Why is the relationship between Es/N0 and SNR different for complex and real signals
53 次查看(过去 30 天)
显示 更早的评论
I'm confused about some statements in the introduction of AWGN Channel. Here is the link AWGN Channel.
It says that
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/410763/image.png)
I wonder why there is a factor of 0.5 for real input signals.
Would you please give me some explanation or introduce me some textbooks that can help me figure out how to derive the equations above?
0 个评论
采纳的回答
Kiran Felix Robert
2020-12-18
Hi Yaowei,
The Symbol rate of a complex input signal is higher when compared to that of a real input signal by a factor of 2.
To understand this, you can think of the complex space as C as being directly mapped to R2 Space. [(x, y) <=> x + i.y]
2 个评论
更多回答(1 个)
Andrew Reibold
2024-3-8
编辑:Andrew Reibold
2024-3-8
Your explanation is quite accurate, and your understanding is correct. The factor of 0.5 in the formula for real input signals is related to how the SNR is specified in MATLAB's AWGN channel model.
In MATLAB, when you specify the SNR for a real signal in the AWGN channel model, it is assumed that the specified SNR corresponds to the power of a complex signal, not a real signal. Since the power of a complex signal is the sum of the powers of its real and imaginary components, for a real signal, you effectively have half the power in each of the real and imaginary parts.
To clarify, let's consider the power relation (Sorry I dont know how to make sub-letters, so I used underscore):
- For a complex signal S=S_i+j*S_q, where S_i and S_q are the real and imaginary parts, the power is ∣S∣^2 = ∣S_i∣^2+∣S_q∣^2∣.
- For a real signal S = S_i, the power is ∣S∣^2=∣S_i|^2 .
Now, if you want the SNR to be specified in terms of the power of the real signal (S_i), you need to adjust the SNR value accordingly. This adjustment involves halving the power, which corresponds to subtracting 3 dB. Hence, the factor of 0.5 in the formula for real input signals.
Your understanding and explanation are correct: if you want to specify an SNR of X dB for a real signal, you would need to set the SNR to X−3 dB in MATLAB's AWGN channel model.
As for textbooks, if you're looking for a comprehensive resource on digital communication systems, "Digital Communications" by John Proakis and Masoud Salehi is a widely used textbook that covers these concepts in detail. It provides a solid foundation in communication theory, including topics like modulation, coding, and noise in communication channels.
0 个评论
另请参阅
类别
在 Help Center 和 File Exchange 中查找有关 Propagation and Channel Models 的更多信息
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!