RADIO SYSTEMS – ETI 051 Contents Lecture no: 5 • Brief overview of a wireless communication link • Radio signals and complex notation (again) • Modulation basics • Important modulation formats Digital modulation Ove Edfors, Department of Electrical and Information Technology Ove.Edfors@eit.lth.se 2010-04-20 Ove Edfors - ETI 051 1 2010-04-20 Ove Edfors - ETI 051 2 A simple structure Speech Speech Chann. A/D Encrypt. Modulation encoder encoding Ampl. Data STRUCTURE OF A WIRELESS Key COMMUNICATION LINK Speech Speech Chann. D/A Decrypt. Demod. decoder decoding Ampl. Data (Read Chapter 10 for more details) 2010-04-20 Ove Edfors - ETI 051 3 2010-04-20 Ove Edfors - ETI 051 4
Simple model of a radio signal • A transmitted radio signal can be written ( ) ( ) = π + φ s t A cos 2 ft Amplitude Frequency Phase RADIO SIGNALS AND • By letting the transmitted information change the amplitude, the frequency, or the phase, we get the COMPLEX NOTATION tree basic types of digital modulation techniques (from Lecture 3) – ASK (Amplitude Shift Keying) – FSK (Frequency Shift Keying) Constant amplitude – PSK (Phase Shift Keying) 2010-04-20 Ove Edfors - ETI 051 5 2010-04-20 Ove Edfors - ETI 051 6 Interpreting the complex The IQ modulator notation ( ) s t Complex envelope (phasor) Transmitted radio signal I I-channel Q ( ) Transmited radio signal (in-phase) π cos 2 f t ( ) s t s t c Re { j 2 f c t } Q s t = s t e ( ) ( ) ( ) f = π s t s t cos 2 f t ( ) ( ) A t φ c I c t Re { A t e j 2 f c t } j t e = ( ) ( ) − π s t sin 2 f t ( ) Q c s t I Re { A t e j 2 f c t t } o -90 = I ( ) ( ) − π sin 2 f t s t = A t cos 2 f c t t c Q Q-channel (quadrature) Polar coordinates: Take a step into the complex domain: By manipulating the amplitude A (t) s t = s I t j s Q t j t Complex envelope s t = s I t j s Q t = A t e and the phase Φ (t) of the complex s t = Re { j 2 f c t } s t e envelope (phasor), we can create any j 2 π f t e Carrier factor type of modulation/radio signal. c 2010-04-20 Ove Edfors - ETI 051 7 2010-04-20 Ove Edfors - ETI 051 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) MODULATION 00 01 11 00 10 BASICS - Amplitude constant (arbitrary) 4PSK - Phase carries information 00 01 11 00 10 - Amplitude constant (arbitrary) - Phase slope (frequency) 4FSK carries information 2010-04-20 Ove Edfors - ETI 051 9 2010-04-20 Ove Edfors - ETI 051 10 Pulse amplitude modulation (PAM) Pulse amplitude modulation (PAM) The modulation process Basis pulses and spectrum Complex domain Bits Assuming that the complex numbers c m representing the data Radio ( ) are independent, then the power spectral density of the b c s t signal m m LP base band PAM signal becomes: Mapping PAM Re{ } S LP f ~ ∣ ∫ − j 2 f t dt ∣ ( ) ∞ 2 π exp j 2 f t g t e Complex c numbers −∞ Symbol ∞ Many possible pulses s LP t = ∑ which translates into a radio signal (band pass) with c m g t − mT s time PAM: ( ) g t m =−∞ 1 ( ) ( ) ( ) ( ) = − + − − S f S f f S f f “Standard” basis pulse criteria t BP LP c LP c 2 ∞ ( ) ∫ 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 2010-04-20 Ove Edfors - ETI 051 11 2010-04-20 Ove Edfors - ETI 051 12
Pulse amplitude modulation (PAM) Pulse amplitude modulation (PAM) Basis pulses and spectrum Basis pulses TIME DOMAIN FREQ. DOMAIN Illustration of power spectral density of the (complex) base-band Rectangular [in time] signal, S L P ( f ), and the (real) radio signal, S B P ( f ). ( ) ( ) S f S f LP BP Normalized time / t T Normalized freq. f × T s − f f f f s c c (Root-) Raised-cosine [in freq.] 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) Normalized freq. f × T s Normalized time / t T - Relatively short in time (low delay) s 2010-04-20 Ove Edfors - ETI 051 13 2010-04-20 Ove Edfors - ETI 051 14 Multi-PAM Pulse amplitude modulation (PAM) Interpretation as IQ-modulator Modulation with multiple pulses For real valued basis functions g ( t ) we can view PAM as: Complex domain Bits Radio ( ) ( ) ( ) ( ) b c s t = s t Re s t signal I LP m m LP ( ) Mapping multi-PAM Re{ } Re c m ( ) g t ( ) π ( ) exp j 2 f t π cos 2 f t c c Radio Pulse b c f signal c m m Mapping shaping ∞ filters s LP t = ∑ g c m t − mT s o -90 multi-PAM: ( ) − π sin 2 f t m −∞ c ( ) g t ( ) “Standard” basis pulse criteria Im c Several m ( ) ( ) ( ) ∫ ∣ g c m t ∣ different 2 dt = 1 or = T s (energy norm.) = s t Im s t Q LP * 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 (Both the rectangular and the (root-) raised-cosine pulses are real valued.) (orthogonality) 2010-04-20 Ove Edfors - ETI 051 15 2010-04-20 Ove Edfors - ETI 051 16
Multi-PAM Continuous-phase FSK (CPFSK) Modulation with multiple pulses The modulation process Complex domain Frequency-shift keying (FSK) with M (even) different transmission Bits Radio frequencies can be interpreted as multi-PAM if the basis functions ( ) b c s t are chosen as: signal m m LP Mapping CPFSK Re{ } − j k f t for 0 ≤ t ≤ T s g k t = e ( ) π exp j 2 f t c and for k = +/- 1, +/- 3, ... , +/- M/2 s LP t = A exp j CPFSK t S LP f S BP f CPFSK: where the amplitude A is constant and the phase is t ∞ CPFSK t = 2 h mod ∑ c m ∫ g u − mT du − f f m =−∞ −∞ c c ∆ f Phase basis where h m d is the modulation index. pulse Bits: 00 01 10 11 o 2010-04-20 Ove Edfors - ETI 051 17 2010-04-20 Ove Edfors - ETI 051 18 Continuous-phase FSK (CPFSK) The Gaussian phase basis pulse In addition to the rectangular phase basis pulse, the Gaussian is the most common. IMPORTANT MODULATION BT s =0.5 FORMATS Normalized time / t T s 2010-04-20 Ove Edfors - ETI 051 19 2010-04-20 Ove Edfors - ETI 051 20
Binary phase-shift keying (BPSK) Binary phase-shift keying (BPSK) Rectangular pulses Rectangular pulses Complex representation Signal constellation diagram Base-band Radio signal 2010-04-20 Ove Edfors - ETI 051 21 2010-04-20 Ove Edfors - ETI 051 22 Binary phase-shift keying (BPSK) Binary phase-shift keying (BPSK) Rectangular pulses Raised-cosine pulses (roll-off 0.5) Base-band Power spectral density for BPSK Radio signal Normalized freq. f × T b 2010-04-20 Ove Edfors - ETI 051 23 2010-04-20 Ove Edfors - ETI 051 24
Binary phase-shift keying (BPSK) Binary phase-shift keying (BPSK) Raised-cosine pulses (roll-off 0.5) Raised-cosine pulses (roll-off 0.5) Complex representation Signal constellation diagram Power spectral density for BAM Normalized freq. f × T b Much higher spectral efficiency than BPSK (with rectangular pulses). 2010-04-20 Ove Edfors - ETI 051 25 2010-04-20 Ove Edfors - ETI 051 26 Quaternary PSK (QPSK or 4-PSK) Quaternary PSK (QPSK or 4-PSK) Rectangular pulses Rectangular pulses Complex representation Power spectral density for QPSK Radio signal Twice the spectrum efficiency of BPSK (with rect. pulses). TWO bits/pulse instead of one. 2010-04-20 Ove Edfors - ETI 051 27 2010-04-20 Ove Edfors - ETI 051 28
Amplitude variations Quadrature ampl.-modulation (QAM) Root raised-cos pulses (roll-off 0.5) The problem Signals with high amplitude variations leads to less efficient amplifiers. Complex representation of QPSK Complex representation 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? Much higher spectral efficiency than QPSK (with rectangular pulses). 2010-04-20 Ove Edfors - ETI 051 29 2010-04-20 Ove Edfors - ETI 051 30 Amplitude variations Amplitude variations A solution A solution Let’s rotate the signal constellation diagram for each Looking at the complex representation ... transmitted symbol! QPSK without rotation QPSK with rotation / 4 2 ×/ 4 etc. A “hole” is created in the center. No close to zero amplitudes. 2010-04-20 Ove Edfors - ETI 051 31 2010-04-20 Ove Edfors - ETI 051 32
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