Bits and Symbols
- A bit is a binary value
- A symbol is one selected transmitted waveform
- Line coding turns a bit stream into a baseband waveform
- NRZ and Manchester encode the same bits with different transitions (below)
Bit Rate and Symbol Rate
- Bit rate : information bits per second
- Symbol rate : selected waveforms per second
Symbol Rate
- Same eight bits, 1 0 1 1 0 0 1 0:
- BPSK, 1 bit/symbol: [1] [0] [1] [1] [0] [0] [1] [0] → 8 symbols
- QPSK, 2 bits/symbol: [10] [11] [00] [10] → 4 symbols
- At 1.0 Mbit/s: BPSK = 1.0 Msymbol/s; QPSK = 0.5 Msymbol/s
- Two identical consecutive states still occupy two symbol intervals
- Symbol rate is what sets the RF bandwidth (RF bandwidth); bit rate is what sets the energy per bit
Line Codes
- Bits 1 0 1 1 0 0 1 0 drawn three ways:
- NRZ-L (non-return-to-zero, level): holds a level for each bit interval
- NRZ-M (mark): changes level on a chosen bit value — in the example, at the start of each 1 (transitions at bit intervals 0, 2, 3, 6)
- Manchester: changes at every bit center
- More transitions can aid timing recovery, but require more bandwidth
Timing Recovery
- Long runs without transitions make timing recovery harder
- Manchester guarantees a transition at each bit center
- NRZ schemes can use scrambling or other structure to aid timing
WARNING
- A line-code symbol, a coded bit, and an RF modulation symbol are different concepts
- References: Gallager, MIT 6.450 Ch. 6; Keysight AN 1298