Virtual Laboratory: Digital Baseband Signals

1. Objectives

Upon completion of this virtual laboratory experiment, the student will be able to:

🎯 Objective 1

Generate and visualize common digital baseband line codes (NRZ-L, NRZ-I, RZ, Manchester, AMI, HDB3) and measure their key time-domain parameters including pulse width, duty cycle, and transition density.

🎯 Objective 2

Analyze the power spectral density (PSD) of different line coding schemes and determine their bandwidth occupancy for satellite transmission.

🎯 Objective 3

Construct and interpret eye diagrams to measure signal quality parameters including eye opening, timing jitter, and noise margin in a satellite link.

🎯 Objective 4

Measure the range of baud rates that a satellite communication system can support for a given channel bandwidth, roll-off factor, and link budget constraints.

🎯 Objective 5

Calculate satellite link parameters (path loss, C/N₀, E_b/N₀) and determine the maximum allowable baud rate while maintaining a specified link margin.

🎯 Objective 6

Evaluate the bit error rate (BER) performance of baseband transmission over a satellite AWGN channel for various modulation and coding schemes.

2. Theory

2.1 Introduction to Digital Baseband Signals

A digital baseband signal is a digital signal that is transmitted without modulation to a carrier wave. In satellite communication systems, baseband signals represent the raw information bits before they are modulated onto an RF carrier (typically in the L, C, Ku, or Ka bands). The characteristics of the baseband signal directly impact the bandwidth efficiency, power efficiency, and error performance of the satellite link.

Figure 1: Digital baseband signal in a satellite communication link

2.2 Line Coding Techniques

Line coding is the process of converting binary data into a digital signal. The choice of line code affects bandwidth, DC content, clock recovery, and error detection capability.

Line Code	Rule	Bandwidth	DC Component	Clock Recovery	Suitable for Satellite?
NRZ-L	1 = +A, 0 = -A	R_b	High	Poor (long strings)	No
NRZ-I	1 = transition, 0 = no change	R_b	High	Poor	No
RZ	1 = +A (50% duty), 0 = 0	2R_b	High	Good	Limited
Manchester	1 = LH, 0 = HL (per bit)	2R_b	None	Excellent	Yes
AMI	1 = ±A alternating, 0 = 0	R_b	None	Fair	Yes
HDB3	AMI + bipolar violation every 4th 0	R_b	None	Good	Yes

Figure 2: Comparison of NRZ-L, Manchester, and AMI line coding waveforms

2.3 Power Spectral Density (PSD)

The power spectral density describes how the power of a baseband signal is distributed across frequencies. For satellite systems, the PSD determines the required transponder bandwidth and adjacent channel interference.

For NRZ rectangular pulses: S(f) = A²T_b [sin(πfT_b) / (πfT_b)]² = A²T_b sinc²(fT_b)

For Manchester coding: S(f) = A²T_b sinc²(fT_b/2) · sin²(πfT_b/2)

where A is the pulse amplitude, T_b is the bit duration, and the null-to-null bandwidth is:

NRZ/RZ/AMI: B_null = R_b (Hz)
Manchester: B_null = 2R_b (Hz)

2.4 Nyquist Criterion for ISI-Free Transmission

Intersymbol interference (ISI) occurs when the channel bandwidth is insufficient to support the baud rate. The Nyquist criterion states that for ISI-free transmission, the overall system response must satisfy:

Σ_n H(f − nR_s) = T_s (constant for |f| ≤ R_s/2)

For a raised-cosine filter with roll-off factor α (0 ≤ α ≤ 1):

Required Bandwidth: B = (1 + α) · R_s / 2 (baseband)
or B = (1 + α) · R_s (passband/modulated)

Satellite Context: Satellite transponders have strictly allocated bandwidth (typically 36 MHz or 54 MHz for Ku-band). The baud rate must be chosen such that the occupied bandwidth fits within the transponder allocation while maximizing spectral efficiency.

2.5 Eye Diagrams

An eye diagram is an oscilloscope display in which the received signal is repetitively sampled and applied to the vertical input, while the data rate triggers the horizontal sweep. It provides a qualitative measure of signal quality.

Figure 3: Eye diagram showing key measurement parameters

2.6 Baud Rate vs Bit Rate

It is essential to distinguish between baud rate (symbol rate) and bit rate:

R_b = R_s · log₂(M)

where M is the number of modulation levels. For binary baseband signals (M=2), R_b = R_s. For higher-order modulation (e.g., QPSK with M=4), the bit rate is twice the baud rate for the same bandwidth.

2.7 Satellite Link Baseband Considerations

In a satellite communication link, the baseband signal must be designed considering:

Free Space Path Loss (FSPL): L_p = (4πd/λ)² = (4πdf/c)², which attenuates the carrier and affects the received SNR.
Noise Power Spectral Density: N₀ = kT_sys (W/Hz), where k is Boltzmann's constant and T_sys is the system noise temperature.
Carrier-to-Noise Density Ratio: C/N₀ = (P_tG_tG_r)/(L_pkT_sys) — often expressed in dB-Hz.
Energy per Bit: E_b/N₀ = (C/N₀) / R_b — the critical parameter determining BER.

Maximum Bit Rate: R_b,max = (C/N₀) / (E_b/N₀)_req
Maximum Baud Rate: R_s,max = R_b,max / log₂(M)

Link Margin: The difference between the available E_b/N₀ and the required E_b/N₀ for a target BER. A typical satellite link requires 3–6 dB of margin to account for rain fade, antenna pointing errors, and equipment aging.

2.8 Bit Error Rate (BER) in AWGN

For a satellite channel modeled as additive white Gaussian noise (AWGN), the theoretical BER for common modulation schemes is:

BPSK: P_e = Q(√(2E_b/N₀))
QPSK: P_e ≈ Q(√(2E_b/N₀)) (per bit, same as BPSK)
16-QAM: P_e ≈ (3/2)Q(√(4E_b/(5N₀)))

where Q(x) is the Q-function: Q(x) = (1/√(2π)) ∫_x^∞ e^−t²/2 dt

3. Experimental Procedure

Perform the following five experiments using the interactive simulations below. Record all measurements in your laboratory notebook.

Experiment 1: Line Code Generation and Parameter Measurement

Open Simulation 1

Navigate to the Baseband Signal Generator. Enter the bit sequence 11010010 or generate a random sequence.

Select Line Codes

Sequentially select NRZ-L, Manchester, AMI, and HDB3. For each code, observe the time-domain waveform and record the measured parameters: pulse width, duty cycle, number of transitions, and estimated DC component.

Analyze Bandwidth

Observe the PSD plot for each line code. Measure the null-to-null bandwidth and compare with theoretical values. Which code has the narrowest bandwidth? Which has the best DC suppression?

Experiment 2: Eye Diagram Analysis

Open Simulation 2

Navigate to the Eye Diagram Analyzer. Set the line code to NRZ-L and baud rate to 10 Mbps.

Vary Noise and Jitter

Gradually increase the noise level (decrease SNR) from 20 dB to 5 dB. Record the eye opening height and width at each step. At what SNR does the eye close completely?

Compare Line Codes

Repeat for Manchester and AMI coding at the same baud rate. Which line code provides the largest eye opening under noisy conditions?

Experiment 3: Baud Rate vs Channel Bandwidth

Open Simulation 3

Navigate to the Baud Rate Analyzer. Set the channel bandwidth to 36 MHz (typical satellite transponder) and roll-off factor α = 0.35.

Calculate Maximum Baud Rate

Calculate the theoretical maximum baud rate using the Nyquist formula. Verify using the simulation by increasing the baud rate until ISI appears.

Vary Roll-off Factor

Change α to 0.2 and 0.5. Record the maximum baud rate for each case. Discuss the trade-off between bandwidth efficiency and ISI immunity.

Experiment 4: Satellite Link Parameter Measurement

Open Simulation 4

Navigate to the Satellite Link Calculator. Use default parameters for a GEO satellite at 36,000 km, 12 GHz (Ku-band), with 2 m antennas.

Measure Link Parameters

Record the calculated path loss, C/N₀, and maximum supported baud rate for a target E_b/N₀ of 10 dB (BER ≈ 10⁻⁶ for BPSK).

Vary System Parameters

Reduce the antenna diameter to 1 m and increase the system noise temperature to 400 K. Measure the new maximum baud rate. Calculate the link margin in each case.

Experiment 5: BER Performance Analysis

Open Simulation 5

Navigate to the BER Analyzer. Select BPSK modulation and plot the BER curve.

Determine Required E_b/N₀

Find the E_b/N₀ required to achieve BER = 10⁻⁵ for BPSK, QPSK, and 16-QAM. Record these values and compare with theoretical predictions.

Link Budget Verification

Using the E_b/N₀ values from Experiment 4, verify whether the satellite link can support the target BER for each modulation scheme.

4. Interactive Simulations

Simulation 1: Baseband Signal Generator & Analyzer

Time Domain

Bit Sequence

Line Code

Bit Rate (Mbps)

Amplitude (V)

Bit Rate (Mbps)

Baud Rate (MBaud)

100

Pulse Width (ns)

100

Duty Cycle (%)

Transitions

0.0

Avg DC (V)

Simulation 2: Eye Diagram Analyzer

Signal Quality

Line Code

Baud Rate (Mbps)

SNR (dB)

Jitter (%)

—

Eye Opening (V)

—

Eye Width (%)

—

Noise Margin (dB)

—

Signal Quality

Simulation 3: Baud Rate vs Bandwidth Analyzer

Nyquist Analysis

Channel Bandwidth (MHz)

Roll-off Factor (α)

Modulation Levels (M)

Test Baud Rate (MBaud)

—

Max Baud Rate (MBaud)

—

Max Bit Rate (Mbps)

—

Spectral Efficiency (bps/Hz)

—

ISI Status

Note: For satellite passband transmission, occupied bandwidth = (1+α) × R_s. The simulation assumes a typical satellite transponder model.

Simulation 4: Satellite Link Baseband Parameter Calculator

Link Budget

Orbit

Frequency (GHz)

Tx Power (dBW)

Tx Antenna (m)

Rx Antenna (m)

System Noise Temp (K)

Required Eₑ/N₀ (dB)

Roll-off (α)

—

Path Loss (dB)

—

C/N₀ (dB-Hz)

—

Max Bit Rate (Mbps)

—

Max Baud Rate (MBaud)

—

Link Margin (dB)

—

Occupied BW (MHz)

Simulation 5: BER Performance Analyzer

AWGN Channel

Modulation

Target BER

—

BPSK Eₑ/N₀ (dB)

—

QPSK Eₑ/N₀ (dB)

—

8-PSK Eₑ/N₀ (dB)

—

16-QAM Eₑ/N₀ (dB)

5. Guidelines for Laboratory Report Writing

Your laboratory report should be a formal technical document following the structure below. Use clear, concise engineering language. All figures must be numbered and captioned.

5.1 Title Page

Experiment title: Digital Baseband Signals in Satellite Communication
Student name, ID, and group number
Course code and name (e.g., SCE 3104: Satellite Communication Systems)
Date of experiment and submission date
Lecturer name

5.2 Abstract (150–200 words)

Summarize the objectives, key methods (line codes analyzed, satellite link parameters measured), principal results (maximum baud rate, link margin, BER performance), and main conclusions.

5.3 Introduction

Explain the importance of digital baseband signals in satellite communication systems.
State the specific objectives of this experiment.
Provide context on why baud rate limitation is critical for satellite transponders.

5.4 Theory

Summarize line coding principles (do not copy the entire theory section).
Present the Nyquist criterion and raised-cosine filtering equations.
Derive the satellite link budget equation used in Experiment 4.
Include the BER equations for the modulation schemes analyzed.

5.5 Equipment and Simulation Setup

List the virtual instruments used (Signal Generator, Eye Diagram Analyzer, Baud Rate Analyzer, Link Calculator, BER Analyzer).
Document the default and modified parameter settings for each experiment.

5.6 Procedure and Results

Present results for each experiment in subsections:

Experiment 1: Include waveform screenshots for each line code. Tabulate measured vs theoretical pulse width, duty cycle, and bandwidth.
Experiment 2: Include eye diagram screenshots at SNR = 20 dB, 10 dB, and 5 dB. Plot eye opening vs SNR.
Experiment 3: Tabulate maximum baud rate for α = 0.2, 0.35, 0.5. Show the ISI threshold.
Experiment 4: Present the complete link budget table. Show calculations for path loss, C/N₀, and maximum baud rate.
Experiment 5: Include the BER curve plot. Tabulate required E_b/N₀ for each modulation scheme at the target BER.

5.7 Discussion and Analysis

Compare the bandwidth efficiency of different line codes. Which is most suitable for bandwidth-limited satellite channels?
Discuss the relationship between baud rate, channel bandwidth, and roll-off factor. What happens when the baud rate exceeds the Nyquist limit?
Analyze the eye diagram results: how does timing jitter affect the sampling instant?
Evaluate the satellite link: is the link margin adequate? How would rain fade (additional 3–6 dB loss) affect the maximum baud rate?
Compare the power efficiency vs spectral efficiency trade-off among BPSK, QPSK, and 16-QAM.

5.8 Conclusion

Summarize the key findings. State whether the objectives were met. Identify any sources of error or limitation in the virtual simulation.

5.9 References

List all textbooks, standards, and papers cited using IEEE citation format. Include at least:

Sklar, B., Digital Communications: Fundamentals and Applications, 2nd ed.
Roddy, D., Satellite Communications, 4th ed.
Proakis, J. G. & Salehi, M., Digital Communications, 5th ed.
ITU-R Recommendations for satellite link design.

5.10 Appendices (if any)

Include raw data tables, additional plots, or MATLAB/Python verification scripts.

Plagiarism Warning: All calculations, plots, and discussions must reflect your own work. Identical submissions will receive zero marks. Cite all external sources properly.

Grading Rubric: Theory (20%), Procedure & Results (30%), Discussion & Analysis (30%), Presentation & Formatting (10%), Conclusion & References (10%).

Virtual Laboratory