Symbol rate
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In a digitally
Symbols
A symbol may be described as either a pulse in digital baseband transmission or a tone in passband transmission using modems. A symbol is a waveform, a state or a significant condition of the
The symbol duration time, also known as
where fs is the symbol rate.
For example, a baud rate of 1 kBd = 1,000 Bd is synonymous to a symbol rate of 1,000 symbols per second. In case of a modem, this corresponds to 1,000 tones per second, and in case of a line code, this corresponds to 1,000 pulses per second. The symbol duration time is 1/1,000 second = 1 millisecond.
Relationship to gross bit rate
The term baud rate has sometimes incorrectly been used to mean bit rate, since these rates are the same in old modems as well as in the simplest digital communication links using only one bit per symbol, such that binary "0" is represented by one symbol, and binary "1" by another symbol. In more advanced modems and data transmission techniques, a symbol may have more than two states, so it may represent more than one binary digit (a binary digit always represents one of exactly two states). For this reason, the baud rate value will often be lower than the gross bit rate.
Example of use and misuse of "baud rate": It is correct to write "the baud rate of my COM port is 9,600" if we mean that the bit rate is 9,600 bit/s, since there is one bit per symbol in this case. It is not correct to write "the baud rate of Ethernet is 100
The difference between baud (or signaling rate) and the data rate (or bit rate) is like a man using a single
If N bits are conveyed per symbol, and the gross bit rate is R, inclusive of channel coding overhead, the symbol rate can be calculated as:
In that case M = 2N different symbols are used. In a modem, these may be sinewave tones with unique combinations of amplitude, phase and/or frequency. For example, in a
By taking information per pulse N in bit/pulse to be the base-2-logarithm of the number of distinct messages M that could be sent, Hartley[1] constructed a measure of the gross bit rate R as:
where fs is the baud rate in symbols/second or pulses/second. (See
Modems for passband transmission
Modulation is used in
In a digital modulation method provided by a modem, each symbol is typically a sine wave tone with a certain frequency, amplitude and phase. Symbol rate, baud rate, is the number of transmitted tones per second.
One symbol can carry one or several bits of information. In voiceband modems for the telephone network, it is common for one symbol to carry up to 7 bits.
Conveying more than one bit per symbol or bit per pulse has advantages. It reduces the time required to send a given quantity of data over a limited bandwidth. A high spectral efficiency in (bit/s)/Hz can be achieved; i.e., a high bit rate in bit/s although the bandwidth in hertz may be low.
The maximum baud rate for a passband for common modulation methods such as
Voiceband modem examples:
- A carrier frequencyis 1800 Hz, meaning that the lower cut off frequency is 1,800 − 1,200/2 = 1,200 Hz, and the upper cutoff frequency is 1,800 + 1,200/2 = 2,400 Hz.
- A V.34modem may transmit symbols at a baud rate of 3,420 Bd, and each symbol can carry up to ten bits, resulting in a gross bit rate of 3420 × 10 = 34,200 bit/s. However, the modem is said to operate at a net bit rate of 33,800 bit/s, excluding physical layer overhead.
Line codes for baseband transmission
In case of a baseband channel such as a telegraph line, a serial cable or a Local Area Network twisted pair cable, data is transferred using line codes; i.e., pulses rather than sinewave tones. In this case, the baud rate is synonymous to the pulse rate in pulses/second.
The maximum baud rate or pulse rate for a
The simplest digital communication links (such as individual wires on a motherboard or the RS-232 serial port/COM port) typically have a symbol rate equal to the gross bit rate.
Common communication links such as 10 Mbit/s
J. M. Emile Baudot (1845–1903) worked out a five-bit code for telegraphs which was standardized internationally and is commonly called Baudot code.
More than two voltage levels are used in advanced techniques such as
1,000 Mbit/s Ethernet LAN cables use four wire pairs in
Digital television and OFDM example
In digital television transmission the symbol rate calculation is:
- symbol rate in symbols per second = (Data rate in bits per second × 204) / (188 × bits per symbol)
The 204 is the number of bytes in a packet including the 16 trailing Reed–Solomon error correction bytes. The 188 is the number of data bytes (187 bytes) plus the leading packet sync byte (0x47).
The bits per symbol is the (modulation's power of 2) × (Forward Error Correction). So for example, in 64-QAM modulation 64 = 26 so the bits per symbol is 6. The Forward Error Correction (FEC) is usually expressed as a fraction; i.e., 1/2, 3/4, etc. In the case of 3/4 FEC, for every 3 bits of data, you are sending out 4 bits, one of which is for error correction.
Example:
- given bit rate = 18096263
- Modulation type = 64-QAM
- FEC = 3/4
then
In digital terrestrial television (
Relationship to chip rate
Some communication links (such as
In these systems, the symbol rate of the physically transmitted high-frequency signal rate is called
Relationship to bit error rate
The disadvantage of conveying many bits per symbol is that the receiver has to distinguish many signal levels or symbols from each other, which may be difficult and cause bit errors in case of a poor phone line that suffers from low signal-to-noise ratio. In that case, a modem or network adapter may automatically choose a slower and more robust modulation scheme or line code, using fewer bits per symbol, in view to reduce the bit error rate.
An optimal symbol set design takes into account channel bandwidth, desired information rate, noise characteristics of the channel and the receiver, and receiver and decoder complexity.
Modulation
Many
Binary modulation
If the carrier signal has only two states, then only one bit of data (i.e., a 0 or 1) can be transmitted in each symbol. The bit rate is in this case equal to the symbol rate. For example, a binary FSK system would allow the carrier to have one of two frequencies, one representing a 0 and the other a 1. A more practical scheme is differential binary phase-shift keying, in which the carrier remains at the same frequency, but can be in one of two phases. During each symbol, the phase either remains the same, encoding a 0, or jumps by 180°, encoding a 1. Again, only one bit of data (i.e., a 0 or 1) is transmitted by each symbol. This is an example of data being encoded in the transitions between symbols (the change in phase), rather than the symbols themselves (the actual phase). (The reason for this in phase-shift keying is that it is impractical to know the reference phase of the transmitter.)
N-ary modulation, N greater than 2
By increasing the number of states that the carrier signal can take, the number of bits encoded in each symbol can be greater than one. The bit rate can then be greater than the symbol rate. For example, a differential phase-shift keying system might allow four possible jumps in phase between symbols. Then two bits could be encoded at each symbol interval, achieving a data rate of double the symbol rate. In a more complex scheme such as
Not power of 2
Although it is common to choose the number of symbols to be a power of 2 and send an integer number of bits per baud, this is not required. Line codes such as
The 4B3T line code uses three 3-ary modulated bits to transmit four data bits, a rate of 1.33 bits per baud.
Data rate versus error rate
Modulating a carrier increases the frequency range, or bandwidth, it occupies. Transmission channels are generally limited in the bandwidth they can carry. The bandwidth depends on the symbol (modulation) rate (not directly on the bit rate). As the bit rate is the product of the symbol rate and the number of bits encoded in each symbol, it is clearly advantageous to increase the latter if the former is fixed. However, for each additional bit encoded in a symbol, the constellation of symbols (the number of states of the carrier) doubles in size. This makes the states less distinct from one another which in turn makes it more difficult for the receiver to detect the symbol correctly in the presence of disturbances on the channel.
The history of
The history of spread spectrum goes in the opposite direction, leading to fewer and fewer data bits per symbol in order to spread the bandwidth. In the case of GPS, we have a data rate of 50 bit/s and a symbol rate of 1.023 Mchips/s. If each chip is considered a symbol, each symbol contains far less than one bit (50 bit/s / 1,023 ksymbols/s ≈ 0.000,05 bits/symbol).
The complete collection of M possible symbols over a particular channel is called a M-ary
modulation) require a different description.Significant condition
In
A significant condition could be an electric current (voltage, or power level), an optical power level, a phase value, or a particular frequency or wavelength. The duration of a significant condition is the time interval between successive significant instants.[3] A change from one significant condition to another is called a signal transition. Information can be transmitted either during the given time interval, or encoded as the presence or absence of a change in the received signal.[4]
Significant conditions are recognized by an appropriate device called a receiver, demodulator, or decoder. The decoder translates the actual signal received into its intended logical value such as a binary digit (0 or 1), an alphabetic character, a mark, or a space. Each significant instant is determined when the appropriate device assumes a condition or state usable for performing a specific function, such as recording, processing, or gating.[3]
See also
- Bandwidth (computing)
- Bitrate
- Chip rate
- Constellation diagram, which shows (on a graph or 2D oscilloscope image) how a given signal state (a symbol) can represent three or four bits at once.
- line rate.
- List of device bandwidths
- Pulse-code modulation
- Signaling rate
References
- ^ D. A. Bell (1962). Information Theory; and its Engineering Applications (3rd ed.). New York: Pitman.
- ^ Goldsmith A. Wireless communications. – Stanford University, 2004. - p. 140, 326
- ^ a b c "Federal Standard 1037C". National Communications System. July 7, 1996.
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(help) - ^ "System Design and Engineering Standard for Tactical Communications". Mil-STD-188-200. United States Department of Defense. May 28, 1983.
External links
- What is the Symbol rate?
- "On the origins of serial communications and data encoding". Archived from the original on December 5, 2012. Retrieved January 4, 2007.
- What’s The Difference Between Bit Rate And Baud Rate?, Electronic Design Magazine