Frequency, Period, Phase

  • Frequency - $ f $
  • Period - $ T = 1/f $
  • Phase - $ \phi $
  • Amplitude - $ A $
  • Wave - $ A \sin(2 \pi ft + \phi) $

I-Q Graph

The I-Q graph is a 2D representation of the phase and amplitude.

In-phase component $ I $ + Quadrature component $ Q $

$ \sin(2 \pi f t + \frac{\pi}{4} ) $
= $ \sin(2 \pi f t) \cos( \frac{\pi}{4}) + \cos(2 \pi f t) \sin (\frac{\pi}{4}) $
= $ \frac{1}{\sqrt{2}} \sin(2 \pi f t) + \frac{1}{\sqrt{2}} \sin (2 \pi f t) $

Wavelength

The distance occupied by one cycle of a wave

$ \lambda = vT $
$ \lambda f = v $

$ c = 3 \times 10^8 m/s $

$ \lambda = c/f $

e.g 2.5 Ghz to Wavelength
$ \lambda = \frac{300 m/\mu s}{2.5 \times 10^9} = 12 cm $

e.g 5mm to Frequency
$ f = \frac{300 m/\mu s}{0.005} = 60 GHz$

Time and Frequency Domain

  • Time Domain
  • Frequency Domain

Wireless Spectrum Allocation

  • Maximise utilisation
  • Adapt to market needs
  • Fair licensing
  • Promote competition
  • Ensure spectrum availability
  • Licensing

Decibels

The unit to measure power, loss, signal-to-noise ratio (SNR)

When measuring power, we have a very large scale (i.e. pico watts to kilo watts)

$ dB = 10 \log_{10}(\frac{P_1}{P_2}) $

  • Path Loss / Attenuation
    • $ P_1 $ - Transmit
    • $ P_2 $ - Receive
  • SNR
    • $ P_1 $ - Signal
    • $ P_2 $ - Noise
  • Signal Power
    • $ P_1 $ - Signal
    • $ P_2 $ - Reference

$ dBm $ - reference to 1 milliwatt
$ dBW $ - reference to 1 watt

$ dBm = dBW + 30 $
When converting dBW to dBm, as 1 W = 1000 mW...
When multiplying the ratio by 1000, we can use the logarithm law $log(a \times b) = log(a) + log(b) $.
This allows us to split the ratio $log(1000 \times \frac{a}{b}) = log(1000) + log(\frac{a}{b}) $
When evaluated, $ log_{10}(1000) = 30 $

Coding

  • Symbol - the smallest element of a signal that can be detected
  • Baud rate (modulation rate / symbol rate) - the rate at which a symbol can change = $ \frac{1}{symbol\ duration} $
  • Data rate - Bits per second
    • $ bps = Bd \times \log_2 (M) $ for an M-ary signal
    • For a binary signal, $ Bps = Bd $

Modulation

The digital version of modulation is called keying

  • ASK - Amplitude Shift Keying
  • FSK - Frequency Shift Keying
  • PSK - Phase Shift Keying
    • DPSK - Differential Phase Shift Keying - Compare to previous wave
      • 0 - No difference
      • 1 - Difference
    • QPSK - Quadrature Phase Shift Keying - Look at new phase offset
      • 11 - 45 degrees
      • 10 - 135 degrees
      • 00 - 225 degrees
      • 01 - 315 degrees
    • Note: We can visualise this with a constellation diagram (I-Q graph)
  • QAM - Quadrature Amplitude and Phase Modulation
    • 4-QAM - 2 bits per symbol
    • 16-QAM - 4 bits per symbol
    • n bits per symbol -> 2^n QAM

Channel Capacity

  • Capacity - Maximum data rate (bps) for a channel
  • Nyquist Theorem - In noiseless channel, error-free transmission can occur when the $ baud\ rate \le 2 \times bandwidth$
    • $ Capacity = 2 \times bandwidth \times log_2(M) $
    • M - number of levels

Shannon's Theory

When noise is present, the maximum data rate for error free communication, is $ B\ log_2 (1 + S/N) $

i.e a SNR of 4.77 dB is required to achieve 10 Mbps through a 5 MHz channel.

$ 10 \times 10^6 = (5 \times 10^6) \times log_2(1 + S/N) $
$ 2 = log_2(1 + S/N) $
$ 1 + S/N = 2^2 = 4 $
$ S/N = 3 $
$ 10log(S/N = 3) = 4.77 dB $

Hamming Distance

The number of different bits, when two sequences are compared.
Increasing the hamming distance between codewords increases the correction rate.

Hamming distance of 3 can detect up to 2 bits of errors, but can only correct one bit errors.

Multiple Access Methods

  • TDMA - Time Division Multiple Access
    • Clients are allocated a portion of time to communicate
    • Only one client at a time
  • FDMA - Frequency Division Multiple Access
    • Clients are allocated to different frequency groups
    • Using FFT, etc... we can extract data from certain frequencies
  • CDMA - Code Division Multiple Access
  • (CDMA) FHSS - Frequency Hopping Spread Spectrum
    • Frequently change to different frequencies
    • Transmitter and Receiver share a pseudo-random seed (code) which produces the next frequency to hop to.
    • Hard to intercept
    • Requires more bandwidth
    • Requires time and frequency synchronisation
  • (CDMA) DSSS - Direct Sequence Spread Spectrum
    • Data XOR code

Doppler Shift

Moving radios will affect the frequency.

  • Moving towards - frequency increase
  • Moving away - frequency decrease
  • Frequency difference = velocity / wavelength = $ \frac{v}{\lambda} $ = $ \frac{vf}{c} $

Doppler Spread

Two rays will be received (due to reflections)

  • Doppler Spread = $ \frac{2vf}{c} $ = 2 $ \times $ doppler shift
    • Spread will either add or cancel out as the receiver moves
  • Coherence time - time during which the channel response is constant
    • $ 1 / doppler\ spread $ = $ \frac{c}{2cf} $ = $ \frac{\lambda}{2v} $

Symbol should be designed to remain for the duration of the coherence time.
High QAM needed for high data rate.

Duplexing

Bidirectional communication.

  • FDD - Frequency Division Duplexing (Full Duplex)
    • Allocate different frequency ranges for Tx and Rx
  • TDD - Time Division Duplexing (Half Duplex)
    • Use the same frequency for Tx and Rx
    • Synchronise time allocation