[Mobile Internet Technology] Physical Layer in Wireless Systems

Physical Layer in Wireless Systems

Notes from RWTH Aachen University course 
“Mobile Internet Technology” Summer semester 2020
professor: Drik Thißen 

Physical Layer in Wireless Systems 

• Radio waves
  $$s(t)=A\cdot\sin(2\cdot\pi ft+\varphi)$$
  $A:$ Amplitude
  $f:$ frequency
  $t:$ time
  $\varphi:$ phase
• wave length $\lambda=\frac{c}{f},c=$ speed of light
  

• Frequency allocation
  • ISM band (Industrial, scientific, medical)

Modulation

• Analog modulation: set parameters to an arbitrary value
• Digital modulation (Digital keying): set parameters from a finite set of values

Amplitude Shift Keying (ASK)

• Encode data with different amplitude
• needs not much bandwidth
• susceptible against distortion

Fourier Transform
Each periodic signals can be represented by a composition of harmonic signals
$$g(t)=\frac{1}{2}c+\sum_{n=1}^\infty a_n\sin (2\pi n f t)+\sum_{n=1}^\infty b_n\cos (2\pi n f t)$$

Digital modulation $\Rightarrow$ Analog signal$=$ periodic signal
Analog signal has infinite bandwidth
bandwidth: width of frequency band needed to represent a signal
wireless communication: restricted bandwidth

• Relationship between bandwidth and signal rate
  $$S_{max}[\text{Hz,baud}]=2\cdot B[\text{Hz}]$$
  $S:$ signal rate
  $B:$ bandwidth
• Nyquist Theorem relationship between signal rate and data rate
  $$R_{max}[\text{bit/s}]=2\cdot B[\text{Hz}]\cdot Id(n)[\text{bit}]$$
  $R:$ data rate
  $Id(n):$ $n$ parameters to represent $m=Id(n)$ bits
  $$\text{Data rate}\Leftrightarrow \text{Bandwidth}$$

1. Digital modulation

• analog baseband signal
• low-pass filtering

2. Analog modulation

• Shift the baseband signal to a given frequency band with carrier frequency $f_c$
• Bandwidth around $f_c$ is necessary for transmission
  
  
  
  
  

Frequency Shift Keying (FSK)

• encode data with different frequency
• needed higher bandwidth than ASK
• bandwidth depends on $f_1,f_2$
  
  
  
  
  

Advanced FSK- MSK (Minimum Shift Keying)

• Pre-computation avoids sudden phase shifts $\Rightarrow$ make the transition more smooth
• encode bit transitions instead of bits

• even	0	1	0	1
  odd	0	0	1	1
  siganl	h	l	l	h
  value	-	-	+	+

  h: high frequency
  l: low frequency
  -: inverted signal
  +: original signal
  
  

  

Advanced FSK-GMSK

• Gaussian MSK
• cut away high frequency side-band
• Used e.g. in GSM

Phase Shift Keying (PSK)

• more robust against distortion than ASK
• bandwidth needed
  
  
  
  
  

Advanced PSK- BPSK (Binary)

• bit 0: sine wave
  bit 1: inverted sine wave
• robust
• low spectral efficiency
• spectral efficiency: relationship between data rate and bandwidth

Advanced PSK-QPSK (Quaternary)

• Two bits coded per signal
• higher spectral efficiency than BPSK
• susceptible to distortion than BPSK
• DQPSK: Different QPSK

Quadrature Amplitude Modulation (QAM)

• Amplitude and phase modulation
• code $m$ bits per siganl, $m=2:$ QPSK
• $m$ increases $\Rightarrow$ bit error rate increase
• error rate less than PSK
• Example: 16-QAM (4 bits = 1 symbol)

Signal-to-Noise ratio

• $SNR=S/N$
• $$\text{dezibel[dB]:}SNR_{max}=10\cdot\log_{10}(S/N)$$

Shannon Theorem

• Noise level has influence on achievable data rate
  $$R_{max}[\text{bit/s}]=B[\text{Hz}]\cdot Id(1+S/N)\text{[bit]}$$

Minimum of Shannon theorem and Nyquist theorem gives maximum achievable data rate

Hierarchical modulation to deal with noise

• DVB-T high priority stream in low priority stream
• poor reception: high priority stream (10)
  good reception: low priority stream (1001)

Demodulation

• Receiver decode signal to $0/1$
• Problem caused by channel imperfections
  • Carrier synchronization
  • Bit (signal) synchronization
  • Frame synchronization
  • (most) interference

Antennas

• electronic signal $\Leftrightarrow$ electromagnetic waves
• Ideal isotropic antenna: radiation pattern = circle/sphere
• Real antenna: size $\propto$ wavelength
• 
  
  
  • best reception with wavelength $\lambda$:
    • dipole of size $\lambda/2$
    • size $\lambda/4$ on car roofs

Antenna gain

• Maximum power in direction of main lobe (葉) compare to isotropic radiator
  $$g[\text{dB}]=10\cdot\log_{10} (P_{antenna}/P_{isotropic})$$
• Whole input power is radiated
  • the smaller radiation area, the higher the signal power
• Directed antenna
  
  
  
• Sectorized antenna
  
  
  

Antenna Diversity

• two or more antennas
• to get receiver antenna gain
• Diversity combining:
  1. increase strength
  2. construct directed antennas
• but interference

Beamforming

• connecting antennas with cables of different length
• to avoid interference
  $\Rightarrow$ Transmit signals with different delays causing different phases. (Through a transmitter)

Signal Propagation

Receiver Power

• in vacuum  $$P_r=P_t\cdot(\frac{\lambda}{4\pi d})^2\cdot G_r\cdot G_t$$
  $P_i:$ power
  $G_i:$ antenna gain
  $d:$ distance
  $r:$ receiver
  $t:$ transmitter

• In reality  $$P_r\propto (1/d)^\alpha$$
  $\alpha$ depends on the material

• Range of received power
  Distance increases $\Rightarrow$ Noise, error rate increase

  
  
  

• Received power influenced by

• attenuation (衰減)
• shadowing
• reflection (反射)
• refraction (折射)
• scattering
• diffraction (散射) at edges

Multipath propagation

• Signals may be directed on several paths to receiver
• Effects:
• receiver has different signal strength
• Time dispersion: signal is dispersed (分散) over time
• constructive or destructive interference
• inner-system interference (ISI)

Mobility

• Quick change $\Rightarrow$ short term fading
  slow change $\Rightarrow$ long term fading

• Conclusion

  reason	effect	Cause
  Multipath Propagation	fast fading	fast fluctuation position
  Multipath Propagation	Time dispersion Delay spread	Signal consists of several components $\Rightarrow$ ISI
  Movement	Doppler Effect Frequency Dispersion	distance change
  Attenuation	Path loss	especially rain and fog
  Shading	slow fading	slow fluctuation

Solution to interference, ISI, movement effects

• Antenna diversity
• Signal spreading: increase bandwidth of a signal
• Orthogonal Frequency Division Multiplexing (OFDM): reduce the signal rate but send on several well-chosen channels simultaneously
• Synchronization sequence: allow receiver to calculate signal distortion

Multiplexing

• Subdivide given spectrum for simultaneous use

Frequency Multiplex

• Separation of spectrum into smaller frequency bands
• Advantages:
  1. No dynamic coordination
  2. Works also for analog signals
• Disadvantages:
  1. Waste of bandwidth
  2. Inflexible
  3. Guard spaces
• Frequency division duplex
  • Used for duplex communication: uplink / downlink
  • two separate antennas or use a "duplexer"

Time Multiplex

• Advantages:
  1. Only one carrier in a medium at any time
  2. Throughput even high for many users
• Disadvantages:
  1. Precise synchronization
  2. Guard time (waste transmission capacity)

  RTT: round-trip time

• Time division duplex (TDD)
  • one frequency carrier
  • uplink / downlink at different time
  • Flexible: adjust time slots

Time and frequency multiplex

• Advantages:
  • protect against tapping
  • protect against frequency selective interference
  • data rate > code multiplex
• Disadvantages:
  • precise coordination

Code division multiplex (CDM)

• each channel (transmitter) has a unique code

• Advantages:
  • protect against tapping and interference
  • bandwidth efficiently used
• Disadvantages:
  • complex signal regeneration, coordination, synchronization
• to avoid noise: orthogonal codes
  $$S\cdot T=0\\ S\cdot\bar{T}=0\\ S\cdot S=1$$

Spread spectrum

• Application of CMD priciples for robust transmission
  $$\text{narrowband signal}\xRightarrow[]{CMD}\text{broadband signal}$$

1. Original signal of sender
   
   
   
   
   
2. spreading to broadband $\Rightarrow$ signal power is distributed
   
   
   
3. $+$ broadband interference
   $+$ narrowband interference
   
   
   
   
   
   
   
   
4. Receiver reconstruct the signal $\Rightarrow$ narrowband interference is spread
   
   
   
   
   
5. Use band pass filter $\Rightarrow$ remove interference
   
   
   

Directed Sequence Spread Spectrum (DSSS)

• $$\text{User data }\oplus \text{ Chipping sequence (random) = resulting signal}$$
• Advantages:
  • Reduces frequency selective fading
  • Base station can use the same frequency band $\Rightarrow$ soft handover
• Disadvantages:
  • precise power control

  Near-far problem
  signal near base band can wipe out signal far from base band
  $\Rightarrow$ base band has to measure and adjust transmit power

  

  
  

Frequency Hopping Spread Spectrum (FHSS)

• Discrete changes of carrier frequency
• Fast hopping: channels/bit
  Slow hopping: bits/channel

• Advantages:
  • frequency selective fading limited to short period
  • Simple implementation
  • Use only small portion of spectrum at any time
• Disadvantages:
  • robust < DSSS
  • simpler to tap

Orthogonal Frequency Division Multiplexing (OFDM)

• Variant of FDM: sub-channels are orthogonal
  $f_n$ maximum power = $f_{n-1},f_{n+1}$ minimum power
• still only one channel (merged before)
• Advantages:
  • Robust against narrowband co-channel interference
  • Robust against ISI
  • High spectral efficiency > FDM
    
    
    
    
    
  • Use Fast Fourier Transform (FFT)
  • Low sensitivity to time synchronization errors
  • Sub-channel can be adapted to dynamic channel conditions

Space Multiplexing

• Limited by transmit power

• Advantage:

  • No coordination

• Disadvantages:

  • No mobility
  • Only useful with other multiplexing

• Cell structure

  • Advantages:
    • Frequency re-use
    • Less transmission power
    • Robust, decentralize
  • Disadvantages:
    • Handover
    • Interference between cells

• Clusters

  • maximum distance $D$ between 2 cells
  • $$D=R\cdot\sqrt{3k}$$
    $R:$ cell radius
    $k:$ cells per cluster
    
    
    
    
    

Coding

• BER: Bit Error Rate
• Packet error probability
  $$P_p=1-(1-\text{BER})^n$$
  $n:$ bit length
• How to deal with high BER?
  • Error detecting code
    • CRC
  • Error correction code
    • Block error correction:
      • Hamming code
      • BCH code
      • Reed-solomon code
    • Convolutional code
      • Trellis code
      • Turbo code

Block code

• process blocks of data independently
• $(n,k)$ protect $k$ bits data with $(n-k)$ FEC-bits
  • ex. $(255,247)$
• Disadvantage:
  • large $k$ causes expensive calculations periodically
  • convolutional code: generate redundant bits continuously

Convolutional code

• Dispere (分散) each bit over time
• $(n,k,K)$
  $K:$ constraint factor (“memory”)
  $n=f(k,K)$
  $n$ bits output depends on $k$ and $K-1$ input bits
• Example
  
  
  
  
  
  • $V_{n1}=u_{n-2}\oplus u_{n-1}\oplus u_{n}$
    $V_{n2}=u_{n-2}\oplus u_{n}$
    $V_i:$ output bits
    $u_i:$ input bits (state)

Trellis Diagram

• Hamming distance
  $$d\geq2\cdot t+1$$
  code can correct $t$ errors
• Search trellis for possible paths

Viterbi Algorithm

• Check if received string gives a valid path through trellis
• Calculate hamming distance, choose the shortest path
• High complexity

Turbo codes

• Faster decoding > Viterbi Algorithm
• RSC codes: recursively systematic convolutional codes
  
  
  
  • systematic: input bit taken over as output bit
  • take interleaved bit sequence
  • guess missing check bit (or set to 0)