The receiver sensitivity is the minimum required rf signal power Pr at its input to achieve certain minimum signal quality measured by the minimum bit error rate. This is by definition,

On the other side to achieve this minimum bit error rate, one has to realize specific minimum signal to noise ratio. More precise, one has to realize minimum Eb/N0 where Eb is the energy per bit to N0 the noise density ratio.

The signal power Pr to noise N ratio= Pr/N is related to Eb/N0 by

Pr/N = Eb fb/ N0 W, where fb is the bit rate and W is the bandwidth,

But we know from the higher order modulation techniques such as QAM, that fb/W is the band width efficiency or the spectral efficiency SE. It is equal to log2 M where M is the modulation order.

So, finally one has: Pr/N = Eb log2 M/ N0 ,

Therefore Pr= N Eb log2M/ N0= W Eb log2 M,

From this relation you can get the required energy per bit as all other parameters may be known for a given receiver. As M increases the required energy per bit increases as clear from the above relation.

An alternative is that you have,

the minimum input power Pr,

You have the Minimum Pr/N from the specific error performance curve for specific modulation technique used fro your receiver, then you can calculate the noise power of the receiver.

Given the noise power you can calculate the link budget for any other modulation order.

Thank you Abdelhalim

Your answer was detailed and helpful. So if I understand correctly, I should compare the BER performance and find the factor to achieve equal BER, e.g. given BER(NRZ)=1/2erfc[sqrt(SNR1)/(2sqrt(2))] and on the other hand BER(RZ)=1/2erfc[sqrt(SNR2)/2)],

and given definition SNR~P^2,

than for same BER: P(NRZ)/(2sqrt(2))=P(RZ)/2

we arrive at a factor of sqrt(2), such that if the detector is defined a sensitivity for NRZ, the required signal power for RZ modulation would be a factor of sqrt(2) less, and so on for other modulations.

If there is a reference for the different dependencies of BER on SNR for existing modulation formats it would be appreciated.

Yishai

Dear Yishai Albeck ,

I just come very late to your answer.

There is a good book which I consider it a good reference in electrical communications. It is the digital communication system by Glover and Grant:https://easyengineering.net/digital-communications-by-lan-glover/

Best wishes

Abdelhalim abdelnaby Zekry Yishai Albeck both of your answers are very helpful to me. I would like to know that can we derive Eb/No and BER relationship (function) given a modulation method? If it is possible, can we derive Eb/No form the BER with a modulation and applied this Eb/No to figure out the receiver sensitivity with given kTB, noise figure?

Thanks,

Danny

Dear @ Da-Ren,

welcome!

The bit error rate rbe is derived as a function of Eb/N0 for the different modulation techniques and order. These relations are drawn in graphs to get characteristic curves for these modulations techniques. Given the minimum bit error rate from the quality of service one can get the minimum Eb/N0 for the intended modulation technique and order.

You can find such formulas and curves in the books of digital communications including the book of Glover and Grant.

Best wishes

Best wishes

I use the alternative approach, which based on the Cramer-Rao Lower Bound (CRLB) for dispersion of amplitude (Re and Im) estimation.

Dear professor Abdelhalim abdelnaby Zekry ,

Thank you for your suggestions and the recommended book.

Another question is that, when the received RSSI is equal or greater (say 3dB) than the receiver sensitivity with specific Eb/No that derived from a modulation curve, can its actual BER approach the BER specified from that modulation curve , or can it be guaranteed within a certain interval?

If it is work, is it realistic that we change RSSI with transmit power in accordance with a pre-trained path loss model to control the receiver BER?

Thank you very much!

Danny

To measure the receiver sensitivity SNR or S/N ratio is one of the direct methods

With following formula it may be calculated:

The sensitivity of a receiver can be calculated if one knows the following performance parameters: the noise figure (NF), the ENBW, and the carrier to noise ratio (C/N) required to achieve the desired quality signal.

The sensitivity is as follows:

Sensitivity=10×log10(kTB)+NF+C⁄N

This equation defines the signal power in dB·

Watts that is present at the demodulator for a desired carrier to noise ratio. Let’s explain each of the terms in this equation.

Dear Da-Ren Chen ,

I come late to your question.

If the received power is that the signal to noise ratio is greater than the minimum required, this will enhance much the bit error rate and the quality of the signal will be improved. This is in accordance with the bit error rate curve for the specific modulation technique and order.

It is a normal practice to make the recieved signal strength greater than the minimum required in order to compensate for any additional random variations of the system parameters including the communication channel. Sometimes it it is called the fading margin.

Best wishes