Flat & Frequency Selective Channels & BER Simulator Fading Distribution Rayleigh (NLOS) Rician (LOS) Nakagami-m (m=2) Signal Frequency: 1.0 MHz Multipath Taps: 3 Path Delay ($\tau$): 2.0 μs SNR (for Spectrum): 30 dB Calculate BER Curve Coh. BW -- Status -- Instantaneous Channel Response $|H(f)|$ Mathematical Foundation & Workflow 1. Signal Generation The simulator generates a discrete-time signal $x[n]$. F...

Understanding Frequency-Selective Channels A student-friendly guide to multipath propagation, channel frequency response, flat fading, frequency-selective fading, and two-path channel simulation. Basic Idea Multipath Two-Path Model Flat vs Selective Simulation Key Concept 1. Basic Idea A frequency-selective channel does not affect all frequencies of a signal equally. Imagine sending a signal containing many frequency components through a wireless channel. Because of multipath propagation, some frequency components may become stronger while others may become weaker. Therefore, the channel gain is not necessarily constant with frequency. Channel Gain at Frequency f1 f2 f3 f4 At one frequency the signal may be strong, while at another frequency it may be strongly attenuated. Key observation: ...

Interactive Signal & Noise Simulator Input Signal Type: Sine Wave Rectangular Pulse Triangular Pulse Noise Type: Gaussian (AWGN) Uniform Noise Laplace Noise Binary Noise Pink Noise Number of Samples: Amplitude: Frequency (Hz): SNR (dB): Noise Variance (σ²): Theory: Waveforms, Noise, Variance, and SNR This simulation generates a noisy periodic signal by combining a waveform with a noise component: x[n] = s[n] + w[n] ...

Analog Signal Chain Simulator Signal Chain Simulator Follow the data from the physical world to the cloud. Instructions--> 1.System ON 2.ADC ON 3.Filter ON POWER MGT: System VOLTAGE: 0.0V RF LINK: Disconnected Encoded Digital Stream (PCM) RF Output (BPSK Modulation) MEMS & Sensors Detects heartbeats as tiny electrical pulses. Raw: 0.01mV Amplifiers Boosts mV signal to V levels for processing. Gain: 1 x Data Converters Sampling & Encoding (8-bit) ADC ON DSP / Processors Mathematical noise filtering & analysis. Filter ON RF ...

Corner Cutoff Frequency RC Low-Pass Filter (LPF): \(f_H = \frac{1}{2\pi RC}\) RC High-Pass Filter (HPF): \(f_L = \frac{1}{2\pi RC}\) RL Low-Pass Filter (LPF): \(f_H = \frac{R}{2\pi L}\) RL High-Pass Filter (HPF): \(f_L = \frac{R}{2\pi L}\) Note: The cutoff frequency is the point where the filter response magnitude falls to \(1/\sqrt{2}\) (approx. 0.707) of its peak passband value, corresponding to −3 dB . Filter Bandwidth (Bandpass contains both fH and fL) Bandwidth represents the frequency range over which a filter permits signals to pass with minimal attenuation. Typically, bandwidth is measured between the lower cutoff frequency (\(f_L\)) and upper cutoff frequency (\(f_H\)) , where the signal response drops −3 dB from its maximum level. Bandwid...

Corner Cutoff Frequency For an RC circuit : f c = 1 / (2πRC) This is the cutoff (corner) frequency in Hz , not the angular frequency. ω c = 1 / RC → angular cutoff frequency (rad/s) f c = 1 / (2πRC) → cutoff frequency (Hz) At this frequency, the output magnitude is 1/√2 ≈ 0.707 of its maximum, corresponding to −3 dB . Remember RL: f c = R / (2πL) RC: f c = 1 / (2πRC) Cutoff (Corner) Frequency in LPF and HPF The calculation of the cutoff (corner) frequency is applicable to both low-pass filters (LPF) and high-pass filters (HPF) . For example, an LPF and an HPF can be constructed using the same component values by changing the circuit configuration or by taking the output from a different point in the circuit. The underlying cutoff-frequency calculation remains the same. For an R...

MIMO Beamforming & Matrix Lab Visualizing Spatial Multiplexing and Channel Orthogonality. (Assuming Antenna Element Spacing is λ/2) 1. System Configuration Antennas (N Rows): 4 Users (K Columns): 2 Note: If two users are at the same angle, the Rank drops and Conditi...

  MIMO Beamforming: Physics to Math MIMO Beamforming & Channel Analysis for (N X 2) How spatial separation determines Matrix Rank and Condition Number (assuming number of users are 2) 1. Physical Config Antennas at Base Station (\(N\)): 4 User 1 Angle (\(\theta_1\)): 60 ° User 2 Angle (\(\theta_2\)): 120 ° Channel Matrix \(H\) (Derived) ...