## What is channel capacity of Gaussian channel?

The capacity of a Gaussian channel is C = 1/2 log(1 + P/N ).

**What is Gaussian channel?**

A Gaussian channel is a time-discrete channel with output Yi, input Xi. and noise Zi at time i such that. Yi = Xi +Zi, Zi∼ N (0,N) where Zi is i.i.d and independent of Xi. The Gaussian channel is the most important continuous alphabet channel, modeling a wide range of communication channels.

**Why Gaussian channel is used for channel capacity?**

It extends that to a continuous signal channel with a bandwidth measure, an arbitrary power spectral density (PSD), and a specified data bit error rate (BER). This creates a Shannon limit that directly compares to concrete transmission systems.

### What is AWGN channel?

The continuous-time AWGN channel is a random channel whose output is a real random process Y (t) = X(t) + N(t), where X(t) is the input waveform, regarded as a real random process, and N(t) is a real white Gaussian noise process with single-sided noise power density N0 which is independent of X(t).

**How do I know my channel capacity?**

According to channel capacity equation, C = B log(1 + S/N), C-capacity, B-bandwidth of channel, S-signal power, N-noise power, when B -> infinity (read B ‘tends to’ infinity), capacity saturates to 1.44S/N.

**What is channel capacity?**

The channel capacity, C, is defined to be the maximum rate at which information can be transmitted through a channel. The fundamental theorem of information theory says that at any rate below channel capacity, an error control code can be designed whose probability of error is arbitrarily small.

#### What is meant by Gaussian noise?

Gaussian noise, named after Carl Friedrich Gauss, is statistical noise having a probability density function (PDF) equal to that of the normal distribution, which is also known as the Gaussian distribution. In other words, the values that the noise can take on are Gaussian-distributed.

**What is the Shannon’s limit for Awgn channel?**

A standard voice-grade telephone channel may be crudely modeled as an ideal band-limited AWGN channel with W ≈ 3500 Hz and SNR ≈ 37 dB. The Shannon limit on spectral efficiency and bit rate of such a channel are roughly ρ < 37/3 ≈ 12.3 (b/s)/Hz and R < 43,000 b/s.

**Why AWGN channel is used?**

The random nature of noise can distort signals and the integrity of electrical systems. Therefore, noise generators can help measure a system’s response to noise, using an AWGN channel to introduce an average number of errors through the system.

## Why AWGN has zero mean?

In words, each noise sample in a sequence is uncorrelated with every other noise sample in the same sequence. Therefore, mean value of a white noise is zero. As a result, the time domain average of a large number of noise samples is equal to zero.

**What is Shannon capacity formula?**

Shannon’s formula C = 12log(1+P/N) is the emblematic expression for the information capacity of a communication channel.

**What is maximum data rate of a channel?**

where Rmax is the maximum data rate and M is the discrete levels of signal. For example, if a transmission system like the telephone network has 3000 Hz of bandwidth, then the maximum data rate = 2 × 3000 log2 2 = 6000 bits/sec (bps). The Shannon theorem states the maximum data rate as follows: (5.2)

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