@n0n0

In digital communication or data transmission,




E

b



/


N

0




{\displaystyle E_{b}/N_{0}}
(energy per bit to noise power spectral density ratio) is a normalized signal-to-noise ratio (SNR) measure, also known as the "SNR per bit". It is especially useful when comparing the bit error rate (BER) performance of different digital modulation schemes without taking bandwidth into account.
As the description implies,




E

b




{\displaystyle E_{b}}
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).




N

0




{\displaystyle N_{0}}
is the noise spectral density, the noise power in a 1 Hz bandwidth, measured in watts per hertz or joules.
These are the same units as




E

b




{\displaystyle E_{b}}
so the ratio




E

b



/


N

0




{\displaystyle E_{b}/N_{0}}
is dimensionless; it is frequently expressed in decibels.




E

b



/


N

0




{\displaystyle E_{b}/N_{0}}
directly indicates the power efficiency of the system without regard to modulation type, error correction coding or signal bandwidth (including any use of spread spectrum). This also avoids any confusion as to which of several definitions of "bandwidth" to apply to the signal.
But when the signal bandwidth is well defined,




E

b



/


N

0




{\displaystyle E_{b}/N_{0}}
is also equal to the signal-to-noise ratio (SNR) in that bandwidth divided by the "gross" link spectral efficiency in bit/s⋅Hz, where the bits in this context again refer to user data bits, irrespective of error correction information and modulation type.




E

b



/


N

0




{\displaystyle E_{b}/N_{0}}
must be used with care on interference-limited channels since additive white noise (with constant noise density




N

0




{\displaystyle N_{0}}
) is assumed, and interference is not always noise-like. In spread spectrum systems (e.g., CDMA), the interference is sufficiently noise-like that it can be represented as




I

0




{\displaystyle I_{0}}
and added to the thermal noise




N

0




{\displaystyle N_{0}}
to produce the overall ratio




E

b



/

(

N

0


+

I

0


)


{\displaystyle E_{b}/(N_{0}+I_{0})}
.

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