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Binary Phase Shift Keying (BPSK) is a form of digital modulation in which each bit of data is represented by one of two phases of a carrier wave. These phases typically represent values like `0` and `1`. In this note, we will focus on Maximum Likelihood (ML) Detection in BPSK and how it helps in recovering the transmitted bits from a noisy signal. 1. What is Maximum Likelihood Detection? Maximum Likelihood (ML) detection is a statistical approach used to estimate the transmitted signal based on the received signal. The principle is to choose the signal that maximizes the likelihood of observing the received data, given a set of possible transmitted symbols. In the context of BPSK, ML detection is about determining which of the two possible transmitted symbols (\(+A\) or \(-A\)) is most likely to have been transmitted based on the received signal. 2. The BPSK Modulation Scheme In BPSK, there are two possible symbols representing binary ...

16-QAM (16 Quadrature Amplitude Modulation) is a popular digital modulation scheme used in many communication systems, including Wi-Fi, cellular, and satellite communications. In this modulation technique, 16 different symbols are used to represent a 4-bit sequence.   1. What is Maximum Likelihood Detection? Maximum Likelihood (ML) Detection is a decision rule used in communication systems to detect the transmitted signal based on the received signal. The goal is to choose the symbol that maximizes the likelihood of observing the received signal, considering the noise in the system. In the context of 16-QAM , ML detection involves choosing the closest point in the 16-QAM constellation to the received signal, where the closeness is measured by the Euclidean distance.   2. 16-QAM Modulation 16-QAM uses both amplitude and phase to represent 16 different combinations of 4 bits. The constellation points are arranged in a grid, where each point co...

MATLAB Code % Example: OFDM with Passband Transmission, Data Rate Calculation, and Signal Visualization clear; clc; % 1. Define bitstream (as a string of bits) bitstream = '1011000110110001'; % Example bitstream % 2. Parameters numSymbols = length(bitstream) / 2; % Each QPSK symbol maps to 2 bits numSubcarriers = 4; % Number of subcarriers nSymbolsPerOFDM = numSubcarriers; % Number of symbols per OFDM symbol (each subcarrier gets 1 symbol) % Carrier Frequency (Passband) f_c = 2e6; % Carrier frequency (in Hz) for passband transmission, e.g., 2 MHz % Sampling Frequency fs = 20e6; % Sampling frequency (in Hz), e.g., 20 MHz % Symbol duration (inverse of symbol rate) symbolDuration = numSubcarriers / fs; % Duration of one OFDM symbol % 3. Map bits to QPSK symbols (2 bits -> 1 symbol) qpskSymbols = zeros(1, numSymbols); for i = 1:numSymbols bits = bitstream(2*i-1:2*i); % Get 2 bits for each symbol if strcmp(bits, '00') qpskSymbols(i) = 1 + 1i; elseif strcmp(bits, '...

In general, the data rate in OFDM is calculated as: Data Rate = Number of Subcarriers × Bits per Symbol × OFDM Symbol Rate In OFDM (Orthogonal Frequency Division Multiplexing) , the achievable data rate depends on several parameters: bandwidth, modulation scheme, number of subcarriers, and the signal-to-noise ratio (SNR). Key Parameters Affecting Achievable Data Rate Total Bandwidth (W): The total available bandwidth for transmission. More bandwidth allows more subcarriers, increasing the data rate. Number of Subcarriers (N): The total bandwidth is divided into smaller subcarriers; more subcarriers means more parallel data streams. Modulation Scheme: Determines bits per symbol: QPSK – 2 bits/symbol 16-QAM – 4 bits/symbol 64-QAM – 6 bits/symbol 256-QAM – 8 bits/symbol Coding Rate (R): The ratio of useful data bits to total transmitted bits (includes error correction). Symbol Duration ...

Generalized Spatial Modulation (GSM) is an advanced technique for wireless communication systems that integrates spatial modulation with a dynamic antenna activation mechanism. This approach allows for significant improvements in both data rate and energy efficiency compared to traditional MIMO systems. In GSM, instead of utilizing all available antennas for transmission, only a subset of antennas are activated at any given time. This selective activation reduces power consumption while still maintaining high throughput, which is a critical requirement for modern wireless communication. Key Concepts of GSM Antenna Activation : n_t = total number of transmit antennas. n_rf = number of active RF chains (active antennas), where n_rf < n_t . Inactive antennas are turned OFF to save power. Transmission with Active Antennas : Symbols are transmitted by activating specific ante...

  GATE Electronics and Communication (EC) Questions Paper With Answer Key Download Pdf [2025] Download Question Paper                 See Answers Answers with Explanations  Q.55 Given: f(t) is a periodic signal with fundamental period T₀ > 0. The signal y(t) = f(αt) , where α > 1. The Fourier series expansions for f(t) and y(t) are given by: f(t) = Σ (from k=-∞ to ∞) cₖ e^(j 2π/T₀ k t) y(t) = Σ (from k=-∞ to ∞) dₖ e^(j 2π/T₀ α k t) Step 1: Find the relationship between the periods of f(t) and y(t). The period of f(t) is T₀ . The signal y(t) = f(αt) effectively compresses or stretches the signal by a factor of α. Therefore, the period of y(t) will be scaled by α, resulting in a period of T₀ / α .    Step 2: Relationship between the Fourier coefficients. The Fourier coefficients of f(t) are cₖ , and for y(t) , they are...

D Flip-Flop, S-R Flip-Flop, and J-K Flip-Flop A D flip-flop (often called a D-type flip-flop ) is a type of edge-triggered flip-flop that is commonly used in digital circuits. The primary function of a D flip-flop is to store and transfer a bit of data (either 0 or 1). It is often used for data storage, synchronization, and signal timing. How It Works Key Inputs and Outputs: D (Data) Input: This is the data input to the flip-flop. The value at this input will be transferred to the output (Q) on the clock edge. CLK (Clock) Input: The clock signal controls when the data at the D input is transferred to the output (Q). The flip-flop is edge-triggered, meaning it only responds to changes on the clock signal (either rising or falling edge, depending on the design). Q Output: This is the main output of the flip-flop, where the stored value is output. Q' (Q Not) Output: This is the inverse of the Q output. Opera...