Noise in a DVB-T System

Transcription

1 Noise in a DVB-T System John Salter Summary This note was written to clarify a simple theoretical noise model of a DVB-T system described in [Reference 1]. This model gives the system carrier-to-noise (C/N) ratio when various noise sources are included. The analysis in this Technical Note uses a more practical approach in that the effects of the channel state measurement and channel equaliser have been incorporated within the demodulator. The analysis shows that excess noise contributions must be kept very low. BBC R&D 1

2 Noise in a DVB-T System John Salter Introduction This note was written to clarify a simple theoretical noise model of a DVB-T system described in [Reference 1]. This model gives the system carrier-to-noise (C/N) ratio when various noise sources are included. The analysis in this Technical Note uses a more practical approach in that the effects of the channel state measurement and channel equaliser have been incorporated within the demodulator. This demodulator is called a practical demodulator, and is defined in Appendix 1. The new model is used to determine the relationship between loss of noise-margin and the total excess noise contribution. It shows that the loss of noise-margin is greatly affected by the different carrier-to-noise requirements between those of a Gaussian channel and those of a difficult channel. Because of this dependence excess noise contributions must be kept very low. Noise Model The mathematical symbols used throughout this paper are defined in Appendix 1. The noise model has two stages as shown in Figure 1. Stage 1 represents degradations which are dependent upon carrier level such as receiver noise figure. Stage 2 represents degradations which are independent of carrier level such as: the intercarrier interference component of phase noise, ADC quantising noise and transmitter intermodulation products. Some degradations are best expressed in terms of noise figure, whilst for others it is more convenient to express them in terms of an excess noise source. There is a simple relationship between excess noise and noise figure. This is shown below. Consider stage 2 only. For a thermal noise input of KTB the output will be F 2 G 2 KTB. The output can be considered to be made up of two parts: a) The amplified input, G 2 KTB b) An excess noise source due to the imperfect amplifier, P x So For convenience, we make G 2 = 1; F 2 G 2 KTB = G 2 KTB + P x = (F 2 1) G 2 KTB. P x P x = (F 2 1) KTB Noise Figure F 1 Power Gain G 1 Noise Figure F 2 Output to a Practical Demodulator BBC R&D 2

3 Input power C Figure 1 We make the power gain of the first amplifier G 1 equal to 1/C, to give constant signal power to the second amplifier. This models ideal AGC action. F 2 will determine the system noise floor. The effective total noise figure of the system is given by the wellknown formula: Ft = F 1 + (F 2 1) / G 1 We have made G 1 = 1/C So Ft = F 1 + C (F 2 1) The carrier to noise ratio at the output to the demodulator is given by: C/N = C / KTBF t So C/N = C / (KTB(F 1 + C (F 2 1)) For an ideal demodulator, the calculated (by computer simulation) C/N ratio required by a 64 QAM rate 2/3 DVB-T system to achieve QEF 1 in a Gaussian channel is 16.5 db 2 [Reference 2]. A practical demodulator, which includes the action of the channel state measurement and equaliser, will require a greater C/N than this. We will call this requirement R 1 and make 1log 1 R 1 = 18.5 db. This probably represents the best performance that a practical demodulator, optimised to cope with time varying as well as Gaussian channels, can achieve at present. C/N can be plotted as a function of C for chosen values of F 1 and F 2. The ideal model is one where F 1 and F 2 are both equal to 1 ( db) and C/N = C / KTB or C = dbm. In the example shown in Figure 2, F 1 (db) = 7 db and P x (db) = -29 dbc. It should be noted that at sufficiently low values of C for the practical system C/N = C/ KTBF 1 ; ie. the curve becomes parallel to, and F 1 db offset from, that of the ideal system. At sufficiently high values of C for the practical system C/N = C/KTB(F 2-1) = C/P x. where 1/P x = -P x db 1 Quasi Error Free is a Bit error ratio of 2 x 1-4 after the Viterbi decoder. 2 Practical experiments with the BBC modem when all significant system degradations were eliminated resulted in a measured C/N of 16.7 db. BBC R&D 3

4 System C/N for a practical demodulator (db) R 1 F 1 (db) Ideal model db I/P Level (dbm) Figure 2 -Px (db) Loss of Noise-Margin An indication as to how well a DVB-T system is performing is the concept of loss of noise-margin. This is the difference (in db) between input C/N ratios of a practical model and of an ideal model when both are operating at QEF. For calculation we will call this difference where db = 1log 1. If N = KTB then this can be expressed in terms of input carrier level C. For our ideal model (which includes a practical demodulator), the C/N requirement to achieve QEF in a Gaussian channel is 1log 1 R 1 = 18.5 db or C = dbm. A practical model will require a greater input C/N than this: ie db or C = dbm. can be calculated as follows: From the noise model the C/N is given by: C/N = C/(KTB(F 1 +C(F 2-1)) Now (F 2-1) = P x /KTB where P x is the noise floor relative to carrier. C/N = C/(KTBF 1 +CP x ) BBC R&D 4

5 The C/N requirement for QEF in a Gaussian channel is R 1 where R 1 (db) = 18.5 db R 1 = C/(KTBF 1 + CP x ) So the carrier level required to achieve QEF in a Gaussian channel is: C = R 1 KTBF 1 /(1-R 1 P x ) For an ideal model where F 1 = 1 and P x = the carrier level required to achieve QEF in a Gaussian channel will be lower. We will call this carrier level C I The ratio 3 between C and C I is C I = R 1 KTB = dbm ie db above KTB = C/C I = F 1 /(1-R 1 P x ) It should be noted that the bulk of this as shown in Figure 2 is due to the contribution of F 1, which includes front-end thermal noise. It is convenient and usual to measure of a receiver with a sufficiently high and known carrier level such that contributions due to front-end thermal noise are negligible. In order to relate to practical measurements made at high carrier levels, is normalised to exclude F 1 contributions. We will call this / and show this in Figure 3 where: / = /F 1 / = 1/(1-R 1 P x ) System C/N for a practical demodulator (db) R 1 / db I/P Level (dbm) Figure 3 3 Note, this would be the difference if C and C I were in db. BBC R&D 5

6 Figure 3 above shows we have put the model noise floor P x to be about -29 dbc. But, this noise floor is dependant upon the sum of excess noise contributions which are independent of carrier level such as: the intercarrier interference component of phase noise, ADC quantising noise and transmitter intermodulation products. / can be plotted as a function of P x. This is shown in Figure 4. / (db) P x (dbc) Figure 4 Difficult channels So far we have considered the system performance requirement R 1 for the case of a Gaussian channel where we have defined 1log 1 R 1 = 18.5 db. A difficult channel will include degradations such as multipath, Co-Channel Interference (CCI) and Adjacent Channel Interference (ACI). The C/N ratio requirement for a difficult channel will be greater than that for the Gaussian channel. We will call this requirement R 2. There has been some debate as to the difficulty of the channel which the receiver should be able to cope with. Field measurements indicate that there is a spread of requirements where 1log 1 R 2 = 1log 1 R 1 + ( to 8) db. We will consider the case for a difficult channel where 1log 1 R 2 = 1log 1 R db = 25 db. This is 2 db greater than the figure used for initial planning studies [References 3 & 4]. We can now include R 2 in the plot of C/N versus I/P level BBC R&D 6

7 System C/N for a practical demodulator (db) R 2 R 1 / db I/P Level (dbm) Figure 5 Here we can clearly see the increase in / when the requirement is R 2. P x for the above example is about -29 dbc. If P x increased to -25 dbc then / for requirement R 2 would approach infinity. This is seen more clearly if we include R 2 in the plot of / versus P x which is done in Figure 6, and tabulated in Appendix 2. / (db) for Gaussian and Difficult Channels Difficult Channel Gaussian Channel Px (dbc) Figure 6 BBC R&D 7

8 Summary Figure 6 shows us that the loss of noise margin in a DVB-T system is greatly affected by the different carrier to noise requirements between those of a Gaussian channel and those of a difficult channel. For example, a system (which includes transmitter degradations) that has a noise floor of dbc has a loss of noise margin of 1 db in a Gaussian channel. This sounds quite small and reasonable. However, if the channel is difficult, which in our example is a 6.5 db increase in C/N requirement, the same system will have a loss of noise margin which is substantial and fast approaching infinity. Low excess noise contributions within a DVB-T system are therefore crucially important to the overall system performance. Recommendations Excess noise contributions P x, which determine the system noise floor are directly related to loss of noise-margin, and may be easier to measure in some circumstances. Consideration should be given to measurement methods that measure P x. It may not be possible to measure BER of a system in which case receivers should be tested under difficult channel conditions. The figures used in the initial planning studies (references 3 & 4) should be revised to take into account the effects of P x. For example: the implementation margin of 1.5 db in addition to the 3dB allowed for multipath, would need to be reduced for the Gaussian channel case. Acknowledgements The author would like to thank his BBC colleagues for useful discussions and in particular Adrian Robinson for clarifying the effects of the channel equaliser. BBC R&D 8

9 References [1] Salter, J.E. A simple noise model of a DVB-T System. DTG Tx Group Doc. 8, Sept BBC reference: DTB document no. 15. [2] European Telecommunication Standard Digital broadcasting systems for television, sound, and data services; Framing structure, channel coding and modulation for digital terrestrial television. ETSI specification ETS 3 744, European Telecommunications Standards Institute, [3] Digital Terrestrial Television Requirements for Interoperability ( UK D Book ). DTG, June [4] ITC/NTL and BBC Digital TV Frequency Planning Project. Technical Parameters and Planning Algorithms. BBC R&D 9

10 Appendix 1: Mathematical symbols and definitions used within the text of this Paper C signal input power K Boltzmann s constant T reference temperature for noise calculations B system noise bandwidth (7.61 MHz) C/N carrier-to-noise ratio F 1 noise figure of Stage 1 of the model: F 1 (db) =1 log 1 F 1 * F 1 (db) 1 log 1 F 1 F 2 noise figure of Stage 2 of the model: F 2 (db) =1 log 1 F 2 * F 2 (db) 1 log 1 F 2 F t effective total noise figure of the system model * F t (db) 1 log 1 F t Px sum of excess noise contributions which are independent of carrier level. This is the system noise floor. = (F 2-1) R 1 C/N requirement for QEF in a Gaussian channel for a demodulator which includes the action of the channel state measurement and channel equaliser. 1log 1 R 1 = 18.5 db R 2 C/N requirement as above except for a non-gaussian (difficult) channel. Figure used in text : 1log 1 R 2 = 25 db QEF Quasi-error-free is a BER of 2 x 1-4 after the Viterbi decoder BER Bit error ratio Loss of noise-margin which includes F 1 contribution * (db) / Loss of noise-margin which excludes F 1 contribution * / (db) Note, both and / exclude any contribution from the action of the channel state measurement and channel equaliser. * (db) 1log 1 * / (db) 1log 1 / Ideal demodulator Only used in (Reference 1). Ideal (noiseless reference) coherent demodulation with reliable finite-accuracy softdecision Viterbi decoding (3 bits). Practical demodulator Used in this paper. As above but the reference for coherent demodulation is derived from the noisy signal in a way which permits tracking of time varying channels e.g. simple linear temporal interpolation between consecutive scattered pilots. Ideal model F 1 = F 2 = 1; (P x = ) with Practical demodulator Practical model Example values: F 1 = 7 db, P x = -29 dbc(variable) BBC R&D 1

11 Appendix 2 - Tabulation of Loss of Noise-Margin as a Function of P x and Channel Difficulty db above Gaussian Px BBC R&D 11