Introduction to Massive MIMO and MUI In a massive MIMO system, a base station is equipped with a large number of antennas \( M \), typically in the order of 100 or more. This system simultaneously serves \( K \) users, each with a single antenna. The key advantage of massive MIMO is the ability to exploit spatial diversity, which allows for significant gains in both signal quality and interference suppression. The signal model in massive MIMO can be described as follows: \( y = \sum_{i=1}^K \sqrt{p_u} g_i x_i + n \) where: \( y \) is the received signal vector. \( p_u \) is the power allocated to each user. \( g_i \) is the channel vector of user \( i \), modeled as a complex Gaussian random vector. \( x_i \) is the transmitted symbol by user \( i \). \( n \) is the noise vector, typically modeled as a complex Gaussian with zero mean and identity covariance, \( \mathcal{CN}(0, I) \). ...

Single Carrier Orthogonal Frequency Division Multiplexing (SC-OFDM) is used for uplink communication in LTE and 5G systems. Unlike traditional OFDM, which uses multiple subcarriers, SC-OFDM employs a single carrier for transmission. This method is particularly effective for communication between a single mobile station (MS) and the base station (BS). The Discrete Fourier Transform (DFT) operation within SC-OFDM divides the original signal into different orthogonal frequency bands, enhancing its resilience to noise and distortion. After the DFT, the Inverse Fast Fourier Transform (IFFT) is applied to convert the signal from the frequency domain back to the time domain for transmission. SC-OFDM (Single-Carrier Orthogonal Frequency Division Multiplexing) is a variation of the traditional OFDM (Orthogonal Frequency Division Multiplexing) technique. It is particularly useful in systems where a single carrier is preferred, such as in some 5G communication systems and LTE (Long-Term Evolution...

  The main difference between OFDM and SC-OFDM is that SC-OFDM transmits the signal using a single carrier, while OFDM uses multiple subcarriers. However, in SC-OFDM, the signal is generated with different sub-bands, but it is transmitted through a single carrier (more technically, through a wideband carrier signal). Block Diagram of OFDM: Data → Modulation → Serial-to-Parallel → IFFT → Add CP → Transmit Received Signal → Remove CP → FFT → Parallel-to-Serial → Demodulation → Data Block Diagram of SC-OFDM: Data → Modulation → DFT → IFFT → Add CP → Transmit Received Signal → Remove CP → FFT → Demodulation → Data    In the case of OFDM, the input modulated data is converted from a serial stream to parallel streams, and different subcarriers are assigned to each chunk. Then, IFFT is applied to these chunks, and a cyclic prefix is added to each one. Each chunk is technically referred to as an OFDM symbol . Unlike OFDM, SC-OFDM does not perform serial-to-parallel conversion o...

   MATLAB Code % The code is developed by SalimWireless.com clc; clear; close all; % Parameters Nbits = 2000; % Number of bits Rb = 1000; % Bit rate (bps) Fs = 10*Rb; % Sampling frequency (Hz) Ts = 1/Fs; % Sampling interval T = 1/Rb; % Bit duration SamplesPerSymbol = Fs/Rb; % Number of samples per bit % Generate random bit sequence data = randi([0 1], 1, Nbits); % Create the baseband message signal (upsampled bits) message_signal = zeros(1, Nbits * SamplesPerSymbol); for i = 1:Nbits message_signal((i-1)*SamplesPerSymbol + 1 : i*SamplesPerSymbol) = data(i); end t_message = (0:length(message_signal)-1)*Ts; % MSK Modulation mskMod = comm.MSKModulator('BitInput', true, 'SamplesPerSymbol', SamplesPerSymbol); mskSig = step(mskMod, data.'); % GMSK Modulation BT = 0.3; % Gaussian BT product gmskMod = comm.GMSKModulator('BitInput', true, 'BandwidthTimeProduct', BT, 'Sa...

In this article, we will discuss how to create an expense tracker mobile app using React Native, Expo, and a smartphone's local SQLite database. SQLite is similar to MySQL but is designed for mobile and embedded applications. Every smartphone has a local SQLite database that apps can use. However, locating these databases on your device can be tricky because they are stored within the app's sandbox, and each app has its own sandboxed storage. In this guide, we will focus on an offline expense tracker that stores your expense data in a local SQLite database. For this example, we have named the database my.db . The app stores information such as the expense ID, day, date, expense amount, and any optional comments related to the expense. Within the my.db database, we have created two tables: users and todos . The users table stores the id , day , date , and expense amount , while the todos table stores the comments. The two tables are ...

In this tutorial, we’ll demonstrate how to create a student management system using Python's FastAPI for the backend and React.js for the frontend. This system includes functionalities for adding, viewing, and updating student data. It uses JWT (JSON Web Token) for secure authentication, ensuring that only authorized users can manage student records. Project Overview Our project is a Student Management System designed to simplify the management of student data for educational institutions. The system allows administrators to: View and manage student records including personal details, courses, GPA, enrollment status, etc. Add new student records into the system. Update existing student records when necessary. Authenticate users with secure JWT tokens to ensure only authorized access. Frontend: React.js The React.js frontend allows users to interact with the system. Below is the component for the student dashb...

What is a Hermitian Matrix? A Hermitian matrix is a special type of square matrix that is equal to its own conjugate transpose: \[ A = A^H \] Where \( A^H \) is the conjugate transpose of \( A \) (also known as the adjoint), defined as: \[ A^H = \overline{A}^T \] Here: \( A^T \) is the transpose of \( A \), where rows become columns. \( \overline{A} \) denotes the complex conjugate of the elements of \( A \). For real-valued matrices, the Hermitian property simplifies to the condition that the matrix is equal to its transpose: \[ A = A^T \] Meaning it is a symmetric matrix. Key Properties of Hermitian Matrices The properties of Hermitian matrices are particularly useful in the context of Eigenvalue Decomposition: Real Eigenvalues The eigenvalues of a Hermitian matrix are always real numbers, which is crucial for numerical stab...

Eigenvalue decomposition helps reduce noise by retaining only the dominant (larger) eigenvalues in the eigenvalue matrix while discarding the smaller ones. It decomposes the covariance matrix of the original data using the Principal Component Analysis (PCA) method. The eigenvectors form an orthogonal basis, and the corresponding eigenvalues indicate how much variance (signal) is captured along each eigenvector direction. In signal processing and data science, noise reduction is critical for improving the quality of data. One effective technique for this is Eigenvalue Decomposition (EVD) applied to the covariance matrix of the dataset. Step-by-Step: Noise Reduction with Eigenvalue Decomposition Let’s say you have a dataset represented by a covariance matrix \( C \). Here’s the process mathematically: 1. Perform Eigenvalue Decomposition on \( C \): \[ C = V \Lambda V^T \] Where: \( V \) contains the eigenvectors (p...