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SNR and MER of Digitally Modulated Signals with Additive Noise

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SNR and MER of Digitally Modulated Signals with Additive Noise BROADCASTING Test tip The right way to measure: SNR and MER of digitally modulated signals with additive noise This test tip describes for different Calculating the SNR Correlation between C/N and SNR digital TV transmission standards The transmission of digitally modulated signals can be accompanied by manifold The ratio of the carrier to the noise in the the correlation between the superim- types of interference that has to be ana- channel (C/N) is determined from the lyzed and quantified – for example, with noise power density N0 of the channel posed noise in the channel (carrier-to- the high-end TV Test Receiver R&S EFA and the noise bandwidth B. With single- from Rohde & Schwarz. Sometimes spe- carrier signals, the symbol rate (with noise ratio, or C/N) and the maximum cial cases such as the influence of addi- VSB methods, half the symbol rate) is tive white Gaussian noise are also of usually used as the noise bandwidth; measurable signal-to-noise ratio interest to users. The noise fed to the in the case of OFDM signals, the band- transmission channel (described by the width of the transmission channel (e.g. (SNR) in the test receiver. Further- ratio of the carrier power C to the noise 8 MHz) is normally used. By applying power N in the transmission channel) the reduction method, the noise compo- more, it portrays software that auto- results in a deviation of the measured nents remain unchanged. The noise in values from the ideal position in the con- the transmission channel (C/N) thus has matically determines the bit error ratio stellation diagram (FIG 1). In extreme an immediate effect on the SNR. How- cases this can cause bit errors. Unlike ever, the following special features have (BER) as a function of C/N. C/N, the SNR is determined on the to be taken into account: basis of the I/Q data and is thus a base- band quantity. By mathematically elim- Single-carrier modulation without inating other causes of interference pilot (QAM, e.g. DVB-C / -S, J.83/B) such as phase noise, carrier suppres- Filtering the receive signal in the root sion, etc (reduction method), appropri- raised cosine filter (Nyquist filter) at the ate test algorithms make it possible to receiver end gives the useful signal a dif- determine the noise components on the ferent shape than the noise. This also basis of the constellation data. The ratio changes the ratio of both components to between the rms value of the payload each other (FIG 2). data and the reduced effective error is referred to as SNR and usually given in FIG 1 Deviation of the measured values from the ideal dB. The modulation error ratio (MER) is Modulation with pilot (e.g. DVB-T) position due to noise (C/N = 25 dB) – here obtained by establishing the relation- If a pilot (subcarrier) exists, it is included shown for 64QAM, measured with the TV Test ship between the rms value of the pay- in the total power but is not part of the Receiver R&S EFA. load data and the effective error with- useful signal components. This also out reduction. The MER value in dB is leads to a change of the attainable SNR thus always lower (worse) than the SNR with the specified C/N and should be value. Another common measurand is taken into account when making calcu- the error vector magnitude (EVM): It is lations (FIG 2). determined by the ratio of the cumula- tive error to the peak value of the pay- Single-carrier modulation with pilot load data, and is specified in %. (e.g. ATSC) Both effects are to be taken into account. 54 News from Rohde&Schwarz Number 178 (2003/II) Modulation and Noise bandwidth BN SNRmax / dB = C/N / dB + k Modulation and Noise bandwidth BN SNRmax / dB = C/N / dB + k TV standard TV standard QAM BN = symbol rate k = –0.1660 dB QAM BN = symbol rate k = –0.1323 dB (DVB-C, r = 0.15) (R&S EFA mod. 60/63) (J.83/B, r = 0.12) QAM BN = channel bandwidth k = –0.1660 dB + 10×log(chan. QAM BN = symbol rate k = –0.1660 dB (DVB-C, r = 0.15) (R&S EFA mod. 20/23) bandw. / symbol rate) (DVB-C, r = 0.15) QAM BN = symbol rate k = –0.1323 dB QAM BN = symbol rate k = –0.2000 dB (J.83/B, r = 0.12) (R&S EFA mod. 70/73) (J.83/B, r = 0.18) QAM BN = symbol rate k = –0.2000 dB QPSK BN = symbol rate k = –0.3977 dB (J.83/B, r = 0.18) (R&S EFA mod. 70/73) (DVB-S, r = 0.35) OFDM BN = channel bandwidth = k = –0.1169 dB OFDM BN = useful bandwidth k = –0.3345 dB (DVB-T, with pilot) 8 or 7 or 6 MHz (DVB-T, with pilot) (R&S EFA mod. 40/43) 8VSB (ATSC, BN = symbol rate/2 k = –0.4387 dB 8VSB (ATSC, BN = symbol rate/2 k = – 0.4387 dB with pilot, r = 0.115) (R&S EFA mod. 50/53) with pilot, r = 0.115) FIG 2 Left: maximum measurable SNR (baseband noise) as a function practice, quantization effects, receiver noise and rounding effects in signal of C/N (noise in transmission channel) taking into account the modula- processing always result in SNR and MER values that are below the spec- tion parameters. Noise source is the TV Test Receiver R&S EFA. With a ified limits. specific C/N, the actually obtainable SNR/MER cannot exceed the speci- Right: Like the table on the left, but here the noise source is the TV Test fied maximum values, which thus represent the theoretical upper limit. In Transmitter R&S SFQ. The BER graphs described in the relevant technical literature usually use the SNR as a parameter, not the C/N. Software for displaying BER as a function of C/N For fully automatic measurement of the bit error ratio (BER) as a function of the channel noise (C/N), Rohde & Schwarz has developed software that makes it easy to control the TV Test Receiver R&S EFA from a PC. The software out- puts the BER values at different points (before or after error correction) and graphically displays them (FIG 3). The noise generator in the R&S EFA is used to set the C/N value. All conversions between C/N and SNR described in the table in FIG 2 are performed automat- ically by the software and displayed FIG 3 Measurement of the bit error ratio BER as a function of the channel C/N, with conversion to the obtainable SNR values (second scale, S/N; see also the left-hand table in FIG 2). The noise is in the form of a double scale (C/N and generated by the noise generator in the TV Test Receiver R&S EFA. The display is for DVB-C. Green: SNR or S/N) if desired. The measure- the theoretically obtainable curve; red: the curve actually measured. The END (equivalent noise degra- ment time is automatically adapted as dation) is determined automatically from the measured values. a function of the measured BER. The software, which is called EFA Noise- Diagram, can be downloaded from the Rohde & Schwarz website free of charge. Christoph Balz 55 News from Rohde&Schwarz Number 178 (2003/II).
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