Question

Need the detailed calculation process about why at the same BER condition, BPSK is 3dB more power efficient that BFSK

Answer 1

BIT ERROR RATE (BER) OF BPSK:

The BER of BPSK is As we increase the transmitted signal per energy bit, E_b, for a specified noise spectral density N₀, the message points corresponding to symbols 1 and 0 move further apart, and the average probability of error P_e is correspondingly reduced in accordance with the above equation.

BIT ERROR RATE (BER) OF BFSK:

Using similar mathematical formula  used for BPSK, BER can be found but the distance between the two signals here is reduced by half, so that the error probability of BFSK becomes

hence

For obtaining the same BER of BPSK the BFSK requires 3 db more E_b/N₀. The BPSK is less erroneous than BFSK.

In general, BFSK modulations tend to be worse than comparable linear modulations by several criteria.

we have these bit error rate versus per bit signal to noise ratio graphs for various modulation schemes. One thing you always see in those graphs is that you need higher E_b/N₀ for same BER in BFSK compared to BPSK. In amateur radio, (clean) power is often relatively limited and getting more with less is respected, giving advantage to BPSK.

One big advantage of BFSK is that we don't need clean power for it! It can work with very non-linear power amplifiers, so a set power level is easier to reach with BFSK than it is with BPSK.

Next, we have the spectral efficiency as well. BFSK is less spectrally efficient compared to BPSK with same number of modulation levels.

For example, for non-coherent orthogonal BFSK, the null-to-null bandwidth is B=(M+1)R_s, while for BPSK (which is same as for non-coherent DPSK as used in say BPSK31) it's 2R_s, so in binary case, we have 3R_b compared to 2R_b for BPSK. If number of modulation levels increases, BFSK starts to lose very quickly, since in BPSK case, bandwidth does not depend on number of modulation levels

After observing both the characteristics we can draw conclusion that BPSK is better than BFSK through AWGN channel with respect to a specific SNR.