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EC-804 · Advanced Communication Engg. Lab/Quick Revision Short Notes

Advanced Communication Engg. Lab (EC-804) - Unit 2 Short Notes

1.0 Digital Modulation Techniques & Spectral Analysis

1.1 Binary Phase Shift Keying (BPSK)

  • Theory:

    • Definition: A digital modulation scheme where the phase of a carrier is shifted by 180° to represent binary '1' and '0'.

    • Constellation: Two points on the real axis (in-phase) at ±A.

    • Mathematical Model:

$$ s(t) = \sqrt{\frac{2E_b}{T_b}} \cos(2\pi f_c t + \pi(1-b)) $$

    where $b \in \{0,1\}$, $$\displaystyle E_b $$ is bit energy, $$\displaystyle T_b $$ is bit duration.

*   **Bandwidth:** Approximately $$\displaystyle 2/T_b $$ (null-to-null) for rectangular pulses.

  • Lab Implementation:

    • Use a function generator to create a binary NRZ data stream.

    • Feed data into a BPSK modulator (balanced mixer or IC) with a continuous wave (CW) carrier.

  • Measurement & Analysis:

    • Spectrum Analyzer: Observe a main lobe with first nulls at $$\displaystyle f_c \pm 1/T_b $$.

    • Eye Diagram: Open eye with maximum vertical opening at the sampling instant.

    • Power Spectral Density (PSD): Single-sided PSD has a $$\displaystyle \text{sinc}^2(fT_b) $$ shape.

[!TIP] Exam Focus: Be able to sketch the BPSK constellation and spectrum. Remember that BPSK has better BER performance than QPSK for the same $$\displaystyle E_b/N_0 $$ but is half as spectrally efficient.

1.2 Quadrature Phase Shift Keying (QPSK) & Offset-QPSK (OQPSK)

  • Theory:

    • QPSK (4-PSK): Transmits 2 bits per symbol using four phase states (45°, 135°, 225°, 315°).

    • Spectral Efficiency: 2 bits/s/Hz (twice BPSK).

    • Phase Transitions: 180° jumps possible (e.g., 45°→225°), causing envelope variations.

    • OQPSK: Offsets the Q-channel data by $$\displaystyle T_b/2 $$ relative to I-channel. Eliminates 180° phase jumps, reducing envelope fluctuations and spectral regrowth.

  • Lab Implementation:

    • I/Q Modulation: Split data into even (I) and odd (Q) bits. Use two BPSK modulators on carriers in quadrature ($$\displaystyle f_c $$ and $$\displaystyle f_c \cos/\sin $$), then sum.

    • For OQPSK, delay one data stream by half a symbol period before I/Q modulation.

  • Measurement & Analysis:

    • Constellation Diagram: Four distinct points. OQPSK shows transitions only through adjacent points.

    • Phase Noise Impact: More sensitive than BPSK due to narrower Euclidean distance between points.

    • Spectral Regrowth: OQPSK spectrum is narrower than QPSK for the same pulse shaping.

Feature BPSK QPSK OQPSK
Bits/Symbol 1 2 2
Phase States 2 4 4
Max Phase Jump 180° 180° 90°
Envelope Variation Constant High Low
Bandwidth (same shaping) $$\displaystyle 2R_b $$ $$\displaystyle R_b $$ $$\displaystyle \approx R_b $$

1.3 Quadrature Amplitude Modulation (QAM) - 16-QAM, 64-QAM

  • Theory:

    • Definition: Modulation using both amplitude and phase of the carrier. 16-QAM has 16 distinct states (4 amplitude levels × 4 phases, or square grid).

    • SNR Requirement: Higher order QAM (e.g., 64-QAM) requires significantly higher $$\displaystyle E_b/N_0 $$ for same BER due to reduced Euclidean distance between constellation points.

    • Spectral Efficiency: 4 bits/s/Hz for 16-QAM, 6 bits/s/Hz for 64-QAM.

  • Lab Implementation:

    • Use a vector modulator. Input I(t) and Q(t) baseband signals (from digital-to-analog converters or filter outputs) control the amplitude and phase of the RF carrier.

  • Measurement & Analysis:

    • Constellation Diagram: Square grid for square QAM. Points should be sharp. Spreading indicates noise, distortion, or synchronization errors.

    • EVM (Error Vector Magnitude): Key metric.

$$ \text{EVM} = \frac{\sqrt{\frac{1}{N}\sum_{i=1}^{N} |e_i|^2}}{|S_{ref}|} \times 100\% $$

    where $$\displaystyle e_i $$ is the error vector, $$\displaystyle S_{ref} $$ is reference constellation point magnitude. Lower EVM is better.

*   **Impact of Non-linearities:** Amplifier compression causes constellation point compression and rotation (AM-AM/AM-PM conversion).

[!TIP] Common Pitfall: Do not confuse EVM with MER (Modulation Error Ratio). EVM is a percentage; MER is in dB. Both measure the same underlying quality.

2.0 Pulse Shaping & Inter-Symbol Interference (ISI)

2.1 Nyquist Criterion for Zero ISI

  • Theory:

    • Goal: Design a pulse shape $p(t)$ such that sampled output at symbol intervals $$\displaystyle kT_s $$ is zero for all $k \neq 0$ (no ISI).

    • Nyquist Criterion (Frequency Domain): The overall system transfer function $H(f)$ must satisfy:

$$ \sum_{k=-\infty}^{\infty} H(f + kR_s) = T_s $$

    where $$\displaystyle R_s = 1/T_s $$ is symbol rate.

*   **Ideal Pulse (Sinc):** $$\displaystyle p(t) = \text{sinc}(t/T_s) $$. Has infinite time duration and zero ISI but unrealistic bandwidth.

*   **Roll-off Factor (α):** Used in practical filters to trade bandwidth for time-domain decay. $0 \leq \alpha \leq 1$.

2.2 Raised Cosine & Root Raised Cosine Filters

  • Theory:

    • Raised Cosine (RC) Filter: Frequency response:

$$ H_{RC}(f) = \begin{cases} T_s & |f| \leq \frac{1-\alpha}{2T_s} \\ \frac{T_s}{2}\left[1 + \cos\left(\frac{\pi T_s}{\alpha}\left(|f| - \frac{1-\alpha}{2T_s}\right)\right)\right] & \frac{1-\alpha}{2T_s} < |f| \leq \frac{1+\alpha}{2T_s} \\ 0 & |f| > \frac{1+\alpha}{2T_s} \end{cases} $$

*   **Bandwidth:** $$\displaystyle B = \frac{1+\alpha}{2T_s} = \frac{R_s(1+\alpha)}{2} $$.

*   **Root Raised Cosine (RRC):** $$\displaystyle |H_{RRC}(f)| = \sqrt{|H_{RC}(f)|} $$. Used in pairs (transmitter and receiver) for matched filtering, minimizing total noise and ISI.

  • Lab Implementation:

    • Implement digitally using FIR filter design (e.g., firrcos in MATLAB/Octave) or use dedicated filter modules.

    • Configure roll-off factor α (common values: 0.2, 0.35, 0.5).

  • Measurement & Analysis:

    • Eye Diagram: Primary tool. Open eye indicates low ISI. α affects the eye closure and rise/fall times.

    • Effect of α:

      • α = 0 (ideal sinc): Minimum bandwidth ($$\displaystyle R_s/2 $$), but slow time decay → hard to implement.

      • α = 1: Maximum bandwidth ($$\displaystyle R_s $$), faster time decay → easier implementation, more tolerance to timing errors.

    • Matched Filter Pair: Transmit RRC, receive RRC → overall response is RC, satisfying Nyquist criterion.

[!TIP] Exam Key: You will likely be asked to plot the frequency response of RC/RRC for given α and symbol rate, and explain the effect of α on bandwidth and eye diagram.

3.0 Carrier & Symbol Synchronization Techniques

3.1 Need for Synchronization

  • Coherent demodulation (BPSK, QPSK, QAM) requires precise knowledge of carrier phase/frequency and symbol timing at the receiver. Mismatch causes performance degradation.

3.2 Carrier Phase Recovery: Costas Loop for BPSK/QPSK

  • Theory:

    • A Phase-Locked Loop (PLL) circuit that locks to the suppressed-carrier phase of the BPSK/QPSK signal.

    • Costas Loop Structure: Uses two mixers (I and Q), low-pass filters, and a multiplier/phase detector. The error signal drives a VCO.

    • Lock Range & Pull-in Range: Range of initial frequency offset over which the loop can acquire lock.

  • Lab Implementation:

    • Simulate using software (e.g., Simulink) or observe on a hardware communication trainer.

    • Inject a frequency offset in the transmitted carrier to test acquisition.

  • Measurement & Analysis:

    • Lock Time: Time from start to stable phase lock. Depends on loop bandwidth.

    • Phase Error: Residual steady-state error after lock. Should be near zero for BPSK/QPSK.

    • Spectrum: VCO control voltage spectrum shows a sharp peak at the offset frequency during acquisition.

3.3 Symbol Timing Recovery: Early-Late Gate, Mueller & Müller Algorithm

  • Theory:

    • Early-Late Gate: Compare signal energy in two partial symbol periods (early and late). Error signal proportional to timing offset.

    • Mueller & Müller (M&M) Algorithm: A decision-directed timing error detector (TED).

$$ e(t) = x(t) \cdot [\text{sign}(x(t-T_s/2)) - \text{sign}(x(t+T_s/2))] $$

    where $x(t)$ is the matched filter output. Works for **Nyquist pulses**.

  • Lab Implementation:

    • Implement TED in software after a matched filter. Use a digital interpolator to adjust sampling phase.

  • Measurement & Analysis:

    • Eye Diagram Sampling Point: The vertical opening should be maximum at the recovered sampling instant.

    • Jitter: Variance of the recovered clock edges. Low jitter indicates stable timing recovery.

    • Convergence: Plot timing error vs. time. Should converge to zero mean.

[!TIP] Common Confusion: The M&M algorithm requires Nyquist pulses (zero-ISI) at the matched filter output. If ISI is present, its performance degrades.

4.0 Channel Coding & Error Performance Analysis

4.1 Linear Block Codes (e.g., Hamming (7,4))

  • Theory:

    • Parameters (n,k): n = total bits, k = message bits. Hamming (7,4): 4 data bits, 3 parity bits.

    • Generator Matrix (G): $$\displaystyle \mathbf{u} \mathbf{G} = \mathbf{c} $$ (encoding).

    • Parity-Check Matrix (H): $$\displaystyle \mathbf{H} \mathbf{c}^T = \mathbf{0} $$ (syndrome calculation).

    • Error Correction: Single-error correcting (SEC) for Hamming codes. Syndrome directly points to error location.

  • Lab Implementation:

    • Simulate encoder/decoder in MATLAB/Python. Generate all 16 possible (7,4) codewords.

    • Introduce single-bit errors, compute syndrome, correct.

  • Measurement & Analysis:

    • Verify all valid codewords satisfy $$\displaystyle \mathbf{H} \mathbf{c}^T = \mathbf{0} $$.

    • Count correctable vs. uncorrectable error patterns.

4.2 Convolutional Codes & Viterbi Decoding

  • Theory:

    • Encoding with memory (constraint length K). Output bits depend on current and previous input bits.

    • Represented by state diagram and trellis diagram.

    • Viterbi Algorithm: Maximum likelihood sequence estimation (MLSE). Finds the most likely path through the trellis (survivor paths).

    • Free Distance ($$\displaystyle d_{free} $$): Minimum Hamming distance between any two diverging paths. Determines error correction capability.

  • Lab Implementation:

    • Simulate a rate-1/2, K=3 convolutional encoder (octal generators, e.g., [7 5]).

    • Implement Viterbi decoder (add-compare-select, traceback).

  • Measurement & Analysis:

    • Traceback Depth: Must be > 5-7 times constraint length for near-optimal performance.

    • BER Performance: Viterbi provides coding gain over uncoded systems at moderate $$\displaystyle E_b/N_0 $$.

4.3 Bit Error Rate (BER) Measurement & Analysis

  • Theory:

    • BER vs. $$\displaystyle E_b/N_0 $$ Curves: Fundamental performance metric.

    • Theoretical BER for BPSK:

$$ P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right) \approx \frac{1}{2}\text{erfc}\left(\sqrt{\frac{E_b}{N_0}}\right) $$

*   **Coding Gain:** Difference in $$\displaystyle E_b/N_0 $$ required to achieve a target BER between coded and uncoded systems.

  • Lab Procedure:

    • Use a BER Tester or simulate an AWGN channel.

    • For each $$\displaystyle E_b/N_0 $$ value: transmit known pseudo-random bit sequence (PRBS), count bit errors, compute BER.

    • Run long enough for at least 100-1000 errors for statistical significance.

  • Analysis:

    • Plot log(BER) vs. $$\displaystyle E_b/N_0 $$ (dB) for uncoded and coded systems on same graph.

    • Compare simulated results with theoretical curves.

    • Calculate coding gain at BER = $$\displaystyle 10^{-5} $$.

    • Discuss discrepancies (finite sequence length, implementation losses, decoder errors at low $$\displaystyle E_b/N_0 $$).

[!TIP] Critical Skill: You must know how to generate an AWGN channel in simulation and calculate $$\displaystyle E_b/N_0 $$ from noise variance: $$\displaystyle \sigma_n^2 = N_0/2 $$ (one-sided) or $$\displaystyle \sigma_n^2 = N_0 $$ (two-sided). $$\displaystyle E_b = P_{signal} \cdot T_b $$.

5.0 Channel Effects & Equalization

5.1 Linear Distortion: Multipath Fading

  • Theory:

    • Multipath: Signal arrives via multiple paths with different delays → delay spread.

    • Channel Impulse Response: $$\displaystyle h(t) = \sum_{i} a_i \delta(t - \tau_i) $$.

    • Frequency-Selective Fading: Occurs when delay spread > 1/(signal bandwidth). Causes notches in frequency response.

    • Coherence Bandwidth ($$\displaystyle B_c $$): Approx. $$\displaystyle B_c \approx 1/(5\tau_{max}) $$. If signal bandwidth $$\displaystyle B_s > B_c $$, fading is frequency-selective → ISI.

5.2 Adaptive Equalization

  • Theory:

    • Goal: Compensate for channel distortion by adjusting filter coefficients automatically.

    • Linear Equalizer (LE): Tries to invert channel. Can amplify noise at frequencies with deep fades.

    • Decision Feedback Equalizer (DFE): Uses past decisions to cancel post-cursor ISI. No noise amplification, but error propagation possible.

    • LMS Algorithm (Stochastic Gradient Descent):

$$ \mathbf{w}(n+1) = \mathbf{w}(n) + \mu \cdot e^*(n) \cdot \mathbf{x}(n) $$

    where $\mathbf{w}$ = weight vector, $\mu$ = step size, $$\displaystyle e(n) = d(n) - y(n) $$ (error), $\mathbf{x}(n)$ = input vector.

  • Lab Implementation:

    • Simulate a multipath channel (e.g., two-tap FIR with specific delays/amplitudes).

    • Implement LMS algorithm for a transversal filter (e.g., 5-10 taps).

  • Measurement & Analysis:

    • Convergence Curve: Plot Mean Square Error (MSE) vs. iterations. Should decrease and stabilize.

    • Step Size (μ): Larger μ → faster convergence but higher steady-state MSE. Smaller μ → slower but lower MSE.

    • Post-Equalization Eye Diagram: Should open significantly compared to unequalized channel.

    • Weight Vector: Plot final coefficients. Should approximate inverse of channel.

[!TIP] Exam Scenario: You may be given a channel impulse response and asked to sketch the equalizer tap weights after convergence (inverse of channel for LE, more complex for DFE).

6.0 Advanced System Measurement & Instrumentation

6.1 Spectrum Analyzer Deep Dive

  • Key Settings:

    • Resolution Bandwidth (RBW): Filter bandwidth in IF stage. Narrower RBW → better frequency resolution, slower sweep, higher noise floor.

    • Video Bandwidth (VBW): Post-detection filter. Narrower VBW → smoother trace, slower response to signal changes.

    • Averaging (VBW or power averaging): Reduces noise variance for stable measurement.

  • Applications:

    • Occupied Bandwidth: Measure bandwidth containing 99% of total power.

    • ACPR (Adjacent Channel Power Ratio):

$$ \text{ACPR} = 10 \log_{10}\left(\frac{P_{adjacent\ channel}}{P_{main\ channel}}\right) \text{ (dB)} $$

    Critical for spectral mask compliance. Measure power in main channel vs. adjacent channel offset by specified frequency.

6.2 Vector Signal Analyzer (VSA) / SDR Basics

  • Theory:

    • VSA: Downconverts RF to baseband I/Q, digitizes, and performs digital demodulation in software.

    • I/Q Data: Complex samples $I + jQ$ represent amplitude and phase.

  • Lab Use:

    • Connect antenna or signal generator output to VSA.

    • Select modulation type (BPSK, QPSK, 16-QAM, etc.) and standard (e.g., WLAN 802.11g).

    • Measurements:

      • Constellation Diagram: Visualize modulation quality.

      • EVM: Quantifies deviation from ideal points.

      • Magnitude/Phase Error: Separate components of EVM.

      • Spectral Flatness: OFDM sub-carrier power variation.

  • Demodulation: Can decode live signals (e.g., LTE, Bluetooth) if modulation parameters are known.

6.3 Noise Figure Measurement (Y-Factor Method)

  • Theory:

    • Noise Figure (NF): Ratio of input SNR to output SNR.

$$ NF = \frac{(S_i/N_i)}{(S_o/N_o)} = \text{SNR}_{in} - \text{SNR}_{out} \text{ (linear)} $$

*   **Noise Temperature:** $$\displaystyle T_e = T_0 (F - 1) $$, where $F$ is noise factor (linear NF), $$\displaystyle T_0 = 290 $$ K.

*   **Y-Factor:**

$$ Y = \frac{P_{out,ON}}{P_{out,OFF}} $$

    where $$\displaystyle P_{out,ON} $$ = output noise power with **noise source ON**, $$\displaystyle P_{out,OFF} $$ = with noise source OFF.

*   **Excess Noise Ratio (ENR):** Specified for noise source (dB above $$\displaystyle kT_0B $$).

*   **NF Calculation:**

$$ NF = \text{ENR} - 10\log_{10}(Y - 1) \text{ (dB)} $$

  • Lab Procedure:

    1. Connect calibrated noise source (with known ENR) to DUT input.

    2. Connect DUT output to spectrum analyzer or noise figure analyzer.

    3. Measure $$\displaystyle P_{out,ON} $$ and $$\displaystyle P_{out,OFF} $$ in a fixed resolution bandwidth (RBW).

    4. Use formula above or instrument's built-in calculation.

[!TIP] Critical: Ensure same RBW for both ON and OFF measurements. The noise source must be properly calibrated and its ENR known at the operating frequency.

7.0 Laboratory Practices & Report Writing (Applied to Unit 2)

  • 7.1 Pre-Lab Preparation:

    • Review theory: modulation equations, filter responses, synchronization algorithms.

    • Draw detailed block diagrams of the experimental setup.

    • Predict expected results (e.g., approximate bandwidth, constellation shape, BER curve slope).

  • 7.2 Safe Operation of RF Equipment:

    • Spectrum Analyzer: Avoid overloading input (use attenuator), correct grounding.

    • Signal Generators: Set safe output power levels, understand modulation sources.

    • General: ESD precautions for sensitive modules, proper cable connections (50Ω systems).

  • 7.3 Data Acquisition & Documentation:

    • Record all instrument settings: frequency, span, RBW, VBW, reference level, modulation parameters.

    • Capture clear screenshots with annotations (measurement markers, cursors).

    • Maintain raw data tables: $$\displaystyle E_b/N_0 $$ values, measured BER counts, EVM values, filter coefficients.

  • 7.4 Results Analysis & Discussion:

    • Compare vs. Theory: Explain deviations (e.g., measured bandwidth > theoretical due to filter roll-off; BER floor due to implementation errors).

    • Error Sources: Identify equipment limitations (phase noise, spurs, quantization noise), channel model imperfections, synchronization inaccuracies.

    • Troubleshooting Log: Document issues encountered (e.g., no carrier lock, unstable eye diagram) and steps taken to resolve.

  • 7.5 Conclusion:

    • Summarize key observations: "QPSK provides 2x spectral efficiency of BPSK but requires 3dB higher SNR for same BER."

    • "RRC filter with α=0.25 reduced occupied bandwidth by 25% compared to α=0.5 but required more precise timing recovery."

    • "LMS equalizer with μ=0.01 converged in ~500 iterations but had 2dB higher residual MSE than μ=0.001."

    • State practical learning: "VSA EVM measurement is sensitive to carrier frequency offset; synchronization must be locked before accurate modulation quality assessment."

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