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What are Time Invariant and Time Variant (TV) Systems

Time invariant system: Any delay provided in input must be reflected in output for a time invariant system.

Time variant system (TV): Abovementioned condition is not applicable for a time variant systems.


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MATLAB Code for QAM (Quadrature Amplitude Modulation)

  One of the best-performing modulation techniques is QAM [↗] . Here, we modulate the symbols by varying the carrier signal's amplitude and phase in response to the variation in the message signal (or voltage variation). So, we may say that QAM is a combination of phase and amplitude modulation. Additionally, it performs better than ASK or PSK [↗] . In fact, any constellation for any type of modulation, signal set (or, symbols) is structured in a way that prevents them from interacting further by being distinct by phase, amplitude, or frequency. MATLAB Script % This code is written by SalimWirelss.Com % This is an example of 4-QAM. Here constellation size is 4 % or total number of symbols/signals is 4 % We need 2 bits once to represent four constellation points % QAM modulation is the combination of Amplitude modulation plus % Phase Modulation. We map the decimal value of the input symbols, i.e., % 00, 01, 10, 11 to 1 + 1i, -1 + 1i, 1 - 1i, and -1 - 1i, respectively. clc;clear all;...
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Star to Delta Conversion and Vice Versa | star delta conversion

The transformation of a star to a delta and a delta to a star circuit is a hot topic in electrical science and engineering. Examiners often ask about the conversion of star to delta and delta to star circuit diagram. When solving complex circuits, the conversion procedure can sometimes ease calculations and save time. Without further ado, we'll go over the characteristics of both a star and a delta circuit. As its title suggests, the star circuit looks like a star. Delta circuit, on the other hand, looks like a delta. Now we'll look at the mathematical method for converting delta to star and star to delta. Delta to Star R1 = RaRb / (Ra + Rb + Rc) R2 = RbRc / (Ra + Rb + Rc) R3 = RaRc / (Ra + Rb + Rc) Use star to delta online converter and vice versa Star to Delta Ra = (R1R2 + R2R3 + R3R1) / R2 Rb = (R1R2 + R2R3 + R3R1) / R3 Rc = (R1R2 + R2R3 + R3R1) / R1 Next Page>>
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MIMO, massive MIMO, and Beamforming

  The term 'MIMO' was originally applied to systems with multiple antennas on both the transmitter (Tx) and receiver (Rx) sides. MIMO is a key component of Wi-Fi 4 and 5, 3G, and 4G cellular networks. This method was introduced to increase the capacity of a channel by sending multiple simultaneous data streams through a single channel. All simultaneous data streams in a MIMO system are encoded orthogonally multiplexed, which reduces interference. Massive MIMO is used extensively in 5G to achieve extremely high capacity and to communicate via  beamforming  or directional transmission. 1. Some essential characteristics of a MIMO system 1.1. Spatial Division Multiplexing Access (SDMA) SDMA is a key feature of MIMO, allowing a base station (BS) to communicate with several devices simultaneously (or even using the same frequency) if they are in different locations. There may be no knowledge of channel information at the transmitter. 1.2. Spatial Multiplexing Another essential ...
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MATLAB Code for Pulse Width Modulation (PWM) and Demodulation

   Pulse Width Modulation (PWM) MATLAB Script   clc; clear all; close all; fs=5; %frequency of the sawtooth signal fm=5; %frequency of the message signal sampling_frequency = 10e3; a=0.5; % amplitide t=0:(1/sampling_frequency):1; %sampling rate of 10kHz sawtooth=1.01*a.*sawtooth(2*pi*fs*t); %generating a sawtooth wave subplot(4,1,1); plot(t,sawtooth); % plotting the sawtooth wave title('Comparator Wave'); msg=a.*sin(2*pi*fm*t); %generating message wave subplot(4,1,2); plot(t,msg); %plotting the sine message wave title('Message Signal'); for i=1:length(sawtooth) if (msg(i)>=sawtooth(i)) pwm(i)=1; %is message signal amplitude at i th sample is greater than %sawtooth wave amplitude at i th sample else pwm(i)=0; end end subplot(4,1,3); plot(t,pwm,'r'); title('PWM'); axis([0 1 0 1.1]); %to keep the pwm visible during plotting. %% Demodulation % Demodulation: Measure the pulse width to reconstruct the signal demodulated_signal = zeros(size(msg)); for i =...
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MATLAB Code for Rank and Condition Number of a Channel Matrix

To assess the signal strengths of various multipaths between TX and RX and enable communication, the rank and condition numbers of a channel matrix are highly helpful characteristics. Signal multipath propagation is a typical occurrence in wireless communication. Phases shift and the signal weakens during this process. We are discussing signal phases in this context. When numerous multipaths arrive at the receiver, the resulting signal may be additive or destructive because of phase alterations. A channel matrix is referred to as a sparse matrix if it only has a few stronger elements and the majority of the other elements are zero. Finding rank and condition number for sparse matrices is important for numerous reasons. That topic has already been covered in another article [ click here ]. We will just talk about the corresponding MATLAB codes here. MATLAB Code for Rank and Condition Number of a Channel Matrix %Author: Salim Wireless For study materials on wireless %com...
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Simulation of ASK, FSK, and PSK using MATLAB Simulink

ASK, FSK & PSK HomePage MATLAB Simulation Simulation of Amplitude Shift Keying (ASK) using MATLAB Simulink      In Simulink, we pick different components/elements from MATLAB Simulink Library. Then we connect the components and perform a particular operation.  Result A sine wave source, a pulse generator, a product block, a mux, and a scope are shown in the diagram above. The pulse generator generates the '1' and '0' bit sequences. Sine wave sources produce a specific amplitude and frequency. The scope displays the modulated signal as well as the original bit sequence created by the pulse generator. Mux is a tool for displaying both modulated and unmodulated signals at the same time. The result section shows that binary '1' is modulated by a certain sine wave amplitude of 1 Volt, and binary '0' is modulated by zero amplitude. Simulation of Frequency Shift Keying (FSK) using MATLAB Simulink   Result The diagram above shows t...
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BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...

Modulation Constellation Diagrams BER vs. SNR BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ... 1. What is Bit Error Rate (BER)? The abbreviation BER stands for bit error rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. It is defined as,  In mathematics, BER = (number of bits received in error / total number of transmitted bits)  On the other hand, SNR refers to the signal-to-noise power ratio. For ease of calculation, we commonly convert it to dB or decibels.   2. What is Signal the signal-to-noise ratio (SNR)? SNR = signal power/noise power (SNR is a ratio of signal power to noise power) SNR (in dB) = 10*log(signal power / noise power) [base 10] For instance, the SNR for a given communication system is 3dB. So, SNR (in ratio) = 10^{SNR (in dB) / 10} = 2 Therefore, in this instance,...
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