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Wireless Transmission
Frequencies Signals Antenna Signal propagation Multiplexing Spread spectrum Modulation Prof. Dr.-Ing. Jochen Schiller,
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Frequencies for communication
Universität Karlsruhe Institut für Telematik Frequencies for communication Mobilkommunikation SS 1998 twisted pair coax cable optical transmission 1 Mm 300 Hz 10 km 30 kHz 100 m 3 MHz 1 m 300 MHz 10 mm 30 GHz 100 m 3 THz 1 m 300 THz VLF LF MF HF VHF UHF SHF EHF infrared visible light UV VLF = Very Low Frequency UHF = Ultra High Frequency LF = Low Frequency SHF = Super High Frequency MF = Medium Frequency EHF = Extra High Frequency HF = High Frequency UV = Ultraviolet Light VHF = Very High Frequency Frequency and wave length: = c/f wave length , speed of light c 3x108m/s, frequency f Prof. Dr. Dr. h.c. G. Krüger E. Dorner / Dr. J. Schiller
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Frequencies for mobile communication
VHF-/UHF-ranges for mobile radio simple, small antenna for cars deterministic propagation characteristics, reliable connections SHF and higher for directed radio links, satellite communication small antenna, focusing large bandwidth available Wireless LANs use frequencies in UHF to SHF spectrum some systems planned up to EHF limitations due to absorption by water and oxygen molecules (resonance frequencies) weather dependent fading, signal loss caused by heavy rainfall etc.
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Signals I physical representation of data
function of time and location signal parameters: parameters representing the value of data classification continuous time/discrete time continuous values/discrete values analog signal = continuous time and continuous values digital signal = discrete time and discrete values signal parameters of periodic signals: period T, frequency f=1/T, amplitude A, phase shift sine wave as special periodic signal for a carrier: s(t) = At sin(2 ft t + t)
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Fourier representation of periodic signals
1 1 t t ideal periodic signal real composition (based on harmonics)
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Signals II Different representations of signals
amplitude (amplitude domain) frequency spectrum (frequency domain) phase state diagram (amplitude M and phase in polar coordinates) Composed signals transferred into frequency domain using Fourier transformation Digital signals need infinite frequencies for perfect transmission modulation with a carrier frequency for transmission (analog signal!) A [V] Q = M sin A [V] t[s] I= M cos f [Hz]
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Antennas: isotropic radiator
Radiation and reception of electromagnetic waves, coupling of wires to space for radio transmission Isotropic radiator: equal radiation in all directions (three dimensional) - only a theoretical reference antenna Real antennas always have directive effects (vertically and/or horizontally) Radiation pattern: measurement of radiation around an antenna z y z ideal isotropic radiator y x x
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Antennas: simple dipoles
Real antennas are not isotropic radiators but, e.g., dipoles with lengths /4 on car roofs or /2 as Hertzian dipole shape of antenna proportional to wavelength Example: Radiation pattern of a simple Hertzian dipole Gain: maximum power in the direction of the main lobe compared to the power of an isotropic radiator (with the same average power) /4 /2 y y z simple dipole x z x side view (xy-plane) side view (yz-plane) top view (xz-plane)
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Antennas: directed and sectorized
Often used for microwave connections or base stations for mobile phones (e.g., radio coverage of a valley) y y z directed antenna x z x side view (xy-plane) side view (yz-plane) top view (xz-plane) z z sectorized antenna x x top view, 3 sector top view, 6 sector
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Antennas: diversity Grouping of 2 or more antennas Antenna diversity
multi-element antenna arrays Antenna diversity switched diversity, selection diversity receiver chooses antenna with largest output diversity combining combine output power to produce gain cophasing needed to avoid cancellation /2 /2 /4 /2 /4 /2 + + ground plane
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Signal propagation ranges
Transmission range communication possible low error rate Detection range detection of the signal possible no communication possible Interference range signal may not be detected signal adds to the background noise sender transmission distance detection interference
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Signal propagation Propagation in free space always like light (straight line) Receiving power proportional to 1/d² (d = distance between sender and receiver) Receiving power additionally influenced by fading (frequency dependent) shadowing reflection at large obstacles refraction depending on the density of a medium scattering at small obstacles diffraction at edges shadowing reflection refraction scattering diffraction
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Real world example
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Multipath propagation
Signal can take many different paths between sender and receiver due to reflection, scattering, diffraction Time dispersion: signal is dispersed over time interference with “neighbor” symbols, Inter Symbol Interference (ISI) The signal reaches a receiver directly and phase shifted distorted signal depending on the phases of the different parts multipath pulses LOS pulses signal at sender signal at receiver
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Effects of mobility Channel characteristics change over time and location signal paths change different delay variations of different signal parts different phases of signal parts quick changes in the power received (short term fading) Additional changes in distance to sender obstacles further away slow changes in the average power received (long term fading) long term fading power t short term fading
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Multiplexing Multiplexing in 4 dimensions
space (si) time (t) frequency (f) code (c) Goal: multiple use of a shared medium Important: guard spaces needed! channels ki k1 k2 k3 k4 k5 k6 c t c s1 t s2 f f c t s3 f
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Frequency multiplex Separation of the whole spectrum into smaller frequency bands A channel gets a certain band of the spectrum for the whole time Advantages: no dynamic coordination necessary works also for analog signals Disadvantages: waste of bandwidth if the traffic is distributed unevenly inflexible guard spaces k1 k2 k3 k4 k5 k6 c f t
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Time multiplex A channel gets the whole spectrum for a certain amount of time Advantages: only one carrier in the medium at any time throughput high even for many users Disadvantages: precise synchronization necessary k1 k2 k3 k4 k5 k6 c f t
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Time and frequency multiplex
Combination of both methods A channel gets a certain frequency band for a certain amount of time Example: GSM Advantages: better protection against tapping protection against frequency selective interference higher data rates compared to code multiplex but: precise coordination required k1 k2 k3 k4 k5 k6 c f t
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Code multiplex Each channel has a unique code
All channels use the same spectrum at the same time Advantages: bandwidth efficient no coordination and synchronization necessary good protection against interference and tapping Disadvantages: lower user data rates more complex signal regeneration Implemented using spread spectrum technology k1 k2 k3 k4 k5 k6 c f t
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Modulation Digital modulation Analog modulation Motivation
digital data is translated into an analog signal (baseband) ASK, FSK, PSK - main focus in this chapter differences in spectral efficiency, power efficiency, robustness Analog modulation shifts center frequency of baseband signal up to the radio carrier Motivation smaller antennas (e.g., /4) Frequency Division Multiplexing medium characteristics Basic schemes Amplitude Modulation (AM) Frequency Modulation (FM) Phase Modulation (PM)
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Modulation and demodulation
analog baseband signal digital data digital modulation analog modulation radio transmitter radio carrier analog baseband signal digital data analog demodulation synchronization decision radio receiver radio carrier
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Digital modulation Modulation of digital signals known as Shift Keying
Amplitude Shift Keying (ASK): very simple low bandwidth requirements very susceptible to interference Frequency Shift Keying (FSK): needs larger bandwidth Phase Shift Keying (PSK): more complex robust against interference 1 1 t 1 1 t 1 1 t
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Advanced Frequency Shift Keying
bandwidth needed for FSK depends on the distance between the carrier frequencies special pre-computation avoids sudden phase shifts MSK (Minimum Shift Keying) bit separated into even and odd bits, the duration of each bit is doubled depending on the bit values (even, odd) the higher or lower frequency, original or inverted is chosen the frequency of one carrier is twice the frequency of the other Equivalent to offset QPSK even higher bandwidth efficiency using a Gaussian low-pass filter GMSK (Gaussian MSK), used in GSM
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Example of MSK 1 1 1 1 data bit even 0 1 0 1 even bits odd 0 0 1 1
1 1 1 data bit even even bits odd signal h n n h value odd bits low frequency h: high frequency n: low frequency +: original signal -: inverted signal high frequency MSK signal t No phase shifts!
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Advanced Phase Shift Keying
BPSK (Binary Phase Shift Keying): bit value 0: sine wave bit value 1: inverted sine wave very simple PSK low spectral efficiency robust, used e.g. in satellite systems QPSK (Quadrature Phase Shift Keying): 2 bits coded as one symbol symbol determines shift of sine wave needs less bandwidth compared to BPSK more complex Often also transmission of relative, not absolute phase shift: DQPSK - Differential QPSK (IS-136, PHS) Q I 1 Q I 11 01 10 00 A t 11 10 00 01
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Quadrature Amplitude Modulation
Quadrature Amplitude Modulation (QAM): combines amplitude and phase modulation it is possible to code n bits using one symbol 2n discrete levels, n=2 identical to QPSK bit error rate increases with n, but less errors compared to comparable PSK schemes Example: 16-QAM (4 bits = 1 symbol) Symbols 0011 and 0001 have the same phase φ, but different amplitude a and 1000 have different phase, but same amplitude. used in standard 9600 bit/s modems Q 0010 0001 0011 0000 φ a I 1000
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Hierarchical Modulation
DVB-T modulates two separate data streams onto a single DVB-T stream High Priority (HP) embedded within a Low Priority (LP) stream Multi carrier system, about 2000 or 8000 carriers QPSK, 16 QAM, 64QAM Example: 64QAM good reception: resolve the entire 64QAM constellation poor reception, mobile reception: resolve only QPSK portion 6 bit per QAM symbol, 2 most significant determine QPSK HP service coded in QPSK (2 bit), LP uses remaining 4 bit Q 10 I 00 000010 010101
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Spread spectrum technology
Problem of radio transmission: frequency dependent fading can wipe out narrow band signals for duration of the interference Solution: spread narrow band signal into broad band signal using special code protection against narrowband interference Side effects: coexistence of several signals without dynamic coordination tap-proof Alternatives: Direct Sequence, Frequency Hopping signal power interference spread signal power spread interference detection at receiver f f
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Effects of spreading and interference
dP/df dP/df user signal broadband interference narrowband interference i) ii) f f sender dP/df dP/df dP/df iii) iv) v) f f f receiver
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Spreading and frequency selective fading
channel quality 2 1 5 6 narrowband channels 3 4 frequency narrow band signal guard space 2 frequency channel quality 1 spread spectrum spread spectrum channels
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DSSS (Direct Sequence Spread Spectrum) I
XOR of the signal with pseudo-random number (chipping sequence) many chips per bit (e.g., 128) result in higher bandwidth of the signal Advantages reduces frequency selective fading in cellular networks base stations can use the same frequency range several base stations can detect and recover the signal soft handover Disadvantages precise power control necessary tb user data 1 XOR tc chipping sequence 1 1 1 1 1 1 1 1 = resulting signal 1 1 1 1 1 1 1 tb: bit period tc: chip period
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DSSS (Direct Sequence Spread Spectrum) II
signal transmit signal user data X modulator chipping sequence radio carrier transmitter correlator lowpass filtered signal sampled sums products received signal data demodulator X integrator decision radio carrier chipping sequence receiver
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FHSS (Frequency Hopping Spread Spectrum) I
Discrete changes of carrier frequency sequence of frequency changes determined via pseudo random number sequence Two versions Fast Hopping: several frequencies per user bit Slow Hopping: several user bits per frequency Advantages frequency selective fading and interference limited to short period simple implementation uses only small portion of spectrum at any time Disadvantages not as robust as DSSS simpler to detect
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FHSS (Frequency Hopping Spread Spectrum) II
tb user data 1 1 1 t f td f3 slow hopping (3 bits/hop) f2 f1 t td f f3 fast hopping (3 hops/bit) f2 f1 t tb: bit period td: dwell time
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FHSS (Frequency Hopping Spread Spectrum) III
transmit signal narrowband signal user data modulator modulator frequency synthesizer hopping sequence transmitter narrowband signal received signal data demodulator demodulator hopping sequence frequency synthesizer receiver
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Physical layer Holger Karl
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Receiver: Demodulation
The receiver looks at the received wave form and matches it with the data bit that caused the transmitter to generate this wave form Necessary: one-to-one mapping between data and wave form Because of channel imperfections, this is at best possible for digital signals, but not for analog signals Problems caused by Carrier synchronization: frequency can vary between sender and receiver (drift, temperature changes, aging, …) Bit synchronization (actually: symbol synchronization): When does symbol representing a certain bit start/end? Frame synchronization: When does a packet start/end? Biggest problem: Received signal is not the transmitted signal!
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Attenuation results in path loss
Effect of attenuation: received signal strength is a function of the distance d between sender and transmitter Captured by Friis free-space equation Describes signal strength at distance d relative to some reference distance d0 < d for which strength is known d0 is far-field distance, depends on antenna technology
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Generalizing the attenuation formula
To take into account stronger attenuation than only caused by distance (e.g., walls, …), use a larger exponent > 2 is the path-loss exponent Rewrite in logarithmic form (in dB): Take obstacles into account by a random variation Add a Gaussian random variable with 0 mean, variance 2 to dB representation Equivalent to multiplying with a lognormal distributed r.v. in metric units ! lognormal fading
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Noise and interference
So far: only a single transmitter assumed Only disturbance: self-interference of a signal with multi-path “copies” of itself In reality, two further disturbances Noise – due to effects in receiver electronics, depends on temperature Typical model: an additive Gaussian variable, mean 0, no correlation in time Interference from third parties Co-channel interference: another sender uses the same spectrum Adjacent-channel interference: another sender uses some other part of the radio spectrum, but receiver filters are not good enough to fully suppress it Effect: Received signal is distorted by channel, corrupted by noise and interference What is the result on the received bits?
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Symbols and bit errors Extracting symbols out of a distorted/corrupted wave form is fraught with errors Depends essentially on strength of the received signal compared to the corruption Captured by signal to noise and interference ratio (SINR) SINR allows to compute bit error rate (BER) for a given modulation Also depends on data rate (# bits/symbol) of modulation E.g., for simple DPSK, data rate corresponding to bandwidth:
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Examples for SINR BER mappings
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Channel models – analog
How to stochastically capture the behavior of a wireless channel Main options: model the SNR or directly the bit errors Signal models Simplest model: assume transmission power and attenuation are constant, noise an uncorrelated Gaussian variable Additive White Gaussian Noise model, results in constant SNR Situation with no line-of-sight path, but many indirect paths: Amplitude of resulting signal has a Rayleigh distribution (Rayleigh fading) One dominant line-of-sight plus many indirect paths: Signal has a Rice distribution (Rice fading)
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Channel models – digital
Directly model the resulting bit error behavior Each bit is erroneous with constant probability, independent of the other bits binary symmetric channel (BSC) Capture fading models’ property that channel be in different states Markov models – states with different BERs Example: Gilbert-Elliot model with “bad” and “good” channel states and high/low bit error rates Fractal channel models describe number of (in-)correct bits in a row by a heavy-tailed distribution good bad
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WSN-specific channel models
Typical WSN properties Small transmission range Implies small delay spread (nanoseconds, compared to micro/milliseconds for symbol duration) Frequency-non-selective fading, low to negligible inter-symbol interference Coherence bandwidth often > 50 MHz Some example measurements path loss exponent Shadowing variance 2 Reference path loss at 1 m
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Wireless channel quality – summary
Wireless channels are substantially worse than wired channels In throughput, bit error characteristics, energy consumption, … Wireless channels are extremely diverse There is no such thing as THE typical wireless channel Various schemes for quality improvement exist Some of them geared towards high-performance wireless communication – not necessarily suitable for WSN, ok for MANET Diversity, equalization, … Some of them general-purpose (ARQ, FEC) Energy issues need to be taken into account!
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Some transceiver design considerations
Strive for good power efficiency at low transmission power Some amplifiers are optimized for efficiency at high output power To radiate 1 mW, typical designs need mW to operate the transmitter WSN nodes: 20 mW (mica motes) Receiver can use as much or more power as transmitter at these power levels ! Sleep state is important Startup energy/time penalty can be high Examples take 0.5 ms and ¼ 60 mW to wake up Exploit communication/computation tradeoffs Might payoff to invest in rather complicated coding/compression schemes
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Choice of modulation One exemplary design point: which modulation to use? Consider: required data rate, available symbol rate, implementation complexity, required BER, channel characteristics, … Tradeoffs: the faster one sends, the longer one can sleep Power consumption can depend on modulation scheme Tradeoffs: symbol rate (high?) versus data rate (low) Use m-ary transmission to get a transmission over with ASAP But: startup costs can easily void any time saving effects For details: see example in exercise! Adapt modulation choice to operation conditions Akin to dynamic voltage scaling, introduce Dynamic Modulation Scaling
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Summary Wireless radio communication introduces many uncertainties and vagaries into a communication system Handling the unavoidable errors will be a major challenge for the communication protocols Dealing with limited bandwidth in an energy-efficient manner is the main challenge MANET and WSN are pretty similar here Main differences are in required data rates and resulting transceiver complexities (higher bandwidth, spread spectrum techniques)
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Chapter 4: Mobile Radio Propagation: Large-Scale Path Loss
Wireless Communications Principles and Practice 2nd Edition T.S. Rappaport Chapter 4: Mobile Radio Propagation: Large-Scale Path Loss
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Co-channel and Adjacent Channel Interference, Propagation
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Small-scale and large-scale fading
Figure 4.1 Small-scale and large-scale fading.
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Typical electromagnetic properties
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Typical large-scale path loss
Fig. 2.15
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Measured large-scale path loss
Fig. 2.16
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Partition losses Fig. 2.16
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Partition losses Fig. 2.16
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Partition losses Fig. 2.16
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Wireless Communications Principles and Practice 2nd Edition T. S
Wireless Communications Principles and Practice 2nd Edition T.S. Rappaport Chapter 5: Mobile Radio Propagation: Small-Scale Fading and Multipath as it applies to Modulation Techniques
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Channel Sounder: Pulse type
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Channel Sounder: PN Type
Fig. 2.4
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Typical RMS delay spreads
Fig. 2.16
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Two independent fading issues
Fig. 2.8
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Flat-fading (non-freq. Selective)
Fig. 2.9
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Frequency selective fading
Fig. 2.10
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Two independent fading issues
Fig. 2.11
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Rayleigh fading Fig. 2.12
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Small-scale envelope distributions
Fig. 2.13
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Ricean and Rayleigh fading distributions
Fig. 2.14
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Wireless Communications Principles and Practice 2/e T.S. Rapppaport
Chapter 6: Modulation Techniques for Mobile Radio
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Amplitude Modulation
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Double Sideband Spectrum
Fig. 3.2
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SSB Modulators
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Tone-in Band SSB Fig. 2.3
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Product Detection
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VCO circuit
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Wideband FM generation
Fig. 2.4
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Slope Detector for FM Fig. 2.5
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Digital Demod for FM Fig. 2.6
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PLL Demod for FM Fig. 2.7
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Phase-shift quadrature FM demod
Fig. 2.8
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FM Demod circuit Fig. 2.9
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Line Coding spectra Fig. 2.10
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RZ and NRZ Line Codes Fig. 2.11
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Nyquist Pulses for zero-ISI
Fig. 2.12
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Raised Cosine Spectrum
Fig. 2.13
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Spectrum of Raised Cosine pulse
Fig. 2.13
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Raised Cosine pulses Fig. 2.14
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RF signal usig Raised Cosine
Fig. 2.15
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Gaussian pulse-shapes
Fig. 2.16
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BPSK constellation Fig. 2.16
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Virtue of pulse shaping
Fig. 2.16
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BPSK Coherent demodulator
Fig. 2.16
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Differential PSK encoding
Fig. 2.16
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DPSK modulation Fig. 2.16
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DPSK receiver Fig. 2.16
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QPSK constellation diagrams
Fig. 2.16
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Virtues of Pulse Shaping
Fig. 2.16
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QPSK modulation Fig. 2.16
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QPSK receiver Fig. 2.16
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Offset QPSK waveforms Fig. 2.16
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Pi/4 QPSK signaling Fig. 2.16
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Pi/4 QPSK phase shifts Fig. 2.16
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Pi/4 QPSK transmitter Fig. 2.16
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Differential detection of pi/4 QPSK
Fig. 2.16
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IF Differential Detection
Fig. 2.16
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FM Discriminator detector
Fig. 2.16
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FSK Coherent Detection
Fig. 2.16
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Noncoherent FSK Fig. 2.16
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Minimum Shift Keying spectra
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MSK modulation Fig. 3.2
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MSK reception
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GMSK spectral shaping Fig. 2.3
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GMSK spectra shaping Fig. 2.16
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Simple GMSK generation
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GMSK Demodulator
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Digital GMSK demodulator
Fig. 2.4
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8-PSK Signal Constellation
Fig. 2.5
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Bandwidth vs. Power Efficiency
Fig. 2.16
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Pulse Shaped M-PSK Fig. 2.6
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16-QAM Signal Constellation
Fig. 2.7
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QAM efficiencies Fig. 2.16
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M-ary FSK efficiencies
Fig. 2.16
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PN Sequence Generator Fig. 2.8
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Direct Sequence Spread Spectrum
Fig. 2.9
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Direct Sequence Spreading
Fig. 2.10
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Frequency Hopping Spread Spectrum
Fig. 2.11
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CDMA – Multiple Users Fig. 2.12
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Effects of Fading Fig. 2.13
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Irreducible Bit Error Rate due to multipath
Fig. 2.14
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Irreducible Bit Error Rate due to multipath
Fig. 2.15
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Simulation of Fading and Multipath
Fig. 2.16
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Irreducible BER due to fading
Fig. 2.16
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Irreducible BER due to fading
Fig. 2.16
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BER due to fading & multipath
Fig. 2.16
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Energy per bit as a function of modulation and packet size (Raghunathan et al)
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Slides from Rahul Mangaram
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Shannon’s Capacity Theorem
States the theoretical maximum rate at which an error-free bit can be transmitted over a noisy channel C: the channel capacity in bits per second B: the bandwidth in hertz SNR: the ratio of signal power to noise power Channel capacity depends on channel bandwidth and system SNR
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Shannon’s Theorem: Example
For SNR of 0, 10, 20, 30 dB, one can achieve C/B of 1, 3.46, 6.66, 9.97 bps/Hz, respectively Example: Consider the operation of a modem on an ordinary telephone line. The SNR is usually about The bandwidth is 3.4 KHz. Therefore: C = 3400 X log2( ) = (3400)(9.97) ≈34 kbps
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Bit Error Rate BER = Errors / Total number of bits
Error means the reception of a “1” when a “0” was transmitted or vice versa. Noise is the main factor of BER performance – signal path loss, circuit noise, …
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Thermal Noise Thermal Noise
white noise since it contains the same level of power at all frequencies kTB, where k is the Boltzmann’s constant = 1.381e-21 W / K / Hz, T is the absolute temperature in Kelvin, and B is the bandwidth. At room temperature, T = 290K, the thermal noise power spectral density, kT = 4.005e-21 W/Hz or –174 dBm/Hz
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Receiver Sensitivity The minimum input signal power needed at receiver input to provide adequate SNR at receiver output to do data demodulation SNR depends on Received signal power Background thermal noise at antenna (Na) Noise added by the receiver (Nr) Pmin = SNRmin ×(Na +Nr)
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Noise Figure Noise Figure (F) quantifies the increase in noise caused by the noise source in the receiver relative to input noise F = SNRinput/SNRoutput = (Na + Nr)/Na Pmin = SNRmin×(Na + Nr) = SNRmin×F ×Na Example: if SNRmin = 10 dB, F = 4 dB, BW = 1 MHz Pmin= ×log(106) = -100 dBm
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802.15.4 - Modulation Scheme 2.4 GHz PHY 868 MHz/915 MHz PHY
250 kb/s (4 bits/symbol, 62.5 kBaud) Data modulation is 16-ary orthogonal O-QPSK 16 symbols are ~orthogonal set of 32-chip PN codes 868 MHz/915 MHz PHY Symbol rate 868 MHz band: 20 kbps (1bit/symbol, 20 Kbaud) 915 MHz band: 40 kbps (1bit/symbol, 40 Kbaud) Spreading code is 15-chip Data modulation is BPSK 868 MHz: 300 Kchips/s 915 MHz: 600 Kchips/s
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802.15.4 - PHY Communication Parameters
Transmit power Capable of at least 0.5 mW Transmit center frequency tolerance ±40 ppm Receiver sensitivity (packet error rate < 1%) − GHz band −92 868/915 MHz band Receiver Selectivity 2.4 GHz: 5 MHz channel spacing, 0 dB adjacent channel requirement Channel Selectivity and Blocking 915 MHz and 2.4 GHz band: 0 dB rejection of interference from adjacent channel 30 dB rejection of interference from alternate channel Rx Signal Strength Indication Measurements Packet strength indication Clear channel assessment Dynamic channel selection
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802.15.4: Receiver Noise Figure Calculation
Channel Noise bandwidth is 1.5 MHz Transmit Power is 1mW or 0 dBm Thermal noise floor is –174 dBm/Hz X 1.5 MHz = –112 dBm Total SNR budget is 0 dBm –(–112 dBm) = 112 dBm To cover ~100 ft. at 2.4 GHz results in a path loss of 40 dB i.e. Receiver sensitivity is –85 dBm Required SNR for QPSK is 12.5 dB packet length is 1Kb Worst packet loss < 1%, (1 –BER)1024= 1 –1%, BER = 10–5 Receiver noise figure requirement NF = Transmit Power – Path Loss – Required SNR – Noise floor = –40 –12.5 = 59.5 dB The design spec is very relaxed Low transmit power enables CMOS single chip solution at low cost and power!
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