bfsk binary frequency shift keying pp.pptx

Binary frequency shift keying

1. Bfsk in wireless communication

2. Bfsk in wireless communication Overview

3. Calculations of bfsk in wireless communication Key Calculations in BFSK
1. Bit Rate (Rb):
* The number of bits transmitted per second.
* Formula: Rb = 1 / Tb, where Tb is the bit duration.
2. Symbol Rate (Rs):
* The number of symbols transmitted per second.
* Formula: Rs = 1 / Ts, where Ts is the symbol duration.
* For BFSK, Rb = Rs, as one bit is represented by one symbol.
3. Frequency Separation (Δf):
* The difference between the two frequencies used to represent ‘0’ and ‘1’.
* Formula: Δf = |f1 – f2|, where f1 and f2 are the two frequencies.
4. Bandwidth (B):
* The range of frequencies occupied by the BFSK signal.
* Formula: B ≈ 2Δf + 2Rb (Carson’s Rule)
5. Signal-to-Noise Ratio (SNR):
* A measure of signal quality, comparing the signal power to the noise power.
* Formula: SNR = Ps / Pn, where Ps is the signal power and Pn is the noise power.
6. Bit Error Rate (BER):
* The probability of a bit being received incorrectly.
* Formula: BER = Q(√(Eb/No)), where Q(x) is the Q-function, Eb is the energy per bit, and No is the noise power spectral density.
7. Power Spectral Density (PSD):
* The distribution of power over different frequencies in the signal.
* For BFSK, the PSD is a sinc-squared function centered at the two carrier frequencies.
Example:
Let’s assume a BFSK system with the following parameters:
* Bit rate (Rb) = 1000 bps
* Frequency separation (Δf) = 100 Hz
* Symbol Rate (Rs):
Rs = Rb = 1000 symbols/s
* Bandwidth (B):
B ≈ 2 * 100 Hz + 2 * 1000 Hz = 2200 Hz
To calculate BER, we need to know the SNR. If we assume a certain SNR value, we can use the Q-function to calculate the BER.
Note: These are basic calculations. Depending on the specific implementation and modulation scheme, other factors like phase shifts, pulse shaping, and channel impairments can influence the performance.
Would you like to delve deeper into a specific calculation or explore a practical example?

4. Derivation of bfsk in wireless communication Derivation of BFSK Binarplement. * It is robust to noise, especially with Derivation of BFSK
Binary Frequency Shift Keying (BFSK) is a digital modulation technique where the frequency of a carrier wave is shifted between two discrete frequencies to represent binary data.
Mathematical Representation of BFSK Signal
Let’s consider a binary data sequence, b(t), which takes on values of 0 or 1. The corresponding BFSK signal, s(t), can be expressed as:
s(t) = A * cos(2πf1t), for b(t) = 0
s(t) = A * cos(2πf2t), for b(t) = 1

where:
* A is the amplitude of the carrier wave
* f1 and f2 are the two frequencies used for ‘0’ and ‘1’ bits, respectively
* t is time
Demodulation of BFSK Signal
Coherent Detection:
* Frequency Shift: The received BFSK signal is multiplied by two locally generated carrier signals, one at frequency f1 and the other at f2.
* Low-Pass Filtering: The product signals from each branch are passed through low-pass filters to remove high-frequency components.
* Decision Making: The output of the low-pass filters is compared, and the larger output indicates the transmitted bit.
Non-Coherent Detection:
* Envelope Detection: The received BFSK signal is passed through an envelope detector to obtain its envelope.
* Comparison: The envelope is compared to a threshold. If the envelope is above the threshold, it’s decided as a ‘1’, otherwise a ‘0’.
Performance Analysis of BFSK
Bit Error Rate (BER):
The BER of BFSK depends on the signal-to-noise ratio (SNR) and the type of detection used. For coherent detection, the BER is given by:
BER = Q(√(Eb/No))

where:
* Q(x) is the Q-function
* Eb/No is the energy per bit to noise power spectral density ratio
For non-coherent detection, the BER is slightly higher:
BER = ½ * exp(-Eb/2No)

Bandwidth:
The bandwidth of a BFSK signal is approximately twice the frequency separation between the two frequencies:
B ≈ 2Δf

where:
Δf = |f1 – f2|

Key Points:
* BFSK is relatively simple to implement.
* It is robust to noise, especially with coherent detection.
* It has lower spectral efficiency compared to other modulation schemes.
* It’s suitable for applications where bandwidth is not a major concern.
By understanding these concepts and derivations, you can gain a deeper insight into the principles of BFSK modulation and its applications in various communication systems.

5. Coherent detection of bfsk BFSK Receiver
A BFSK receiver is designed to demodulate the frequency-shifted signal and recover the original binary data. There are primarily two types of BFSK receivers: coherent and non-coherent.
1. Coherent Detection
In coherent detection, the receiver requires precise knowledge of the carrier phase and frequency. This is typically achieved using a Phase-Locked Loop (PLL).
* Frequency Shift: The received BFSK signal is multiplied by two locally generated carrier signals, one at frequency f1 and the other at f2.
* Low-Pass Filtering: The product signals from each branch are passed through low-pass filters to remove high-frequency components.
* Decision Making: The output of the low-pass filters is compared, and the larger output indicates the transmitted bit.
2. Non-Coherent Detection
Non-coherent detection is simpler and does not require precise phase information.
* Envelope Detection: The received BFSK signal is passed through an envelope detector to obtain its envelope.
* Comparison: The envelope is compared to a threshold. If the envelope is above the threshold, it’s decided as a ‘1’, otherwise a ‘0’.
Key Components of a BFSK Receiver:
* Bandpass Filter: Filters the received signal to remove unwanted noise and interference.
* Frequency Discriminators: Separates the two frequency components of the BFSK signal.
* Low-Pass Filter: Removes high-frequency components and extracts the baseband signal.
* Clock Recovery Circuit: Recovers the clock signal for timing synchronization.
* Decision Circuit: Compares the received signal to a threshold to determine the transmitted bit.
Performance Considerations:
* Noise Immunity: Coherent detection offers better noise immunity than non-coherent detection.
* Implementation Complexity: Coherent detection is more complex to implement due to the need for a PLL.
* Bandwidth Efficiency: BFSK is not very bandwidth-efficient compared to other modulation schemes.
By understanding the principles of BFSK modulation and demodulation, you can design and implement effective BFSK communication systems for various applications.

6. Coherent detection of bfsk with diagram

7. Coherent detection diagram explanation

8. Non coherent detection of bfsk in wireless communication

9. Non coherent detection of bfsk with diagram

10. Non coherent detection of bfsk with diagram explanation

11. Spectrum and Bandwidth of BFSIC signals As the complex envelope of an FSK signal is a nonlinear fi.inction of the message signal m (t) , evaluation of the spectra of an FSK signal is, in general, quite involved, and is usually performed using actual time averaged measure- ments. The power spectral density of a binary FSK signal consists of discrete fre- quency components at + nEil, where it is an integer. It can be shown that the PSD of a continuous phase FSK ultimately falls off as the inverse fourth power of the frequency offset from – However, if phase discontinuities exist, the PSD falls off as the inverse square of the frequency offset from [Cou93]. The transmission bandwidth BT of an FSK signal is given by Carson’s rule as BT = 2af+ 2B (5.98) where B is the bandwidth of the digital baseband signal. Assuming that first null bandwidth is used, the bandwidth of rectangular pulses is B = R. Hence, the FSK transmission bandwidth becomes = 2(af+R) (5.99) If a raised cosine pulse-shaping filter is used, then the transmission bandwidth reduces to = 2Eif+ (I +c4R (5.100) where a is the rolloff factor of the filter. Coherent Detection of Binary FSK A block diagram of a coherent detection schem