RADIO SYSTEMS – ETIN15 Lecture no: 5 Digital modulation Ove Edfors, Department of Electrical and Information Technology Ove.Edfors@eit.lth.se 2011-03-28 Ove Edfors - ETIN15 1
Contents • Brief overview of a wireless communication link • Radio signals and complex notation (again) • Modulation basics • Important modulation formats 2012-03-26 Ove Edfors - ETIN15 2
STRUCTURE OF A WIRELESS COMMUNICATION LINK 2012-03-26 Ove Edfors - ETIN15 3
A simple structure Speech Speech Chann. A/D Encrypt. Modulation encoder encoding Data Key Speech Speech Chann. D/A Decrypt. Demod. decoder decoding Data (Read Chapter 10 for more details) 2012-03-26 Ove Edfors - ETIN15 4
RADIO SIGNALS AND COMPLEX NOTATION (from Lecture 3) 2012-03-26 Ove Edfors - ETIN15 5
Simple model of a radio signal • A transmitted radio signal can be written ( ) ( ) = π + φ s t A cos 2 ft Amplitude Frequency Phase • By letting the transmitted information change the amplitude, the frequency, or the phase, we get the tree basic types of digital modulation techniques – ASK (Amplitude Shift Keying) – FSK (Frequency Shift Keying) Constant amplitude – PSK (Phase Shift Keying) 2012-03-26 Ove Edfors - ETIN15 6
The IQ modulator ( ) s t I I-channel ( ) Transmited radio signal (in-phase) π cos 2 f t c ( ) ( ) ( ) = π f s t s t cos 2 f t c I c ( ) ( ) − π s t sin 2 f t Q c o -90 ( ) − π ( ) sin 2 f t s t c Q Q-channel (quadrature) Take a step into the complex domain: s t = s I t j s Q t Complex envelope s t = Re { j 2 f c t } s t e π j 2 f t e Carrier factor c 2012-03-26 Ove Edfors - ETIN15 7
Interpreting the complex notation Complex envelope (phasor) Transmitted radio signal Q ( ) s t s t Re { j 2 f c t } Q s t = s t e ( ) ( ) A t φ t Re { A t e j 2 f c t } j t e = ( ) s t I Re { A t e j 2 f c t t } = I = A t cos 2 f c t t Polar coordinates: By manipulating the amplitude A (t) j t s t = s I t j s Q t = A t e and the phase Φ (t) of the complex envelope (phasor), we can create any type of modulation/radio signal. 2012-03-26 Ove Edfors - ETIN15 8
Example: Amplitude, phase and frequency modulation ( ) ( ) ( ) ( ) = π + φ s t A t cos 2 f t t c ( ) ( ) φ A t t Comment: 00 01 11 00 10 - Amplitude carries information 4ASK - Phase constant (arbitrary) 00 01 11 00 10 - Amplitude constant (arbitrary) 4PSK - Phase carries information 00 01 11 00 10 - Amplitude constant (arbitrary) - Phase slope (frequency) 4FSK carries information 2012-03-26 Ove Edfors - ETIN15 9
MODULATION BASICS 2012-03-26 Ove Edfors - ETIN15 10
Pulse amplitude modulation (PAM) The modulation process Complex domain Bits Radio ( ) b c s t signal m m LP Mapping PAM Re{ } ( ) π exp j 2 f t Complex c numbers Symbol ∞ Many possible pulses s LP t = ∑ c m g t − mT s time ( ) PAM: g t m =−∞ “Standard” basis pulse criteria t ∞ ( ) ∫ 2 dt = 1 or = T s g t ∣ g t ∣ (energy norm.) −∞ ∞ ∫ * t − mT s dt = 0 for m ≠ 0 (orthogonality) g t g t T −∞ s 2012-03-26 Ove Edfors - ETIN15 11
Pulse amplitude modulation (PAM) Basis pulses and spectrum Assuming that the complex numbers c m representing the data are independent, then the power spectral density of the base band PAM signal becomes: S LP f ~ ∣ ∫ − j 2 f t dt ∣ ∞ 2 g t e −∞ which translates into a radio signal (band pass) with 1 ( ) ( ) ( ) ( ) = − + − − S f S f f S f f BP LP c LP c 2 2012-03-26 Ove Edfors - ETIN15 12
Pulse amplitude modulation (PAM) Basis pulses and spectrum Illustration of power spectral density of the (complex) base-band signal, S LP ( f ), and the (real) radio signal, S BP ( f ). ( ) ( ) S f S f LP BP − f f f f c c Can be asymmetric, since it is a complex Symmetry (real radio signal) signal. What we need are basis pulses g ( t ) with nice properties like: - Narrow spectrum (low side-lobes) - Relatively short in time (low delay) 2012-03-26 Ove Edfors - ETIN15 13
Pulse amplitude modulation (PAM) Basis pulses TIME DOMAIN FREQ. DOMAIN Rectangular [in time] Normalized time / t T Normalized freq. f × T s s (Root-) Raised-cosine [in freq.] Normalized freq. f × T s Normalized time / t T s 2012-03-26 Ove Edfors - ETIN15 14
Pulse amplitude modulation (PAM) Interpretation as IQ-modulator For real valued basis functions g ( t ) we can view PAM as: ( ) ( ) ( ) = s t Re s t I LP ( ) Re c m ( ) g t ( ) π cos 2 f t c Radio Pulse b c f signal c m m Mapping shaping filters o -90 ( ) − π sin 2 f t c ( ) g t ( ) Im c m ( ) ( ) ( ) = s t Im s t Q LP (Both the rectangular and the (root-) raised-cosine pulses are real valued.) 2012-03-26 Ove Edfors - ETIN15 15
Multi-PAM Modulation with multiple pulses Complex domain Bits Radio ( ) b c s t signal m m LP Mapping multi-PAM Re{ } ( ) π exp j 2 f t c ∞ s LP t = ∑ g c m t − mT s multi-PAM: m −∞ “Standard” basis pulse criteria Several ∫ ∣ g c m t ∣ 2 dt = 1 or = T s different (energy norm.) * t − kT s dt = 0 for k ≠ 0 pulses ∫ g c m t g c m (orthogonality) * t dt = 0 for c m ≠ c n ∫ g c m t g c n (orthogonality) 2012-03-26 Ove Edfors - ETIN15 16
Multi-PAM Modulation with multiple pulses Frequency-shift keying (FSK) with M (even) different transmission frequencies can be interpreted as multi-PAM if the basis functions are chosen as: − j k f t for 0 ≤ t ≤ T s g k t = e and for k = +/- 1, +/- 3, ... , +/- M/2 S LP f S BP f − f f c c ∆ f Bits: 00 01 10 11 2012-03-26 Ove Edfors - ETIN15 17
Continuous-phase FSK (CPFSK) The modulation process Complex domain Bits Radio ( ) b c s t signal m m LP Mapping CPFSK Re{ } ( ) π exp j 2 f t c s LP t = A exp j CPFSK t CPFSK: where the amplitude A is constant and the phase is t ∞ CPFSK t = 2 h mod ∑ c m ∫ g u − mT du m =−∞ −∞ Phase basis where h mod is the modulation index. pulse 2012-03-26 Ove Edfors - ETIN15 18
Continuous-phase FSK (CPFSK) The Gaussian phase basis pulse In addition to the rectangular phase basis pulse, the Gaussian is the most common. BT s =0.5 Normalized time / t T s 2012-03-26 Ove Edfors - ETIN15 19
IMPORTANT MODULATION FORMATS 2012-03-26 Ove Edfors - ETIN15 20
Binary phase-shift keying (BPSK) Rectangular pulses Base-band Radio signal 2012-03-26 Ove Edfors - ETIN15 21
Binary phase-shift keying (BPSK) Rectangular pulses Complex representation Signal constellation diagram 2012-03-26 Ove Edfors - ETIN15 22
Binary phase-shift keying (BPSK) Rectangular pulses Power spectral density for BPSK Normalized freq. f × T b 2012-03-26 Ove Edfors - ETIN15 23
Binary phase-shift keying (BPSK) Raised-cosine pulses (roll-off 0.5) Base-band Radio signal 2012-03-26 Ove Edfors - ETIN15 24
Binary phase-shift keying (BPSK) Raised-cosine pulses (roll-off 0.5) Complex representation Signal constellation diagram 2012-03-26 Ove Edfors - ETIN15 25
Binary phase-shift keying (BPSK) Raised-cosine pulses (roll-off 0.5) Power spectral density for BAM Normalized freq. f × T b Much higher spectral efficiency than BPSK (with rectangular pulses). 2012-03-26 Ove Edfors - ETIN15 26
Quaternary PSK (QPSK or 4-PSK) Rectangular pulses Complex representation Radio signal 2012-03-26 Ove Edfors - ETIN15 27
Quaternary PSK (QPSK or 4-PSK) Rectangular pulses Power spectral density for QPSK Twice the spectrum efficiency of BPSK (with rect. pulses). TWO bits/pulse instead of one. 2012-03-26 Ove Edfors - ETIN15 28
Quadrature ampl.-modulation (QAM) Root raised-cos pulses (roll-off 0.5) Complex representation Much higher spectral efficiency than QPSK (with rectangular pulses). 2012-03-26 Ove Edfors - ETIN15 29
Amplitude variations The problem Signals with high amplitude variations leads to less efficient amplifiers. Complex representation of QPSK It is a problem that the signal passes through the origin, where the amplitude is ZERO. (Infinite amplitude variation.) Can we solve this problem in a simple way? 2012-03-26 Ove Edfors - ETIN15 30
Amplitude variations A solution Let’s rotate the signal constellation diagram for each transmitted symbol! / 4 2 ×/ 4 etc. 2012-03-26 Ove Edfors - ETIN15 31
Amplitude variations A solution Looking at the complex representation ... QPSK without rotation QPSK with rotation A “hole” is created in the center. No close to zero amplitudes. 2012-03-26 Ove Edfors - ETIN15 32
Recommend
More recommend
