yucaoxilin的个人空间 http://blog.eetop.cn/814670 [收藏] [复制] [RSS]


Relation between Eb/N0 and SNR

已有 817 次阅读2013-8-21 14:54


I have seen a lot of questions being posted in several forums on the relationship between Eb/N0 and SNR. Like, whether SNR and Eb/No are same or not. In fact , the relationship is very easier to understand.

Lets start with the basic equation and try to verify its authenticity.

\frac{S}{R_{b}}=E_{b}\;\;\;\;\; \rightarrow (1)

Rb = bit rate in bits/second
Eb = Energy per bit in Joules/bit
S = Total Signal power in Watts

We all know from fundamental physics that Power = Energy/Time. Using SI units, lets verify the above equation.


\frac{Watts}{\frac{bits}{second}} = \frac{Joules}{bit}

\Rightarrow Watts = \frac{Joules}{second}

This verifies the power, energy relationship between S and Eb. Now, introducing the noise power N_{0} in equation (1)

\Rightarrow \frac{Eb}{N0} = \frac{S}{ \left( Rb*N0 \right )}

\Rightarrow SNR = \frac{Rb*Eb}{N0}\;\;\;\;\; \rightarrow (2)

This equation implies that the SNR will be more than \frac{Eb}{N_{0}} by a factor of R_{b} (if Rb > 1 bit/second)

Increasing the data rate will increase the SNR, however , increasing Rb will also cause more noise and noise term also increases ( due to ISI – intersymbol interference , since more bits are packed closer and sent through the channel).

So we cannot increase SNR by simply increasing Rb. We must strike a compromise between the data rate and the amount of noise our receiver can handle.

Always engineering is about where and when we want to compromise …



\frac{S}{N} = \frac{\left( Rb*Eb \right)}{B*N0}

where B is the noise bandwidth. Here, I have taken an unity noise bandwidth (ie. B=1) for simplification.


评论 (0 个评论)


您需要登录后才可以评论 登录 | 注册


站长推荐上一条 /2 下一条

小黑屋| 关于我们| 联系我们| 在线咨询 |  EETOP 创芯网 ( 京ICP备:10050787号 京公网安备:11010502037710 )

GMT+8, 2020-9-24 19:49 , Processed in 0.027749 second(s), 5 queries , Gzip On, Redis On.

Powered by Discuz! X3.4

© 2001-2017 Comsenz Inc.