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In digital communications , symbol rate , also known as baud rate and modulation rate , is the number of symbol changes, waveform changes, or signaling events, across the transmission medium per time unit using a digitally modulated signal or a line code. The symbol rate is measured in baud Bd or symbols per second.
In the case of a line code, the symbol rate is the pulse rate in pulses per second. Each symbol can represent or convey one or several bits of data. The symbol rate is related to the gross bitrate expressed in bits per second. 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 communication channel that persists , for a fixed period of time. A sending device places symbols on the channel at a fixed and known symbol rate, and the receiving device has the job of detecting the sequence of symbols in order to reconstruct the transmitted data. There may be a direct correspondence between a symbol and a small unit of data.
For example, each symbol may encode one or several binary digits or 'bits'. The data may also be represented by the transitions between symbols, or even by a sequence of many symbols.
The symbol duration time , also known as unit interval , can be directly measured as the time between transitions by looking into an eye diagram of an oscilloscope.
The symbol duration time T s can be calculated as:. 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 not correct to write "the baud rate of Ethernet is megabaud " or "the baud rate of my modem is 56," if we mean bit rate. See below for more details on these techniques. The difference between baud or signalling rate and the data rate or bit rate is like a man using a single semaphore flag who can move his arm to a new position once each second, so his signalling rate baud is one symbol per second.
The flag can be held in one of eight distinct positions: Each signal symbol carries three bits of information. It takes three binary digits to encode eight states. The data rate is three bits per second. In the Navy, more than one flag pattern and arm can be used at once, so the combinations of these produce many symbols, each conveying several bits, a higher data rate.
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 a line code, these may be M different voltage levels. Modulation is used in passband filtered channels such as telephone lines, radio channels and other frequency division multiplex FDM channels.
In a digital modulation method provided by a modem , each symbol is typically a sine wave tone with 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.
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. The maximum baud rate or pulse rate for a base band channel is called the Nyquist rate , and is double the bandwidth double the cut-off frequency. Emile Baudot — worked out a five-level code five bits per character for telegraphs which was standardized internationally and is commonly called Baudot code. In digital television transmission the symbol rate calculation is:.
The is the number of bytes in a packet including the 16 trailing Reed-Solomon error checking and correction bytes. The is the number of data bytes bytes plus the leading packet sync byte 0x See the OFDM system comparison table for further numerical details. Some communication links such as GPS transmissions, CDMA cell phones, and other spread spectrum links have a symbol rate much higher than the data rate they transmit many symbols called chips per data bit. Representing one bit by a chip sequence of many symbols overcomes co-channel interference from other transmitters sharing the same frequency channel, including radio jamming , and is common in military radio and cell phones.
In these systems, the symbol rate of the physically transmitted high-frequency signal rate is called chip rate , which also is the pulse rate of the equivalent base band signal. However, in spread spectrum systems, the term symbol may also be used at a higher layer and refer to one information bit, or a block of information bits that are modulated using for example conventional QAM modulation, before the CDMA spreading code is applied.
Using the latter definition, the symbol rate is equal to or lower than the bit 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.
Many data transmission systems operate by the modulation of a carrier signal. For example, in frequency-shift keying FSK , the frequency of a tone is varied among a small, fixed set of possible values. In a synchronous data transmission system, the tone can only be changed from one frequency to another at regular and well-defined intervals. The presence of one particular frequency during one of these intervals constitutes a symbol.
The concept of symbols does not apply to asynchronous data transmission systems. In a modulated system, the term modulation rate may be used synonymously with symbol rate. If the carrier signal has only two states, then only one bit of data i. 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. Again, only one bit of data i.
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.
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 QAM , four bits of data are transmitted in each symbol, resulting in a bit rate of four times the symbol rate. 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 bipolar encoding and MLT-3 use three carrier states to encode one bit per baud while maintaining DC balance. More interestingly, the 4B3T line code uses three 3-ary modulated bits to transmit four data bits, a rate of 1.
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 modems is the attempt at increasing the bit rate over a fixed bandwidth and therefore a fixed maximum symbol rate , leading to increasing bits per symbol.
For example, the V. 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.
The complete collection of M possible symbols over a particular channel is called a M-ary modulation scheme.
Most popular modulation schemes can be described by showing each point on a constellation diagram , although a few modulation schemes such as MFSK , DTMF , pulse-position modulation , spread spectrum modulation require a different description. In telecommunication , concerning the modulation of a carrier , a significant condition is one of the signal 's parameters chosen to represent information. 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. Information can be transmitted either during the given time interval, or encoded as the presence or absence of a change in the received signal. 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.