Probability Of Error For Binary Fsk
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Krishna Sankar on August 30, 2007 Following the request by Siti Naimah, this post discuss the bit error probability for coherent probability of error in fsk demodulation of binary Frequency Shift Keying (BFSK) along with a small Matlab probability of error in ask psk fsk code snippet. Using the definition provided in Sec 4.4.4 of [DIG-COMM-SKLAR]), in binary Frequency shift keying (BFSK), fsk bit error rate 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 probability of error for noncoherent fsk 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
Probability Of Error For Non-coherent Fsk
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:
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Coherent And Noncoherent Fsk
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