Non-coherent Orthogonal Modulation

1. Non-coherent Orthogonal Modulation • Non-coherent implies that phase information is not available to the receiver • As a result, zero phase of the receiver can mean any phase of the transmitter • Any modulation techniques that transmits information through the phase; such as BPSK, M-ary PSK; must be demodulated only coherently

2. sin(2ft) cos(2ft) Transmitter Non-coherent Orthogonal Modulation sin(2ft) cos(2ft) Receiver

3. Non-coherent Orthogonal Modulation • It is impossible to draw the signal constellation since we do not know where the axes are • However, we can still determine the distance of the each signal constellation from the origin • As a result, the modulation techniques that put information in the amplitude can be detected • FSK uses the amplitude of signals in two different frequencies. Hence non-coherent receivers can be employed to demodulate FSK signals

4. Non-coherent Orthogonal Modulation • Consider the BFSK system where two frequencies f1 and f2 are used to represented two “1” and “0” • The transmitted signal is given by • If the carrier phase  is unknown to the receiver, we can still be able to demodulate the transmitted signal using non coherent demodulation

5. Non-coherent Orthogonal Modulation • The previous BFSK signal, can be rearranged as shown below • The amplitude (envelope) of the transmitted signal is given by

6. Non-coherent Orthogonal Modulation • Recall that • The amplitude (envelope) of the received signal is given by

7. Non-coherent BFSK • There are three common implementations for the equation li • Quadrature receiver using correlator • Quadrature receiver using matched filter • Matched filter using envelope detector

8. Quadrature receiver using correlators

9. Quadrature receiver using Matched Filter

10. Non-coherent matched filter using envelope detector Since the equation Represent the envelope of the received signal we can demodulate the received signal using an envelope detector as shown in the next slide The envelope detector finds the square root of

11. Non-coherent Matched Filter envelope detector

12. Non-coherent matched filter envelope detector An alternate way to show the equivalence between the non-coherent matched filter using envelope detector and the non-coherent detector using quadrature detector is illustrated in mathematically in the next few slides

13. Noncoherent Orthogonal Modulation • Consider the output of y(t) a filter matched to cos(2fit)

14. Noncoherent Orthogonal Modulation • The detected envelope at is • Which is exactly the same as in correlator receiver

15. Generalized binary receiver for noncoherent orthogonal modulation.

16. Noncoherent Orthogonal Modulation • Decision rule: Let if li> lkfor all k. For examples, decide if l1> l2 • This decision rule suggests that if the envelope (amplitude) of the received signal described in terms of cos(2f1t) is greater than the envelope of the received signal described in terms of cos(2f2t), we say s1(t) was sent

17. Quadrature receiver equivalent to either one of the two matched filters in part

18. Noncoherent Orthogonal Modulation • The average probability of error in non-coherent detector can be given by • Where E is the symbol energy and is the power spectral density of the noise

19. Noncoherent: BFSK • For BFSK, the transmitted symbols are defined by • The receiver can be implemented as shown in the block diagram detailed in the next slide

20. Non-coherent: BFSK demodulator

21. Non-coherent BFSK, probability of error • Probability of Errors

22. Differential PSK • Differential PSK is the non coherent version of phase shift keying (PSK) • It eliminates the need for a coherent reference signal by combining two basic operations • Differential encoding of the input binary stream (as explained at the end of Ch. 3) • Applying phase shift keying modulation to the encoded binary data

23. Differential PSK Differential PSK Instead of finding the phase of the signal on the interval 0<t≤Tb. This receiver determines the phase difference between adjacent time intervals. If “1” is sent, the phase remains unchanged If “0” is sent, the phase changed by 180◦

24. Differential PSK • Suppose that the transmitted DPSK signal equals to for , where is the bit duration and is the signal energy per bit • Let denote the transmitted DPSK signal for for the case when symbol 1 is being transmitted for the second part of the this time interval • The transmission of symbol 1 leaves the carrier unchanged over the interval • and

25. Differential PSK • The transmission of symbol 1 leaves the carrier unchanged over the interval , therefore we can define as

26. Differential PSK Similary we can define for the transmission of symbol 0 for DPSK encoding over the time interval as

27. Average probability of error of DPSK signals • The average probability of error of DPSK signal is given by • A comparison between the average probability of error of DPSK and non-coherent BFSK shows that the DPSK has a better average probability of error compared with non-coherent BFSK

28. Generation of DPSK Let the binary sequence represents the binary data to be transmitted using DPSK Let the sequence represents the differentially encoded sequence The encoding rule can be as follows (there is a reference bit as explained in Ch.3)

29. Generation of DPSK • If the incoming binary symbol is 1, leave the symbol unchanged with respect to the previous bit • If the incoming binary symbol is 0, change the symbol with respect to the previous bit • The differentially encoded sequence is used to phase-shift a carrier with phase angles and representing symbols 1 and 0, respectively

30. Example of differential encoding process Consider the binary sequence shown below find the differentially encoded sequence and the transmitted phase of the carrier

31. Generation of DPSK Differential PSK modulator can be realized by the block diagram shown below, where (Xnor operation)

32. DPSK: Receiver

33. DPSK: Receiver • From the block diagram, we have that the decision rule as • If the phase of signal is unchanged (send “1”) the sign (“+” or “-”) of both xi and xQ should not change. Hence, thel(x) should be positive. • If the phase of signal is unchanged (send “0”) the sign (“+” or “-1”) of both xi and xQ should change. Hence, thel(x) should be negative.

34. Signal-space diagram of received DPSK signal.

35. Comparison of digital modulation schemes using a single carrier