Advanced Communication Engg. Lab (EC-804) - Unit 3 Short Notes

EC-804: Advanced Communication Engineering Lab - UNIT 3 SHORT NOTES

Core Theme: Implementation, Simulation & Performance Analysis of Digital & Advanced Modulation Schemes in AWGN.

3.1 Fundamentals & Review (Prerequisite for Lab)

3.1.1 Review of Key Digital Modulation Schemes

• Binary Modulation:

  • BPSK (Binary Phase Shift Keying): 2 phases (0°, 180°). Most power-efficient among binary schemes.

  • BASK (Binary Amplitude Shift Keying): 2 amplitudes (on/off). Sensitive to noise/non-linearities.

  • BFSK (Binary Frequency Shift Keying): 2 frequencies. Better noise immunity than BASK, larger bandwidth.

• M-ary Modulation (M > 2): Transmits log2(M) bits per symbol. Trade-off: Higher bandwidth efficiency vs. higher power requirement (closer constellation points).

  • M-PSK (e.g., QPSK): Constant envelope. QPSK (4 phases) has same BER as BPSK but doubles bandwidth efficiency.

  • M-QAM (e.g., 16-QAM, 64-QAM): Both amplitude & phase. Higher bandwidth efficiency but not constant envelope (sensitive to non-linearities). BER increases with M.

  • M-FSK: Orthogonal signals. Very high bandwidth requirement, excellent error performance in low SNR.

3.1.2 Review of Noise and Channel Models

• AWGN Channel: Additive White Gaussian Noise. r(t) = s(t) + n(t), where n(t) is zero-mean Gaussian with PSD N0/2.

• Key Parameters:

  • SNR (Signal-to-Noise Ratio): SNR = (Signal Power) / (Noise Power).

  • Eb/N0 (Energy per Bit to Noise PSD): Fundamental performance metric. Eb/N0 = (SNR) / (R_b / B) where R_b is bit rate, B is bandwidth.

  • Es/N0 (Energy per Symbol to Noise PSD): Es/N0 = (log2(M)) * (Eb/N0).

3.1.3 Review of Performance Metrics

• BER (Bit Error Rate): P_b = (Number of bit errors) / (Total bits transmitted).

• SER (Symbol Error Rate): P_s = (Number of symbol errors) / (Total symbols transmitted). For M-PSK/M-QAM: P_b ≈ P_s / log2(M) (high SNR).

• Theoretical BER in AWGN (Coherent Detection):

  • BPSK/QPSK:

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

*   **M-PSK (M>4):** 

$$P_s \approx 2Q\left(\sqrt{\frac{2E_b}{N_0} \log_2 M} \sin\left(\frac{\pi}{M}\right)\right)$$

*   **Square M-QAM:** 

$$P_s \approx 4\left(1 - \frac{1}{\sqrt{M}}\right) Q\left(\sqrt{\frac{3E_b}{N_0 (M-1)}}\right)$$

> [!TIP] **Exam Focus:** Remember BPSK/QPSK have same BER curve. QAM's `3/(M-1)` factor shows its inferior noise immunity compared to PSK at same `Eb/N0`.

• Bandwidth Efficiency (η): η = (R_b) / (B) [bits/sec/Hz]. For M-ary signaling: η ≈ log2(M) (with ideal Nyquist pulses).

3.2 ★ High-Frequency Lab Experiment: Simulation & BER Analysis

3.2.1 Experiment 1: BER vs. Eb/N0 Performance in AWGN

• Objective: Simulate and plot theoretical vs. simulated BER curves for BPSK, QPSK, 16-QAM.

• MATLAB/Python Implementation Flow:

  1. bits = randi([0 1], N, 1);

  2. Modulate: Map bits to symbols (e.g., qammod, pskmod). Apply pulse shaping (e.g., rcosdesign).

  3. AWGN Channel: rx_sig = awgn(tx_sig, EbN0_dB, 'measured'); or manually scale noise variance: σ = sqrt(N0/2).

  4. Demodulate: Matched filter, downsample, symbol detection (qamdemod, pskdemod).

  5. [num_errors, ber] = biterr(bits, rx_bits);

  6. Loop over EbN0_dB range, store ber.

• Key Plot: Semilogy plot (semilogy(EbN0_dB, ber_theory, 'b-', EbN0_dB, ber_sim, 'r*')).

• Viva Q&A:

  • Why does 16-QAM have higher BER than QPSK for same Eb/N0? Because 16-QAM constellation points are closer together (smaller minimum Euclidean distance d_min), making them more susceptible to noise-induced mis-detection.

  • Effect of Pulse Shaping? Raised Cosine filters eliminate ISI (Inter-Symbol Interference) but increase bandwidth slightly (B = (1+α)R_s, where α is roll-off). Without it, ISI degrades BER.

3.2.2 Experiment 2: Constellation & Eye Diagram Analysis

• Constellation Diagram: Plot I vs. Q of received symbols.

  • Clean Signal: Sharp, distinct points.

  • With Noise: Points spread around ideal locations (Gaussian cloud). Spread ∝ noise variance.

  • With Phase Offset: Constellation rotates.

• Eye Diagram: Overlay multiple symbol-period segments of baseband I/Q waveform.

  • Open Eye: Good timing recovery, low ISI.

  • Closed Eye: Severe ISI, timing jitter, or insufficient bandwidth.

  • Vertical Opening: Related to noise margin.

  • Horizontal Opening: Related to timing jitter/uncertainty.

3.3 ★ High-Frequency Lab Experiment: Advanced & Multi-Carrier Systems

3.3.1 Experiment 3: OFDM System Simulation

• Objective: Simulate OFDM and demonstrate robustness against frequency-selective fading.

• OFDM Transmitter Block Diagram:

  
  Serial Bits → Parallel (N_sub groups) → QAM/PSK Mapper → IFFT (N_sub) → Add Cyclic Prefix (N_cp) → Parallel-to-Serial → DAC/Upconversion → Channel
  
  

• Cyclic Prefix (CP): Copy last N_cp samples of IFFT output to prefix. Purposes:

  1. Convert linear convolution (multipath channel) into cyclic convolution.

  2. Combat ISI by making channel appear "flat" per subcarrier (if CP length > channel delay spread).

  3. Maintain subcarrier orthogonality.

• Channel Models:

  • Flat Fading: All frequencies fade equally. Single-tap channel in frequency domain.

  • Frequency-Selective Fading: Different gains/phases across bandwidth. Multi-tap channel. OFDM excels here by dividing wideband channel into many narrowband flat-fading subcarriers.

• Viva Focus: Why CP? It preserves orthogonality in multipath and provides a guard interval against ISI from previous OFDM symbols.

3.3.2 Experiment 4: Introduction to DSSS (Direct Sequence Spread Spectrum)

• Objective: Simulate DSSS and measure processing gain.

• Core Concept: Spread narrowband data d(t) with wideband PN (Pseudo-Noise) sequence c(t) (chip rate R_c >> R_b). Transmitted signal: s(t) = d(t) * c(t).

• Processing Gain (G_p): G_p = (Spread Bandwidth) / (Original Data Bandwidth) ≈ R_c / R_b (for BPSK). In dB: G_p(dB) = 10 log10(R_c / R_b).

• Jamming Resistance: Narrowband jammer's power is spread over wide bandwidth at receiver after despreading. Desired signal is de-spread (correlated with synchronized PN) back to original bandwidth, while jammer remains spread. BER improvement ≈ G_p.

• Viva Focus: CDMA Principle: Multiple users use orthogonal or quasi-orthogonal PN sequences to share same spectrum. Despreading selects intended user's signal.

3.4 ★ High-Frequency Lab Experiment: Error Control Coding

3.4.1 Experiment 5: Block Codes (Hamming (7,4))

• Objective: Encode, introduce error, correct using syndrome.

• Generator Matrix (G): [I_k | P] where I_k is k×k identity, P is parity submatrix. For (7,4): k=4, n=7.

• Parity-Check Matrix (H): [P^T | I_{n-k}]. Syndrome: S = r * H^T.

• Syndrome Decoding: Each single-bit error pattern has unique non-zero syndrome. Lookup table corrects error.

• Coding Gain: Improvement in Eb/N0 for a given BER due to coding. For Hamming(7,4), theoretical coding gain ≈ 1.5 dB at BER=10^-5.

• Rate (R): R = k/n = 4/7 ≈ 0.57. Bandwidth expansion by factor 1/R.

3.4.2 Experiment 6: Convolutional Codes & Viterbi Decoding

• Encoder: Shift registers (constraint length K) with modulo-2 adders. Outputs n bits per input bit (rate R=1/n or k/n).

• Trellis Diagram: State diagram vs. time. Each branch labeled with input & output bits.

• Viterbi Algorithm (Hard Decision):

  1. Branch Metric (BM): Hamming distance between received bits & expected branch output.

  2. Path Metric (PM): Cumulative BM for a path to a state.

  3. Add-Compare-Select (ACS): For each state, add BM to PMs of predecessor states, select minimum.

  4. Traceback: After L symbols (traceback depth), trace back from state with minimum PM to recover path (information bits).

• Free Distance (d_free): Minimum Hamming distance between any two diverging-then-remerging trellis paths. Determines error floor: P_b ≈ (d_free) * Q(d_free * sqrt(2R Eb/N0)).

• Viva Focus: Traceback Depth (L): Must be ≥ 5K for near-optimal performance. Larger L → more delay & memory.

3.5 ★ High-Frequency Lab Experiment: Practical System & Hardware Aspects

3.5.1 Experiment 7: SDR-Based Modulation/Demodulation

• Tools: USRP, ADALM-Pluto, RTL-SDR with GNU Radio or MATLAB/Simulink.

• Key Practical Challenges:

  • Carrier Frequency Offset (CFO): Mismatch between TX & RX local oscillators. Causes constellation rotation.

  • Phase Noise: Random phase jitter in oscillators → constellation blurring.

  • Timing Offset/Synchronization: Need Timing Recovery Loop (e.g., Gardner, Mueller & Müller) to sample at optimal instants.

  • Carrier Synchronization: Need Phase-Locked Loop (PLL), e.g., Costas Loop for BPSK/QPSK, to remove CFO and phase noise.

• Viva Focus: Costas Loop Operation: Uses error signal from multiplying I & Q branches to drive VCO, locking to carrier phase. Suppresses 180° ambiguity for BPSK.

3.5.2 Experiment 8: Spectrum Sensing & Analysis

• Tools: Spectrum Analyzer (hardware) or SDR with FFT visualization (software).

• Tasks:

  • Capture Power Spectral Density (PSD) of BPSK, QPSK, 16-QAM, OFDM.

  • Measure Occupied Bandwidth: Bandwidth containing ~99% of signal power.

  • Observe Pulse Shaping Effect: Compare spectra of rectangular pulses (sinc^2 shape, high sidelobes) vs. Raised Cosine (faster roll-off, lower out-of-band emissions).

• Key Relationships:

  • BPSK/QPSK: Bandwidth ≈ 2 * R_s (for rectangular pulses) or (1+α)R_s (with RC filter), where R_s = symbol rate.

  • 16-QAM: Same symbol rate as QPSK → same bandwidth, but carries 2x bits/symbol → higher bandwidth efficiency.

  • OFDM: Bandwidth ≈ N_sub * Δf (subcarrier spacing), but with CP overhead → effective rate lower.

3.6 Synthesis & Advanced Topics (For Report/Exam Essays)

3.6.1 Comparative Analysis of Modulation Schemes

3.6.2 Fundamental Trade-off: Bandwidth Efficiency vs. Power Efficiency

• Trade-off: As M increases in M-ary schemes (PSK/QAM):

  • Bandwidth Efficiency (η) ↑ (more bits/symbol).

  • Minimum Euclidean Distance (d_min) ↓ → Power Efficiency ↓ (higher Eb/N0 needed for same BER).

• Design Choice: Depends on channel & system constraints.

  • Power-limited channel (deep fade, satellite): Use BPSK/QPSK (low Eb/N0 req.).

  • Bandwidth-limited channel (spectrum scarce): Use High-M QAM/OFDM (high η).

3.6.3 Role of Channel Coding (FEC)

• Concept: Add redundant bits to detect/correct errors at receiver.

• Impact on BER Curve: Coding Gain – entire BER curve shifts left (requires lower Eb/N0 for same BER).

• Price Paid: Bandwidth Expansion. Effective rate R_eff = R * R_c (where R_c is code rate <1). So, Eb/N0 for coded system is compared to un-coded Eb/N0 but bandwidth-expanded.

• Net Effect: For a fixed information bit rate, coding increases required bandwidth but decreases required transmit power (or improves BER at same power).

3.6.4 Modern Context (4G/5G)

• Downlink (eNodeB/gNB → UE): Uses high-order QAM (64-QAM, 256-QAM) for high throughput.

• Waveform: OFDM (LTE) / Filtered-OFDM (5G NR) for robustness to multipath & flexible numerology.

• Channel Coding: Turbo Codes (LTE), LDPC Codes (5G NR data), Polar Codes (5G NR control).

• Multiple Access: OFDMA (orthogonal users in frequency) & SC-FDMA (uplink, lower PAPR). CDMA concepts from DSSS used in earlier 3G (WCDMA).

\boxed{\text{Core Lab Takeaway: Simulate, visualize (constellation/eye), compare BER curves, and analyze trade-offs (η vs. SNR, coding gain vs. bandwidth).}}