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Bit Error Rate (BER) for frequency shift keying with coherent demodulation

Posted by Krishna Pillai
August 30, 2007

Following the request by Siti Naimah, this post discuss the bit error probability for coherent demodulation of binary Frequency Shift Keying (BFSK) along with a small Matlab code snippet.

Using the definition provided in Sec 4.4.4 of [DIG-COMM-SKLAR]), in binary Frequency shift keying (BFSK), the bits 0’s and 1’s are represented by signals and having frequencies and respectively, i.e.

,

where

is the energy ,

is the symbol duration and

is an arbitrary phase (assume to be zero).


The two frequencies and are orthogonal, i.e.

and

.

Simple transmit-receive block diagram for binary frequency shift keying (FSK) can be as shown below.

Figure: Block diagram of FSK modulation and coherent demodulation

For analyzing the bit error rate with coherent FSK demodulation, let us compare the signaling waveform used by binary FSK when compared with binary PSK. The distance between the energy of the signaling waveform for:

(a) binary phase shift keying (BPSK) is (uses antipodal signaling)

(b) binary frequency shift keying (BFSK) is (uses orthogonal signaling)

Figure: Orthogonal and antipodal signaling

Using similar mathematical formulation used for BPSK, but with the distance between the signals reduced by half, the bit error probability for coherent binary frequency shift keying is

.

For obtaining the same bit error rate as BPSK, binary frequency shift keying requires around 3dB more . More details on the bit error curves with orthogonal and antipodal signals is discussed in Sec 3.2.5 of [DIG-COMM-SKLAR].

Simulation Model

Simple Matlab/Octave script for computing the bit error rate with FSK modulation. The code performs the following:

(a) Generation of random 1’s and 0’s

(b) Converting bits to appropriate frequency

(c) Passing through Additive White Gaussian Noise channel

(d) Demodulation at the receiver

(e) Counting the number of errors.

Click here to download Matlab/Octave script for computing Bit Error Rate with FSK modulation

Figure: Bit error probability with coherent demodulation of frequency shift keying

Hope this helps

Krishna

Reference

[DIG-COMM-SKLAR] Digital Communications: Fundamentals and Applications (2nd Edition), Bernard Sklar

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    • Comments
    Comment by davis on October 30, 2008 @ 10:54 pm

    Hi Krishna
    i see that in the code the freqency for 0 is 1 Hz
    and for 1 2 Hz
    and that bit period is 1sec witch means that the data band width is the same as the seperation between the to carriers
    How is this possible?
    Thanks

    Comment by Krishna Pillai on November 3, 2008 @ 8:51 am

    @davis: Well, given that we need to send both 1Hz and 2Hz, I do not think that the data bandwidth becomes equal to the carrier separation. Given the above understanding, am unable to understand your perspective. Can you please provide more details.

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