Dear Afsaneh,

I would like to pay your attention that there are some information missed to answer your question quantitatively. The terms in your equation must be defined thoroughly. Your wireless communication system must be described in sufficient detail. For example what is R?. you ask about gamma and you said that that is a function of bit error rate.

In addition i could not get a copy of the referenced paper such that i could get the details of the problem.

In calculating the bit rate one starts from the Shannon capacity limit of a communication channel, that is 

rb= B log2 (1+ sinr),

If the system is a spatial multiplexing mimo system with number of antennas  N=Nt=Nr for the transmission and reception , then the bit rte will be increased by  a factor N so that rb for mimo= N B log2 (1+ sinr), Here rb is the error free rate, 

On the other side one can express the bit error rate as a function of sinr and the modulation order M. These expression can be readily found in the literature for the M-PSK and M-QAM.

At the end one can determine the spectral efficiency as a function of bit error rate and the modulation order.

This just an approach to solve the problem rather tan a rigorous answer. 

wish you success

There is inverse relation between SNR (Signal to Noise Ratio) and BER (Bit Error Rate).

When BER is increases the SNR decrees and When BER deceases the SNR increases.

Generally you may consider

SNR: Show the Quality of Signal

BER: Show the Error Rate in Signal

thank you so much for your time.

the problem is, I need an exact numerical relationship.

for example:

BER=10-6, SINR(Signal to Noise + Interference)=0.2, B(Bandwidth)=3 MHz, R=15

now, how much is the rate?

Dear all,

to my knowledge, BER and rate can be drawn from the SINR. In fact, rate, usually called capacity of a channel can be expressed as

R = E{B.log2(1+SINR)},

where E is the mathematical expectation, and B the bandwidth of the signal. See for instance the papers:

- Ergodic capacity, outage capacity, and information

transmission over Rayleigh fading channels, by Choudhury and Gibson,

- WIRELESS COMMUNICATIONS, by A. Goldsmith

and references therein.

For the BER, it is a bit more complex, since it depends on the modulation and the receiver, however see for instance :

- Lecture 10: Wireless Network Capacity (ppt)

- Bit Error Rate Estimation for a Joint Detection Receiver in the Downlink of UMTS/TDD

Best,

Vincent

thank you dear Vincent for your time.

the rate formula I'm speaking of is -as said in the article I attached- this:

B/R log10(1+SINR/gamma)

which should somehow be related to the original formula you have mentioned, and the question is, how?

Article Transmission Scheduling and Game Theoretical Power Allocatio...

Dear Afsaneh,

I would like to pay your attention that there are some information missed to answer your question quantitatively. The terms in your equation must be defined thoroughly. Your wireless communication system must be described in sufficient detail. For example what is R?. you ask about gamma and you said that that is a function of bit error rate.

In addition i could not get a copy of the referenced paper such that i could get the details of the problem.

In calculating the bit rate one starts from the Shannon capacity limit of a communication channel, that is 

rb= B log2 (1+ sinr),

If the system is a spatial multiplexing mimo system with number of antennas  N=Nt=Nr for the transmission and reception , then the bit rte will be increased by  a factor N so that rb for mimo= N B log2 (1+ sinr), Here rb is the error free rate, 

On the other side one can express the bit error rate as a function of sinr and the modulation order M. These expression can be readily found in the literature for the M-PSK and M-QAM.

At the end one can determine the spectral efficiency as a function of bit error rate and the modulation order.

This just an approach to solve the problem rather tan a rigorous answer. 

wish you success

thaks alot for your time Mr. Zekry.

the formula I am questioning is different from what I've seen in other resources of shannon! and my case is SISO.

B is the total bandwidth , and R is the number of resource blocks.

other details are provided in the copy I attached.

 Dear Afsaneh,

Welcome!

Thank you for the source. Now your question became clear. But before giving an answer i would like to pay your attention to the error in the equation: In the reference, it is log2 and not log10. So, the things return to its origin.

Let us start with Shannon again: rb= B log2 (1+ sinr),

In your equation the bit rate rb is substituted by the rate of the physical resource blocks r prb multiplied by the number of bits in one PRB which is termed R in your equation above. B is the total bandwidth of the channel as usual. 

The problem with Shannon is that it is a theoretical limit of the channel capacity. It is higher than real rate since Shannon assumed infinite number of symbols while in the real systems the number of symbols M is limited. For M-PSK the number of bits per symbol n= log2M. In the real communication systems, the bit error rate Pe depends on the ratio of the signal to interference plus noise.

So, one has to modify Shannon to reflect the performance of the real communication channel. This is accomplished by dividing sinr by the constant gamma. It is so that one calculates the sinr required for certain bit error rate defined by the quality of the service say Pe= 10^-6 for certian modulation order and type.

If one substitutes this value directly into Shannon,  one would get a much larger theoretical bit rate for the same channel bandwidth. So, one has to scale sinr by an empirical constant  GAMMA such that one gets the real bit rate when substituting the real sinr.

wish you success

thank you so so so much 

Best Regards

gama = 10^(((2/3)*(erfcinv(Pe))^2)/10);

Rate=W*log2(1+SINR/gama)

Madam,

Refer Wireless Communication by Andrea Goldsmith or Rappaport book for your clarification.

wish you all success

thank you so much R.Suresh Babu .

Best regards

Just beer in mind that Bit Error is generated due to encoding and decoding techniques while SnR is a fundamental problem generated by noise.

Dear Afsaneh,

Thanks for the rate expression but do have a reference for it ?

I must to appreciate the questioner and all the answers. It is very encouraging and helpful. Best of luck for all.

P.S. to discussion. SNR in Shannon's formula for the capacity is SNR at the output of the channel (C.Shannon, Mathematical theory of communications, sect. 25).

Distance between the transmitter and receiver decreases SNR.

Do we correctly evaluate (or call) the capacity using SNR at the channel input, but not output?

I agree that SNR is a matrix associated with the channel, however the error probability is an end-to-end system matrix. Although the error in the destination depends on the the SNR received, but it also depends on the deciding rule, modulation scheme.

The sentence " the error probability is an end-to-end system matrix". To omit misunderstanding, let's confine a discussion by SISO systems. On the other hand, Shannon's formula depends on the modulation scheme implicitly, only on the received power. But the power depends on the distance. Just this is a question - what we call the channel capacity? Maximal bit rate at the channel output or input?

I do agree with you that Shannon's formula depends on the modulation scheme implicitly however when we talk about SNR I am of the view that the SNR is a channel dependent factor. For example, received SNR for two differently modulated signals if transmitted with same power (which generally happens) depends on the channel (yes i agree that channel response is function of distance) and not on the modulation. However, two differently modulated signal transmitted with same power may yield different error probabilities.

Dependence of bit rate on SINR is known and confirmed in practice. However no explicit relationships between the bit rate (also capacity) and BER exist. Therefore, the question of Afsaneh Saeidanezhad can be answered only in SINR part.

Nevertheless, bit rate and capacity should implicitly depend on BER. This is evident - each not corrected transmission error causes losses of information in the sequences of signals or bits (packages) delivered to addressee.

This creates the question in development of the question asked by Afsaneh: can influence of BER on the bit rate (or capacity) be evaluated in any way? Do we know?

This question is not abstract. For instance: if we use good correcting code (BER

i want to know the relation between BER with increase in the channel order for diversity order 1 can anyone please help regarding this issue

Be careful. You asked question about the channel but did not define its model. There is a lot of models. Term "order"" may suggest you employ polinomial , AR - ARMA or other models.

The relationship is very simple. When Bandwidth is high, data rate is high.

When SINR is high, BER (Bit Error Rate) is low