Wireless Notes
Learn FSK Frequency Shift Keying with working principle, BFSK, MFSK, MSK, GFSK, GMSK, bandwidth calculation, BER performance, detection methods, and applications in Bluetooth GSM for engineering students.
In FSK, the carrier's frequency is changed to represent digital data (0 and 1). One frequency (f1) is used for Bit 1 and another frequency (f2) is used for Bit 0.
🎯 What is FSK?
FSK is the digital version of Frequency Modulation. Different frequencies are assigned to different digital bits.
| │ Digital Data | │ 1 │ 0 │ 1 │ 1 │ 0 │ 0 │ 1 │ │ |
| │ FSK Signal | │ |
| │ Bit 1 | Frequency f1 (higher) │ |
| │ Bit 0 | Frequency f2 (lower) │ |
⚙️ Working Principle
Mathematical Expression:
┌──────────────────────────────────────────────────────┐
│ │
│ Binary FSK: │
│ │
│ s(t) = { Ac × cos(2πf1×t) for bit 1 (mark) │
│ { Ac × cos(2πf2×t) for bit 0 (space) │
│ │
│ Where: │
│ f1 = fc + Δf (frequency for bit 1) │
│ f2 = fc - Δf (frequency for bit 0) │
│ Δf = Frequency deviation │
│ fc = Center frequency │
│ │
└──────────────────────────────────────────────────────┘
FSK Generation:
📊 Types of FSK
1. Binary FSK (BFSK)
- 2 frequencies: f1 and f2
- 1 bit per symbol
- Simple, widely used
2. M-FSK (M-ary FSK)
- M different frequencies
- log₂(M) bits per symbol
- More bandwidth needed, better BER per bit
3. MSK (Minimum Shift Keying)
- Special BFSK with minimum frequency separation
- Δf = 1/(4Tb) → modulation index h = 0.5
- Continuous phase (no abrupt phase jumps)
- Better spectral efficiency than standard FSK
- Used in: GSM (GMSK variant)
4. GFSK (Gaussian FSK)
- FSK with Gaussian pulse shaping
- Reduces bandwidth (smooth transitions)
- Used in: Bluetooth, DECT, Zigbee
5. CPFSK (Continuous Phase FSK)
- Phase continuous at bit transitions
- Better spectral properties
- MSK is a special case of CPFSK
| │ Standard FSK | Phase discontinuity at transitions │ |
| │ CPFSK/MSK | Smooth phase transitions │ |
| │ GFSK | Gaussian filtered, extra smooth │ |
📡 Bandwidth
| │ BFSK Bandwidth | │ |
| │ Where | │ |
| │ Modulation Index | h = 2Δf/Rb = 2Δf×Tb │ |
| │ MSK | h = 0.5, BW ≈ 1.5 × Rb │ |
| │ GFSK | BW < MSK (depends on BT product) │ |
| FSK Type | Bandwidth | Spectral Efficiency |
|---|---|---|
| Wide-deviation FSK | 2Δf + 2Rb | Low |
| Narrow-deviation FSK | ≈ 2Rb | Moderate |
| MSK | 1.5 × Rb | Good |
| GFSK (BT=0.5) | ≈ 1.0 × Rb | Better |
📉 BER Performance
| Coherent BFSK | BER = (1/2) × erfc(√(Eb/2N₀)) |
| Non-coherent BFSK | BER = (1/2) × exp(-Eb/2N₀) |
| Coherent BFSK | Eb/N₀ ≈ 13.5 dB |
| Non-coherent BFSK | Eb/N₀ ≈ 14.2 dB |
| Compare | BPSK needs only 10.5 dB (3 dB better) |
The BER performance of FSK is better than ASK (constant amplitude = better against noise) but worse than PSK.
Ranking (best to worst BER): BPSK > Coherent BFSK > Non-coherent BFSK > ASK
🔍 FSK Detection Methods
1. Coherent Detection
- Uses local oscillator synchronized with carrier
- Better performance (lower BER)
- More complex receiver
2. Non-Coherent Detection
- No phase synchronization needed
- Slightly worse BER (0.7 dB penalty)
- Simpler receiver
- Used in most practical FSK systems
3. Discriminator Detection
- Frequency-to-voltage converter
- Simple analog approach
- Used in legacy FM/FSK receivers
✅ Advantages & Disadvantages
Advantages:
- Constant amplitude → immune to amplitude fading/noise
- Simple non-coherent detection possible
- Better BER than ASK
- Good performance in fading channels
- Easy to implement with VCO
Disadvantages:
- Larger bandwidth than PSK (needs 2 frequencies + gap)
- Lower spectral efficiency than PSK/QAM
- BER worse than PSK for same Eb/N₀
- For M-FSK: bandwidth grows linearly with M
🌐 Applications
| Application | FSK Variant | Why? |
|---|---|---|
| Bluetooth | GFSK | Low power, simple, narrow BW |
| Zigbee (868 MHz) | BFSK | Simple IoT devices |
| DECT cordless phones | GFSK | Good quality, simple |
| Caller ID | BFSK (Bell 202) | Simple modem standard |
| Pagers | BFSK/4-FSK | Non-coherent, simple RX |
| LoRa | CSS (chirp spread) | Long range variant |
| Old dial-up modems | FSK | Simple, reliable |
| GSM | GMSK (Gaussian MSK) | Spectral efficiency + constant envelope |
📝 Summary
| Parameter | BFSK |
|---|---|
| Frequencies | 2 (f1 for 1, f2 for 0) |
| Amplitude | Constant |
| Bandwidth | 2(Δf + Rb) |
| BER (coherent) | (1/2)erfc(√(Eb/2N₀)) |
| vs ASK | Better (constant amplitude) |
| vs PSK | Worse (needs more BW) |
| Best for | Fading channels, simple receivers, IoT |
| Modern use | Bluetooth (GFSK), GSM (GMSK), Zigbee |
❓ FAQ
Q: Why does Bluetooth use GFSK instead of PSK? A: Bluetooth is designed for low-power, low-cost devices. GFSK has a constant envelope (efficient power amplifier), simple non-coherent detection is possible, and for short-range it works well enough.
Q: Why is GMSK used in GSM? A: GMSK has a constant envelope (power efficient), good spectral containment (Gaussian filter), and MSK's smooth phase ensures low out-of-band emissions. 3G/4G/5G use OFDM+QAM for higher data rates.
Q: FSK mein Δf kitna rakhein? A: Minimum Δf for orthogonality = 1/(2Tb) (coherent) ya 1/Tb (non-coherent). MSK uses exactly Δf = 1/(4Tb) which is the minimum for non-coherent while maintaining good properties.
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