How to establish the relationship between transmission rate and energy consumption?
Abdullah Ahmed Yaqot
Hi. I think your question is not clear enough. However, If I understand it well, you need a formula showing the relationship.
- I would say Shannon capacity draws a theoretical bound for the data rate as a function of the signal-to-noise SNR ratio at the receiver side. If any modulation scheme is used, there should be a gap in the data rate, for example the gap of QAM scheme can be expressed as: gamma= - ln(5 BER)/1.5 given that Shannon bound = bandwidth * log2(1+channel power*signal power/ (gamma*noise power)). This means that based on the bit error rate (BER) required for the system, we can tune the system energy to get (Eb/No) which is the SNR of digital communication system at the receiver side. The error function erfc(x) draws the relationship between BER and Eb/No for a couple of modulation schemes as you might know.
- The second point is we can transmit any data rate with any transmit power, however the main concern is what is the BER we get at the end, in other words very high data rate at very small transmit power produces many errors and consequently unreliable communication system. Thus to tighten the relationship between power and data rate theoretically we have Shannon bound which guarantees negligible BER. Physically, we need to involve a high-order modulation scheme like QAM to get the required system performance. I wish this answer helps.
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Abdullah Ahmed Yaqot
- Book --> Digital Communications: Fundamentals and Applications, Bernard Sklar.
- Book --> Thomas M. Cover, Joy A. Thomas (2006). Elements of Information Theory. John Wiley & Sons, New York.
- Paper --> A. J. Goldsmith and S.-G. Chua, “Variable-rate variable-power MQAM for fading channels,” IEEE Trans. Commun., vol. 45, no. 10, pp. 1218–1230, Oct. 1997.
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