Table of contents
introduce
During the transmission process, signals will be affected by various factors.
As shown in the picture, this is a digital signal.
When it passes through the actual channel, the waveform will be distorted; when the distortion is not severe, the transmitted symbols can be restored at the output end based on the distorted waveform.
But when the distortion is severe, it is difficult to determine when the signal is 1 and when it is 0 at the output end.
The signal waveform loses the clear boundaries between symbols, a phenomenon called inter-symbol crosstalk.
The main reasons for distortion are:
- code element transmission rate
- Signal transmission distance
- Noise interference
- Transmission media quality, etc.
Nye's criterion
(Nyquist formula)
As early as 1924, Nyquist derived the famous Nyquist criterion. He gave the upper limit of the code element transmission rate in order to avoid inter-code crosstalk under assumed ideal conditions.
- The highest symbol transmission rate of an ideal low-pass channel = 2W Baud = 2W symbols/second
- The highest symbol transmission rate of an ideal bandpass channel = W Baud = W symbols/second
W: Channel bandwidth (unit: Hz)
Baud: Baud, that is, code units/second
The symbol transmission rate is also called the baud rate, modulation rate, waveform rate or symbol rate. It has a certain relationship with bitrate:
- When a symbol carries only 1 bit of information, the baud rate (symbol/second) and the bit rate (bit/second) are numerically equal;
- When a symbol carries n bits of information, when the baud rate is converted into a bit rate, the value must be multiplied by n.
To increase the information transmission rate (bit rate), we must try to make each symbol carry more bits of information. This requires pluralism.
Do you still remember the three basic modulation methods we introduced earlier, namely amplitude modulation, frequency modulation and phase modulation?
They belong to binary modulation and can only produce two different symbols, that is, two different basic waveforms. Therefore, each symbol can only carry 1 bit of information.
Hybrid modulation is a multi-element modulation. For example, QAM16 can modulate 16 different symbols. Therefore, each symbol can carry 4 bits of information.
It should be noted:
The highest symbol rate that the actual channel can transmit is significantly lower than the upper limit given by the Nys' criterion.
This is because the Neyslaw criterion is derived under assumed ideal conditions and does not consider other factors, such as transmission distance, noise interference, transmission media quality, etc.
Judging from the formula alone, as long as a better modulation method is used so that the symbols can carry more bits, wouldn't it be possible to increase the information transmission rate without limit?
the answer is negative. The ultimate information transmission rate of the channel is also limited by the signal-to-noise ratio of the actual signal transmitted in the channel.
Because the noise in the channel will also affect the recognition of symbols by the receiving end, and the greater the noise power relative to the signal power, the greater the impact.
Shannon formula
In 1948, Shannon used information theory to derive the ultimate information transmission rate for a channel with limited bandwidth and interference from Gaussian white noise.
The specific formula is as follows:
where c is the limit information transmission rate of the channel, in bits per second; W is the channel bandwidth, in Hertz; S is the average power of the signal transmitted in the channel; N is the Gaussian noise power in the channel; S/N is the signal Noise ratio, measured in decibels.
Signal-to-noise ratio (db) =
As shown below, it can be seen from the same formula: the greater the channel bandwidth or the channel ratio in the channel, the greater the ultimate transmission rate of information.
It should be noted:
On the actual channel, the information transmission rate that can be achieved is much lower than the limit transmission rate of this formula.
This is because in the actual channel, the signal is also subject to other damages, such as various pulse interferences. Factors such as signal attenuation and distortion during transmission are not considered in the Shannon formula.
Taken together, if you want toincrease the information transmission rate when the channel bandwidth is certain, Nye's criterion and Shannon's formula must be Must adoptmultiple system (better modulation method) and striveto improve the signal-to-noise ratio in the channel.
- Since the publication of Shannon's formula, various new signal processing and modulation methods have continued to appear, all of which aim to maximize the Close to the transmission rate limit given by Shannon's formula.
END
Study from: Lake University of Science and Technology - Computer Network Micro Classroom