Digital Modulation

Why Put Information on a Carrier?

• Information (bit levels) × carrier (fixed frequency ) in a modulator → RF output whose phase carries the bits
  • The data selects the carrier phase (illustrative BPSK; only a few RF cycles per bit drawn)
  • The antenna radiates the RF output
• Low-rate information moves to a band suited to antennas and spectrum allocation (bands and spectrum)
• The bits themselves first become a baseband waveform: Bits, Symbols, and Line Coding

On-Off Keying

• OOK: one state sends a carrier, the other sends no carrier
• The information changes the carrier amplitude
• For unbalanced on/off levels, a residual carrier component may remain

Frequency-Shift Keying

• FSK: a 0 and a 1 select different carrier frequencies
• The receiver decides which tone is present
• Required bandwidth depends on tone spacing and pulse shaping

BPSK: A Bit Selects the Carrier Phase

• BPSK (binary phase-shift keying): two phases separated by 180°
• One bit per modulation symbol
• For rectangular bit pulses, the null-to-null RF bandwidth is approximately (RF bandwidth)
• Constellation: the symbol states after carrier removal
  • I = in-phase (horizontal axis), Q = quadrature (vertical), relative to the carrier reference
  • Ideal BPSK: two values (±) and ; each point is one possible symbol

QPSK: Two Bits per Symbol

• QPSK (quadrature phase-shift keying): four carrier phases represent four possible two-bit symbols
  • Constellation: one point in each quadrant
• Each transmitted symbol carries two bits
• For an uncoded QPSK link: (bit rate and symbol rate)

Summary: Amplitude, Frequency, and Phase

• The same data (1 0 1 1 0 0 1 0) controls each carrier:
  • ASK: amplitude changes with the bit
  • FSK: frequency changes with the bit
  • BPSK: phase changes with the bit
• Adjacent equal bits need no state change

The I and Q View of a Modulator

• 
• Serial bits → serial-to-parallel → and
• Carrier oscillator → on the branch; +90° shift → on the branch
• Multiply, then sum → RF output

I/Q Modulator Output

Question: BPSK or QPSK?

• Uncoded information rate = 1.0 Mbit/s. Keep received power, noise density, and pulse shaping fixed. Change BPSK to QPSK. Which statement is correct?
  1. Symbol rate halves, so the RF bandwidth is about halved
  2. The received energy per information bit doubles
  3. The symbol rate doubles
• Answer: 1 — half the symbol rate and RF bandwidth
  • : BPSK 1.0 Msymbol/s; QPSK 0.5 Msymbol/s
  • 2 is false: fixed power and information rate give the same energy per bit
  • 3 is false: symbol rate halves
• At a fixed symbol rate instead, QPSK carries twice as many information bits per second

NOTE

• So QPSK saves bandwidth, not power: it cannot rescue a power-limited link (the 4 Mbit/s question)

Higher-Order Constellations

• M-PSK places more phase states on a circle; QAM (quadrature amplitude modulation) uses amplitude and phase (e.g. a 4 × 4 grid of 16 states)
• More coded bits per symbol can reduce the required symbol rate
• At fixed average symbol energy, more closely spaced states are harder to distinguish
• Envelope variation and amplifier linearity become important

Modulation Selection Is a Mission Trade

Need	Signal design implication
Weak signal acquisition	Consider tracking aids and residual-carrier power
High data rate in limited spectrum	More bits per symbol and appropriate pulse shaping
Efficient spacecraft power amplifier	Control envelope variation and amplifier backoff
Navigation or tracking on the same link	Allocate signal power and spectrum to each function

• Choose the waveform with the receiver, amplifier, and mission requirements in view
• Related: pulse-shaping costs, residual carrier and power allocation

Analog Modulation

• Optional reference slide; message , carrier amplitude :
• FM bandwidth, Carson’s approximation:
• No blanket AM/FM/PM performance ranking applies without assumptions
• References: Gallager, MIT 6.450 Ch. 6 (Channels, Modulation, and Demodulation); Keysight AN 1298 (Digital Modulation in Communications Systems)