGL 1777 I855212 052877b
33、 I80 Rec. ITU-R SM.1235 1 o- 10-2 10-3 10-4 %- 10-5 1 o“ 10-7 10-8 10-9 FIGURE 5 P, versus EIN, and E/Ze for I-ary CPSK 10 14 18 22 26 30 34 EINo (dB) FIGURE 6 Ps versus EIN, and EMe for 16-ary CPSK 1 o- 1 0-2 10-3 1 0-4 %- 10-5 1 0-6 1 0-7 1 o-* 1 16 20 24 28 32 36 40 EINo (dB) STD-ITU-R RECMN SM*L
34、235-ENGL 1777 Li855212 0528777 317 Rec. ITU-R SM.1235 7 FIGURE 7 P, versus EINo and EII, for binary DPSK FIGURE 8 P, versus EINO and EM, for 4-ary DPSK 1 0-8 1 0-9 12 14 16 18 20 22 24 EINO (dB) STDOITU-R RECMN SM*1235-ENGL 3777 W 4855232 0528778 253 8 Rec. ITU-R SM.1235 1 1 o- 1 0-2 1 0-3 1 o“ CL:
35、10-5 1 0-6 1 0-7 10-8 FIGURE 9 P, versus ElNo and EM, for 8-ary and 16-ary DPSK EIc (dB) = _ 10 - 15 12 EINo (dB) 1 1 o- 1 o-* %* 10-3 1 o“ 1 0-5 20 _ 25 30 FIGURE 10 Pb versus EbINo for Mary CFSK FIGURE 11 P,versus EINo and EIZe for binary CFSK d 1 1 o- 10-2 1 cr3 1 0-l 10-5 1 0-6 1 0-7 9 1 1 o- 1
36、0-2 1 0-3 4- 10-4 1 o- 1 0-6 10-7 6 10 14 18 22 26 30 “0 (dB) FIGURE 12 P, versus EalNo for M-ary NCFSK - M= 2 4 .8 . 16 32 10 STD-ITU-R RECMN SM*1235-ENGL 1997 q855212 0528780 701 Rec. ITU-R SM.1235 1 1 o- 10-2 1 &* 10-4 10-5 10-6 10-7 FIGURE 13 P, versus E/No and E/Ze for binary NCFSK with interfe
37、ring in one channel 1 1 o- 10-2 10-3 &- 10-4 1 o- 1 0-6 10-7 6 10 14 18 22 26 30 EIN, (dB) Tg$Qgr$ FIGURE 14 with equal interfering tones in each channel P,versus EIN, and E/Ze for binary NCFSK 6 10 14 18 22 26 30 “0 (dB) STD-ITU-R RECMN SM.LZ35-ENGL 1997 9855212 0528781 894 Rec. ITU-R SM.1235 d FIG
38、URE 15 P, versus EINo and E/Ze for 4-ary NCFSK 1 1 o- 1 0-2 1 0-3 1 0-4 10-5 1 0-6 1 0-7 11 6 10 14 18 22 26 30 EIN, (dB) gptp FIGURE 16 P, versus EIN, and EIZe for I-ary NCFSK 1 1 o- 1 0-2 1 0-3 10-4 10-5 1 0-6 1 0-7 6 10 14 18 22 26 30 EIN, (dB) $2335% 12 STDDITU-R RECMN SM.1235-ENGL 1997 Li855212
39、 0528782 7811 Rec. ITU-R SM.1235 FIGURE 17 P, versus Eb/No for Wary bipolar CASK 1 1 o- 1 0-2 1 0-3 4“ 1 04 10-5 1 0-6 1 0-7 O 4 8 12 16 20 24 EbNQ (dB) FIGURE 18 P, versus EIN, and EMe for 16-ary bipolar CASK 1 1 o- 10-2 10-3 4“ 10-4 10-5 1 o“ 10-7 STD-ITU-R RECMN SM*L235-ENGL 1777 = 4855212 052878
40、3 bLO Rec. ITU-R SM.1235 FIGURE 19 P, versus Eb/No for M-ary unipolar CASK 1 1 o- 1 0-2 1 0-3 10-4 %* 10-5 1 1 1 o- 10-2 10-3 %* io“ 1 0-5 10-6 1 13 FIGURE 20 P, versus Eb/No and Elre for binary unipolar CASK (OOK) 14 STDOITU-R RECMN SM.1235-ENGL 1777 i855212 0528784 557 Rec. ITU-R SM.1235 10 10-2 1
41、0-3 %* 1 o“ 10-5 1 0-6 10-7 FIGURE 21 Ps versus EblNo for M-ary NCASK 8 12 1 1 1 o- 10-2 10-3 io4 10-5 d 1 0-6 1 0-7 FIGURE 22 P, versus E,INo for M-ary QAM and comparison to selected M-ary PSK O 4 8 12 16 20 24 EbNo (dB) STD=ITU-R RECMN SM*3235-ENGL 3777 4855232 0528785 q73 B 1 lo- 1 0-2 10-3 a: lo
42、“ 1 0-5 104 1 0-7 Rec. ITU-R SM.1235 15 FIGURE 23 P, versus EINo and EIIe for 16-ary QAM 10 14 18 22 26 30 34 EINo (dB) FIGURE 2.4 P, versus EINo and EMe for 64-ary QAM 1 1 o- 10-2 10-3 4: 10-4 10-5 10-6 10-7 20 24 28 32 36 40 EINo (dB) ANNEX 2 Performance function for multiple PSK systems with more
43、 than one interfering systems NOTE 1 - All graphs in this Annex with K = 1 (a single interfering system) duplicate similar graphs in Annex 1, where SIN and Mvaiues are equal. 1 Introduction I Several ITU-R Questions, such as ITU-R ISII, ITU-R 44/1 and ITU-R 45I1, seek methods and results of communic
44、ation theory that would increase the efficiency of spectrum use. A case of considerable present - and even greater future - interest to high speed data technology deals with the performance of MPSK systems (coherent M-ary, M= 2, 3, 4, ) in the presence of noise and Co-channel interference. 2 Definit
45、ions Assume that each M-ary symbol, same as a binary or non-binary signal element, has duration T, and that the received signal waveform in absence of other input is: where the instantaneous coherent phase (t) is some 211 mlM, with m an integer O I m 1 is to further deteriorate the performance. The
46、effect is shown in Figs. 27a and 27b, each chosen for a fixed SII value but both with M= 2. It seems that K = CO should have the worst effect of all choices of K. When the Co-channel interference contains modulated constant envelope signals, the effects become far more complex and are not well docum
47、ented. While theoretical estimates for a single, K = 1, angle modulated interference suggest performance degradation shown in Fig. 28, more results can be deduced through simulation. Figure 29 shows the results from a simulated QPSK (M = 4) receiver being interfered with by a modulated undesired QPS
48、K signal. The data shows that for high signal-to- interference ratios the theoretical derivation agrees reasonably well with the simulated results. For low signal-to-interference ratios there is considerable difference between the two procedures which is caused by the approximations inherent in the
49、analytic approach. The results in general indicate that the theoretical bounds are valid and for low signal-to-interference ratios additional analytic complexity needs to be considered. In particular, the simulation should be extended to the arbitrary Mphase case and to a multiplicity K of interferers. 3.2 Measured results The probability of errors for a 4-phase PSK receiver subjected to interference were measured using the test set up shown in F
