Carrier
Understanding the RF Carrier
The carrier wave is the fundamental building block of all RF communications. At its simplest, a carrier is an unmodulated sinusoid at frequency fc, carrying no information by itself. Information is added through modulation, which systematically varies one or more carrier parameters (amplitude, frequency, phase) in proportion to the baseband signal. The modulated carrier then occupies a bandwidth centered on fc, and the receiver must recover the original information by demodulation, which requires a coherent or near-coherent local reference.
Carrier quality is governed by three primary metrics. Frequency stability (ppm) determines how accurately the carrier remains on its assigned channel. Phase noise L(f) in dBc/Hz at a given offset describes the spectral purity and limits close-in signal detection. Carrier-to-noise ratio (C/N) sets the theoretical ceiling on achievable data rate via the Shannon capacity theorem: C = B·log2(1 + C/N). Modern OFDM systems subdivide the carrier into thousands of orthogonal subcarriers spaced at Δf = 1/Tsymbol, enabling robust wideband transmission over frequency-selective fading channels.
Carrier and Modulation Mathematics
s(t) = A·cos(2πfct + φ)
AM modulated:
sAM(t) = Ac[1 + m·x(t)]cos(2πfct)
m = modulation index (0–1 for no distortion)
FM modulated:
sFM(t) = Accos(2πfct + 2πkf∫x(τ)dτ)
Δf = kf·max|x(t)| = peak deviation
Carrier-to-noise ratio:
C/N = Pcarrier / (kTB) [linear]
C/N(dB) = Pcarrier(dBm) − 10log(kTB)
Phase noise → RMS jitter:
σφ = √(2·∫L(f)df) [radians]
Modulation Scheme Comparison
| Modulation | Type | Spectral Eff. | C/N for 10−6 BER | Phase Noise Sensitivity | Application |
|---|---|---|---|---|---|
| BPSK | Digital phase | 1 bps/Hz | ~10.5 dB | Low | Deep-space, spread spectrum |
| QPSK | Digital phase | 2 bps/Hz | ~10.5 dB | Moderate | Satellite, 4G uplink |
| 16-QAM | Amplitude+phase | 4 bps/Hz | ~17 dB | High | Wi-Fi, LTE |
| 64-QAM | Amplitude+phase | 6 bps/Hz | ~23 dB | Very high | Cable, 5G |
| 256-QAM | Amplitude+phase | 8 bps/Hz | ~30 dB | Extreme | Wi-Fi 6/7, DOCSIS |
| FM (analog) | Frequency | ~0.5 bps/Hz | ~12 dB (SINAD) | Low | Land mobile, broadcast |
Phase Noise Requirements by Standard
| Standard | Carrier Freq. | Offset | L(f) Requirement | Stability |
|---|---|---|---|---|
| GSM | 900/1800 MHz | 200 kHz | −121 dBc/Hz | ±0.1 ppm |
| LTE | 700–3500 MHz | 100 kHz | −113 dBc/Hz | ±0.05 ppm |
| 5G NR FR1 | 410–7125 MHz | 100 kHz | −110 dBc/Hz | ±0.05 ppm |
| 5G NR FR2 | 24–52 GHz | 1 MHz | −93 dBc/Hz | ±0.1 ppm |
| Wi-Fi 7 | 2.4/5/6 GHz | 1 MHz | −105 dBc/Hz | ±20 ppm |
Frequently Asked Questions
What is C/N ratio?
Carrier-to-noise ratio is C/N = Pcarrier/(kTB), measured before demodulation. It determines achievable BER for any modulation. BPSK needs ~10.5 dB; 256-QAM needs ~30 dB for BER = 10−6. C/N differs from SNR, which is measured after demodulation and processing gain.
How does phase noise affect the carrier?
Phase noise L(f) at offset f degrades EVM, limits adjacent-channel rejection, and causes reciprocal mixing. Integrated phase noise gives RMS jitter: σφ = √(2·∫L(f)df). GSM requires −121 dBc/Hz at 200 kHz; 5G FR2 needs −93 dBc/Hz at 1 MHz due to wider subcarrier spacing.
Carrier recovery methods?
Costas loop: removes data modulation via squaring, recovers BPSK/QPSK phase. Decision-directed PLL: uses symbol decisions for phase error estimation in higher-order QAM. Pilot-tone insertion: unmodulated subcarriers provide explicit reference (OFDM/DVB). Each trades complexity vs. acquisition speed.