Why MSE Is Often Used in Wireless Communication Understanding MSE and MMSE In wireless communication systems, signals transmitted over the air are distorted by noise, multipath effects, and interference. To measure how well a receiver can recover the original transmitted signal, engineers frequently use Mean Squared Error (MSE) , which calculates the average of the squares of errors between estimated and true values. The Minimum Mean Square Error (MMSE) approach finds the estimator that minimizes this squared error.  Channel Estimation and Equalization In systems like MIMO and OFDM, receivers must estimate channel characteristics to undo the distortion caused by the propagation environment. Using pilot symbols or known training sequences, the receiver compares the observed signal with expected values and computes estimates of the channel. Minimizing the MS...

Optical Camera Communication (OCC) Optical Camera Communication (OCC) is a wireless communication method that uses light to send data and a camera (or image sensor) to receive it. Think of it as: Wi-Fi, but with light + a camera instead of radio waves + an antenna How OCC Works Transmitter: Light source (LED, screen, traffic light, car headlight) Light is modulated (on/off or intensity changes) Modulation is too fast for the human eye to notice Receiver: Camera or image sensor Captures...

RNN vs Transformer RNN (Recurrent Neural Network) — Word-by-Word Processing RNNs process text sequentially , one word at a time. At each step, the model reads the current word and updates a hidden memory state that carries information from all previous words. This means each new word depends on the previous words through that hidden state. :contentReference[oaicite:0]{index=0} RNNs are inherently sequential — the next step cannot start until the previous one finishes. :contentReference[oaicite:1]{index=1} Analogy: Imagine an assembly line where each worker only knows what the previous worker passed on — nothing else. Transformers — All Words at Once Using Self-Attention Instead of processing words one by one, Transformers look at the entire sentence simultaneously using a mechanism called ...

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MSD and GMSD Algorithms 1. Why MSD and GMSD Are Used In Wireless Communication, signals suffer from: Scattering by surrounding objects Reflections The above two leads non-line-of-sight (NLOS) propagation As a result, the received signal is composed of multiple delayed replicas of previously transmitted symbols, causing inter-symbol interference (ISI) . Discrete-time channel model Let binary symbols \( b[k] \in \{0,1\} \) be transmitted using IM/DD modulation. The received signal is: \[ r[k] = \sum_{i=0}^{L} h[i]\; b[k-i] + n[k] \] \(h[i]\): channel impulse response taps \(L\): ISI memory length \(n[k]\): noise (shot + thermal) Hence, detecting a symbol independently is suboptimal. 2. Maximum Likelihood Sequence Detection (MLSD) \[ \hat{\...

What is an LSTM? LSTM (Long Short-Term Memory) is a special kind of Recurrent Neural Network (RNN) designed to remember important information over long time sequences and forget useless stuff. A smart notebook that decides what to remember , what to forget , and what to use right now . Classic RNNs forget quickly. LSTMs were invented to fix that. Mathematical Intuition Each LSTM cell has 3 gates + memory . Let: x t = input at time t h t-1 = previous hidden state c t-1 = previous memory (cell state) Forget Gate – What should I forget? f_t = σ(W_f [h_{t-1}, x_t] + b_f) Outputs values between 0 and 1 0 → forget completely 1 → keep completely Input Gate i_t = σ(W_i [h_{t-1}, x_t] + b_i) ~c_t = tanh(W_c [h_{t-1}, x_t] + b_c) Update Me...

  Question A uniformly distributed random variable X with probability density function f X (x) = (1/10) ( u(x+5) − u(x−5) ) where u(.) is the unit step function, is passed through a transformation given in the figure below. The probability density function of the transformed random variable Y would be... Y = 1 when X ∈ [−2.5, 2.5], else 0 (a) f Y (y) = (1/5)(u(y+2.5) − u(y−2.5)) (b) f Y (y) = 0.5δ(y) + 0.5δ(y−1) (c) f Y (y) = 0.25δ(y+2.5) + 0.25δ(y−2.5) + 0.5δ(y) (d) f Y (y) = 0.25δ(y+2.5) + 0.25δ(y−2.5) Correct Answer The transformation maps X to Y such that: If X ∈ [-2.5, 2.5], then Y = 1 If X < −2.5 or X...

Object vs Function vs Method (Python) In Python, these three concepts are closely related, which is why they can feel confusing at first. The key idea is who owns what . 1. Function A function is a reusable block of code that performs a task. It exists independently . def greet(name): return "Hello " + name greet("Alex") Stands alone Not tied to any object Can be called from anywhere Think: “Do this task.” 2. Object An object represents a thing. It holds data (attributes) and behavior (methods) . user = { "name": "Alex", "age": 25 } Or more commonly in Python, using a class: class User: pass u = User() Objects store related data Created from classes Almost everything i...