0. Chapter 4: Bandpass Modulation and Demodulation/Detection

1. 4.1 Why Modulate?
이번 발표자료는
연구배경
연구복적
제안시스템
시뮬레이션
향후 연구방향으로 구성되어 있습니다.

2. digital symbol : waveform compatible with the characteristic
4.1 Why Modulate?
Digital modulation :
digital symbol : waveform compatible with the characteristic
of the channel
Why use carrier?
ⓐ reduce size of antenna (=3108m/fc)
e.g.) fc = 3kHz : antenna span : /4 = 25km
fc = 900 MHz : antenna diameter : /4 = 9cm
ⓑ frequency-division multiplexing
ⓒ minimize the effect of interference : spread spectrum
ⓓ place a signal in a frequency band where design
requirements are met (e.g.)RF->IF
이번 발표자료는
연구배경
연구복적
제안시스템
시뮬레이션
향후 연구방향으로 구성되어 있습니다.

3. 4.1 Why Modulate?
고속의 멀티미디어 서비스를 위하여 고속의 data rate과 고품질의 서비스를 요구 하게되었습니다. MC-CDMA는 이러한 요구를 만족하는 기술중에 하나입니다.
MC-CDMA는 직교하는 여러개의 부반송파를 이용하여 전송함으로써 주파수 선택적페이딩에 강합니다. 또한, 복수의 사용자가 코드를 사용하여 다중화 함으로써 주파수 효율을 높일수 있습니다. 세 번째로, 사용자가 같은 데이터를 다른 캐리어를 사용하여 전송하므로, 주파수 다이버시티 이득을 얻을 수 있다.

4. 4.2 Digital Bandpass Modulation Technique
General form of a carrier wave
4.2.1 Phasor Representation of a Sinusoid
complex notation of a sinusoidal carrier wave

5. 4.2 Digital Bandpass Modulation Technique
Analytical form of transmitted waveform
Analytical representation of narrowband FM(NFM)

6. 4.2 Digital Bandpass Modulation Technique
4.2.2 Phase Shift Keying
4.2.3 Frequency Shift Keying
4.2.4 Amplitude Shift Keying

7. 4.2 Digital Bandpass Modulation Technique

8. 4.3 Detection of signals in Gaussian Noise
Two-dimensional signal space (M=2)
Detector decides which of the signals s1 or s2 was transmitted,
after receiving r
=>Minimum-error decision rule chooses the signal class s.t.
distance is minimized
Decision region
Decision rule
4.3.1 Decision Regions

9. 4.3 Detection of signals in Gaussian Noise
4.3.2 Correlation Receiver
Received signal
Detection process
Step 1 : Transform the waveform r(t) into a single random variable(R.V.)
Matched filter (Correlator) maximizes SNR
Another detection approach (Fig.4.7.(b)) Any signal set can be expressed in terms of some set of basis functions
Step 2 : Choose waveform si(t) that has the largest correlation with r(t)
Choose the si(t) whose index corresponds to the max Zi(T)

10. 4.3 Detection of signals in Gaussian Noise
Signal N symbol M
Signal N< symbol M
Ex) M-ary PSK
N=2

11. 4.3 Detection of signals in Gaussian Noise
Binary Detection Threshold
Decision stage : choose the signal best matched to the
coefficients aij (with the set of output Zj(T))

12. 4.3 Detection of signals in Gaussian Noise
Two conditional pdfs : likelihood of s1(s2)

13. 4.3 Detection of signals in Gaussian Noise
Minimum error criterion for equally likely binary signals
corrupted by Gaussian noise
For antipodal signals,

14. 4.4 Coherent Detection 4.4.1Coherent Detection of PSK(BPSK)
Coherent detector
BPSK example
Orthonormal basis function

15. 4.4 Coherent Detection 4.4.1Coherent Detection of PSK(BPSK)
When s1(t) is transmitted, the expected values of product integrator
Decision stage
Choose the signal with largest value of zi(T)

16. 4.4.2 Sampled Matched Filter
Example 4.1 Sampled Matched Filter Consider the BPSK waveform set
Illustrate how a sampled matched filter or correlator can be used to detect a received signal, say s1(t), from the BPSK Waveform set, in the absence of noise.
Sampled MF (N samples per symbol)

17. 4.4 Coherent Detection Ex) Sampled MF (4 samples per symbol)
sampled s1
sampled s2

18. 4.4 Coherent Detection
4.4.3 Coherent Detection of Multiple Phase Shift Keying
Signal space for QPSK(quadri-phase shift keying), M=4 (N=2)
For typical coherent MPSK system,
Orthonormal basis function

19. 4.4.3 Coherent Detection of Multiple PSK
Signal can be written as
Received signal
Demodulator
decision

20. Demodulator of multiple-PSK

21. 4.4.4 Coherent Detection of FSK
Typical set of FSK signal waveforms
Orthonormal set
Distance between any two prototype signal vectors is constant
The ith prptotype signal vector is located on the ith coordinated axis a displacement from origin

22. 4.4 Coherent Detection
Example:3-ary FSK signal

23. 4.5 Non-coherent Detection
Non-coherent detection : actual value of the phase
of the incoming signal is not required
4.5.1 Detection of Differential PSK
For coherent detection, MF is used
For non-coherent detection, this is not possible because MF
output is a function of unknown angle α

24. 4.5.1 Detection of Differential PSK
Differential encoding : information is carried by
the difference in phase between two successive
waveforms. To sent the i-th message (i=0,…,M),
the present signal must have its phase advanced by
over the previous signal
Differential coherent detection : non-coherent because
it does not require a reference in phase with received
carrier Assuming that αvaries slowly relative to 2T,
phase difference is independent of α as

25. 4.5.1 Detection of Differential PSK
DPSK Vs. PSK
DPSK : 3dB worse than PSK
PSK compares signal with clean reference
DPSK compares two noisy signals,
reducing complexity

26. 4.5.2 Binary Differential PSK Example
Sample index k
Original message
encoder
Differential message
Correspondng phase 1
Arbitrary setting
decoder

27. 4.5 .3 Non-coherent Detection of Binary Differential FSK
Just an energy detector without phase measurement
Twice as many channel branches
Quadrature receiver

28. 4.5 .3 Non-coherent Detection of Binary Differential FSK
Three different cases :
Another implementation for
non-coherent FSK detection
Envelop detector :
rectifier and LPF
Looks simpler, but (analog)
filter require more complexity

29. 4.5.4 Required Tone Spacing for Non-coherent Orthogonal FSK Signaling
In order for the signal set to be orthogonal, any
pair of adjacent tones must have a frequency
separation of a multiple of 1/T[Hz] cf) Nyquist filter
Minimum tone separation:1/T[Hz]

30. 4.5 Non-coherent Detection : Example 4.3
⊙ Non-coherent FSK signal :
⊙ Coherent FSK signal :
Non-coherent이면 둘 다 0이어야 함

31. 4.7 Error Performance for Binary Systems
4.7.1Probability of Bit Error for Coherently Detected BPSK
Antipodal signals
Basis function
Decision rule is

32. The same a priori probability
4.7 Error Performnace for Binary Systems
The same a priori probability a1 a2

33. 4.7 Error Performnace for Binary Systems

34. 4.7 Error Performance for Binary Systems
Another approach (1)

35. 4.7 Error Performance for Binary Systems
Another approach (2)
BPSK
BFSK s2 s2 s1 s1

36. (dfferentially coherent)
4.7 Error Performance for Binary Systems
Probability of bit error for several types of binary systems
TABLE 4.1 Probability of Error for Selected
Binary Modulation Schemes
Modulation
PSK(coherent)
DPSK
(dfferentially coherent)
Orthogonal FSK
(coherent) PB
(noncoherent)

37. 4.8 M-ary Signaling and Performance
4.8.2 M-ary Signaling(M=2k k:bits, M=# of waveforms)
M-ary orthogonal
k↑ BER↑ BW↑ ①
M-ary PSK
k↑ BER↑
same BW
Shannon
Limit
-1.6dB
k=∞ ②
(R, Eb/No, BER, BW) : fundamental “trade-off”

38. 4.8.3 Vectorial View of MPSK Signaling
① (M=2k↑, the same Eb/No)
 bandwidth efficiency (R/W) ↑, PB ↑
② (M=2k↑, the same PB)
 bandwidth efficiency (R/W) ↑, Eb/No ↑

39. 4.8.4 BPSK and QPSK : the same bit error probability
General relationship
QPSK = two orthogonal BPSK
channel (I stream, Q stream)
BPSK
QPSK
Magnitude
(A)
I stream ( A/root(2) )
Q stream ( A/root(2) )
Power/bit
Half
Bit rate

40. 4.8 M-ary Signaling and Performance
If original QPSK is given by R[bps], S[watt],
Same BER, BW efficiency : BPSK=1,QPSK=2[bit/s/Hz]
Eb/N0 vs. SNR

41. 4.8 M-ary Signaling and Performance
Fig : M-ary orthogonal signaling at PE=10-3 in
dB(decibel, nonlinear), factor(linear)
k=10 (1024-ary symbol), 20SNR(factor)→2SNR per bit(factor);
each bit require 2.

42. 4.9 Symbol Error Performance for M-ary System(M>2)
4.9.4 Bit Error Probability vs. Symbol Error Probability for Multiple Phase Signaling
Assume that the symbol(011) is transmitted
If an error occur, (010) or (100) is likely→3bit errors
Gray code : neighboring symbols differ from one another in only one bit position
BPSK vs. QPSK