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Tele4653 l3 Tele4653 l3 Presentation Transcript

  • TELE4653 Digital Modulation & Coding Digital Modulation Wei Zhang w.zhang@unsw.edu.au School of Electrical Engineering and Telecommunications The University of New South Wales
  • Outline CPFSK CPM MSK Offset QPSK TELE4653 - Digital Modulation & Coding - Lecture 2. March 15, 2010. – p.1/2
  • Modulation with Memory Modulation is the mapping between the digital sequence and the signal sequence to be transmitted over the channel. Modulation with memory: the mapping depends on the current and the past bits. Example: differential encoding. bk = ak ⊕ bk−1 TELE4653 - Digital Modulation & Coding - Lecture 2. March 15, 2010. – p.2/2
  • from Digital Communications (5th Ed.) – John G. Proakis and Masoud Salehi
  • from Digital Communications (5th Ed.) – John G. Proakis and Masoud Salehi
  • from Digital Communications (5th Ed.) – John G. Proakis and Masoud Salehi
  • CPFSKWhy do we need Continuous-Phase FSK (CPFSK)? A conventional FSK signal is generated by shifting the carrier by m∆f , 1 ≤ m ≤ M . It can be accomplished by having M separate oscillators tuned to the desired frequencies. The abrupt switching from one oscillator output to another results in large spectral side lobes of the signal. To address spectral side lobes, the frequency is changed continuously. CPFSK. TELE4653 - Digital Modulation & Coding - Lecture 2. March 15, 2010. – p.6/2
  • CPFSKThe signal waveform of CPFSK is given by 2E s(t) = cos [2πfc t + φ(t; I) + φ0 ] (1) Twhere φ(t; I) represents the time-varying phase of the carrier, as t φ(t; I) = 4πT fd d(τ )dτ (2) −∞with a PAM signal d(t) = In g(t − nT ). (3) nIn denotes the sequence of amplitudes and g(t) is the 1rectangular pulse of amplitude of 2T and duration of T . TELE4653 - Digital Modulation & Coding - Lecture 2. March 15, 2010. – p.7/2
  • CPFSK Although d(t) contains discontinuities, φ(t; I) is continuous. The phase φ(t; I) in the interval nT ≤ t ≤ (n + 1)T is n−1 φ(t; I) = 2πfd T Ik + 4πfd T q(t − nT )In (4) k=−∞ = θn + 2πhIn q(t − nT ) (5) n−1 where h = 2fd T is the modulation index, θn = πh k=−∞ Ik represents the accumulation of all symbols, and   0  t<0   q(t) = t 0≤t≤T (6)  2T   1  2 t>T TELE4653 - Digital Modulation & Coding - Lecture 2. March 15, 2010. – p.8/2
  • CPMFor continuous-phase modulation (CPM) signals, n φ(t; I) = 2π Ik hk q(t − kT ), nT ≤ t ≤ (n + 1)T (7) k=−∞where {Ik } is the sequence of M -ary symbols selected from{±1, ±3, · · · , ±(M − 1)}, {hk } is a sequence of modulationindices, and q(t) is some normalized waveform shape as t q(t) = g(τ )dτ (8) 0Full-response CPM if g(t) = 0 for t > T , and Partial-responseCPM if g(t) = 0 for t > T . TELE4653 - Digital Modulation & Coding - Lecture 2. March 15, 2010. – p.9/2
  • from Digital Communications (5th Ed.) – John G. Proakis and Masoud Salehi
  • from Digital Communications (5th Ed.) – John G. Proakis and Masoud Salehi
  • MSKMinimum-shift keying (MSK) is a special case of binary CPFSK(and CPM) in which h = 1 and g(t) is a rectangular pulse of 2duration T . The phase of the carrier in the intervalnT ≤ t ≤ (n + 1)T is [obtained from Eq. (5)] t − nT φ(t; I) = θn + πIn , nT ≤ t ≤ (n + 1)T (9) 2Tand the MSK signal is s(t) = A cos [2πfc t + φ(t; I)] (10) 1 1 = A cos 2π fc + In t − nπIn + θn , (11) 4T 2for nT ≤ t ≤ (n + 1)T . TELE4653 - Digital Modulation & Coding - Lecture 2. March 15, 2010. – p.12/2
  • MSKFor binary CPFSK, i.e., In = {±1}, the signal may be written as 1 si (t) = A cos 2πfi t + θn + nπ(−1)i−1 , i = 1, 2 (12) 2where 1 f1 = fc − (13) 4T 1 f2 = fc + (14) 4TNote ∆f = f2 − f1 = 1/2T , i.e., the minimum frequencyseparation that is necessary to ensure the orthogonality ofsignals s1 (t) and s2 (t). This explains why binary CPFSK withh = 1 is called the MSK. 2 TELE4653 - Digital Modulation & Coding - Lecture 2. March 15, 2010. – p.13/2
  • from Digital Communications (5th Ed.) – John G. Proakis and Masoud Salehi
  • from Digital Communications (5th Ed.) – John G. Proakis and Masoud Salehi
  • Offset QPSK For conventional QPSK signals, the possible 180◦ phase change can occur when both I and Q components change simultaneously. To prevent 180◦ phase changes that cause abrupt changes in the signal, resulting in large spectral side lobes, offset QPSK (OQPSK) is introduced, by misalignment of the I and Q components. The OQPSK signal can be written as ∞ s(t) = A I2n g(t − 2nT ) cos 2πfc t n=−∞ ∞ + I2n+1 g(t − 2nT − T ) sin 2πfc t (15) n=−∞ TELE4653 - Digital Modulation & Coding - Lecture 2. March 15, 2010. – p.16/2
  • from Digital Communications (5th Ed.) – John G. Proakis and Masoud Salehi
  • from Digital Communications (5th Ed.) – John G. Proakis and Masoud Salehi
  • OQPSK vs. MSK Conventional QPSK contains phase jumps of ±180◦ or ±90◦ . Offset QPSK contains phase jumps of ±90◦ . It has constant frequency, but there exist jumps in its waveform. MSK may be represented as a form of OQPSK. MSK has continuous phase, so there exist no jumps in the waveform. But there are jumps in its instantaneous frequency. GMSK can smooth the frequency jumps of MSK by shaping the lowpass signal before being applied to the MSK modulator. TELE4653 - Digital Modulation & Coding - Lecture 2. March 15, 2010. – p.19/2
  • from Digital Communications (5th Ed.) – John G. Proakis and Masoud Salehi