Advanced Wireless Communication

Cheatsheet Content

UNIT 1: Fundamentals of Wireless Communications 1. Evolution of Wireless Communication 1G (1980s - Analog): Fully analog, FDMA, voice only (e.g., AMPS), poor security, low capacity. 2G (1990s - Digital Voice): Digital voice, better spectral efficiency/security. Technologies: GSM (TDMA), IS-95 (CDMA). Introduced SMS. 2.5G / 2.75G: GPRS, EDGE. Packet-switched data, moderate rates. 3G (2000s - Multimedia): High data rates for internet/video. Technologies: UMTS, CDMA2000. Supports circuit & packet switching. 4G (LTE/LTE-A): Fully packet-switched IP. High data rates (100 Mbps - 1 Gbps). Uses OFDM, MIMO. 5G (Present - Ultra-Low Latency & Massive Connectivity): Supports eMBB, URLLC, mMTC. Uses Massive MIMO, mmWave. Applications: IoT, autonomous vehicles, AR/VR. 2. Review of Cellular Communication Divides large area into small cells. Frequency Reuse: Improves capacity by reusing frequencies in non-adjacent cells. Key Components: Mobile Station (MS), Base Station (BS), Mobile Switching Center (MSC). Cell Splitting: Increases capacity by reducing cell size. Sectoring: Uses directional antennas to reduce co-channel interference. Handoff: Transfers an ongoing call between cells without interruption. 3. Radio Wave Propagation Reflection: Occurs when radio waves hit large obstacles (e.g., buildings, ground). Diffraction: Waves bend around sharp edges or obstacles. Scattering: Occurs when waves encounter objects smaller than the wavelength (e.g., foliage, street signs). Multipath Propagation: Multiple delayed versions of the same signal arrive at the receiver, causing fading and inter-symbol interference (ISI). 4. Free Space Path Loss (FSPL) Path loss in line-of-sight (LOS) conditions. Depends on distance ($d$) and wavelength ($\lambda$). Formula: $L_{FSPL} = \left(\frac{4\pi d}{\lambda}\right)^2$ or $L_{FSPL} = 20 \log_{10}(d) + 20 \log_{10}(f) + 20 \log_{10}\left(\frac{4\pi}{c}\right) \text{ (in dB)}$ 5. Short-Term and Long-Term Fading Short-Term (Small Scale) Fading: Rapid fluctuations in signal strength over short distances or times. Caused by multipath propagation. Examples: Rayleigh, Rician fading. Long-Term (Large Scale) Fading: Signal strength variation due to shadowing by large obstacles (buildings, terrain). Modeled by log-normal distribution. 6. Channel Modelling Wireless channel is represented as a time-varying impulse response $h(\tau, t)$. Channel coefficients are random variables. Rayleigh Fading Channel: Occurs when there is no dominant Line-of-Sight (LOS) path. Envelope of the received signal follows a Rayleigh distribution. Rician Fading Channel: Occurs when there is a strong dominant LOS path in addition to multipath components. Envelope follows a Rician distribution. 7. Power Delay Profile (PDP) Represents the average received power as a function of excess delay. Used to characterize the multipath structure of a channel. RMS Delay Spread ($\tau_{rms}$): A measure of the time dispersion of the channel, indicating the duration over which multipath components are significant. 8. Coherence Bandwidth & Coherence Time Coherence Bandwidth ($B_C$): Range of frequencies over which the channel experiences similar fading characteristics. Inversely proportional to RMS Delay Spread: $B_C \approx \frac{1}{5\tau_{rms}}$. Flat Fading: Signal bandwidth ($B_S$) Frequency Selective Fading: $B_S$ > $B_C$. Different frequency components fade independently, causing ISI. Coherence Time ($T_C$): Time duration over which the channel impulse response remains approximately constant. Inversely proportional to Doppler spread ($f_D$): $T_C \approx \frac{1}{f_D}$. Slow Fading: Symbol duration ($T_S$) Fast Fading: $T_S$ > $T_C$. Channel changes significantly within a symbol period. UNIT 2: Capacity and Coding for Wireless Channels 1. Wireless vs. Wired Communication (BER) Aspect Wired Wireless Noise AWGN Fading + Noise BER Lower Higher Reliability High Variable 2. BER in AWGN Channel Channel affected only by Additive White Gaussian Noise (AWGN). BPSK BER: $P_b = Q\left(\sqrt{\frac{2E_b}{N_0}}\right)$, where $Q(x) = \frac{1}{\sqrt{2\pi}} \int_x^\infty e^{-t^2/2} dt$. 3. BER in Wireless Fading Channel Channel gain is a random variable, varying with time/location. Average BER is obtained by averaging the conditional BER (given a fixed channel gain) over the fading distribution. For Rayleigh fading, the average BER is significantly higher than in AWGN for the same $E_b/N_0$. 4. Capacity of Wireless Channels Shannon Capacity (AWGN): $C = B \log_2\left(1 + \frac{P}{N_0 B}\right)$ bits/s, where $B$ is bandwidth, $P$ is signal power, $N_0$ is noise power spectral density. Flat Fading Channel Capacity: Channel gain ($h$) is random. Capacity depends on whether Channel State Information (CSI) is available at the transmitter and/or receiver. If CSI at Rx only, capacity is averaged over fading. If CSI at Tx & Rx, adaptive power/rate allocation can be used. Frequency Selective Channel Capacity: Can be decomposed into multiple parallel flat-fading subchannels (e.g., using OFDM). Water-filling Principle: Optimal power allocation across subchannels to maximize capacity, allocating more power to stronger subchannels. UNIT 3: Deep Fade and Diversity Techniques 1. Deep Fade A phenomenon where the received signal power drops severely (e.g., by 20-30 dB or more) for a short duration. Caused by destructive interference of multipath components. Leads to a significant increase in Bit Error Rate (BER) and can cause communication outages. 2. Diversity Concepts Techniques used to mitigate fading by providing the receiver with multiple, statistically independent versions of the same signal. Diversity Gain: The improvement in signal-to-noise ratio (SNR) or reduction in BER achieved by diversity. Goal: Reduce the probability of a deep fade affecting all signal paths simultaneously. 3. Space Diversity (Receive Diversity) Uses multiple antennas at the receiver to exploit independent fading paths. Selection Combining (SC): Selects the branch with the highest instantaneous SNR. Simplest, but not optimal. Threshold Combining: Switches to another branch when the current branch's SNR drops below a predefined threshold. Maximal Ratio Combining (MRC): Weights each received signal according to its SNR and sums them coherently. Optimal combining technique, achieving the highest possible SNR. Equal Gain Combining (EGC): Combines branches with equal weights but corrects their phases to ensure coherent summation. Simpler than MRC, performance close to MRC. 4. Transmit Diversity Uses multiple antennas at the transmitter to create diversity. Transmit Beamforming: If CSI is available at the transmitter, signals are weighted and phased to constructively interfere at the receiver, directing energy towards the desired user. Improves received SNR. Alamouti Code (Space-Time Block Code - STBC): A 2x1 (2 transmit, 1 receive antenna) STBC. Provides full diversity order (equal to the number of transmit antennas) with simple linear decoding at the receiver. Requires no CSI at the transmitter. 5. Time and Frequency Diversity Time Diversity: Transmitting the same information over different time slots (e.g., repetition coding, interleaving). Effective against fast fading if symbol duration is less than coherence time. Frequency Diversity: Transmitting the same information over different frequency bands (e.g., spread spectrum, OFDM with subcarriers far apart). Effective against frequency-selective fading if frequency separation is greater than coherence bandwidth. 6. MIMO Systems Multiple-Input Multiple-Output: Employs multiple antennas at both the transmitter and receiver. Significantly improves both capacity (spatial multiplexing) and reliability (diversity gain). MIMO Receiver Types: Zero Forcing (ZF): Eliminates interference from other spatial streams by inverting the channel matrix. Enhances noise. Minimum Mean Square Error (MMSE): Balances interference cancellation and noise enhancement. Generally better than ZF. Maximum Likelihood (ML): Jointly searches for the most likely transmitted symbols. Optimal but computationally complex. 7. Spatial Multiplexing using SVD Singular Value Decomposition (SVD): A mathematical tool to decompose the MIMO channel matrix $\mathbf{H}$ into $\mathbf{H} = \mathbf{U} \mathbf{\Sigma} \mathbf{V}^H$. Decomposes the MIMO channel into a set of parallel, independent subchannels (eigenmodes). Allows for transmitting independent data streams over these subchannels, maximizing data rate (spatial multiplexing gain). UNIT 4: Multi-Carrier Modulation (MCM) 1. Single Carrier vs. Multi-Carrier Feature Single Carrier Multi-Carrier Symbol Duration Short Long ISI High in frequency selective channels Low (due to long symbol duration and CP) Equalization Complex in frequency selective channels Simple (per subcarrier, often 1-tap) Implementation Simpler RF front-end IFFT/FFT complexity 2. OFDM (Orthogonal Frequency Division Multiplexing) A multi-carrier modulation technique where a high-rate data stream is split into multiple lower-rate streams. Each stream modulates a separate, orthogonal subcarrier. Converts a frequency-selective wideband channel into multiple parallel flat-fading narrowband subchannels. Achieved efficiently using Inverse Fast Fourier Transform (IFFT) at the transmitter and Fast Fourier Transform (FFT) at the receiver. 3. OFDM Block Diagram Transmitter: Serial to Parallel Converter: Divides high-rate data into $N$ parallel streams. Modulation Mapper: Maps bits to complex symbols (e.g., QPSK, 16-QAM). IFFT: Transforms $N$ frequency-domain symbols into $N$ time-domain samples. Cyclic Prefix (CP) Insertion: Copies the end of the IFFT output to the beginning. Parallel to Serial Converter: Transmits the time-domain samples serially. Digital to Analog Converter (DAC) & RF up-conversion. Receiver: Reverse process (RF down-conversion, ADC, Serial to Parallel, CP Removal, FFT, Demodulation, Parallel to Serial). 4. Cyclic Prefix (CP) A copy of the last part of the OFDM symbol is inserted at its beginning. Purpose: Prevents ISI: Absorbs the channel's multipath delay spread, ensuring that multipath components from preceding symbols do not interfere with the current symbol. Maintains Orthogonality: Makes the linear convolution with the channel appear as a circular convolution, preserving the orthogonality between subcarriers at the FFT output. Length of CP must be greater than the maximum channel delay spread. 5. BER of OFDM The overall BER of an OFDM system depends on the BER of each individual subcarrier. Since each subcarrier experiences flat fading, its BER can be calculated using standard modulation BER formulas (e.g., for BPSK, QPSK) for its specific SNR. The overall BER is then typically an average over the BERs of all subcarriers. 6. Problems in OFDM Carrier Frequency Offset (CFO): Mismatch between transmitter and receiver oscillator frequencies. Causes inter-carrier interference (ICI) and rotation of constellation points, leading to loss of subcarrier orthogonality and increased BER. Requires accurate frequency synchronization. Peak-to-Average Power Ratio (PAPR): High PAPR occurs when many subcarriers align constructively, leading to large instantaneous signal peaks. Requires highly linear power amplifiers, which are less efficient and more expensive. Techniques like clipping, selected mapping (SLM), partial transmit sequences (PTS) are used to reduce PAPR.