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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 scheme.
In a noisy channel, the BER is often expressed as a function of the normalized carrier-to-noise ratio measure denoted Eb/N0, (energy per bit to noise power spectral density ratio), or Es/N0 (energy per modulation symbol to noise spectral density).
It is, however, only able to modulate at 1 bit/symbol (as seen in the figure) and so is unsuitable for high data-rate applications. In the presence of an arbitrary phase-shift introduced by the communications channel , the demodulator (see, e.g. Costas loop ) is unable to tell which constellation point is which.
It leads to a maximal rate of information of 10 6 log 2 (1 + 10 −3) = 1443 bit/s. These values are typical of the received ranging signals of the GPS, where the navigation message is sent at 50 bit/s (below the channel capacity for the given S/N), and whose bandwidth is spread to around 1 MHz by a pseudo-noise multiplication before transmission.
In MSK the difference between the higher and lower frequency is identical to half the bit rate. Consequently, the waveforms used to represent a 0 and a 1 bit differ by exactly half a carrier period. Thus, the maximum frequency deviation is δ = 0.5 f m where f m is the maximum modulating frequency. As a result, the modulation index m is 0.5.
As the description implies, is the signal energy associated with each user data bit; it is equal to the signal power divided by the user bit rate (not the channel symbol rate). If signal power is in watts and bit rate is in bits per second, E b {\displaystyle E_{b}} is in units of joules (watt-seconds).
Each symbol is encoded as a different combination of amplitude and phase of the carrier, so each symbol is represented by a point on the constellation diagram, called a constellation point. The constellation diagram shows all the possible symbols that can be transmitted by the system as a collection of points.
The symbol rate is related to gross bit rate expressed in bit/s. The term baud has sometimes incorrectly been used to mean bit rate , [ 3 ] 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 digit "0" is represented by one symbol, and binary digit ...