DSB-SC Modulation & Demodulation Message Frequency (Hz) Carrier Frequency (Hz) Cutoff Frequency (Hz) Sampling Frequency (Hz) Generate & Demodulate Message Signal Carrier Signal Modulated Signal (DSB-SC) Demodulated Signal

Bilateral Laplace Transform Mathematical concept used in signal processing and system analysis The bilateral Laplace transform (also called the two-sided Laplace transform ) is a form of Laplace transform where integration is taken over all time, from \( -\infty \) to \( +\infty \). Definition For a function \(x(t)\), the bilateral Laplace transform is \[ X(s) = \int_{-\infty}^{\infty} x(t)e^{-st} dt \] where: \(x(t)\) = time-domain function \(X(s)\) = Laplace transform \(s = \sigma + j\omega\) (a complex variable) Comparison with the usual Laplace transform Type Formula Integration Range Unilateral Laplace Transform \(X(s)=\int_{0}^{\infty}x(t)e^{-st}dt\) \(0 \rightarrow \infty\) Bilateral Laplace Transform \(X(s)=\int_{-\infty}^{\infty}x(t)e^{-st}dt\) \(-\infty \rightarrow \infty\) Unilateral: used for solving differential equations and systems with initial conditions. Bilateral: use...

Single Phase and Three Phase Wiring Explained Understanding Electrical Power Systems Contents Single Phase Supply Three Phase Supply Frequently Asked Questions 1. Single Phase Supply Yes. A single-phase electrical supply normally needs two wires to work.  The two essential wires Live (Phase / Hot) – carries the voltage from the source. Neutral – completes the circuit and returns current to the source. Electric current flows from live → through the appliance → back through neutral . Without both wires, the circuit is incomplete and the device will not operate. Optional third wire Many installations also include a third wire called Earth (Ground) for safety. Live (L) Neutral (N) Earth (E) The earth wire is mainly used for safety and protection from electric shock . Typical Single Phase System Voltage: About 230 V Minimum Wires: 2 (Live + Neutral) Safer Wiring: 3 (Live + Neutral + Earth) 2. Th...

For practical 5G phased arrays , the beamforming effect is generated primarily by antenna spacing.  1. How 5G phased arrays work 5G base stations use multi-element antenna arrays (often 8×8, 16×16, or even more elements for Massive MIMO). Each antenna element transmits the same signal , but the phase of each element is controlled electronically . The physical spacing between antennas —usually ~0.5λ (half-wavelength) to λ—creates inherent phase differences when the signal reaches a user at an angle. φ total,n = φ steering,n - (2π/λ) n d sin(θ) Where: n = antenna index d = antenna spacing θ = angle of the target φ steering,n = electronic phase shift applied to steer the beam The steering phase compensates for the inherent phase from spacing to direct the beam toward the desired angle. 2. Why not use a single antenna with time delays? Software time delays can emulate phased ar...

Golden Band in Wireless Communications The term “Golden Band” is commonly used in wireless communications to refer to a radio frequency range that offers an excellent balance between coverage and data capacity .  1. What is the Golden Band? The Golden Band typically refers to the mid-band spectrum around 3–4 GHz , especially the 3.3–3.8 GHz range , which is widely used in modern mobile networks. Example bands often called golden: 3.3 GHz 3.5 GHz 3.7 GHz These frequencies are heavily used in 5G NR deployments worldwide. 2. Why is it called “Golden”? Because it sits between low-band and high-band frequencies , giving the best compromise: Band Type Frequency Coverage Speed Low band < 1 GHz Excellent Low Golden band (mid-band) ...

AI-RAN, RIS, ISAC and Spectrum Coexistence AI-RAN, RIS, ISAC, and Spectrum Coexistence are major technologies being developed for advanced 5G and future 6G networks . These technologies aim to improve spectrum efficiency, signal quality, and wireless communication performance. 1. AI-RAN (Artificial Intelligence Radio Access Network) Concept AI-RAN integrates artificial intelligence directly into the Radio Access Network (RAN) to optimize wireless communication in real time. The RAN includes: Base stations Antennas Beamforming systems User scheduling Power control Instead of fixed algorithms, AI dynamically learns optimal decisions. Optimization Model The network tries to maximize system performance: $$ \max_{\mathbf{x}} R(\mathbf{x}) $$ Where: \(R\) = network throughput \(\mathbf{x}\) = control parameters Example control variables: $$ \mathbf{x} = \{P, W, f, B\} $$ \(P\) = transmit power \(W\) = beamforming weights \(f\) = frequency ...

  MATLAB Code clc; clear; close all ; %% Step 1: Define Parameters M = 3; % Number of transmitters N = 200; % Number of time samples SNR = 10; % Baseline SNR (dB) P_max = 1; % Maximum transmit power I_th = 0.1; % Interference threshold (arbitrary unit) fprintf( 'Step 1: Parameters initialized\n' ); %% Step 2: Generate Original Signals t = 1:N; s = zeros(M,N); frequencies = [0.05 0.08 0.12]; % normalized frequency for each transmitter for k = 1:M s(k,:) = exp(1j*2*pi*frequencies(k)*t); % narrowband signals end figure; plot(real(s.')); title( 'Original Transmitter Signals (Real Part)' ); xlabel( 'Time samples' ); ylabel( 'Amplitude' ); %% Step 3: Define Random Channel Matrix H = (randn(M) + 1j*randn(M))/sqrt(2); % channel gains h_mk % Each row = receiver, each column = transmitter %% Step 4: Simulate Received Signals n = (randn(M,N) + 1j*randn(M,N))/sqrt(2); % noise n = n * 10...

1. Concept of AI-Driven Spectrum Sharing AI-driven spectrum sharing uses artificial intelligence / machine learning to manage spectrum dynamically and efficiently: Multiple users or systems share the same frequency band. AI algorithms predict spectrum usage, interference patterns, and optimal allocation . The system adapts power, beamforming, or frequency allocation in real time based on learned patterns. Goal: Maximize throughput, minimize interference, and improve spectrum utilization without human intervention. 2. Mathematical Model Suppose: \(M\) transmitters share the same band. \(s_k(t)\) is the signal from transmitter \(k\). Channel from transmitter \(k\) to receiver \(m\): \(h_{mk}\). Noise at receiver \(m\): \(n_m(t)\). Received signal: $$ y_m(t) = \sum_{k=1}^{M} h_{mk} s_k(t) + n_m(t) $$ Interference at receiver \(m\): $$ I_m = \sum_{k \ne m} |h_{mk}|^2 P_k $$ AI agent uses this data to predict interference patterns and decide optimal po...