Advanced Communication Engg. Lab (EC-804) - Unit 5 Short Notes

UNIT 5: Advanced Digital & Wireless Communication Systems Lab

Module 1: Advanced Digital Modulation & Detection Techniques

Core Concepts:

• Quadrature Amplitude Modulation (QAM): Modulates both amplitude and phase of the carrier. An M-ary QAM signal has M distinct constellation points. Spectral Efficiency is given by:

$$\eta = \frac{\log_2 M}{T_s} \text{ (bits/s/Hz)}$$

where `T_s` is the symbol period. Higher `M` increases bandwidth efficiency but reduces noise immunity.

• Phase-Shift Keying (PSK): Modulates only the phase.

  • BPSK: 2 phases (0°, 180°). Most robust.

  • QPSK: 4 phases (45°, 135°, 225°, 315°). Equivalent to 2 BPSK streams on quadrature carriers.

  • DPSK: Differential encoding avoids need for coherent carrier recovery.

  • π/4-QPSK: Alternate constellation between 45° and 135° to reduce amplitude variations.

• Performance Metric: Bit Error Rate (BER) vs. Energy per bit to Noise Power Spectral Density ratio (E_b/N_0). Theoretical BER for coherent BPSK/QPSK in AWGN:

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

where $$\displaystyle Q(x) = \frac{1}{\sqrt{2\pi}}\int_x^\infty e^{-t^2/2} dt $$.

Lab Focus:

• Simulate M-QAM (e.g., 16-QAM, 64-QAM) and M-PSK (QPSK, 8-PSK) systems.

• Generate and visualize constellation diagrams at receiver.

• Measure and plot BER vs. E_b/N_0 curves over AWGN channel.

• Compare performance: BPSK > QPSK > 16-QAM > 64-QAM in noise (for same E_b/N_0).

[!TIP] Exam Focus: Be prepared to sketch constellation diagrams for different modulations and explain why higher-order QAM is more bandwidth-efficient but less power-efficient.

Module 2: Orthogonal Frequency Division Multiplexing (OFDM)

Core Concepts:

• Principle: Splits high-rate data stream into N parallel low-rate subcarriers. Orthogonality between subcarriers allows tight spacing without ICI (Inter-Carrier Interference).

$$f_k = \frac{k}{T_s}, \quad k=0,1,...,N-1$$

where `T_s` is the OFDM symbol duration.

• Implementation: Uses IFFT at transmitter to generate parallel subcarriers, and FFT at receiver.

• Cyclic Prefix (CP): Copy of end of OFDM symbol prepended to front. Length T_g must be > maximum channel delay spread to combat ISI (Inter-Symbol Interference).

  Effective Symbol Duration: $$\displaystyle T_{total} = T_s + T_g $$

  Spectral Efficiency Loss: $$\displaystyle \frac{T_s}{T_s + T_g} $$

• Advantages: Robust against frequency-selective fading (each subcarrier sees flat fading). Simple equalization (one-tap per subcarrier).

Lab Focus:

• Implement OFDM transceiver chain (IFFT -> CP add -> serial -> channel -> FFT -> CP remove).

• Vary CP length and observe BER performance in a multipath channel.

• Compare OFDM vs. single-carrier system in a channel with deep fades.

• Analyze ICI if Doppler spread is high (loss of orthogonality).

[!TIP] Common Pitfall: Confusing the role of CP. It converts linear convolution (from multipath) into circular convolution, which FFT can invert. Without CP, ISI is severe.

Module 3: Error Control Coding & Decoding

Core Concepts:

• Block Codes (n, k): Maps k info bits to n code bits. Adds n-k parity bits.

  • Hamming Code (7,4): Can correct single-bit error. Syndrome S = rH^T identifies error location.

  • BCH/Reed-Solomon: Correct multiple errors (t). RS is non-binary, good for burst errors.

• Convolutional Codes: Generated by shift registers and modulo-2 adders. Specified by (n, k, K) where K is constraint length.

  • Viterbi Algorithm (VA): Maximum Likelihood (ML) decoding via trellis diagram. Uses traceback depth (typically 5-7 times K).

• Turbo Codes & LDPC: Iterative decoding (e.g., BCJR algorithm for Turbo, belief propagation for LDPC). Near-Shannon limit performance. Coding Gain = improvement in E_b/N_0 for same BER.

Lab Focus:

• Simulate Hamming (7,4) encoder/decoder (syndrome table).

• Implement convolutional encoder and Viterbi decoder (hard/soft decision). Plot BER vs. E_b/N_0 for uncoded vs. coded system.

• Simulate Turbo/LDPC encoder and iterative decoder. Observe error floor at high SNR.

• Measure coding gain at a target BER (e.g., 10^-5).

[!TIP] Key Formula: Coding Gain (dB) = (E_b/N_0)_uncoded - (E_b/N_0)_coded at same BER.

Module 4: Multiple Input Multiple Output (MIMO) Systems

Core Concepts:

• System Model: y = Hx + n, where H is N_r x N_t channel matrix, x is N_t x 1 transmit vector.

• Gains:

  1. Spatial Multiplexing Gain: Transmit parallel data streams. Capacity increases linearly with min(N_t, N_r).

  2. Diversity Gain: Improves reliability (e.g., Alamouti STBC).

• Channel Capacity (Water-Filling): For parallel eigen-channels of H^H H:

$$C = \sum_{i=1}^{N_{min}} \log_2 \left(1 + \frac{P_i \lambda_i}{N_0}\right)$$

where `λ_i` are eigenvalues, `P_i` power allocated (water-filling).

• Alamouti STBC (2x1 or 2x2): Transmits two symbols over two time slots using orthogonal code. Full diversity order, simple ML decoding.

$$\begin{bmatrix} s_1 & -s_2^* \\ s_2 & s_1^* \end{bmatrix}$$

• Detection Techniques:

  • Zero-Forcing (ZF): x̂ = (H^H H)^{-1} H^H y. Noise enhancement.

  • Minimum Mean Square Error (MMSE): x̂ = (H^H H + N_0 I)^{-1} H^H y. Balances interference and noise.

  • Maximum Likelihood (ML): Optimal but complex (exponential in N_t).

Lab Focus:

• Simulate flat-fading MIMO channel (H with i.i.d. Rayleigh entries).

• Plot MIMO capacity vs. SNR for different (N_t, N_r) configurations.

• Implement Alamouti STBC encoder/decoder and compare BER with SISO.

• Compare ZF, MMSE, and ML detectors for 2x2 MIMO.

Module 5: Spread Spectrum & CDMA Techniques

Core Concepts:

• Direct Sequence Spread Spectrum (DSSS): Data modulated by high-rate PN sequence (chip rate R_c >> R_b).

  • Processing Gain (PG): $$\displaystyle G_p = \frac{R_c}{R_b} = \frac{T_b}{T_c} $$. Measures interference/jamming suppression.

  • Correlation Property: PN sequences have low cross-correlation (for different users) and high auto-correlation (for synchronization).

• Frequency Hopping (FHSS): Carrier frequency changes according to PN sequence.

• CDMA:

  • Uses orthogonal codes (Walsh-Hadamard) for different users in same band.

  • Near-Far Problem: Strong signal from nearby user overwhelms weak signal from distant user. Requires power control.

  • RAKE Receiver: For multipath channels. Uses multiple fingers to align and combine delayed multipath components (each finger correlates with PN sequence at a specific delay).

Lab Focus:

• Generate m-sequences (maximal length LFSR) and Gold codes. Measure their auto/cross-correlation.

• Simulate DSSS system: Spread BPSK with PN, transmit over AWGN + narrowband jammer, despread at receiver. Show BER improvement with higher PG.

• Simulate basic CDMA with 2-3 users using orthogonal codes. Demonstrate near-far effect.

• Implement a simple 2-finger RAKE receiver for a 2-path channel.

[!TIP] Key Insight: DSSS's interference rejection comes from despreading: only the desired signal's PN correlates to a peak; interferers (including other users if codes not perfectly orthogonal) spread to noise-like power.

Module 6: Software Defined Radio (SDR) Platforms & Practical Measurements

Core Concepts:

• SDR Architecture: RF Front-end (up/down conversion, filtering) -> ADC/DAC -> FPGA/DSP/CPU (baseband processing). Flexibility in waveform definition.

• Common Platforms:

  • USRP (Ettus): High-performance, with FPGA and host CPU.

  • RTL-SDR: Low-cost DVB-T dongle (receive-only, limited bandwidth).

  • ADALM-PLUTO: Low-cost, full-duplex transceiver.

• Software Framework: GNU Radio (most common) provides blocks for modulation, filtering, channel coding, etc., connected in a flowgraph.

Lab Focus (Typical GNU Radio Experiments):

1. Spectrum Sensing: Use osmocom_fft or qtgui_freq_sink_c to visualize RF spectrum (FM band, Wi-Fi channels).

2. Passive Reception: Demodulate FM radio (WBFM block), decode ADS-B messages (from aircraft).

3. Active Transceiver: Build a BPSK/QPSK transceiver flowgraph. Transmit a file/packet, receive, and calculate BER.

4. Channel Emulation: Insert channel_model block (AWGN, fading, multipath) and observe performance degradation.

5. Implement Simple Coding: Add convolutional encoder/decoder blocks to transceiver.

[!TIP] Practical Note: SDR experiments highlight real-world impairments: frequency/phase offset, sampling clock error, non-linearities. Use frequency_modulator_fc and costas_loop blocks for carrier recovery.

Module 7: Channel Modeling & Simulation

Core Concepts:

• Large-Scale Fading: Path Loss (distance-dependent, $$\displaystyle PL \propto d^{-\alpha} $$) and Shadowing (log-normal distribution).

• Small-Scale Fading (Multipath):

  • Rayleigh Fading: No dominant line-of-sight (LoS). Envelope |h| is Rayleigh distributed. Phase uniform [0, 2π).

  • Rician Fading: Dominant LoS component. K-factor = power of LoS / power of scattered.

  • Doppler Shift: $$\displaystyle f_d = \frac{v f_c}{c} $$ (max shift). Doppler Spread determines channel coherence time.

• Channel Models:

  • Flat Fading: Bandwidth < coherence bandwidth. Single tap h(t).

  • Frequency-Selective Fading: Bandwidth > coherence bandwidth. Multi-tap tapped-delay-line model. Power Delay Profile (PDP).

  • Clarke's Model: Simulates Rayleigh fading with Doppler spectrum (Jakes' method).

Lab Focus:

• Generate Rayleigh/Rician fading coefficients (using randn + filtering for Doppler).

• Simulate a two-path channel (e.g., h = [1, 0.5*exp(j*2*pi*f_d*t)]). Observe frequency selectivity (notches in frequency response).

• Plot Doppler Power Spectrum (Jakes' spectrum).

• Run a communication system (e.g., QPSK) over generated fading channel. Compare BER with AWGN case.

• (If equipment available) Use a channel sounder to measure impulse response of a real environment.

[!TIP] Critical Relationship: Coherence Time T_c ≈ 1/(2f_d) and Coherence Bandwidth B_c ≈ 1/(5τ_max) (τ_max = max delay spread) determine if channel is flat/fast fading.

Module 8: Advanced System-Level Analysis & Trade-offs

Core Concepts:

• Link Budget: $$\displaystyle P_{rx} = P_{tx} + G_{tx} - PL + G_{rx} $$. Must be > receiver sensitivity.

• Key Metrics:

  • Spectral Efficiency (SE): $$\displaystyle \eta = R_b / B $$ (bits/s/Hz). Target for 5G: > 30 b/s/Hz.

  • Energy Efficiency (EE): $$\displaystyle \frac{R_b}{P_{tx}} $$ (bits/Joule). Crucial for IoT.

  • Latency & Reliability: e.g., URLLC requires < 1ms latency, > 99.999% reliability.

• Fundamental Trade-offs:

  • Bandwidth vs. Power: Higher bandwidth (higher SE) allows lower E_b/N_0 for same rate (Shannon: $$\displaystyle C = B \log_2(1+SNR) $$).

  • Modulation vs. Coding: High-order modulation (high SE) needs strong coding (low rate) to maintain BER.

  • Diversity vs. Multiplexing (MIMO): Diversity improves reliability (lower BER), multiplexing improves rate (higher SE). Alamouti gives diversity, spatial multiplexing gives rate.

Lab Focus (Capstone Project):

• Design a point-to-point link (e.g., indoor Wi-Fi-like) with specifications: Data rate, range, BER target.

• Choose & Simulate: Modulation (QPSK/16-QAM), Coding (Turbo/LDPC rate 1/2), MIMO (2x2 Alamouti or spatial multiplexing), OFDM (N=64, CP=16).

• Perform Link Budget: Calculate required P_tx given path loss model (e.g., log-distance).

• Simulate End-to-End: Generate bits -> encode -> modulate -> OFDM -> MIMO -> channel (multipath fading) -> MIMO detector -> OFDM demod -> decode -> measure BER.

• Analyze: Vary one parameter (e.g., coding rate, MIMO config) and plot SE vs. EE or BER vs. SNR. Discuss trade-offs made.

[!TIP] Exam Strategy: For system design questions, always state assumptions (channel model, mobility, hardware constraints) and justify choices based on the required trade-off (e.g., "For high SE, we choose 64-QAM with rate-1/2 LDPC, accepting higher required SNR").