Skip to main content

Frequency Selective Fading vs Flat Fading in MATLAB


In the MATLAB code below, a comparison between frequency-selective fading and flat fading is shown.
In frequency-selective fading, multipath propagation causes multiple delayed copies of the signal to arrive at the receiver. When the channel delay spread exceeds the symbol duration, these delayed components overlap, resulting in inter-symbol interference (ISI). In flat fading, ISI does not occur because the signal bandwidth is much smaller than the channel’s coherence bandwidth. Therefore, the channel response remains approximately constant across the signal bandwidth, and all symbols experience the same fading.

MATLAB Code for frequency selective fading channel


% OFDM over frequency selective Rayleigh fading channel
clc; clearvars; close all;
% Simulation parameters
nSym = 10^4; % Number of OFDM symbols
EbN0dB = 0:2:20; % Eb/N0 range
MOD_TYPE = 'MPSK'; % 'MPSK' or 'MQAM'
M = 4; % QPSK
N = 64; % Total number of subcarriers
Ncp = 16; % Cyclic prefix length
L = 10; % Number of channel taps
k = log2(M); % Bits per symbol
EsN0dB = 10*log10(k*(N/(N+Ncp))) + EbN0dB; % account CP loss
errors = zeros(1,length(EsN0dB));
% Monte Carlo simulation
for i = 1:length(EsN0dB)
for j = 1:nSym
% -------- Transmitter --------
d = ceil(M*rand(1,N)); % Random symbols
[X , ref] = modulation_mapper(MOD_TYPE,M,d);
x = ifft(X,N); % IDFT
s = add_cyclic_prefix(x,Ncp); % Add CP
% -------- Channel (Freq-selective Rayleigh) --------
h = 1/sqrt(2)*(randn(1,L)+1i*randn(1,L)); % CIR
H = fft(h,N); % Freq response
hs = conv(h,s); % Channel filtering
r = awgn(hs,EsN0dB(i)); % Add noise
% -------- Receiver --------
y = remove_cyclic_prefix(r,Ncp,N); % Remove CP
Y = fft(y,N); % DFT
V = Y ./ H; % Equalization
[~, dcap] = iqOptDetector(V,ref);
errors(i) = errors(i) + sum(d ~= dcap);
end
end
% SER results
simulatedSER = errors/(nSym*N);
theoreticalSER = ser_rayleigh(EbN0dB,MOD_TYPE,M);
% Plot
semilogy(EbN0dB,simulatedSER,'ko'); hold on;
title(['Performance of ',num2str(M),'-',MOD_TYPE,...
' OFDM over Freq Selective Rayleigh channel']);
xlabel('Eb/N0 (dB)');
ylabel('Symbol Error Rate');
function [X, ref] = modulation_mapper(MOD_TYPE, M, d)
% Modulation mapper for OFDM transmitter
% MOD_TYPE - 'MPSK' or 'MQAM'
% M - Modulation order (BPSK=2, QPSK=4, 16-QAM=16, etc.)
% d - Data symbols drawn from {1,2,...,M}
%
% Outputs:
% X - Modulated complex symbols
% ref - Ideal constellation points (for IQ detector)
if strcmpi(MOD_TYPE, 'MPSK')
[X, ref] = mpsk_modulator(M, d); % M-PSK modulation
elseif strcmpi(MOD_TYPE, 'MQAM')
[X, ref] = mqam_modulator(M, d); % M-QAM modulation
else
error('Invalid modulation type. Use ''MPSK'' or ''MQAM''.');
end
end
function [s,ref]=mpsk_modulator(M,d)
%Function to MPSK modulate the vector of data symbols - d
%[s,ref]=mpsk_modulator(M,d) modulates the symbols defined by the
%vector d using MPSK modulation, where M specifies the order of
%M-PSK modulation and the vector d contains symbols whose values
%in the range 1:M. The output s is the modulated output and ref
%represents the reference constellation that can be used in demod
ref_i= 1/sqrt(2)*cos(((1:1:M)-1)/M*2*pi);
ref_q= 1/sqrt(2)*sin(((1:1:M)-1)/M*2*pi);
ref = ref_i+1i*ref_q;
s = ref(d); %M-PSK Mapping
end
function s = add_cyclic_prefix(x,Ncp)
%function to add cyclic prefix to the generated OFDM symbol x that
%is generated at the output of the IDFT block
% x - ofdm symbol without CP (output of IDFT block)
% Ncp-num. of samples at x's end that will copied to its beginning
% s - returns the cyclic prefixed OFDM symbol
s = [x(end-Ncp+1:end) x]; %Cyclic prefixed OFDM symbol
end
function y = remove_cyclic_prefix(r,Ncp,N)
%function to remove cyclic prefix from the received OFDM symbol r
% r - received ofdm symbol with CP
% Ncp - num. of samples at beginning of r that need to be removed
% N - number of samples in a single OFDM symbol
% y - returns the OFDM symbol without cyclic prefix
y=r(Ncp+1:N+Ncp);%cut from index Ncp+1 to N+Ncp
end
function [idealPoints,indices]= iqOptDetector(received,ref)
%Optimum Detector for 2-dim. signals (MQAM,MPSK,MPAM) in IQ Plane
%received - vector of form I+jQ
%ref - reference constellation of form I+jQ
%Note: MPAM/BPSK are one dim. modulations. The same function can be
%applied for these modulations since quadrature is zero (Q=0).
x=[real(received); imag(received)]';%received vec. in cartesian form
y=[real(ref); imag(ref)]';%reference vec. in cartesian form
[idealPoints,indices]= minEuclideanDistance(x,y);
end
function [idealPoints,indices]= minEuclideanDistance(x,y)
%function to compute the pairwise minimum Distance between two
%vectors x and y in p-dimensional signal space and select the
%vectors in y that provides the minimum distances.
% x - a matrix of size mxp
% y - a matrix of size nxp. This acts as a reference against
% which each point in x is compared.
% idealPoints - contain the decoded vector
% indices - indices of the ideal points in reference matrix y
[m,p1] = size(x);[n,p2] = size(y);
if p1~=p2
error('Dimension Mismatch: x and y must have same dimension')
end
X = sum(x.*x,2);
Y = sum(y.*y,2)';
d = X(:,ones(1,n)) + Y(ones(1,m),:) - 2*x*y';%Squared Euclidean Dist.
[~,indices]=min(d,[],2); %Find the minimum value along DIM=2
idealPoints=y(indices,:);
indices=indices.';
end
function [ser] = ser_rayleigh(EbN0dB,MOD_TYPE,M)
%Compute Theoretical Symbol Error rates for MPSK or MQAM modulations
%EbN0dB - list of SNR per bit points
%MOD_TYPE - 'MPSK' or 'MQAM'
%M - Modulation level for the chosen modulation
% - For MPSK M can be any power of 2
% - For MQAM M must be even power of 2 (square QAM only)
gamma_b = 10.^(EbN0dB/10); %SNR per bit in linear scale
gamma_s = log2(M)*gamma_b; %SNR per symbol in linear scale
switch lower(MOD_TYPE)
case {'bpsk'}
ser = 0.5*(1-sqrt(gamma_b/(1+gamma_b)));
case {'mpsk','psk'}
ser = zeros(size(gamma_s));
for i=1:length(gamma_s), %for each SNR point
g = sin(pi/M).^2;
fun = @(x) 1./(1+(g.*gamma_s(i)./(sin(x).^2))); %MGF
ser(i) = (1/pi)*integral(fun,0,pi*(M-1)/M);
end
case {'mqam','qam'}
ser = zeros(size(gamma_s));
for i=1:length(gamma_s) %for each SNR point
g = 1.5/(M-1);
fun = @(x) 1./(1+(g.*gamma_s(i)./(sin(x).^2)));%MGF
ser(i) = 4/pi*(1-1/sqrt(M))*integral(fun,0,pi/2)-4/pi*(1-1/sqrt(M))^2* ...
integral(fun,0,pi/4);
end
case {'mpam','pam'}
ser = zeros(size(gamma_s));
for i=1:length(gamma_s) %for each SNR point
g = 3/(M^2-1);
fun = @(x) 1./(1+(g.*gamma_s(i)./(sin(x).^2)));%MGF
ser(i) = 2*(M-1)/(M*pi)*integral(fun,0,pi/2);
end
end
end

Output 

 



MATLAB Code for flat fading channel


% OFDM over flat Rayleigh fading channel
clc; clearvars; close all;
% Simulation parameters
nSym = 10^4; % Number of OFDM symbols
EbN0dB = 0:2:20; % Eb/N0 range
MOD_TYPE = 'MPSK'; % 'MPSK' or 'MQAM'
M = 4; % QPSK
N = 64; % Total number of subcarriers
Ncp = 16; % Cyclic prefix length
k = log2(M); % Bits per symbol
EsN0dB = 10*log10(k*(N/(N+Ncp))) + EbN0dB; % account CP loss
errors = zeros(1,length(EsN0dB));
% Monte Carlo simulation
for i = 1:length(EsN0dB)
for j = 1:nSym
% -------- Transmitter --------
d = ceil(M*rand(1,N)); % Random symbols
[X , ref] = modulation_mapper(MOD_TYPE,M,d);
x = ifft(X,N); % IDFT
s = add_cyclic_prefix(x,Ncp); % Add CP
% -------- Channel (Flat Rayleigh) --------
h = 1/sqrt(2)*(randn + 1i*randn); % Single-tap flat fading
H = h; % Frequency response
r = h*s; % Flat-fading multiplication
r = awgn(r,EsN0dB(i),'measured'); % Add AWGN noise
% -------- Receiver --------
y = remove_cyclic_prefix(r,Ncp,N); % Remove CP
Y = fft(y,N); % DFT
V = Y ./ H; % Equalization
[~, dcap] = iqOptDetector(V,ref);
errors(i) = errors(i) + sum(d ~= dcap);
end
end
% SER results
simulatedSER = errors/(nSym*N);
theoreticalSER = ser_rayleigh(EbN0dB,MOD_TYPE,M);
% Plot
semilogy(EbN0dB,simulatedSER,'ko'); hold on;
title(['Performance of ',num2str(M),'-',MOD_TYPE,...
' OFDM over Flat Rayleigh channel']);
xlabel('Eb/N0 (dB)');
ylabel('Symbol Error Rate');
%% ------------------------ Functions ------------------------
function [X, ref] = modulation_mapper(MOD_TYPE, M, d)
if strcmpi(MOD_TYPE, 'MPSK')
[X, ref] = mpsk_modulator(M, d);
elseif strcmpi(MOD_TYPE, 'MQAM')
[X, ref] = mqam_modulator(M, d);
else
error('Invalid modulation type. Use ''MPSK'' or ''MQAM''.');
end
end
function [s, ref] = mpsk_modulator(M,d)
ref_i= 1/sqrt(2)*cos(((1:M)-1)/M*2*pi);
ref_q= 1/sqrt(2)*sin(((1:M)-1)/M*2*pi);
ref = ref_i + 1i*ref_q;
s = ref(d);
end
function s = add_cyclic_prefix(x,Ncp)
s = [x(end-Ncp+1:end) x];
end
function y = remove_cyclic_prefix(r,Ncp,N)
y = r(Ncp+1:N+Ncp);
end
function [idealPoints,indices] = iqOptDetector(received,ref)
x = [real(received); imag(received)]';
y = [real(ref); imag(ref)]';
[idealPoints,indices] = minEuclideanDistance(x,y);
end
function [idealPoints,indices] = minEuclideanDistance(x,y)
[m,p1] = size(x); [n,p2] = size(y);
if p1 ~= p2, error('Dimension mismatch'); end
X = sum(x.*x,2);
Y = sum(y.*y,2)';
d = X(:,ones(1,n)) + Y(ones(1,m),:) - 2*x*y';
[~,indices] = min(d,[],2);
idealPoints = y(indices,:);
indices = indices.';
end
function ser = ser_rayleigh(EbN0dB,MOD_TYPE,M)
gamma_b = 10.^(EbN0dB/10); % SNR per bit linear
gamma_s = log2(M)*gamma_b; % SNR per symbol linear
switch lower(MOD_TYPE)
case {'bpsk'}
ser = 0.5*(1-sqrt(gamma_b./(1+gamma_b)));
case {'mpsk','psk'}
ser = zeros(size(gamma_s));
for i=1:length(gamma_s)
g = sin(pi/M)^2;
fun = @(x) 1./(1 + (g*gamma_s(i)./(sin(x).^2)));
ser(i) = (1/pi)*integral(fun,0,pi*(M-1)/M);
end
case {'mqam','qam'}
ser = zeros(size(gamma_s));
for i=1:length(gamma_s)
g = 1.5/(M-1);
fun = @(x) 1./(1 + (g*gamma_s(i)./(sin(x).^2)));
ser(i) = 4/pi*(1-1/sqrt(M))*integral(fun,0,pi/2) ...
- 4/pi*(1-1/sqrt(M))^2*integral(fun,0,pi/4);
end
end
end
 

 

 Output

 

 


Further Reading


📊 MATLAB & ONLINE SIMULATIONS (Web-Based)
🎓 GATE & UGC - NET SOLUTIONS
📡 WIRELESS & SIGNAL PROCESSING


Contact Us

Name

Email *

Message *

Popular Posts

MIMO Channel Matrix | Rank and Condition Number

MIMO / Massive MIMO MIMO Channel Matrix | Rank and Condition...   The channel matrix in wireless communication is a matrix that describes the impact of the channel on the transmitted signal. The channel matrix can be used to model the effects of the atmospheric or underwater environment on the signal, such as the absorption, reflection or scattering of the signal by surrounding objects. When addressing multi-antenna communication, the term "channel matrix" is used. Let's assume that only one TX and one RX are in communication and there's no surrounding object. Here, in our case, we can apply the proper threshold condition to a received signal and get the original transmitted signal at the RX side. However, in real-world situations, we see signal path blockage, reflections, etc.,  (NLOS paths [↗]) more frequently. The obstruction is typically caused by building walls, etc. Multi-antenna communication was introduced to address this issue. It makes diversity app...
Read more

BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...(MATLAB Code + Simulator)

Bit Error Rate (BER) & SNR Guide Analyze communication system performance with our interactive simulators and MATLAB tools. 📘 Theory 🧮 Simulators 💻 MATLAB Code 📚 Resources BER Definition SNR Formula BER Calculator MATLAB Comparison 📂 Explore M-ary QAM, PSK, and QPSK Topics ▼ 🧮 Constellation Simulator: M-ary QAM 🧮 Constellation Simulator: M-ary PSK 🧮 BER calculation for ASK, FSK, and PSK 🧮 Approaches to BER vs SNR Calculation What is Bit Error Rate (BER)? The BER indicates how many corrupted bits are received compared to the total number of bits sent. It is the primary figur...
Read more

UGC NET Electronic Science Previous Year Question Papers with Solutions

Home / Engineering & Other Exams / UGC NET 2026 PYQ ⬇️ Download Papers and Solutions 📋 Exam Pattern 💡 Preparation Tips ❓ FAQs 📊 Exam Highlights: Electronic Science (88) Feature Details Junior Research Fellowship (JRF) ₹37,000 + HRA per month Eligibility M.Sc/M.Tech in Electronics (55%) Validity of Certificate JRF (3 Years) | Lectureship (Lifetime) 📥 Download UGC NET Electronics PDFs Complete collection of previous year question papers, answer keys and explanations for Subject Code 88. Start Downloading 📂 View All Question Papers June 2025 - Question Paper Download PDF June 2025 - Solved Paper + Explanation ...
Read more

How to Mount Google Drive in Google Colab

How to Mount Google Drive in Google Colab Google Colab provides temporary storage during a session. Any files stored in the /content directory will be deleted when the runtime disconnects. To store datasets, trained models, and results permanently, it is recommended to mount your Google Drive in Colab. Mounting Google Drive allows your notebook to access files directly from your Drive and save outputs there so they remain available even after the Colab session ends. Step 1: Import the Drive Module First import the Google Colab drive module. from google.colab import drive Step 2: Mount Google Drive Run the following command to mount your Google Drive. from google.colab import drive drive.mount('/content/drive') After running the command: A link will appear in the output. Click the link and log in to your Google account. Copy the authentication code provided. Paste the code back into the notebook. Or, a Google authentication page will a...
Read more

Wiener Filter in MATLAB

  MATLAB Code  % Wiener Filter Based on Wiener-Hopf Equation % This script demonstrates how to apply the Wiener filter to recover % a reference signal from a noisy signal using the Wiener-Hopf equation. % The filter minimizes the mean squared error between the noisy signal and the reference signal. clear; close all; clc; % Signal Parameters fs = 4000; % Sampling frequency (Hz) T = 1; % Total recording time (seconds) L = T * fs; % Signal length (samples) tt = (0:L-1) / fs; % Time vector ff = (0:L-1) * fs / L; % Frequency vector % Generate Reference Signal (a sinusoid) y = sin(2 * pi * 120 * tt); % Reference sinusoidal signal y = y(:); % Ensure column vector % Create Noisy Signal by Adding Gaussian Noise x = 0.50 * randn(L, 1) + y; % Noisy signal x = x(:); % Ensure column vector % Define Filter Order (Number of Coefficients) N = 200; % Apply Wiener Filter using custom function [xest, b, MSE] = wienerFilt(x, y, N); % Plot Results figure; subplot(411); plot(tt, x, 'k'), hold on, p...
Read more

Overmodulation & Distortion in AM

Overmodulation in AM and How It Causes Distortion 1. AM Signal Equation s(t) = A c [1 + μ m(t)] cos(2Ï€ f c t) A c = carrier amplitude m(t) = normalized modulating signal (|m(t)| ≤ 1) μ = modulation index 2. Modulation Index μ = A m / A c - Normal AM: 0 < μ ≤ 1 → no distortion - Overmodulation: μ > 1 → distortion occurs 3. Envelope and Overmodulation A(t) = A c [1 + μ m(t)] - For undistorted AM: 1 + μ m(t) ≥ 0 at all times - If μ > 1: 1 + μ m(t) < 0 at negative peaks → carrier flips Example: Let m(t) = cos(2Ï€ f m t), A c = 1 V, μ = 1.2 Minimum envelope: A min = A c [1 - 1.2] = -0.2 V Negative amplitude → envelope crosses zero → 180° phase flip 4. Mathematical Consequence -A c cos(θ) = A c cos(θ + Ï€) This phase reversal is what causes distortion in the demodulated signal. 5. Instantaneous AM Signal s...
Read more

Phase Modulation (PM) & Demodulation

Advanced Analysis of Phase Modulation Phase Modulation (PM): Theoretical Foundations and Spectral Dynamics 1. Analytical Characterization Phase Modulation (PM) is a subset of Angle Modulation , where the information residing in the message signal \( m(t) \) is mapped linearly onto the instantaneous phase of a high-frequency carrier. Unlike Amplitude Modulation (AM), PM is a non-linear modulation process, resulting in an expansion of the signal bandwidth into an infinite dimensional Hilbert space. \[ S_{PM}(t) = A_c \cos\left[ 2\pi f_c t + \phi(t) \right] = A_c \cos\left[ 2\pi f_c t + K_p m(t) \right] \] The instantaneous frequency \( f_i(t) \) is defined as the time derivative of the total angle: \[ f_i(t) = \frac{1}{2\pi} \frac{d\theta_i(t)}{dt} = f_c + \frac{K_p}{2\pi} \frac{dm(t)}{dt} \] ...
Read more

QPSK Online Simulator (Signal Generation)

Simulator for QPSK Modulation Quadrature (4-PSK) Bitstream (Even length) Carrier Freq (Hz) Samples Per Symbol Run QPSK Simulation The Math Behind QPSK Quadrature Phase Shift Keying (QPSK) is a form of digital modulation that transmits two bits per symbol by changing the phase of a carrier wave. s(t) = A cos(2Ï€f c t + θ n ) Phase (θ n ): Each pair of bits (dibit) corresponds to a specific phase shift. In Gray coding, we use: "00" → Ï€/4 (45°) "01" → 3Ï€/4 (135°) "11" → 5Ï€/4 (225°) "10" → 7Ï€/4 (315°) Efficiency: Since 4 phases are used, QPSK carries double the data of BPSK in the same bandwidth. ...
Read more