Carrier-to-Noise Ratio (C/N)

Carrier-to-Noise Ratio (C/N or CNR) quantifies the quality of a received signal by comparing the carrier signal power to the noise power in a communication system. It is typically expressed in decibels (dB) and is a fundamental parameter in analog systems and a supporting metric in digital communication link design.

Definition and Mathematical Expression

C/N is defined as the ratio between carrier power (P_carrier) and noise power (P_noise).

C/N = P_carrier / P_noise

Expressed in decibels:

C/N (dB) = 10 × log₁₀(P_carrier / P_noise)

This logarithmic form is commonly used in system specifications and performance assessments.

Relationship to Signal-to-Noise Ratio (SNR)

In bandwidth-limited systems, C/N relates to the signal-to-noise ratio (SNR), which considers both the signal bandwidth (B_s) and the noise bandwidth (B_n):

SNR = C/N × (B_n / B_s)

This relationship helps engineers convert measured carrier power levels into meaningful performance metrics for digital signal processing and demodulation.

C/N vs. SNR: Functional Differences

Although related, C/N and SNR describe different aspects of signal performance:

• C/N: Measures carrier power relative to noise; used in analog systems and intermediate stages of digital systems.

• SNR: Evaluates total signal power relative to noise; relevant for bit error rate (BER) and system reliability.

• In AM systems, a strong carrier is needed for proper demodulation, even though it carries no information.

• In FM systems, maintaining a sufficient C/N is critical to avoid the FM threshold effect, where signal quality drops sharply below a certain level.

• In digital systems, C/N is often used alongside E_b/N₀ for precise performance evaluation.

Example: C/N in Satellite TV

Different systems require different minimum C/N values:

• Analog satellite TV: Acceptable image quality at C/N ≈ 12 dB

• Digital DVB-S2 systems: Require C/N ≥ 8–10 dB for reliable, error-free decoding due to efficient modulation and forward error correction

This illustrates how modern systems leverage improved coding techniques to reduce C/N requirements while maintaining link quality.

Applications and Design Implications

Carrier-to-Noise Ratio is essential in:

• FM and AM radio: Determines coverage and audio clarity

• Satellite communications: Critical for maintaining link quality under varying atmospheric conditions

• Cable and microwave links: Ensures signal fidelity over long distances

• Wireless and digital systems: Used to define receiver sensitivity and margin against noise

System designers establish minimum C/N thresholds based on environmental noise, link margin, and quality-of-service (QoS) requirements. In digital systems, C/N is often supplemented by E_b/N₀ to evaluate error performance more precisely.