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# Relation between data rate and carrier frequency under BPSK modulation

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#### chessmath2009

##### Newbie level 6
Hi
I have seen in different simulations for BER vs SNR under BPSK modulation, the relationship like Rb=2*Fc where Rb is the data rate and Fc is carrier frequency.
Can anyone please tell me what is the justification behind these formulas? How can I relate data rate(bit rate ) to carrier frequency under certain modulation?:thinker:
Thanks

Hi
I have seen in different simulations for BER vs SNR under BPSK modulation, the relationship like Rb=2*Fc where Rb is the data rate and Fc is carrier frequency.
Can anyone please tell me what is the justification behind these formulas? How can I relate data rate(bit rate ) to carrier frequency under certain modulation?:thinker:
Thanks

Are you sure that Fc is the carrier frequency? To my understanding carrier frequency just shift the signal to an appropriate portion of the spectrum.

These ratios are often optimized using matched filters. Shannon's Law determines the tradeoff for bit rate vs SNR at a fixed BER. Bandwidth expansion or compression trades off power density efficiency and BER.

Thus depending on your SNR and noise threshold of receiver with sub-optimal filter and discrimination, your results can vary widely and be worse than expected optimum.

e.g. Integrate and dump detector vs centre sampling Detector or wideband Rx vs "matched Filter" Rx affects results significantly for BER vs BW and SNR

As I recall channel spacing is recommended to be equal to bit rate, with low ISI filtering (raised cosine)

if BR is 2x bandwidth, then very aggressive and matched filtering group delay ISI becomes a challenge and depends how you define BW as -3dB (idealistic) or say -20dB or -40 dB in the presence of strong adjacent channels

Hi,

As per my understanding bandwidth = 2 * data rate. Carrier frequency is the frequency at which you will transmit the signal.

Suppose your data rate is 9600 bps and you are modulating that using gold code of length 1023 then your bandwidth will become 2*9600*1023 ~= 20Mhz. It means your signal power will be distributed in that bandwidth. After that you have to choose which frequency you want to transmit. If you are choosing some x frequency as carrier then your signal power will be distributed in band x+/- 10MHz.

Amit

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