Objectives. Presentation Outline. Digital Modulation Lecture 04

Transcription

1 Digital Modulation Leture 04 Filters Digital Modulation Tehniques Rihard Harris Objetives To be able to disuss the purpose of filtering and determine the properties of well known filters. You will be able to: Desribe I/Q diagrams and their uses Provide an overview of digital modulation appliation areas Desribe the harateristis of the various forms of filters and their use in digital transmission Communiation Systems Digital Modulation Slide Presentation Outline Filtering methods Raised osine Square-root raised osine Gaussian filters Detetion methods for standard Digital Modulation tehniques PSDs for ommon Digital Modulation shemes Communiation Systems Digital Modulation Slide 3 1

2 Referenes Digital Modulation in Communiation Systems An Introdution (Hewlett Pakard Appliation Note 198) Priniples of Digital Modulation, by Dr Mike Fitton, Teleommuniations Researh Lab Toshiba Researh Europe Limited Communiation Systems Digital Modulation Slide 4 Filtering 1 Filtering allows the transmitted bandwidth to be signifiantly redued without losing the ontent of the digital data. Spetral effiieny of the signal is improved using filtering. Many possible varieties: Raised osine Square-root raised osine Gaussian filters Any fast transition in a signal, irrespetive of whether it is amplitude, phase or frequeny, will need wide oupied bandwidth. Thus, if we have a tehnique that an help to slow down these transitions then it will narrow the oupied bandwidth. Communiation Systems Digital Modulation Slide 5 Filtering Filtering helps to smooth these transitions (in I and Q). It also redues interferene sine it lowers the tendeny of one signal to interfere with another. On the reeiver side, the redued bandwidth inreases the sensitivity beause more noise and interferene are rejeted. Tradeoffs may be neessary though: Some types of filtering may ause the trajetory of the signal (the paths of transitions between states) to overshoot. Overshooting implies more arrier power and phase from the transmitter amplifiers Communiation Systems Digital Modulation Slide 6

3 f 0 Filtering 3 Other problems Filtering may make radios more omplex and larger. Filtering an reate ISI problems Can our if heavy filtering so that the symbols blur together and eah symbol affets those around it. This is determined by the time response or the impulse response of the filter. Communiation Systems Digital Modulation Slide 7 Nyquist or Raised-Cosine Filters The following graph shows the impulse or time domain response of a Nyquist filter. We have seen this figure before. Nyquist filters have the property that their impulse response rings at the symbol rate. The filter is hosen to ring or have the impulse response of the filter ross through zero at the symbol lok frequeny. 1 Communiation Systems Digital Modulation Slide 8 Nyquist or Raised-Cosine Filters The time response of the filter goes through zero with a period that exatly orresponds to the symbol spaing. Adjaent symbols do not interfere with eah other at the symbol times beause the response equals zero at all symbol times exept the entre (desired) one. Nyquist filters heavily filter the signal without blurring the symbols together at the symbol times. This is important for transmitting information without errors aused by Inter-Symbol Interferene. Note that Inter-Symbol Interferene does exist at all times exept the symbol (deision) times. Usually the filter is split, half being in the transmit path and half in the reeiver path. In this ase root Nyquist filters (ommonly alled root raised osine) are used in eah part, so that their ombined response is that of a Nyquist filter. Communiation Systems Digital Modulation Slide 9 3

4 Nyquist or Raised-Cosine Filters Sometimes filtering is desired at both the transmitter and reeiver. Filtering in the transmitter redues the adjaenthannel-power radiation of the transmitter, and thus its potential for interfering with other transmitters. Communiation Systems Digital Modulation Slide 10 Nyquist or Raised-Cosine Filters Filtering at the reeiver redues the effets of broadband noise and also interferene from other transmitters in nearby hannels. To get zero Inter-Symbol Interferene (ISI), both filters are designed until the ombined result of the filters and the rest of the system is a full Nyquist filter. Potential differenes an ause problems in manufaturing beause the transmitter and reeiver are often manufatured by different ompanies. The reeiver may be a small hand-held model and the transmitter may be a large ellular base station. If the design is done orretly, the results are the best data rate, the most effiient radio, and redued effets of interferene and noise. This is why root-nyquist filters are used in reeivers and transmitters as Nyquist x Nyquist = Nyquist. Mathed filters are not used in Gaussian filtering. Communiation Systems Digital Modulation Slide 11 Gaussian Filter - 1 In ontrast, a GSM signal will have a small blurring of symbols on eah of the four states beause the Gaussian filter used in GSM does not have zero Inter-Symbol Interferene. The phase states vary somewhat ausing a blurring of the symbols as shown in the figure below. Wireless system arhitets must deide just how muh of the Inter-Symbol Interferene an be tolerated in a system and ombine that with noise and interferene. Communiation Systems Digital Modulation Slide 1 4

5 Gaussian Filter Communiation Systems Digital Modulation Slide 13 Gaussian Filter 3 Gaussian filters are used in GSM beause of their advantages in arrier power, oupied bandwidth and symbol-lok reovery. The Gaussian filter is a Gaussian shape in both the time and frequeny domains, and it does not ring like the raised osine filters do. Its effets in the time domain are relatively short and eah symbol interats signifiantly (or auses ISI) with only the preeding and sueeding symbols. This redues the tendeny for partiular sequenes of symbols to interat whih makes amplifiers easier to build and more effiient. Communiation Systems Digital Modulation Slide 14 Filter Bandwidth Parameter r - 1 The sharpness of a raised osine filter is desribed by the value of r the roll-off parameter. Thus r gives a diret measure of the oupied bandwidth of the system and is alulated as Oupied bandwidth = Symbol rate X (1 + r). If the filter had a perfet harateristi with sharp transitions and r = 0, the oupied bandwidth would be: Oupied bandwidth = Symbol rate X (1 + 0) = symbol rate. Communiation Systems Digital Modulation Slide 15 5

6 Filter Bandwidth Parameter r - Communiation Systems Digital Modulation Slide 16 Filter Bandwidth Parameter r - 3 An r-value of one uses twie as muh bandwidth as an r-value of zero. In pratie, it is possible to implement an r-value below 0. and make good, ompat, pratial radios. Typial values range from 0.35 to 0.5, though some video systems use an r-value as low as The orresponding term for a Gaussian filter is BT (bandwidth time produt). Oupied bandwidth annot be stated in terms of BT beause a Gaussian filter s frequeny response does not go identially to zero, as does a raised osine. Common values for BT are 0.3 to 0.5. Communiation Systems Digital Modulation Slide 17 Different Filter Bandwidths Different filter bandwidths show different effets. For example, look at a QPSK signal and examine how different values of r effet the vetor diagram. If the radio has no transmitter filter as shown on the left of the graph, the transitions between states are instantaneous. No filtering means an r of infinity. Communiation Systems Digital Modulation Slide 18 6

7 Power Spetral Densities and Detetion Methods for Digital Modulation Rihard Harris Coherent Reeption An estimate of the hannel phase and attenuation is reovered. It is then possible to reprodue the transmitted signal, and demodulate. It is neessary to have an aurate version of the arrier, otherwise errors are introdued. Carrier reovery methods inlude: Pilot Tone (suh as Transparent Tone in Band) Less power in information bearing signal High peak-to-mean power ratio Pilot Symbol Assisted Modulation Less power in information bearing signal Carrier Reovery (suh as Costas loop) The arrier is reovered from the information signal Communiation Systems Digital Modulation Slide 0 Differential Reeption In the transmitter, eah symbol is modulated relative to the previous symbol, for example in differential BPSK: 0 = no hange 1 = +180 o In the reeiver, the urrent symbol is demodulated using the previous symbol as a referene. The previous symbol ats as an estimate of the hannel. Differential reeption is theoretially 3dB poorer than oherent. This is beause the differential system has two soures of error: a orrupted symbol, and a orrupted referene (the previous symbol). Non-oherent reeption is often easier to implement. Communiation Systems Digital Modulation Slide 1 7

8 Computing the PSD of OOK The Power Spetral Density of the omplex envelope is omputed using our PSD formula as: A sinπ ft b Pg( f) = δ ( f) + Tb π ft b Assuming that m(t) has a peak value of The PSD of OOK is then given by 1 Pg( f f) + Pg( f f) 4 Note: We have already onsidered this in a tutorial Communiation Systems Digital Modulation Slide Plot of PSD for OOK The null-null bandwidth is R The transmission bandwidth of OOK is B T = B where B is the baseband bandwidth With raised osine rolloff filtering, B= ½(1+r)R, hene B T = (1+r)R Note: For binary signalling, D = R. Communiation Systems Digital Modulation Slide 3 Detetion of OOK 1 The following set up is used to detet OOK signals: OOK in Envelope detetor Binary output Non-oherent Detetion OOK in Low-pass filter Binary output Coherent Detetion with Low-Pass Filter Proessing Communiation Systems Digital Modulation Slide 4 8

9 Detetion of OOK Note: When the reeived OOK signal is orrupted by Additive White Gaussian Noise (AWGN), the optimal detetion (to obtain the lowest possible Bit Error Rate BER ) requires oherent detetion with mathed filter proessing. Communiation Systems Digital Modulation Slide 5 Binary Phase-Shift Keying Computing the PSD for the omplex envelope of BPSK gives the following: sinπftb Pg ( f ) = A Tb πftb Assuming that m(t) has peak values of ±1 The PSD of BPSK is then given by 1 4 [ P ( f f ) + P ( f f )] g g Communiation Systems Digital Modulation Slide 6 The PSD of BPSK The bandwidth for BPSK is the same as for OOK. Raised osine-rolloff filtering an be used to onserve bandwidth Communiation Systems Digital Modulation Slide 7 9

10 Detetion of BPSK [ ] s()( t sinω t LP reovers m(t) Coherent detetion must be used. Communiation Systems Digital Modulation Slide 8 Orthogonal Signalling 1 Consider transmitting a binary 1 over the bit interval 0<t<T b using an FSK signal given by: s () t = A os( ω t+ θ ) The binary 0 is transmitted using the signal Where θ 1 = θ for ontinuous phase FSK, the two signals are orthogonal if b T s 1() ts () tdt= 0 That is: s () t = A os( ω t+ θ ) 0 T b A os( ω1t+ θ1)os( ωt+ θ) dt = 0 0 Communiation Systems Digital Modulation Slide 9 Orthogonal Signalling This means that A sin[( ω1 ω) Tb + ( θ1 θ)] sin( θ1 θ) ( ω1 ω) A sin[( ω1+ ω) Tb + ( θ1+ θ)] sin( θ1+ θ) + = 0 ( ω1+ ω) The seond term is negligible sine we assume ω 1 +ω is large. Therefore sin[ π h + ( θ1 θ)] sin( θ1 θ) = 0 π h Communiation Systems Digital Modulation Slide 30 10

11 Orthogonal Signalling 3 Where ( ω1 ω) Tb = π( F) Tb and h= FT b For θ 1 = θ the minimum value for orthogonality is h=0.5, or a peak frequeny deviation of 1 1 F = = R 4Tb 4 For θ 1 θ the disontinuous phase FSK ase, the minimum value for the orthogonality is h=1, or a peak frequeny deviation of 1 1 F = = R T b Communiation Systems Digital Modulation Slide 31 Minimum Shift Keying (MSK) Minimum Shift Keying is ontinuous phase FSK with a minimum modulation index (h=0.5) that will produe orthogonal signalling. The omplex envelope is jθ () t gt () = Ae = Ae t m( λ ) dλ Where F= ¼R and m(t) = ±1 MSK is a onstant amplitude signal Communiation Systems Digital Modulation Slide 3 MSK MSK an be generated by using a simple FM modulator, viz: FM Transmitter F= ¼R MSK is equivalent to OQPSK with sinusoidal pulse shaping. Communiation Systems Digital Modulation Slide 33 11

12 PSD of MSK The PSD of the omplex envelope is given by: 16AT b os πtb f Pg ( f) = π [1 (4 Tf b ) ] Communiation Systems Digital Modulation Slide 34 GMSK 1 Gaussian-filtered MSK The data (retangular shaped pulses) are filtered by a filter having a Gaussian shaped frequeny response ( f / B) (ln/) H( f) e = Where B is the 3dB bandwidth of the filter The PSD of GMSK an be obtained via omputer simulation Communiation Systems Digital Modulation Slide 35 GMSK BT b = 0.3 (ie. the 3dB bandwidth is 0.3 of the bit rate) gives a good ompromise for relatively low side-lobes and tolerable ISI GMSK has a onstant envelope GMSK with BT b = 0.3 is the modulation format used in GSM ellular telephone systems GMSK and MSK an be deteted either oherently or non-oherently Communiation Systems Digital Modulation Slide 36 1

13 Detetion of DPSK Partially oherent detetion: Does not require arrier phase synhronisation Reeiver detets the relative phase differene between the waveforms of e n and e n-1 to determine d n In the previous example, d n =1 if phase differene is π and d n =0 if no phase differene Communiation Systems Digital Modulation Slide 37 PSD of FSK h is the digital modulation index, the peak frequeny deviation F = D f /π for m(t) having values of ±1. (See pages for the mathematial expression for the PSD in this ase) Communiation Systems Digital Modulation Slide 38 Bandwidth of FSK The approximate bandwidth is given by Carson s rule: BT = ( β + 1) B Where β = F/ B and B is the bandwidth of the squarewave data waveform. Using the first null bandwidth, B=R, thus B = ( F + R) T With raised osine filtering, B = 1/ (1+r)R, hene B = F + (1 + r) R T Communiation Systems Digital Modulation Slide 39 13

14 Detetion of FSK Communiation Systems Digital Modulation Slide 40 14