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What are SNR and Eb/No?
Iain Explains Signals, Systems, and Digital Comms
Overview
This video explains the difference between Signal-to-Noise Ratio (SNR) and Energy per Bit to Noise Power Spectral Density Ratio (Eb/No), two crucial metrics in communication systems. It starts by defining SNR in the context of analog signals, explaining it as a ratio of signal power to noise power within a specific bandwidth. Then, it transitions to digital signals, introducing Eb/No as a more relevant metric that considers the energy of a single bit relative to the noise power spectral density. The explanation involves visualizing signals and noise in the frequency domain and understanding how filtering affects them.
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Chapters
- SNR is a measure of the power of a desired signal relative to the power of background noise.
- In the frequency domain, signal power is represented by the area under its power spectral density curve.
- Noise, often modeled as white noise, has a flat power spectral density across all frequencies.
- A bandpass filter is used to isolate the signal's frequency band, reducing noise power within that band.
- SNR is calculated as the ratio of the filtered signal power to the filtered noise power, simplified to signal power divided by (noise power spectral density * bandwidth).
SNR is fundamental for understanding the quality of analog communication signals and determining how much information can be reliably transmitted.
The power of a voice signal (signal power) is compared to the power of random electrical interference (noise power) within the specific frequency range the voice occupies after filtering.
- Digital communication involves sending discrete symbols (waveforms) over time slots, where each symbol can represent one or more bits.
- Instead of average power, the energy contained within a symbol or a bit becomes the critical factor.
- The ideal pulse shape for digital signals in the time domain is a sync function, which has a rectangular power spectral density in the frequency domain.
- The bandwidth (W) in the digital case is inversely related to the symbol duration (T), specifically W = 1/T.
- Noise power within the signal's bandwidth is considered, and over a symbol duration T, the total noise energy is calculated.
Eb/No is essential for digital communications because it directly relates the energy used to transmit information to the noise level, impacting error rates.
When sending a digital '1' or '0', a specific waveform is transmitted for a duration T. The energy of this waveform is what matters, not just its average power.
- The energy collected from noise over a symbol period (T) is calculated as noise power spectral density (N0) multiplied by the bandwidth (W) and the symbol duration (T).
- Since W = 1/T, the noise energy collected over time T simplifies to N0.
- The energy per bit (Eb) is derived from the energy per symbol (Es) by dividing by the number of bits per symbol (log2(M)).
- Eb/No is the ratio of the energy used to send a single bit to the noise energy collected over the time it takes to send that bit.
- This ratio is a key performance indicator for digital communication systems, directly influencing the probability of bit errors.
Eb/No provides a standardized way to compare the performance of different digital modulation schemes and assess their resilience to noise.
If a symbol represents 4 bits (M=16), the energy of that symbol is divided by 4 to find the energy per bit (Eb), which is then compared to the noise energy (N0).
Key takeaways
- SNR is a power ratio used for analog signals, comparing signal power to noise power within a defined bandwidth.
- Eb/No is an energy ratio crucial for digital signals, comparing the energy of a single bit to the noise power spectral density.
- Bandpass filtering is essential in both analog and digital systems to reduce out-of-band noise.
- The relationship between bandwidth and symbol duration (W=1/T) simplifies noise energy calculations in digital systems.
- Eb/No is a more relevant metric than SNR for evaluating the performance and reliability of digital communication links.
- Understanding these metrics helps in designing and analyzing communication systems for optimal data transmission.
Key terms
Signal-to-Noise Ratio (SNR)Eb/NoPower Spectral Density (PSD)White NoiseBandpass FilterBandwidth (W)Symbol Duration (T)Energy per Bit (Eb)Noise Power Spectral Density (N0)Amplitude Modulation (AM)Pulse Amplitude Modulation (PAM)Quadrature Amplitude Modulation (QAM)
Test your understanding
- What is the fundamental difference between how SNR and Eb/No measure signal quality?
- How does a bandpass filter help in improving the effective signal quality in a communication system?
- Why is energy per bit (Eb) a more relevant metric than average power for digital communication systems?
- Explain the relationship between symbol duration (T) and bandwidth (W) in the context of digital signal transmission.
- How does the number of bits per symbol (M) affect the calculation of Eb/No?