Choose Input Type: Sine Wave Number of Samples: AWGN Mean: AWGN Variance: SNR (dB): Amplitude: Frequency (Hz): Reset Simulator Generate (Signal + AWGN) Theory: Sine Wave, Noise, Variance, and SNR In our simulation, we generate a noisy sinusoidal signal: x[n] = A * sin(2π f n / N) + w[n] Where: A = amplitude of the sine wave f = frequency of the sine wave N = total number of samples w[n] = additive noise with zero mean and variance σ² The variance of the noise determines how strong the noise is compared to the sine wave: σ² = P_signal / (10^(SNR_dB / 10)) The Signal-to-Noise Ratio (SNR) in decibels is given by: SNR_dB = 10 * log10(P_signal / σ²) ...

When MSE Loss Is Used in Machine Learning What Is Mean Squared Error (MSE)? Mean Squared Error (MSE) is a loss function that measures the average of the squares of the differences between predicted and actual values. It is widely used to evaluate the quality of predictions in models where outputs are continuous numeric values. Common Use Cases for MSE Loss Regression Problems: MSE is most commonly used in regression tasks where the model predicts continuous outputs like house prices, temperatures, or stock values. It penalizes large prediction errors more heavily due to squaring the differences. Neural Network Training: When training neural networks for tasks that require predicting real-valued numbers (not categories), MSE is often chosen as the loss function beca...

Gold Sequences and m-Sequences Gold Sequence Gold sequence (or Gold code ) is a type of pseudo-random binary sequence used in digital communications and signal processing, especially in spread-spectrum systems. It belongs to a family of sequences known for: Good cross-correlation properties Predictable structure Easy hardware implementation Basic Idea Generate two different maximal-length sequences (m-sequences) of the same length. Combine them using bitwise XOR (modulo-2 addition) . Shift one sequence relative to the other to create multiple distinct sequences. If each m-sequence has length: $$ N = 2^n - 1 $$ then the Gold code family contains: $$ N + 2 $$ different sequences. Why They’re Important 1. Bounded Cross-Correlation The cross-correlation between different sequences is small and limited to three values. This is critical in multi-user systems ....

When a Tree Becomes a Graph Minimal Change from Tree to Graph A tree is a special type of graph. To convert a tree into a general graph, you just need to make a small change: Add one edge that creates a cycle. Example: Tree: 10 / \ 5 15 Graph (after adding edge 5 → 15): 10 / \ 5────15 Now there is a cycle (10 → 5 → 15 → 10), so it is a graph. Benefits of Graphs over Trees Feature Tree Graph Benefit of Graph Cycles Not allowed Allowed ...

Comparison of Nakagami-m, Rayleigh, and Rician Fading Models Wireless fading models describe how the received signal strength fluctuates due to multipath propagation. This article provides an intuitive, mathematical, and practical comparison of the three most widely used fading models. 1. Why Fading Models Are Needed In wireless communication, signals reach the receiver through multiple paths caused by reflection, diffraction, and scattering. These paths interfere constructively and destructively, producing random fluctuations in signal amplitude and SNR. Fading models statistically characterize these fluctuations. 2. Rayleigh Fading Applicable scenario: Non-line-of-sight (NLOS) environments with many scatterers. Probability density function (PDF): \[ f_R(r) = \frac{r}{\sigma^2} e^{-\frac{r^2}{2\sigma^2}}, \quad r \ge 0 \] Severe fading No dominant LOS...

Quantum Communication Underwater using hBN Single Photon Emitters Challenges in Underwater Communication Acoustic waves: work over long distances but low data rates, insecure, omni-directional Electromagnetic waves (Radio, Infrared) cannot propagate underwater Optical wavelengths mostly absorbed → communication limited to few meters Current Optical Communication Issues Blue/green light (~417 nm) reduces absorption Attenuated lasers used for underwater communication Probabilistic photon generation → not ideal for high-security applications Need for reliable, on-demand quantum light sources Hexagonal Boron Nitride (hBN) Single Photon Emitters B-centres in hBN emit at 436 nm Engineered using electron beam Photostable and reliable Emission near water absorption minimum Suitable for underwater quantum communication T...

Understanding Diversity Order (DO) At high SNR, the Bit Error Rate (BER) behaves like: BER ≈ k / (SNR^DO) Where: k is a constant depending on modulation and channel. DO is the diversity order, indicating how steeply BER decreases with SNR. Mathematical Concept of DO Formally, diversity order is defined as: DO = - lim_{SNR → ∞} (log(BER) / log(SNR)) This means: if you plot log(BER) vs log(SNR), the slope at high SNR is the diversity order. Slopes can be fractional depending on the fading channel statistics. Case 1: DO = 1 BER ∝ 1 / SNR^1 = 1 / SNR BER decreases linearly on a log-log scale with SNR. Doubling SNR roughly halves BER. Steep slope → faster improvement → more robust system. Case 2: DO = 0.5 BER ∝ 1 / SNR^0.5 = 1 / √SNR BER decreases more slowly than DO = 1. Doubling SNR decreases BER by ~1/√2 ≈ 0.707. Flatter slope → slower improvement → less robust system. Intuition with Numbers Suppose BER = 0.01 at some SNR,...

BER and Outage Probability in Atmospheric Turbulence After modeling turbulence using log-normal, Gamma–Gamma, and exponential distributions, the next step is to understand how turbulence affects bit error rate (BER) and outage probability . 1. What BER and Outage Mean in Turbulent Channels Bit Error Rate (BER) BER is the probability that a transmitted bit is detected incorrectly. In free-space optical (FSO) links, turbulence causes random fading of the received intensity, which makes the instantaneous SNR random. Therefore, BER must be averaged over the turbulence statistics: Average BER = E_I[ BER(γ(I)) ] Outage Probability Outage probability measures the likelihood that the received signal is too weak to maintain reliable communication. P_out = P( γ < γ_th ) Since SNR is proportional to received intensity: γ = γ̄ · I 2. Relation Between Inten...