ENSC37 Communication Systems 7: Digital Bandpass Modulation (Ch. 7) Jie Liang School of Engineering Science Simon Fraser University 1
Outline 7.1 Preliminaries 7. Binary Amplitude-Shift Keying (BASK) 7.3 Phase-Shift Keying (PSK) 7.4 Frequency-shifting Keying (FSK) 7.7 M-ary Digital Modulation 7.8 Mapping of digitally modulated waveforms onto constellations of signal points
7.1 Preliminaries If the channel is low-pass (e.g., coaxial cale), we can transmit the pulses corresponding to digital data directly. If the channel is and-pass (e.g. wireless, satellite), we need to use the digital data to modulate a high-freq sinusoidal carrier: c( t) = Ac cos(π fct+ φc ) Amplitude-Shift Keying (ASK): Use two Ac s to represent 0 and 1. Phase-Shift Keying (PSK): φ c : use 0 and π Frequency-Shift Keying (ASK): use two fc s to represent 0 and 1. to represent 0 and1. 3
7.1 Preliminaries he amplitude of the carrier is usually chosen as A= c such that the carrier has unit energy measured over one it duration.. 4
7. Binary Amplitude-Shift Keying (BASK) In BASK, the modulated wave is s( t) = ( t) cos(πf c E t) = 0, cos(πf c t), for symol1, for symol 0. (t) is the on-off signalling coding of the input inary data. his is a special case of Amplitude Modulation (AM): ( 1+ k m( t) ) cos(πf ), s( t) = A t c a c herefore the BASK spectrum has a carrier component. Envelope detector can e used to demodulate the digital signal. 5
7. Binary Amplitude-Shift Keying (BASK) he average transmitted signal energy is 6
7.3 Phase-Shift Keying (PSK) We first consider inary PSK (BPSK): s( t) = E E cos(πf cos( π f c c t), for symol1, E t + π ) = cos(π f c t ), for symol 0. he two possile values are called antipodal signals. A special case of DSB-SC: No carrier component in the freq domain. BPSK has constant envelope constant transmitted power. Desired in many systems. But cannot use envelope detector in the receiver, need coherent detection. 7
7.3 Phase-Shift Keying (PSK) Detection of BPSK signals: Coherent DSB-SC receiver Sample & decision-making: new to digital communication Can reduce error rate. Advantage over analog comm. 8
Quadriphase-Shift Keying (QPSK) Recall Chap 3.5: Quadrature-amplitude modulation (QAM): ransmit two DSB-SC signals in the same spectrum region. Use two modulators with orthogonal carriers. ransmitted signal: s( t) = Ac m1 ( t)cos(π fct) + Ac m ( t)sin(πfct ) he two signals do not affect each other. 9
Quadriphase-Shift Keying (QPSK) QAM can e generalized to digital modulation In QPSK, the transmitted signal has four possile phases: π/4, 3π/4, 5π/4, 7π/4. E s i ( t ) = 0, Index i: 1,, 3, 4. cos(πf c π t + (i 1) ), 0 t, 4 elsewhere. i= i=1 i=3 i=4 Each signal can represent two its of inary data, called diits. : it duration. : Symol duration. It s easy to see that the energy of si(t) is E. his is the Symol Energy. Since each symol represents its, the average transmitted energy per it is 10
Quadriphase-Shift Keying (QPSK) o see the link with QAM: + = elsewhere. 0,, 0 ), 4 1) ( cos( ) ( t i t f E t s c i π π E E 11 ) sin( ) ( ) cos( ) ( ) )sin( 4 1) sin(( ) )cos( 4 1) cos(( ) ( 1 t f t a t f t a t f i E t f i E t s c c c c i π π π π π π + = =
Quadriphase-Shift Keying (QPSK) Detection of QPSK: si ( t) = a1( t) cos(π fct) + a( t) sin(πf ct) Similar to QAM wo coherent BPSK detectors. 1
7.4 Frequency-Shift Keying (FSK) Binary FSK (BFSK): symol 0 and 1 are represented y two sinusoidal waves with different frequencies si ( t) = E E cos(πf 1 t), cos(π f t ), for symol 1corresponds to i = 1, for symol f1 and f can e chosen such that neighoring signals have continuous phases. his can reduce the andwidth of the transmitted waveforms. his is called the Sunde BFSK. 0 corresponds to i =. 13
Frequency-Shift Keying (FSK) Example: Continuous phase can reduce andwidth 14
7.7 M-ary Digital Modulation M-ary PSK M-ary QAM M-ary FSK Mapping waveforms to signal points 15
7.7 M-ary Digital Modulation During each symol interval of duration, the transmitter sends one of M possile signal s1(t),, sm(t). M is usually a power of : M = ^m. M-ary modulation is necessary if we want to conserve the andwidth. But M-ary system needs more power and more complicated implementation to achieve the same error rate as inary system. 16
M-ary Phase-Shift Keying Generalization of the QPSK E π si ( t) = cos(πf ct+ i), i= 0,...,M -1, 0 t. M his can e expressed as 17
Signal Space Diagram As the increase of M, the receiver of the M-ary modulation can ecome more complicated, ecause for each input symol, a naive receiver needs to compare with M references. It is thus necessary to simplify the signal representation and therefore reduce the complexity of the receiver. he concept of signal space is useful here. 18
Signal Space Diagram he signals si(t) can e written as We can visualize the transmitted signals as points in a K-dimensional space, with axes { } (t) φ j 19
M-ary Phase-Shift Keying π M In M-ary PSK: si ( t) = E cos i cos( πf ct) E sin i sin( πf ct). π M We can define two orthonormal asis functions: {si(t)} can e represented y points on a signal space diagram. he coordinate of each point: In MPSK, the distance from the origin to each point is equal to the signal energy E. 8-PSK 0
M-ary QAM Recall Chap 3.5: QAM s( t) = Ac m1 ( t)cos(π fct) + Ac m( t)sin(πfct ) If m1(t) and m(t) are discrete, we get digital QAM: E0 E0 s( t) = ai cos(πf ct) i sin(πf ct). Example of signal space diagram: 16-QAM Possile values for ai, i: -3, -1, 1, 3. Envelope is not constant. 1
Mapping of Modulated Waveforms to Constellations of Signal Points he correlator method is used in receiver in many systems: Calculate the correlation of input with a pulse template, Sample the output of the correlator, Compare the sample with some thresholds to decode the its. For example, in BPSK, the template is simply the asis function: φ 1( t) = cos(πf ct). If the transmitter sends s1(t): its correlation with the asis function is:
Mapping of Modulated Waveforms to Constellations of Signal Points If the transmitter sends s(t): its correlation with the asis function is: his can e represented y a one-dimensional diagram: 3
Mapping of Modulated Waveforms to Constellations of Signal Points his diagram is useful in studying the effect of the noise. When noise is considered, the received signal will e r ( t) = s ( t) n ( t), n ( t) i i + he output of the correlator will e s i ' i i is noise. ( s ( t) + n ( t) ) φ ( t) dt= s+ n ( t) φ ( t) dt= s+ v. = i i 1 i i 1 i i 0 0 he noise ni(t) introduces some disturs to the position of the desired point on the signal space diagram. Decoding could e wrong if the noise is too large. BPSK: 4
Mapping of Modulated Waveforms to Constellations of Signal Points BFSK: he transmitted signals can e written as: s s t) = E / cos(πf ( 1 1 t), ( t ) = E / cos(π ft ). t he receiver takes correlation of the received signal with two asis functions: φ φ 1 ( t) = ( t) = / / cos(πf 1 cos(πf t), t). 5
Mapping of Modulated Waveforms to Constellations of Signal Points If s1(t) is sent, the outputs of the two correlators are: If s(t) is sent, the outputs are: 6
Mapping of Modulated Waveforms to Constellations of Signal Points So each signal can e represented y a point on a -D diagram: φ φ 1 he noise introduces some disturs to the position of the desired point on the signal space diagram. Decoding could e wrong if the noise is too large. 7
Mapping of Modulated Waveforms to Constellations of Signal Points Compare the diagrams of BPSK and BFSK, we can see that the distance of the two points are Since noise changes the position of the signal in the signal space diagram at the receiver, we can see from these figures that BPSK is more roust to noise than the BFSK. his will e studied in details in Chapter 10. BPSK: BFSK: E E 8