Skip to main content

Antenna Gain-Combining Methods - EGC, MRC, SC, and RMSGC



 There are different antenna gain-combining methods. They are as follows.


1. Equal gain combining (EGC)

2. Maximum ratio combining (MRC)

3. Selective combining (SC)

4. Root mean square gain combining (RMSGC)

5. Zero-Forcing (ZF) Combining 


1. Equal gain combining method

Equal Gain Combining (EGC) is a diversity combining technique in which the receiver aligns the phase of the received signals from multiple antennas (or channels) but gives them equal amplitude weight before summing.

This means each received signal is phase-corrected to be coherent with others, but no scaling is applied based on signal strength or channel quality (unlike MRC).

Mathematically, for received signals y1, y2, ..., yN with complex channel gains h1, h2, ..., hN, the EGC output is:

yegc = ∑i=1N (hi* / |hi|) · yi

Here:

  • hi is the complex channel gain
  • hi* / |hi| is a unit-magnitude phasor that corrects the phase of each path
  • All corrected signals are added with equal magnitude

2. Maximum ratio combining method

Maximum Ratio Combining (MRC) multiplies each received signal by the complex conjugate of its corresponding channel coefficient. This corrects the phase distortion introduced by the channel and gives more weight to signals with higher power (|h|2).

For example, if y1 and y2 are received signals, and h1, h2 are the complex channel gains, then:

ymrc = h1* · y1 + h2* · y2

MATLAB Code for Maximum Ratio Combining (MRC)


3. Selective combining method

In the selective combing method, we select a few data streamwise with higher SNR values than others. Then we combine them.


4. Root mean square gain combining method. 


We first take the square of individual data stream in the root mean square combining method. Then we sum them. And finally, we take the square root values of the composite data streams. This method shows the near-optimal performance as the maximum ratio combining, as some researcher claims.

5. Zero Forcing Combining

Zero Forcing is a linear combining technique used in MIMO systems to nullify inter-stream interference by inverting the channel. It works under the assumption of perfect channel knowledge (CSI).

The idea:

Given: y = Hx + n
Want to recover: x
Multiply both sides by W = (HHH)-1 HH (or pinv(H) in MATLAB)
Result: x = Wy ≈ x + Wn

It forces WH ≈ I, effectively "undoing" the channel.

 

MATLAB Code for Zero Forcing Combining

%The code is written by SalimWireless.com

clc; clear; close all;

%% Parameters
Nt = 4; % Transmit antennas
Nr = 4; % Receive antennas
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 for each run
bits = randi([0 1], Nt, numBits); % Size: [4 x 10000]
txSymbols = 1 - 2 * bits; % BPSK: 0→+1, 1→-1

% Generate random Rayleigh fading channel (4x4)
H = (randn(Nr, Nt) + 1j * randn(Nr, Nt)) / sqrt(2);

% Generate AWGN noise
noise = noiseSigma * (randn(Nr, numBits) + 1j * randn(Nr, numBits)) / sqrt(2);

% Received signal
y = H * txSymbols + noise;

% Zero Forcing equalizer
W_zf = pinv(H);
rxSymbols = W_zf * y;

% BPSK demodulation
rxBits = real(rxSymbols) < 0;

% Count errors
totalErrors = totalErrors + sum(rxBits(:) ~= bits(:));
end

%% Final BER
BER = totalErrors / (Nt * numBits * numRuns);
fprintf('Average BER over %d runs for 4x4 MIMO ZF at %d dB SNR: %.5f\n', numRuns, SNRdB, BER);
web('https://www.salimwireless.com/search?q=antenna%20combining%20methods', '-browser');

Further Reading 

People are good at skipping over material they already know!

View Related Topics to







Admin & Author: Salim

s

  Website: www.salimwireless.com
  Interests: Signal Processing, Telecommunication, 5G Technology, Present & Future Wireless Technologies, Digital Signal Processing, Computer Networks, Millimeter Wave Band Channel, Web Development
  Seeking an opportunity in the Teaching or Electronics & Telecommunication domains.
  Possess M.Tech in Electronic Communication Systems.


Contact Us

Name

Email *

Message *

Popular Posts

Comparisons among ASK, PSK, and FSK | And the definitions of each

📘 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 Comparison among ASK, FSK, and PSK Parameters ASK FSK PSK Variable Characteristics Amplitude Frequency ...

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...

📘 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 ...

Constellation Diagrams of ASK, PSK, and FSK

📘 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...

Theoretical BER vs SNR for BPSK

Let's simplify the explanation for the theoretical Bit Error Rate (BER) versus Signal-to-Noise Ratio (SNR) for Binary Phase Shift Keying (BPSK) in an Additive White Gaussian Noise (AWGN) channel.  Key Points Fig 1: Constellation Diagrams of BASK, BFSK, and BPSK [↗] BPSK Modulation: Transmits one of two signals: +√Eb ​ or -√Eb , where Eb​ is the energy per bit. These signals represent binary 0 and 1 . AWGN Channel: The channel adds Gaussian noise with zero mean and variance N0/2 (where N0 ​ is the noise power spectral density). Receiver Decision: The receiver decides if the received signal is closer to +√Eb​ (for bit 0) or -√Eb​ (for bit 1) . Bit Error Rate (BER) The probability of error (BER) for BPSK is given by a function called the Q-function. The Q-function Q(x) measures the tail probability of the normal distribution, i.e., the probability that a Gaussian random variable exceeds a certain value x.  Understanding the Q...

MATLAB Code for ASK, FSK, and PSK

📘 Overview & Theory 🧮 MATLAB Code for ASK 🧮 MATLAB Code for FSK 🧮 MATLAB Code for PSK 🧮 Simulator for binary ASK, FSK, and PSK Modulations 📚 Further Reading ASK, FSK & PSK HomePage MATLAB Code MATLAB Code for Amplitude Shift Keying (ASK) % The code is written by SalimWireless.Com % Clear previous data and plots clc; clear all; close all; % Parameters Tb = 1; % Bit duration fc = 10; % Carrier frequency N = 10; % Number of bits % Generate carrier signal t = 0:Tb/100:1; carrier_signal = sqrt(2/Tb) * sin(2*pi*fc*t); % Generate message signal rng(10); % Set random seed for reproducibility binary_data = rand(1, N); % Generate random binary data t_start = 0; t_end = Tb; for i = 1:N t = [t_start:0.01:t_end]; % Generate message signal if binary_data(i) > 0.5 binary_data(i) = 1; message_signal = ones(1, length(t)); ...

Simulation of ASK, FSK, and PSK using MATLAB Simulink

📘 Overview 🧮 How to use MATLAB Simulink 🧮 Simulation of ASK using MATLAB Simulink 🧮 Simulation of FSK using MATLAB Simulink 🧮 Simulation of PSK using MATLAB Simulink 🧮 Simulator for ASK, FSK, and PSK 🧮 Digital Signal Processing Simulator 📚 Further Reading 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 b...

MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...

🧮 MATLAB Code for BPSK, M-ary PSK, and M-ary QAM Together 🧮 MATLAB Code for M-ary QAM 🧮 MATLAB Code for M-ary PSK 📚 Further Reading MATLAB Script for BER vs. SNR for M-QAM, M-PSK, QPSK, BPSK % Written by Salim Wireless clc; clear; close all; num_symbols = 1e5; snr_db = -20:2:20; psk_orders = [2, 4, 8, 16, 32]; qam_orders = [4, 16, 64, 256]; ber_psk_results = zeros(length(psk_orders), length(snr_db)); ber_qam_results = zeros(length(qam_orders), length(snr_db)); for i = 1:length(psk_orders) psk_order = psk_orders(i); for j = 1:length(snr_db) data_symbols = randi([0, psk_order-1], 1, num_symbols); modulated_signal = pskmod(data_symbols, psk_order, pi/psk_order); received_signal = awgn(modulated_signal, snr_db(j), 'measured'); demodulated_symbols = pskdemod(received_signal, psk_order, pi/psk_order); ber_psk_results(i, j) = sum(data_symbols ~= demodulated_symbols) / num_symbols; end end for ...

Online Simulator for ASK, FSK, and PSK

Try our new Digital Signal Processing Simulator!   Start Simulator for binary ASK Modulation Message Bits (e.g. 1,0,1,0) Carrier Frequency (Hz) Sampling Frequency (Hz) Run Simulation Simulator for binary FSK Modulation Input Bits (e.g. 1,0,1,0) Freq for '1' (Hz) Freq for '0' (Hz) Sampling Rate (Hz) Visualize FSK Signal Simulator for BPSK Modulation ...