Signal-to-noise
Standard Physical Layers

• Signal to Noise Ratio
  • Decibel
  • Shannon Capacity
  • Quantization Noise
• Standard Physical Layers
  • SONET
  • RS-232-C
  • ADSL

Signal-to-noise Ratio

• Noise can (sometimes) be characterized by its average power N
• Signals can be characterized by their average power S
• Ratio is S/N
• 1 Bel = 10 dB = 10
• 2 Bel = 20 dB = 100
• 3 Bel = 30 dB = 1000
• n Bel = n * 10 dB = 10^n
• A dB = 10^{A / 10}

Shannon Capacity

• thermal noise with power N
• signal with power S
• channel bandwidth B (in Hertz)
• capacity of channel in bits/second is:

Shannon Capacity -- Example

• telephone line with bandwidth B = 3100 Hz (from 300 Hz to 3400 Hz)
• S/N ratio of 30 dB C = B log2(1+S/N) = 3100 * log2(1+1000) = 3100 * 10 = 31 Kb/s

Quantization Noise

• signal quantized using N bits
• signal value is (-1, +1)
• error e(nT) is difference between actual and quantized value
• error power is e^2(nT)
• if all values are equally likely:
  • average e^2(nT) = 2^{-2N}/3
  • average power v^2(t) = 1/3
  • average S/N = 2^{2N} =~ 6N dB

Quantization Noise Example

• telephone line
  • 8000 samples/second
  • 8 bits per sample
  • voice signal filtered to (300Hz, 3400Hz)
  • S/N = 2^{16} =~ 48 dB
  • Shannon capacity (with only quantization noise) C = 3100 * 16 = 49,600 b/s
  • Bits used to encode signal 8000 * 8 = 64,000

SONET/SDH

• Synchronous Optical Network
• continuous flow of frames in both directions
• common clock, recovered from framing bytes
• 2430 total bytes per frame, 2340 user bytes per frame
• suitable for real-time transmission (e.g. telephone traffic)
• slower channels interleaved (Time-domain multiplexing) into one SONET channel
• defined speeds:
  • STS-1, 51.84 Mb/s
  • STS-3, 155.52 Mb/s (8000 frames/second)
  • STS-12, 622.08 Mb/s

RS-232-C

• Serial line connection
• Data Terminal Equipment (DTE, i.e. computer) talking to Data Circuit-Terminating Equipment (DCE, i.e.. modem)
• Asynchronous Baseband Transmission with Bipolar Modulation
• Two-way transmission
• Receiver can always stop transmission
• Universal Asynchronous Receiver/Transmitter (UART) adds start and stop/parity bits, interprets received data

ADSL

• Asymmetric Digital Subscriber Line
• similar to ISDN, Integrated Services Data Network
• Carrierless Amplitude/Phase modulation (CAP) or Discrete Multitone (DMT)
• CAP: like QAM, but no carrier
• DMT: split wire into channels, only use channels with low noise
• Error correction codes for burst errors
• 100KHz-1MHz CO-to-home, 25KHz-100KHz home-to-CO, voice channel