Beamforming Techniques Hybrid Beamforming... Page 1 | Page 2 | clear all; close all; clc; Nt = 64; Nr = 16; NtRF = 4; NrRF = 4; At both the transmitter and receiver ends, there are four RF chains only for a hybrid beamforming system. Alternatively, every 16 antenna elements on the transmitter side is connected to a single RF chain, while every 4 antenna elements on the receiver side are connected to a single RF chain. Mixers, amplifiers, and other critical wireless communication components make up the RF chain. Now, in the case of hybrid beamforming, there can be four different data streams between the transmitter and receiver, as both sides have four RF chains, each of which is accountable for a separate data stream. For Analog Beamforming: All 64 Tx antenna elements create a beam or focus the resultant correlated signal spread from adjacent antennas to a particular direction. Similarly, it may be used for beam...
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📘 Overview & Theory 🧮 MATLAB Codes 📚 Further Reading Theoretical Ber vs SNR for Amplitude Shift Keying (ASK) The theoretical bit error rate (BER) for binary Amplitude Shift Keying (ASK) as a function of the signal-to-noise ratio (SNR) can be derived using the following expression: If we map the binary signals to 1 and -1 in ASK , the probability of bit error will be: BER = Q(√(2*SNR)) If we map the binary signals to 0 and 1 in ASK , the probability of bit error will be: BER = Q(√(SNR/2)) Where: Q(x) is the Q-function, which is the tail probability of the standard normal distribution. SNR is the signal-to-noise ratio. N0 is the noise power spectral density. Where Q is the Q function In mathematics Q(x) = 0.5 * erfc(x/ √ 2) Calculate the Probability of Error using Q-function for ASK: For ASK with amplitudes 0 and 1 : When bit '0' is transmitted, the received signal is noise only . When bit '1' is transmitted, the re...
Channel Impulse Response (CIR) 📘 Overview & Theory 📘 How does the channel impulse response affect the signal? 🧮 Online Channel Impulse Response Simulator 🧮 MATLAB Codes 📚 Further Reading Wireless Signal Processing CIR, Doppler Shift & Gaussian Random Variable The Channel Impulse Response (CIR) is a concept primarily used in the field of telecommunications and signal processing. It provides information about how a communication channel responds to an impulse signal. What is the Channel Impulse Response (CIR) ? It describes the behavior of a communication channel in response to an impulse signal. In signal processing, an impulse signal has zero amplitude at all other times and amplitude ∞ at time 0 for the signal. Using a Dirac Delta function, we can approximate this. ...(i) δ( t) now has a very intriguing characteristic. The answer is 1 when the Fourier Transform of δ(...
🧮 Coherence Bandwidth 🧮 Coherence Time 🧮 Coherence Time Calculator 🧮 Relationship between Coherence Time and Delay Spread 🧮 MATLAB Code to find Relationship between Coherence Time and delay Spread 📚 Further Reading Coherence Bandwidth Coherence bandwidth is a concept in wireless communication and signal processing that relates to the frequency range over which a wireless channel remains approximately constant in terms of its characteristics. coherence bandwidth is The inverse of Doppler spread delay time, or any spread delay time due to fading in general. The coherence bandwidth is related to the delay spread of the channel, which is a measure of the time it takes for signals to traverse the channel. The two are related by the following formulae: Coherence bandwidth = 1/(delay spread time) Or, Coherence Bandwidth = 1/(root-mean-square delay spread time) (Coherence bandwidth in Hertz) For instance, the coherence bandwidth is...
📘 Overview of Energy per Bit (Eb / N0) 🧮 Online Simulator for constellation diagrams of ASK, FSK, and PSK 🧮 Theory behind Constellation Diagrams of ASK, FSK, and PSK 🧮 MATLAB Codes for Constellation Diagrams of ASK, FSK, and PSK 📚 Further Reading 📂 Other Topics on Constellation Diagrams of ASK, PSK, and FSK ... 🧮 Simulator for constellation diagrams of m-ary PSK 🧮 Simulator for constellation diagrams of m-ary QAM BASK (Binary ASK) Modulation: Transmits one of two signals: 0 or -√Eb, where Eb is the energy per bit. These signals represent binary 0 and 1. BFSK (Binary FSK) Modulation: Transmits one of two signals: +√Eb ( On the y-axis, the phase shift of 90 degrees with respect to the x-axis, which is also termed phase offset ) or √Eb (on x-axis), where Eb is the energy per bit. These signals represent binary 0 and 1. BPSK (Binary PSK) Modulation: Transmits one of two signals...
MATLAB Code for Zero-Forcing (ZF) Beamforming in 4×4 MIMO Systems clc; clear; close all; %% Parameters Nt = 4; % Transmit antennas Nr = 4; % Receive antennas (must be >= Nt for ZFBF) numBits = 1e4; % Number of bits per stream SNRdB = 0; % SNR in dB numRuns = 100; % Number of independent runs for averaging %% Precompute noise standard deviation noiseSigma = 10^(-SNRdB / 20); %% Accumulator for total errors totalErrors = 0; for run = 1:numRuns % Generate random bits: [4 x 10000] bits = randi([0 1], Nt, numBits); % BPSK modulation: 0 → +1, 1 → -1 txSymbols = 1 - 2 * bits; % Rayleigh channel matrix: [4 x 4] H = (randn(Nr, Nt) + 1j * randn(Nr, Nt)) / sqrt(2); %% === Zero Forcing Beamforming at Transmitter === W_zf = pinv(H); % Precoding matrix: [Nt x Nr] txPrecoded = W_zf * txSymbols; % Apply ZF precoding % Normalize transmit power (optional but useful) txPrecoded = txPrecoded / sqrt(mean(abs(txPrecoded(:)).^2)); %% Channel transmission with AWGN noise = noiseSigma * (randn(...
📘 Comparisons among ASK, FSK, and PSK 🧮 Online Simulator for calculating Bandwidth of ASK, FSK, and PSK 🧮 MATLAB Code for BER vs. SNR Analysis of ASK, FSK, and PSK 📚 Further Reading 📂 View Other Topics on Comparisons among ASK, PSK, and FSK ... 🧮 Comparisons of Noise Sensitivity, Bandwidth, Complexity, etc. 🧮 MATLAB Code for Constellation Diagrams of ASK, FSK, and PSK 🧮 Online Simulator for ASK, FSK, and PSK Generation 🧮 Online Simulator for ASK, FSK, and PSK Constellation 🧮 Some Questions and Answers Modulation ASK, FSK & PSK Constellation MATLAB Simulink MATLAB Code Comparisons among ASK, PSK, and FSK Comparisons among ASK, PSK, and FSK Simulator for Calculating Bandwidth of ASK, FSK, and PSK The baud rate represents the number of symbols transmitted per second. Both baud rate and bit rate a...
📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 📚 Further Reading 📂 View Other Topics on M-ary QAM, M-ary PSK, QPSK ... 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 MATLAB Code for BER calculation of ASK, FSK, and PSK 🧮 MATLAB Code for BER calculation of Alamouti Scheme 🧮 Different approaches to calculate BER vs SNR 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 ...