Binary Phase Shift Keying (BPSK)! ( π ) { } ( t) carrier bursts that corresponds to the information bit being a 1 or 0. Binary 0: I

Transcription

1 Binary Phase Shift Keying (BPSK)! l In BPSK, the symbol mapping table encodes bits (b n ) 1 and 0 to transmission symbols (a n ) 1 and 1, respectively l Every T b seconds the modulator transmits one of the two carrier bursts that corresponds to the information bit being a 1 or 0 Binary 1: s () t = A cos(2 π f t), 0 t T 1 c c b Binary 0: s () t = A cos(2 π f t+ π) = A cos(2 π f t) 2 c c c c l The resultant BPSK signal can be expressed as ( ) ( t) ( π ) { } x() t = Ac anπ t ntb / Tb cos 2 fct, an A2 = 1 1 n= I l x(t) contains only the in-phase component I(t); Q(t) is zero 11/18/14 1

2 BPSK Modulation! 11/18/14 2

3 BPSK Coherent Demodulation! 11/18/14 3

4 Error Performance! l If we choose the basis function 2 φ 1 ( t) = cos(2πf ct), 0 T b we can write BPSK waveforms as s s 1 2 ( t) ( t) = A c = A c Tb φ1( t) 2 Tb φ1( t) 2 φ ( t) l BPSK is thus polar signaling with = E = b 1 E l The BER performance of BPSK is, therefore, identical to that of polar NRZ signaling 11/18/14 4 b t φ ( t) d min 2E b BERBPSK = Q = Q 2N N o o 1 T b dmin = 2 E b

5 Binary Frequency Shift Keying (BFSK)! l In BFSK, information is transmitted by sending carrier bursts of two different frequencies, f 1 = f c +Δf /2 and f 2 = f c - Δf /2, to transmit binary data. Δ f is called the frequency deviation Binary 1: s ( t) = A cos(2 π f t+ πδ ft+ φ ), 0 t T 1 c c 1 b Binary 0 : s ( t) = A cos(2 π f t πδ ft+ φ ), 0 t T 2 c c 2 b l A simple way to generate a BFSK signal is to use two separate oscillators tuned to frequencies f 1 and f 2 and switch between their outputs in accordance with the amplitude of the random data bit during that bit interval l φ 1 and φ 2 are arbitrary phases of two frequency bursts generated by separate oscillators 11/18/14 5

6 Other Demodulation Techniques! l Coherent demodulation may neither be desirable nor feasible in many practical applications. l The propagation delay on some radio channels changes too rapidly to permit accurate tracking of the carrier phase at the demodulator l Tracking the incoming signal s carrier phase and synchronizing the demodulator to it requires additional hardware complexity with cost and power efficiency ramifications l Differentially Coherent Demodulator demodulator uses the carrier phase of the previous symbol period as phase reference for the current period l Noncoherent Demodulator demodulator does not exploit phase information in the received signal for its demodulation 11/18/14 6

7 DBPSK (contd)! DBPSK modulator DBPSK demodulator 11/18/14 7

8 DBPSK (contd)! l The output of the sampler is given by r o E + n( T ), a = a = E + n( T ), a a b b n n 1 b b n n 1 where n(t) is non-gaussian noise. l Since we have polar symmetry, V T = 0 is selected. We can now write the following decision rule for decoding r > 0 aˆ = aˆ bˆ = 0 o n n 1 n r < 0 aˆ aˆ bˆ = 1 o n n 1 n l The probability of bit error for DBPSK scheme is given by BERDBPSK 1 = 2 E N e b o 11/18/14 8

9 DBPSK (contd)! 11/18/14 9

10 BER Comparison! 10 0 Probability of Bit Error Rate vs. (Eb/No)dB BPSK DBPSK Coherent ASK/FSK Noncoherent ASK/FSK 10-3 BER Eb/No [db] 11/18/14 10

11 Quadrature Modulation Schemes! l In BPSK the phase of the carrier burst is shifted 0 or 180 degrees every pulse or symbol interval depending upon the information sequence. Thus each modulated carrier pulse transmits 1 bit of information l If, on the other hand, the modulation scheme can use phase shifts of 45, 135, 225, or 315 degrees, each modulated carrier pulse transmits 2 bits of information. This technique is called Quadrature Phase Shift Keying (QPSK) l Using QPSK, we can double the data rate over the same channel bandwidth. l QPSK is one of the modulation methods in the family known as Quadrature modulation schemes which are widely used, including in cellular and cable modem applications 11/18/14 11

12 Quadrature Modulation Schemes (contd)! l Suppose an information source generates M-ary symbols at a rate of D symbols/second T = 1/D l The symbol stream is split into 2 sequences that consist of I Q odd and even symbols, say, a n and a n, respectively I l Let an AM modulate in-phase carrier A c cos(2π f c t) every T seconds to produce the signal I c an c c c n= ( ) cos( 2 π ) = I( )cos( 2π ) A v t nt f t A t f t I l This signal is identical to the BPSK signal if a n is polar binary symbol sequence Q l Similarly, let an AM modulate the quadrature carrier A c sin(2π f c t) every T seconds to produce the signal Q Ac anw( t nt) sin ( 2 π fct) = AcQ( t)sin ( 2π fct) n= 11/18/14 12

13 Quadrature Modulation Schemes (contd)! l v(t) and w(t) are unit energy pulses of width T seconds. For example v() t = w() t = (1/ T ) Π[( t nt)/ T] l Both modulated waveforms will have their power spectrum located within the same frequency band l The composite modulated signal x(t) is ( π ) ( π ) x( t) = Ac I( t)cos 2 fct Q( t)sin 2 fct I Q a ( ) cos( 2π ) a ( ) sin ( 2π ) = A v t nt f t w t nt f t c n c n c n= 11/18/14 13

14 Quadrature Modulation Schemes (contd)! l The in-phase and quadrature pulse trains I(t) and Q(t) can be recovered by, respectively, multiplying x(t) with 2cos(2π f c t) and 2sin(2π f c t) and then LP filtering resultant waveforms I Q l The M-ary symbols a n and a n are then detected from I(t) and Q(t), respectively, as discussed in Chapter 10 11/18/14 14

15 Quaternary Phase Shift Keying (QPSK)! l QPSK is the most common form of phase-shift keying. By using phase shifts of 45, 135, 225, or 315 degrees, each modulated carrier pulse transmits 2 bits of information l QPSK is a quadrature modulation scheme: each orthogonal carrier is modulated by a statistically independent polar NRZ symbol sequence l The block diagram of a QPSK modulator is shown in Figure l Binary data arriving at rate R b is split by a serial to parallel converter into two data streams, one containing even bits (b 2n ) and other odd bits (b 2n+1 ) l The symbol mapping tables in the upper and lower branches of the modulator encode even and odd bits into polar transmission symbols a 2n and a 2n+1, respectively 11/18/14 15

16 QPSK Modulator! l The output of the pulse shaping filter in the upper branch is a binary polar NRZ pulse train I(t) that modulates the in-phase carrier Ac cos( 2π fct) l Similarly, a binary polar NRZ pulse train Q(t) generated by the pulse shaping filter in the lower branch modulates the quadrature carrier Acsin ( 2π fct) l The QPSK signal x(t) is now obtained by adding the in-phase and quadrature components 2n 2n+ 1 ( π ) ( π ) x( t) = Ac I( t)cos 2 fct Q( t)sin 2 fct where ( ) I() t = a v t nt n= ( ) Q() t = a v t nt 11/18/14 16 n=

17 QPSK Modulator Block Diagram! 11/18/14 17

18 QPSK! l The carrier-modulated pulse during the first symbol interval is ( ) ( ) s( t) = Av c ( t) a0cos 2π fct a1sin 2 π fct, 0 t T 1 a1 = Av c ( t)cos( 2 π ft c + ψ0), ψ0 = tan a0 ` where phase of the transmitted carrier burst ψ 0 is a discrete random variable assuming one of the four possible values {π/ 4, 3π/4, 5π/4, 7π/4} depending on the binary pair (a 0, a 1 ) ψ 0 π 3π 5π 7π,,, /18/14 18

19 QPSK Demodulator Block Diagram! l The coherent demodulation of the QPSK signal is shown in Figure 11/18/14 19

20 Error Performance! l By choosing the basis functions φ 1( t) = 2v( t)cos(2π fct) φ 2 ( t) = 2v( t)sin(2πf ct) it is possible express all four possible carrier bursts in table as vectors in the plane spanned by φ 1 and φ 2 Es Es s= ( a2n Es, a2n+ 1 Es) = ( ±, ± ) = ( ± Eb, ± Eb) 2 2 l The nearest neighbor estimate for the BER of for QPSK is (K = 4, M =4 ) 2K d min 2E E b b = Es BERQPSK = Q = Q M log2 M 2N N o o dmin = 2 It is exact value 11/18/14 20 /2 E b

21 Offset QPSK (OQPSK)! l OQPSK is a minor but important variation on QPSK l In QPSK, there is no constraint on allowed phase transitions (0, 90 or 180 degrees as shown by dotted lines) as shown in Figure l I(t) and Q(t) in QPSK can switch signs simultaneously (e.g. if 11 is followed by 00) the phase ψ(t) changes by 180 o l Constant envelope nature of the QPSK signal destroyed with the filtered pulses - the waveform can t change instantaneously from one peak to another when 180 o phase transitions occur l However, Class-C amplifiers are highly nonlinear and restore the filtered sidelobes causing adjacent channel interference, when amplifying a waveform with envelope variation l In OQPSK, either a 2n or a 2n+1 can change but not both because of a single bit delay in the quadrature path ±90 o phase transitions only to adjacent neighbors. Less envelope variation 11/18/14 21

22 OQPSK Modulator! 11/18/14 22

23 OQPSK Demodulator! l The OQPSK demodulator is identical to that of QPSK demodulator except for a single bit delay in the inphase path l Since OQPSK constellation is identical to that of QPSK, its BER performance is identical to that of QPSK 11/18/14 23

24 M-ary Phase Shift Keying! l In M-ary PSK, M different phase shifts of the carrier are used to convey the information. The M = 2 k signal waveforms, each representing k information bits, are represented as s() t = Av()cos[2 t π f t+ ψ + ϕ], 0 t T i= 1,..., M i c c i where π ϕ = 0 or M = Fixed phase offset 2 ( i 1) ψ i = π = M possible phases of the carrier M v(t)= unit energy pulse Phase of the carrier during l M-ary PSK signal the nth symbol interval 2Es x() t = v( t nt)cos[2 π fct+ ψ n + ϕ] T n= All M-ary PSK waveforms have equal energy E s 11/18/14 24

25 M-ary PSK (contd)! l By choosing the same basis functions as for QPSK, it is possible to express all waveforms in the M-PSK signal set as vectors in the plane spanned by φ 1 and φ 2 as I Q s = ( a E, a E ) where a a I n Q n n s n s = cos( ψ + ϕ) n = sin( ψ + ϕ) n l The signal vectors lie around a circle of radius The constellation for 8- PSK (M = 8) is shown in Figure E s. 11/18/14 25

26 M-ary PSK (contd)! l As illustrated in Figure, the minimum distance between two adjacent signal points is π dmin = 2D= 2 E s sin M l The nearest-neighbor estimate of P e is P e 2E s 2 2Q sin N o 2E log b 2 2 = 2Q sin N o π M M π M BER MPSK 1 2E log M π log2 M No M b 2 2 2Q sin 11/18/14 26

27 M-PSK BER Performance! 11/18/14 27

28 Digital Carrier Modulation Schemes!