Advanced Communication Engg. Lab (EC-804) - Unit 4 Short Notes

UNIT 4: ADVANCED MODULATION, MULTIPLE ANTENNA TECHNIQUES & SYSTEM INTEGRATION

4.1 Advanced Digital Modulation & Demodulation Techniques (Software-Defined Radio Focus)

4.1.1 Implementation & Performance Analysis of Higher-Order QAM

• Definition: Quadrature Amplitude Modulation (QAM) encodes information in both the amplitude and phase of the carrier. Higher-order QAM (e.g., 64-QAM, 256-QAM) increases spectral efficiency by packing more bits per symbol.

• Constellation Diagram: Visual representation of symbol mapping. For M-QAM, constellation is a square grid of $\sqrt{M} \times \sqrt{M}$ points.

• Key Performance Metrics:

  • Error Vector Magnitude (EVM): Measures accuracy of received symbol relative to ideal.

$$ \text{EVM} = \sqrt{\frac{\frac{1}{N}\sum_{k=1}^{N} |e_k|^2}{\frac{1}{N}\sum_{k=1}^{N} |s_k|^2}} \times 100\% $$

  where $$\displaystyle e_k = r_k - s_k $$ (error vector), $$\displaystyle r_k $$ is received, $$\displaystyle s_k $$ is ideal symbol.

*   **Modulation Error Ratio (MER):** Similar to EVM but often averaged over time.

$$ \text{MER} = \frac{\text{Avg. Power of Ideal Symbols}}{\text{Avg. Power of Error Vectors}} $$

• Impact of Non-linearities & Phase Noise:

  • Non-linearities (e.g., HPA): Cause amplitude compression and phase distortion, leading to constellation point spreading and rotation. Severely degrades high-order QAM.

  • Phase Noise: Causes constellation rotation blurring, increasing symbol error rate (SER).

[!TIP] Exam Focus: Be prepared to sketch a 16-QAM/64-QAM constellation, define EVM/MER, and explain why higher-order QAM is more susceptible to impairments.

4.1.2 Pulse Shaping & Matched Filtering

• Objective: Limit signal bandwidth, minimize Inter-Symbol Interference (ISI).

• Raised Cosine (RC) Filter: Frequency response $H(f)$ has a flat passband and a roll-off region (cosine shape).

  • Roll-off factor ($\beta$): $0 \leq \beta \leq 1$. Bandwidth $$\displaystyle B = \frac{R_s}{2}(1+\beta) $$, where $$\displaystyle R_s $$ is symbol rate.

  • Impulse Response: $$\displaystyle h(t) = \frac{\sin(\pi t / T_s)}{\pi t / T_s} \cdot \frac{\cos(\pi \beta t / T_s)}{1 - (2\beta t / T_s)^2} $$ (sinc function with cosine roll-off).

• Root-Raised Cosine (RRC) Filter: $$\displaystyle |H_{RRC}(f)|^2 = |H_{RC}(f)| $$. Used in transmitter and receiver (matched filter pair) to achieve overall RC response and avoid ISI.

• Eye Diagram: Oscilloscope display of overlayed received symbols. Open eye indicates low ISI; closed eye indicates high ISI. Used to assess timing jitter and noise margin.

[!TIP] Common Pitfall: Remember RRC filters are split between Tx and Rx. The product of their transfer functions gives the overall RC response.

4.1.3 Differential Modulation Techniques (DPSK, DQPSK)

• Coherent vs. Non-coherent Detection:

  • Coherent: Requires accurate carrier phase reference at receiver. Better performance (lower BER for same $$\displaystyle E_b/N_0 $$).

  • Non-coherent (Differential): Encodes information in phase change between consecutive symbols. Does not require absolute phase reference. More robust to phase ambiguities.

• DPSK (Differential PSK): $$\displaystyle s_k = s_{k-1} \cdot e^{j\theta_k} $$, where $$\displaystyle \theta_k $$ is data bit phase ($0$ or $\pi$ for DBPSK). Demodulation by comparing phase of $$\displaystyle r_k $$ and $$\displaystyle r_{k-1} $$.

• DQPSK (Differential QPSK): Encodes 2 bits per symbol via 4 possible phase changes ($\pi/4, 3\pi/4, -\pi/4, -3\pi/4$).

• Performance in Fading: Differential detection suffers from error propagation (one error affects next decision). In fast fading, performance degrades more than coherent detection with perfect channel state information (CSI).

4.2 Multiple Input Multiple Output (MIMO) Systems

4.2.1 MIMO System Model & Capacity Fundamentals

• System Model: $$\displaystyle n_T $$ transmit, $$\displaystyle n_R $$ receive antennas.

$$ \mathbf{y} = \mathbf{H}\mathbf{x} + \mathbf{n} $$

*   $\mathbf{y}$: $$\displaystyle n_R \times 1 $$ received vector.

*   $\mathbf{H}$: $$\displaystyle n_R \times n_T $$ channel matrix (complex Gaussian entries for flat fading).

*   $\mathbf{x}$: $$\displaystyle n_T \times 1 $$ transmitted symbol vector (power constraint $$\displaystyle E[\|\mathbf{x}\|^2] \leq n_T $$).

*   $\mathbf{n}$: $$\displaystyle n_R \times 1 $$ AWGN vector ($$\displaystyle \mathcal{CN}(0, N_0\mathbf{I}) $$).

• Capacity (ergodic, with perfect CSI at receiver only):

$$ C = \mathbb{E}_{\mathbf{H}} \left[ \log_2 \det \left( \mathbf{I}_{n_R} + \frac{\rho}{n_T} \mathbf{H}\mathbf{H}^H \right) \right] \text{ bits/s/Hz} $$

where $$\displaystyle \rho = E_b/N_0 \cdot R $$ (SNR per receive antenna).

• Key Gains:

  • Spatial Multiplexing Gain: Increase data rate linearly with $$\displaystyle \min(n_T, n_R) $$.

  • Diversity Gain: Improve reliability (lower BER) by providing multiple independent fading paths.

4.2.2 Alamouti Space-Time Block Coding (STBC)

• Encoding (Rate-1, 2 Tx antennas): For two consecutive symbols $$\displaystyle s_1, s_2 $$:

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

Column 1 sent from Antenna 1, Column 2 from Antenna 2 at times $t, t+T$.

• Decoding (2 Rx antennas, flat fading):

  Received signals: $$\displaystyle \mathbf{y}_1 = \mathbf{h}_1 s_1 + \mathbf{h}_2 s_2 + \mathbf{n}_1 $$, $$\displaystyle \mathbf{y}_2 = -\mathbf{h}_1 s_2^* + \mathbf{h}_2 s_1^* + \mathbf{n}_2 $$.

  Form combined variables:

$$ \tilde{s}_1 = h_1^* y_1 + h_2 y_2^* $$

$$ \tilde{s}_2 = h_2^* y_1 - h_1 y_2^* $$

Then make decisions: $$\displaystyle \hat{s}_1 = \text{slice}(\tilde{s}_1) $$, $$\displaystyle \hat{s}_2 = \text{slice}(\tilde{s}_2) $$.

• Performance: Provides full diversity order $$\displaystyle 2n_R $$ with simple linear processing. BER curve has same slope as SISO with 3 dB worse SNR (due to two Tx antennas sharing power).

4.2.3 MIMO-OFDM System Implementation

• Motivation: MIMO for spatial multiplexing/diversity + OFDM to combat frequency-selective fading (turns wideband channel into many flat-fading subcarriers).

• Implementation per subcarrier: MIMO processing (e.g., Alamouti, spatial multiplexing with V-BLAST) is applied independently on each OFDM subcarrier. Channel $\mathbf{H}$ becomes a set of $$\displaystyle N_{sub} $$ matrices $\mathbf{H}(k)$.

• Simple 2x2 MIMO-OFDM Link:

  1. Tx: Serial bits → Channel Encoder → Interleaver → MIMO Encoder (Alamouti) → OFDM Modulator (IFFT + CP) per antenna.

  2. Channel: Frequency-selective MIMO channel (per subcarrier $\mathbf{H}(k)$).

  3. Rx: OFDM Demodulator (CP removal + FFT) per antenna → MIMO Detector (Alamouti combiner per subcarrier) → Channel Decoder → Bits.

4.3 Channel Coding for Reliability

4.3.1 Convolutional Codes & Viterbi Decoding

• Encoder: Shift register (constraint length $K$) and modulo-2 adders. Described by generator polynomials (octal), e.g., $(7,5)$ for $$\displaystyle K=3 $$.

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

• Viterbi Algorithm (VA): Maximum Likelihood Sequence Estimation (MLSE).

  1. Branch Metric (BM): Hamming distance (hard-decision) or Euclidean distance (soft-decision) between received bits/symbols and expected branch output.

  2. Path Metric (PM): Cumulative BM along a path.

  3. Add-Compare-Select (ACS): For each state at time $t$, add BM to PM of predecessor states, select survivor path with max PM.

  4. Traceback: After $5K$ to $10K$ steps, trace back from state with max PM to get decoded sequence.

• Soft-decision vs. Hard-decision: Soft (e.g., 3-bit quantization) provides ~2 dB coding gain over hard.

4.3.2 Turbo Codes & Iterative Decoding

• Structure: Parallel Concatenated Convolutional Codes (PCCC). Two or more constituent encoders (typically RSC codes) separated by an interleaver.

• Encoding: Information bits $\mathbf{u}$ → Interleaver $\pi$ → Encoder 1 (output $$\displaystyle \mathbf{c}_1 $$) & Encoder 2 (output $$\displaystyle \mathbf{c}_2 $$). Often punctured to get higher rates.

• Decoding:

  • Iterative (Turbo Principle): Two decoders (for each constituent code) exchange extrinsic information (LLRs) via the interleaver/de-interleaver.

  • Algorithm: Typically Log-MAP or Max-Log-MAP (approximation).

  • Steps per iteration:

    1. Decoder 1: Takes channel LLRs + a priori LLRs (from Decoder 2) → computes posteriori LLRs → splits into extrinsic LLRs for Decoder 2.

    2. Decoder 2: Same process, feeds extrinsic LLRs back to Decoder 1.

  • Convergence: After 4-8 iterations, performance near Shannon limit.

4.3.3 Low-Density Parity-Check (LDPC) Codes

• Definition: Linear block codes with sparse parity-check matrix $\mathbf{H}$ ($n \times (n-k)$).

• Tanner Graph: Bipartite graph with variable nodes (bits) and check nodes (parity checks). Edges indicate $$\displaystyle \mathbf{H}_{i,j}=1 $$.

• Sum-Product (Belief Propagation) Algorithm:

  1. Initialization: Set variable node messages to channel LLRs.

  2. Horizontal Pass (Check → Variable): Each check node computes message to connected variable nodes based on incoming messages from other variable nodes.

  3. Vertical Pass (Variable → Check): Each variable node updates message to connected check nodes using channel LLR and incoming messages from other check nodes.

  4. Decision & Update: After each iteration, compute tentative codeword by summing LLRs at each variable node. If $$\displaystyle \mathbf{H}\hat{\mathbf{x}}^T = \mathbf{0} $$, stop (valid codeword).

• Performance: Approaches Shannon limit with large block lengths and proper design (avoid short cycles in Tanner graph).

4.4 Orthogonal Frequency Division Multiplexing (OFDM) - Deep Dive

4.4.1 OFDM Transmitter/Receiver Chain

• Transmitter:

  1. Serial bits → Mapper (QPSK, 16-QAM, etc.) → $N$ parallel symbols $$\displaystyle \mathbf{X} = [X_0, ..., X_{N-1}] $$.

  2. IFFT: $$\displaystyle \mathbf{x} = \text{IFFT}(\mathbf{X}) $$ (converts frequency-domain to time-domain).

  3. Cyclic Prefix (CP) Insertion: Copy last $L$ samples of $\mathbf{x}$ to front. Length $L \geq$ channel delay spread $$\displaystyle L_{max} $$.

  4. Parallel-to-Serial → DAC → RF Up-conversion.

• Receiver:

  1. RF Down-conversion → ADC → Serial-to-Parallel.

  2. CP Removal: Discard first $L$ samples.

  3. FFT: $$\displaystyle \mathbf{Y} = \text{FFT}(\text{remaining } \mathbf{x}) $$ (converts to frequency-domain).

  4. Channel Equalization (per subcarrier) → Demapper → Serial bits.

• Impact of CP Length:

  • ISI Immunity: $$\displaystyle L \geq L_{max} $$ ensures no ISI between OFDM symbols.

  • Spectral Efficiency Penalty: Overhead = $L/(N+L)$. Longer CP reduces net data rate.

4.4.2 Synchronization in OFDM

• Timing Offset (TO):

  • Problem: FFT window misalignment causes ISI and ICI (Inter-Carrier Interference).

  • Estimation: Use preamble (known sequence). Cross-correlate received signal with known preamble. Peak indicates start of OFDM symbol (after CP).

• Carrier Frequency Offset (CFO):

  • Problem: Due to oscillator mismatch/Doppler. Causes ICI (subcarrier orthogonality lost).

  • Estimation: Use preamble with repeated structure (e.g., two identical halves). Phase difference between halves $$\displaystyle \Delta\phi = 2\pi \epsilon \cdot N_{sub} / N_{FFT} $$, where $\epsilon$ is normalized CFO.

  • Compensation: Multiply time-domain signal by $$\displaystyle e^{-j2\pi \epsilon n / N} $$ before FFT.

4.4.3 Peak-to-Average Power Ratio (PAPR) in OFDM

• Definition: Ratio of peak power to average power of OFDM time-domain signal.

$$ \text{PAPR} = \frac{\max_{n} |x[n]|^2}{E[|x[n]|^2]} $$

*   $x[n]$: IFFT output (sum of $N$ complex sinusoids). Can have very high peaks when all subcarriers are in phase.

• Impact: Forces Power Amplifier (PA) to operate in linear region with large back-off → low power efficiency.

• Reduction Techniques:

  • Clipping & Filtering: Clip peaks above threshold, then filter to reduce out-of-band noise.

  • Tone Reservation: Reserve some subcarriers to carry signals that reduce PAPR.

  • Selected Mapping (SLM): Generate multiple candidate signals (phase rotations), choose one with lowest PAPR.

  • Partial Transmit Sequences (PTS): Partition subcarriers into clusters, optimize phase factors.

4.5 Software-Defined Radio (SDR) Platform Integration

4.5.1 Introduction to SDR Hardware

• Core Components:

  • RF Front-end: Up/down-conversion, filtering, amplification (Duplexer, LNA, PA).

  • ADC/DAC: High-speed, high-resolution converters (e.g., 100 MS/s, 12-bit).

  • FPGA/Processor: Real-time signal processing (FPGA for low-latency, CPU/GPP for flexibility).

• Examples: USRP (Universal Software Radio Peripheral), RTL-SDR (receiver-only), ADALM-PLUTO.

4.5.2 SDR Framework (GNU Radio / MATLAB)

• GNU Radio: Open-source toolkit. Flowgraph = blocks connected by streams/messages.

  • Source/Sink Blocks: UHD: USRP Source/Sink, File Source/Sink, Throttle.

  • Processing Blocks: FFT, Filter, Constellation Decoder, Viterbi Decoder.

• MATLAB/Simulink: SDR Support Packages (for USRP, RTL-SDR). Simulink blocks for RF transmission/reception.

• Integrating Custom Blocks: Write Python/C++ blocks for proprietary algorithms (e.g., custom MIMO detector, LDPC decoder).

4.5.3 End-to-End System Implementation Project

• Typical Flowgraph:

  Random Source → Channel Encoder (Conv/Turbo) → Interleaver → Modulator (QAM) → OFDM Mod (IFFT+CP) → MIMO Encoder (Alamouti) → SDR Tx → Channel Model (AWGN/Fading) → SDR Rx → MIMO Decoder → OFDM Demod (FFT+CP remove) → Demodulator → Channel Decoder → Decision → Error Rate Calc.

• System-Level Metrics:

  • BER vs. $$\displaystyle E_b/N_0 $$: Primary performance measure.

  • Throughput: $$\displaystyle R_b \times (1 - \text{FER}) $$ (bits/sec).

  • Spectral Efficiency: $$\displaystyle \eta = \frac{R_b}{B} $$ (bits/sec/Hz), where $B$ is occupied bandwidth.

4.6 Advanced Channel Models & Equalization

4.6.1 Multipath Fading Channel Models

• Rayleigh Fading: No LOS component. Channel impulse response $$\displaystyle h(t) = \sum_{l=1}^{L} \alpha_l e^{j\phi_l} \delta(t-\tau_l) $$.

  • $$\displaystyle \alpha_l \sim \text{Rayleigh} $$, $$\displaystyle \phi_l \sim \text{Uniform}[0,2\pi) $$.

• Rician Fading: Includes LOS component. $$\displaystyle h(t) = \sqrt{\frac{K}{K+1}} h_{LOS} + \sqrt{\frac{1}{K+1}} h_{scatter} $$.

  • $K$-factor = ratio of LOS power to scattered power.

• Clarke's Model (Doppler): Simulates time-varying Rayleigh channel. $$\displaystyle h(t) = \sum_{n=1}^{N} \cos(2\pi f_{D,n} t + \phi_n) $$ (sum of sinusoids with Doppler shifts $$\displaystyle f_{D,n} $$).

• Key Parameters:

  • Delay Spread ($$\displaystyle \sigma_\tau $$): Spread of path delays → frequency-selective fading if $$\displaystyle B_{signal} \gg 1/\sigma_\tau $$.

  • Doppler Spread ($$\displaystyle f_D $$): Spread of Doppler shifts → time-selective fading if $$\displaystyle T_{symbol} \gg 1/f_D $$.

  • Coherence Time ($$\displaystyle T_c \approx 1/f_D $$): Channel stays roughly constant.

  • Coherence Bandwidth ($$\displaystyle B_c \approx 1/\sigma_\tau $$): Frequency range over which channel is flat.

4.6.2 Equalization Techniques

• Problem: Compensate for ISI caused by frequency-selective channel.

• Linear Equalizers:

  • Zero-Forcing (ZF): Inverts channel: $$\displaystyle \mathbf{W}_{ZF} = \mathbf{H}^{-1} $$. Amplifies noise at deep fades.

  • Minimum Mean Square Error (MMSE): Balances inversion and noise enhancement.

$$ \mathbf{W}_{MMSE} = (\mathbf{H}^H\mathbf{H} + \frac{N_0}{E_s}\mathbf{I})^{-1}\mathbf{H}^H $$

  For SISO: $$\displaystyle W(z) = \frac{H^*(z)}{|H(z)|^2 + N_0/E_s} $$.

• Decision-Feedback Equalizer (DFE):

  • Feedforward Filter (FFF): Similar to linear equalizer.

  • Feedback Filter (FBF): Cancels post-cursor ISI using previous detected symbols.

  • Advantage: Avoids noise enhancement of ZF/MMSE. Disadvantage: Error propagation.

[!TIP] Comparison: DFE > MMSE > ZF in severe multipath, but DFE is non-linear and suffers from error propagation.

4.7 Laboratory Core Principles & Measurements

4.7.1 Key Performance Metrics

• Bit Error Rate (BER): $$\displaystyle P_b = \frac{\text{# of erroneous bits}}{\text{Total # of bits transmitted}} $$.

• Symbol Error Rate (SER): $$\displaystyle P_s = \frac{\text{# of erroneous symbols}}{\text{Total # of symbols transmitted}} $$.

  • For M-PSK: $$\displaystyle P_s \approx 2Q\left(\sqrt{2\frac{E_s}{N_0}\sin(\pi/M)}\right) $$.

  • For square M-QAM: $$\displaystyle P_s \approx 4\left(1-\frac{1}{\sqrt{M}}\right)Q\left(\sqrt{\frac{3}{M-1}\frac{E_s}{N_0}}\right) $$.

• SNR Estimation: Use known pilot symbols: $$\displaystyle \hat{SNR} = \frac{\text{mean}(|s|^2)}{\text{mean}(|r-s|^2)} $$.

• Spectral Efficiency: $$\displaystyle \eta = \frac{\log_2 M}{T_s(1+\beta)} $$ for pulse-shaped QAM (bits/sec/Hz).

4.7.2 Instrumentation & Tools

• Vector Signal Generator (VSG): Generates custom modulated waveforms (QAM, OFDM). Used for Tx simulation.

• Vector Signal Analyzer (VSA): Captures and demodulates signals. Measures EVM, MER, ACPR (Adjacent Channel Power Ratio).

• Spectrum Analyzer: Measures spectral mask, occupied bandwidth, out-of-band emissions.

• SDR Debugging:

  • Flowgraph Monitoring: Use Probe blocks, Message Debug in GNU Radio.

  • Data Logging: Write received symbols/errors to file for offline analysis (MATLAB/Python).

  • Timing Analysis: Use Time Sink to view waveforms.

[!TIP] Exam Viva: Be ready to explain how you would measure PAPR (capture time-domain waveform, compute peak/average power) or EVM (using VSA or by comparing received symbols to ideal constellation).