Coherent GMSK Demodulation in
Communication Systems
Lecture by [Your Name]
Course: Digital Communication Systems
February 4, 2025
1
Introduction to GMSK Demodulation
1.1
Overview of GMSK
Gaussian Minimum Shift Keying (GMSK) is a continuous-phase frequency shift keying
(CPFSK) modulation scheme used in wireless communication systems like GSM, Bluetooth,
and satellite communication. It offers bandwidth efficiency, low power consumption, and
resilience to nonlinear distortions.
1.2
Why Use Coherent Demodulation?
Coherent demodulation of GMSK is based on precise carrier phase tracking. Compared to
non-coherent detection, coherent detection offers:
• Better Bit Error Rate (BER) performance.
• Higher spectral efficiency.
• Robust synchronization mechanisms.
• Reduced inter-symbol interference (ISI).
Coherent demodulation requires a synchronized local oscillator and phase-locked loop
(PLL) for carrier recovery.
2
Theoretical Basis of Coherent GMSK Demodulation
2.1
Mathematical Representation of GMSK
The transmitted GMSK signal is given by:
s(t) = A cos (2πfc t + ϕ(t))
where:
• A is the signal amplitude.
1
(1)
• fc is the carrier frequency.
• ϕ(t) is the modulated phase:
ϕ(t) = πh
X
ak q(t − kTb )
(2)
k
• h = 0.5 (modulation index).
• ak is the NRZ-modulated bit sequence (±1).
• q(t) is the Gaussian-filtered impulse response.
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Coherent GMSK Demodulation Process
3.1
Quadrature Decomposition
To demodulate GMSK coherently, we use Quadrature Demodulation:
3.2
I(t) = s(t) · cos(2πfc t)
(3)
Q(t) = s(t) · sin(2πfc t)
(4)
Low-Pass Filtering
The signals I(t) and Q(t) contain high-frequency terms that must be removed using lowpass filters (LPFs):
If (t) = A cos(ϕ(t))
(5)
Qf (t) = A sin(ϕ(t))
3.3
Phase Extraction
The phase of the received signal is extracted using:
Qf (t)
−1
θ(t) = tan
If (t)
3.4
(6)
(7)
Differential Phase Detection
Since GMSK carries information in phase transitions, we compute the differential phase:
∆θ(t) = θ(t) − θ(t − Tb )
3.5
Bit Decision
A threshold decision rule is applied:
• If ∆θ(t) > 0 ⇒ Bit = 1
• If ∆θ(t) < 0 ⇒ Bit = 0
2
(8)
4
Implementation in Vivado (FPGA-Based Design)
4.1
System Overview
To implement coherent GMSK demodulation on an FPGA, the following components are
required:
• ADC (Analog-to-Digital Converter) – Converts received RF signals to digital.
• IQ Demodulator – Extracts I(t) and Q(t).
• Low-Pass FIR Filters – Removes high-frequency noise.
• CORDIC Algorithm – Computes θ(t).
• Differential Decoder – Extracts binary data.
• NRZI Decoder – Converts data into final output.
4.2
HDL Implementation
The core components are implemented in Verilog:
Listing 1: IQ Demodulator (Mixers)
assign I = R F s i g n a l ∗ c o s ( 2 ∗ p i ∗ f c ∗ t ) ;
assign Q = R F s i g n a l ∗ s i n ( 2 ∗ p i ∗ f c ∗ t ) ;
Listing 2: Phase Extraction Using CORDIC
t h e t a = atan2 (Q, I ) ;
Listing 3: Differential Phase Calculation
delta theta = theta − theta previous ;
5
Performance Considerations
Parameter
Impact
Carrier Frequency Offset Demodulation errors
Phase Noise
Degrades BER
Multipath Interference
Increases ISI
Solution
Use PLL-based tracking
Use adaptive filtering
Apply equalization techniques
Table 1: Performance Factors in Coherent GMSK Demodulation
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Conclusion
• Coherent GMSK demodulation provides better performance than non-coherent
methods.
• IQ demodulation, CORDIC phase detection, and differential decoding are the
core building blocks.
• Vivado and FPGA-based implementation allows real-time high-speed processing.
3
7
References
1. Proakis, J. G., & Salehi, M. (2008). Digital Communications. McGraw-Hill. 2. Haykin, S.
(2001). Communication Systems. John Wiley & Sons. 3. Vivado Design Suite User Guide,
Xilinx.
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